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How I Interpret C.S. Peirce

AI3:::Adaptive Information (Mike Bergman) - Wed, 09/20/2017 - 22:55

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Another Rung on the Ladder of Knowledge

I suppose, like most philosophers, that Charles Sanders Peirce (1839-1914) often engenders much passion and strongly held views. Among the prominent authors who have written about Peirce are scholars, engineers, arm-chair philosophers, charlatans, physicists, confused thinkers, pendants, academics, linguists, mathematicians, cosmologists, biosemioticians, atheists, religionists, scientists, and writers, among other disciplines and viewpoints. Peirce maintained the discovery of truth is a community exercise, yet that consensus about many aspects of his writings eludes the Peircean community [1]. The strength of Peirce’s theories, I believe, resides most in the generals that may be derived from his world view. Despite the areas of disagreement, I think that a general conclusion shared in the Peircean community is that much can be learned about the nature of the world and knowledge of it by studying Peirce.

In this article, the last in my current series of why and how I study Peirce, I discuss the methods and approach — the methodeutic in Thirdness according to Peirce — that I use to interpret his writings. I want to continue to emphasize the general in Peirce’s writings, the Thirdness, that fixes my own beliefs [2]. These beliefs, while sufficient as a basis for action and learning (or habit), are not fixed in the sense of being inviolate. Quite the contrary. I am continuing to learn about Peirce, changing my views and beliefs as evidence presents itself. This evidence comes from either studying more of Peirce’s writings directly or learning from others’ scholarship and insightful interpretation.

Belief is not truth, and what we take today to be truth is fallible. Continuity, change, growth and learning are core concepts within Peirce’s conception of Thirdness. Peirce continued to question and test his own views, leading to changing statements and interpretation in many areas across his five decades of writings. Peirce would have never seen himself as infallible, and would disdain any of those who hold him as such. So we shall not [3].

The very scheme of Peirce’s beliefs, what he rightfully termed his architectonic, is grounded in his universal categories of Firstness, Secondness, and Thirdness [4]. Each of these formative concepts is both necessary and sufficient for building all aspects of an understanding of reality, which in Secondness also gives us a basis for understanding the fictional as a contrast to that reality. All aspects of the knowable, experienced reality, what Peirce called the phaneron, can be reduced to one or more of these universal categories, in full or degenerate form [5]

Having died more than a century ago, Peirce was part of an age just on the cusp of electricity, wireless communications, the automobile, and the airplane. The discovery of relativity, atomic energy, quantum mechanics, and computers still resided mostly into the future. So how can Peirce speak to us about these modern things and knowledge? Well, at the most fundamental levels, Peirce is very much a big picture guy, seeking to understand the essences of existence and reality. By trying to grok Peirce’s mindset and methods, I believe we can address problems Peirce did not directly address himself. Because of his timeless insights, Peirce continues to provide adaptive guidance for our changing, modern world.

Why Important to Interpret Peirce

I have maintained throughout this series that Peirce is the greatest thinker ever in the realm of knowledge representation. Yet KR, as a term of art, was not a phrase used in Peirce’s time. True, Peirce wrote much on relations and representation (via his semiotic theory of signs) and provided many insights on the nature of information and knowledge, but he never used the specific phrase of “knowledge representation” [6]. Further, while he categorized the realm of science at least 20 different times (see below), and wrote on Charles Babbage and posited the use of electricity and logic gates for reasoning machines [7], he never attempted to categorize knowledge such as what we have undertaken with the KBpedia Knowledge Ontology (KKO). While I think Peirce had more than a glimmer of an idea that reasoning machines might someday be a reality, there was no need within his time to attempt to provide the specific representational framework for doing so.

Thus, the importance of studying Peirce for me has been to tease out those principles, design bases and mindsets that can apply Peircean thinking to the modern challenge of knowledge representation. This knowledge representation is like Peirce’s categorization of science or signs, but is broader still in needing to capture the nature of relations and attributes and how they become building blocks to predicates and assertions. In turn, these constructs need to be subjected to logical tests in order to provide a defensible basis for what is knowledge and truth given current information. Then, all of these representations need to be put forward in a manner (symbolic representation) that is machine readable and computable.

In reading and studying Peirce for more than a decade it has become clear that he had insights and guidance on every single aspect of this broader KR problem. The objective has been how to take these piece parts and recombine them into a coherent whole that is consistent with Peirce’s architectonic. How can Peirce’s thinking be decomposed into its most primitive assumptions in order to build up a new KR representation? As I argue in this article, the key to unlocking this challenge has been through an understanding of the universal categories and the mindset that resides behind them. In Peirce’s own term, the universal categories are the most “indecomposable” elements of his world view.

Of course, since Peirce himself never addressed the specific challenge of knowledge representation for computers, there is no guarantee that Peirce himself would endorse this current interpretation. Further, Peirce was a stickler for terminology and evolved and changed in his thinking over his long intellectual career. An appreciation of these factors is also important to do justice in posing a Peircean view of knowledge representation.

The Terminology Tarpits

Though Peirce frequently railed against nominalism, arguing instead for a realistic view of the world, he also was very attuned to names, labels and definitions. For example, he authored some 6,000 definitions of technical terms over the years for the Century Dictionary [8]. He was in constant search for the “correct” way to label his constructs. As one instance, at various times, Peirce called abductive reasoning hypothesis, abduction, presumption, and retroduction. He also called the methodeutic speculative rhetoric, general rhetoric, formal rhetoric, and objective logic. Such changing names were not uncommon with Peirce.

Because Peirce held that the understanding of a language symbol is a process of shared consensus among its community of users, he was generally loathe to use common terms for many of his constructs. Indeed, when one of his terms, pragmatism, was adopted by William James who gave it a different spin and interpretation, Peirce disavowed his earlier term and replaced it with the term pragmaticism. “So then, the writer [Peirce], finds his bantling ‘pragmatism’ so promoted, feels that it is the time to kiss his child good-by and relinquish it to its higher destiny; while to serve the precise purpose of expressing the original definition, he begs to announce the birth of the word ‘pragmaticism’, which is ugly enough to be safe from kidnappers” [9, pp 165-166].

This penchant for “ugly” terms is not uncommon with Peirce. As examples, here are some other terminology uses from Peirce’s writings:

agapism coenoscopy interpretant phaneroscopy semeiotic anancasticism cyclosy legisign pragmastic definition sinsign apeiry dicent medisense pragmaticism speculative rhetoric antethics entelechy methodeutic precission stecheotic architectonic fallibilism objective idealism qualisign synechism axiagastics hylozoism percipuum representamen transuasion ceno-pythagorean hypostatic abstraction periphraxy retroduction tychasticism chorisy idioscopy phaneron rheme tychism Examples of Obscure Peirce Terminology

Changing and “ugly” terminology is but the first of the difficulties in reading and understanding Peirce. His own evolution as a thinker, plus the interpretations of those who study them, also complicate matters. I cover this topic in the next section.

But a real point about interpretation, I think, is to try to get past his sometimes off-putting terminology. Mostly what is hard to understand are terms you may be encountering for the first time. There are rewards if you can see through the newness of this terminology to get to the meat underneath.

Eras and Changing Viewpoints

Peirce was often the first to acknowledge how he changed his views, with one set of quotes from early 1908 showing how his thinking about the nature of signs had changed over the prior two or three years [10]. Yet that was but a small snapshot of the changes Peirce made to his sign theories over time, or of his acknowledgments that his views on one matter or another had changed.

In his analysis of Peirce’s 70-plus definitions of the sign, Robert Marty distinguishes between the original three correlates of the triadic relation as ‘global triadic’ and the later six-element definition as being ‘analytic triadic’ [11, in reference to 5]. Besides this first elaboration, Peirce undertook a further extensive expansion of his theory of signs after the turn of the 20th century. In a new book [12], Jappy provides an intelligent analysis of this evolution of Peirce’s sign theories, focusing on his latter 28-sign scheme, what Jappy feels to be Peirce’s most mature (but still incomplete). Thus, with respect to signs alone, we can trace an evolution or maturation of Peirce’s sign theories that went from 3 → 6 → 10 → 28 66 elaborations. The latter 28 and 66 schemes remained incompletely developed at the time of Peirce’s death.

Similarly, Peirce’s classification of the sciences also went through considerable changes. Beverly Kent conducted a thorough analysis in 1987, much based on unpublished manuscripts at the time, that documents at least 20 different classifications of the sciences from Peirce over the period of 1866 to 1903 (the last “perennial”), with minor ones in between [13]. In addition to signs and the classification of the sciences, examples abound of evolving terminology or thinking by Peirce for other topics for which he is commonly known, such as logic (deductive v inductive v abductive), pragmatism, continuity, infinitesimals, and mathematics.

Of course, it is not surprising that an active writing career, often encompassing many drafts, conducted over a half of a century, would see changes and evolution in thinking. Many scholars have looked to specific papers or events in order to understand this evolution in thinking. Max Fisch divided Peirce’s philosophy development into three periods: 1) the Cambridge period (1851-1870); 2) the cosmopolitan period (1870-1887); and 3) the Arisbe period (1887-1914) [14]. Murphey split Peirce’s development into four phases: 1) the Kantian phase (1857-1866); 2) three syllogistic figures (1867-1870); 3) the logic of relations (1879-1884); and 4) quantification and set theory (1884-1914) [15]. Brent has a different split more akin to Peirce’s external and economic fortunes [16]. Parker tends to split his analysis of Peirce into early and mature phases [17]. It is a common theme within major scholars of Peirce to note these various changes and evolutions.

Some of this analysis asserts breakpoints and real transitions in Peirce’s thinking. Others tend to see a more gradual evolution or maturation of thinking. Some of the arguments are clearly aimed at bolstering whatever particular thesis the author is putting forward. Such is the nature of scholarship, and to be expected.

For me, I take a pragmatic view of these changes. First, some of Peirce’s earliest writings, particular his 1867 “On a New List of Categories’ [18], but also mid-career ones, are amazingly insightful and thought-provoking. There is tremendous value in these earlier writings, often infused with genius. Peirce, after all, was in the prime of his powers. Sure, I can see where some points have evolved or prior assertions have changed, but Peirce is also good at flagging those areas he sees as having been important and earlier in error. I therefore tend to rely most on his later writings, when a hard life lived, maturity and experience added wisdom and perspective to his thoughts. I tend to see his later changes more as nuanced or mature, rather than fundamental breaks with prior writings. I see tremendous continuity and consistency of world view in Peirce over time.

Sure, at the level of how specific items or ideas change over time it is important to be cognizant of when a Peirce quote or writing occurred. The jumbled nature of the original Collected Papers means they need to be used with caution, since they have no chronology. Most contemporary Peirce scholars now tend to date by year the passages they quote in order to overcome this problem. I think this is good practice, and for which I am increasingly trying to adhere. Also, I tend to not like his later terminology, since I think it errs on the side of obscurity in order to be precise, which limits its understandability to a broader community. Peirce should have realized that understandability holds sway over individualized perspective. He was silly to argue with James about the term pragmatism, as James was doing so much to promote awareness of Peirce’s ideas.

The Lens of the Universal Categories

Chronologies, terminologies, or evolutions aside, still the question remains: How can one apply Peirce and his ideas to today’s challenges? What is the essence of trying to approach and solve problems by Peircean means? Is there a mindset by which we can think through contemporary problems in domains unheard of in Peirce’s time? Are there indeed timeless truths?

I think there are.

To me, slicing through all of the complexity and the noise, are Peirce’s universal categories of Firstness, Secondness and Thirdness. I find it amazing and consistent how much Peirce himself relies on the universal categories in his own thinking and analysis. There must be something at the heart of these universal categories that make them such a powerful lodestone.

The first hurdle, I think, in attempting to understand the universal categories is the absolute abstractness of the terms Firstness, Secondness and Thirdness. In this case, I believe Peirce’s terminology fussiness to be exactly what is proper. Since, ultimately, all reality, all potential, and all emergence derives from these elements, nothing other than one, two and three will do. Everything that is, may be, or could surprise us arises from these elements. This is the absolute ground. Nothing further can be decomposed from these elements, yet everything that is and is conceivable is built from these categories. I don’t mean to be or sound religious; just logical.

So, if we have such fundamental building blocks at hand, how can we begin to understand their nature, use and implications? How can we incorporate the universal categories into our own methodeutic?  How can our thinking, the ultimate Thirdness, leverage these elements?

As might be expected, Peirce tried to get at this very question through the idea of continuity, the force at the heart of Thirdness. The universal categories are not static, but dynamic. The occasional “surprising fact” alters what we think we know about reality, which causes us to re-inspect and re-categorize our world. The dynamic universal categories, faced with the unexpected chance arising in Firstness, ripple through our awareness (reality) to cause a new understanding of the state of existence (Secondness). The universal categories give us the primitive elements by which we can again categorize and generalize our new world, a factor of Thirdness. And so the cycle continues. Truth, understood to be a limit function, gets constantly exposed as all of us test and affirm these new realities.

Peirce, the logical categorizer, concerned with methods, and interested in pragmatic approaches and solutions, understood that how we categorize our constantly emerging worlds was fundamental. His pragmatic maxim helps us decide among many possible alternatives. Perhaps we can follow his natural classification guidelines, an item of keen interest to him, and one which I have previously discussed [19], as a way to better appreciate what these universal categories of Firstness, Secondness and Thirdness are and mean, as we work to categorize our emerging world anew.

One way to do that is to follow Peirce’s directive for determining a natural class by “an enumeration of tests by which the class may be recognized in any one of its members” [20]. So, as to better understand the ideas of Firstness, Secondness and Thirdness, I have assembled as many examples as I could find from Peirce’s writings of these members of the universal categories. The following table lists these 70 or so examples of Firstness, Secondness and Thirdness, the contexts in which they arose, and a citation where to find the supporting material in Peirce’s writings:

Firstness Secondness Thirdness Moods or Tones first second third [21] Conceptions of First, Second, Third independent relative mediating [22] The Categories monads particulars generals [23] Time “present” “past” “future” [24] Cognition / Space point line triangle / sphere [25] Movement position velocity acceleration [26] Modes of Being possibility existence law [27] Seconds internal external Thirdness [28] Thirds mixtures comparisons intelligibles [29] Modality possibility actuality necessity [30] Phenomena 1 sensations reactions generals [31] Phenomena 2 qualities of phenomena actual facts laws (and thoughts) [32] Active Elements chance law habit-taking [33] Existence chaos regularity continuity [34] Continuity feeling effort habit [35] Mathematics quality facts laws [36] Ceno-Pythagorean Categories originality obsistence transuasion [37] Form tone token type [38] Being quality relation representation [39] Protoplasm sensibility motion growth [40] Natural Selection individual variation heritability elimination of unfavored characters [41] Modes of Evolution absolute chance mechanical necessity law of love [42] Doctrines of Evolution tychasticism anancasticism agapasticism [43] Consciousness 1 feeling sense of action/reaction sense of learning [44] Consciousness 2 feeling altersense medisense [45] Consciousness 3 immediate feeling polar sense synthetical consciousnes [46] Thought 1 abstraction suggestion association [47] Thought 2 possibility information cognition [48] Thought 3 thought-sign connected interpreted [49] Synthetical Consciousness association by contiguity association by resemblance intelligibility [50] Mind feelings reaction-sensations conceptions [51] Logical Mind ideas ideas from prior ideas ideas from prior processes [52] Experiences simples recurrences comprehensions [53] Information intensions extensions comprehensions [54] Knowledge Representation attributes individuals types [55] Characters or Predicates internal external conceptual [56] Relations attributes external relations representations [57] Representation sign object interpretant [58] Sign-Object icon index symbol [59] Nature of Signs qualisign sinsign legisign [60] Kinds of Characters singular characters dual characters plural characters [61] Symbols words (or terms) propositions arguments [62] Sign-Interpretant 1 emotional interpretant energetic interpretant logical interpretant [63] Sign-Interpretant 2 rhemes dicisigns arguments [64] Signs 1 possibles things collections [65] Signs 2 abstractives concretetives collectives [66] Propositions hypothetical categorical relative [67] Logical Terms monads dyads triads [68] Assertions possible modality actual modality necessary modality [69] Reasoning what is possible what is actual what is necessary [70] Logical Thinking clearness of conceptions clearness of distinctions clearness of practical implications [71] Logic Methods abductions deductions inductions [72] Logic speculative grammar logic and classified arguments methods of truth-seeking [73] Sciences of Discovery mathematics philosophy special sciences [74] Philosophy phenomenology normative science metaphysics [75] Normative Science logic ethics aesthetics [76] Concepts of Metaphysics spontaneity dependence mediation [77] Others complete in itself, freedom, free, measureless variety, freshness, multiplicity, manifold of sense, peculiar, idiosyncratic, suchness, one, new, spontaneous, vivid, sui generis otherness, comparison, action, dichotomies, mutual action, will, volition, involuntary attention, shock, sense of change, here and now, compulsion, state, occurrence, negation idea of composition, continuity, moderation, comparative, reason, sympathy, intelligence, structure, regularities, conduct, representation, middle, learning, conditional [78] C.S. Peirce’s Universal Categories in Relation to Various Topics

Though atheists and religionists alike argue Peirce’s belief or not in God, I also find this statement by him to be another powerful expression of the universal categories: “The starting-point of the universe, God the Creator, is the Absolute First; the terminus of the universe, God completely revealed, is the Absolute Second; every state of the universe at a measurable point of time is the third.” (CP 1.362)

It took me a while to realize that Firstness, Secondness, and Thirdness are not a linear sequence, nor one in time. In fact, Peirce likens Firstness to the present, Secondness to the past, and Thirdness to the future [24]. All possibilities, Firstness, reside in the absolute present, “for nothing is more occult” (CP 2.85), the instance at which they act or are acted upon or perceive such changes causes them to come into existence, or Secondness, in relation or contrast with other instances and events, because what is real is past. The continuity of these instances through space and time, the future, enables new contexts and generalities arising from what we can learn from Secondness and Firstness. Chance events in Firstness may spring “surprises” in Secondness that trigger new cognition or mediation in Thirdness, which potentially predicates a new basis for categorization, certainly in the sense of knowledge representation, my chosen frame of reference.

My thesis is that studying these assignments in relation to the various contexts is one way to internalize the mindset of the universal categories. At the most fundamental level we can see Firstness as the raw, unexpressed possibilities of the current problem set, the building blocks for the new category, if you will. Chance is the root aspect of Firstness, which means any of these possibilities may express themselves in surprising ways, perhaps causing the need for new categorization. The actual things or events of the new category, as made manifest by their interaction or contact with what also exists in the domain at hand, provide the actual instances of Secondness. And, the generalities or continuities among these instances, classed as best we can in a natural manner, provide the Thirdness of this domain. The best way to glean meaning from this table is through deep study and contemplation.

In the context of knowledge representation, we begin with these foundational aspects of the universal categories and then keep analyzing and categorizing following this mindset. I think it is evident in the table above, sometimes to multiple levels depending on context (which requires studying some of the supporting material to the table), that Peirce applied this same method. Where questions arise about which universal category to assign something, we look to Peirce and later scholars to see if prior determinations have been postulated and argued. If so, we test those assumptions and adopt or not those assignments, based on our own logical assessments. We continue this process as we get deeper and more specific in our categorizations. No matter what the assignment, each should be subject to questioning and testing by the community of users, perhaps altering those assignments as better information or better logic is applied to the assignments. This is the process that has been followed in developing the KBpedia Knowledge Ontology (KKO), the knowledge graph of some 200 concepts that provides the upper-level scaffolding for our knowledge representation efforts.

As of the date of this writing, there is NO other knowledge representation framework besides KKO that explicitly embraces Peirce’s universal categories of Firstness, Secondness and Thirdness. While many, many insights from Peirce’s writings contribute to how we approach representing knowledge in our systems, the adoption of the mindset of universal categories is by far the most important element in how we go about constructing our representations.

A Synthetic Mindset Through Peirce’s Architectonic

Unfamiliar terminology and a triadic foundation to his philosophy make Charles Peirce a difficult guide to initially follow. Further, there are many dimensions, each richly layered, to his guidance. For those who have stayed the course, Peirce has become an invaluable guide.

The overarching framework of Peirce’s philosophy — his architectonic — is grounded in his universal categories of Firstness, Secondness and Thirdness. As a scientist and logician, Peirce applied this mindset in pragmatic and testable ways. These methods, indeed the scientific method itself, further guide how and where to apply this mindset in ways that are economical and promise the most knowledge among all of the possible paths of inquiry. Peirce’s fierce realism, the belief there is reality beyond our own minds, and his insistence that this reality is subject to inquiry and the fixation of belief leading ever closer to truth, is distinctly different than the mind-body duality put forward by Descartes.

Richard Bernstein in a recent book [79], calls this viewpoint a sea change:

“Pragmatism begins with a radical critique of Cartesianism. In one fell swoop, Peirce seeks to demolish the inter-related motifs that constitute Cartesianism [mind-body duality; primacy of personal experience; doubt as a starting condition; there are incontrovertible truths to be discovered] . . . . We can view the development of pragmatism from Peirce until its recent resurgence as developing and refining this fundamental change of philosophical orientation — this sea change. A unifying theme in all the classical pragmatists as well as their successors is the development of a philosophical orientation that replaced Cartesianism (in all its varieties).” (pp 18-19)

Our real world is constantly changing, constantly unfolding. Our real world is viewed by all of us differently, based on background, predilection, perspective and context. What we think we know about the world today is subject to inquiry and new insights. New factors are constantly arising to shift what we think we know about ourselves and our place in the world.

Knowledge representation by computers that does not explicitly account for perspective, meaning, and interpretation is doomed to be wooden and unable to handle context. Such is the state of art today. We do not all need to agree on the specifics or any single interpretation of what our domains of inquiry may be. But we do need a framework that can respect and model those differences.

To sum up, how I interpret Peirce embraces three perspectives. First, given the breadth of Peirce’s insights, I try to read as much by him and about his writings by others as I can. This exposure helps set a rich milieu for my own insights, but also in interpretation and critical judgment. Second, despite my awe of Peirce’s genius, I do not treat his writings as gospel. Were he alive today, I have no doubt that the massive increase in knowledge and information since his day would cause him to alter his own viewpoints — perhaps substantially so in some areas. There is no similar reason why any of us should shy from questioning any of Peirce’s assertions. Yet, given Peirce’s immense powers of logic, one better be well prepared with evidence and sound reasoning before undertaking such a challenge.

And, third, and most fundamentally, I try to view how to represent knowledge through the lens of Peirce’s universal categories. The tasks of defining and organizing knowledge demand that we bring meaning, context and perspective to the task. Peirce stood on the shoulders of the giants before him. We can now stand on Peirce’s shoulders to mount the next rung on the ladder of knowledge. I believe Peirce’s universal categories and what they imply offer the next adaptive climb upward for knowledge representation. As Bernstein states, “Peirce opened up a new way of thinking that is still being pursued today in novel and exciting ways by all those who have taken the pragmatic turn. This is the sea change he helped initiate.” (p 52)

[1] Many of the Peirce quotations are drawn from The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme used for these sources is commonly seen in Peirce scholarship, and is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [2] Peirce discusses this topic in his seminal paper, Charles S. Peirce, 1877. “The Fixation of Belief,” Popular Science Monthly 12:1-15, November 1877 [3] “To be blinded by the peculiar strength of his thinking into a type of reverence that has always been common, would certainly be to violate the very spirit which animated him.” p. xv; from the editor’s introduction to Justus Buchler, ed., 1940. Philosophical Writings of Peirce, Routledge and Kegan Paul Ltd., reissued by Dover Publications, New York NY, 1955. [4] M.K. Bergman, 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness,” AI3:::Adaptive Information blog, March 21, 2016. [5] Peirce’s original three universal categories were expanded to six by adding what he called one “degenerate” form to Secondness and two “degenerate” forms to Thirdness, increasing the original three by an additional three. See further CP 1.365-367. [6] The exact origin of the phrase “knowledge representation” is unclear. Given its role in symbolic representations to computers, a branch of artificial intelligence, the phrase would not be expected to be used in that sense until the mid-20th century. Knowledge representation first became prominent through systems like the GPS problem-solving program (A. Newell, J.C. Shaw, and Herbert A. Simon, 1959. “Report on a General Problem-solving Program,” in Proceedings of the International Conference on Information Processing, pp. 256–264, KRL (the Knowledge Representation Language, see Daniel G. Bobrow and Terry Winograd, 1976. “An Overview of KRL, A Knowledge Representation Language,” Stanford Artificial Intelligence Laboratory Memo AIM 293, 1976), and then the KR thesis work of Ron Brachman at Harvard (1978) followed by his early technical papers and books; see especially the popular Hector J. Levesque and Ronald J. Brachman, 2004. Knowledge Representation and Reasoning. Amsterdam: Elsevier/Morgan Kaufmann. ISBN 1-55860-932-6. [7] References to Charles Babbage may be found at CP 2.56 and CP 4.611. For electrical logical machines, see Charles S. Peirce, 1993, “Letter, Peirce to A. Marquand” dated 30 December 1886, in Kloesel, C. et al., eds., Writings of Charles S. Peirce: A Chronological Edition: Volume 5: 1884–1886. Indiana University Press: 421-422, with an image of the letter page with the circuits on p. 423. [8] Charles S. Peirce, 1982. Writings of Charles S. Peirce: A Chronological Edition – Volume 1, 1857-1866, compiled by the editors of the Peirce Edition Project, Indiana University Press, August 1982, 736 pages,ISBN: 978-0-253-37201-7. The editors note Peirce contributed to 16,000 entries, most in mathematics and logic, with 6,000 written solely by Peirce [9] Charles S. Peirce, “What Pragmatism Is,” The Monist, Vol. 15, No. 2 (April, 1905), pp. 161-181; see http://www.jstor.org/stable/27899577; also CP 5.414. He also expands on this general theme in Charles S. Peirce, 1906. “Prolegomena to an Apology for Pragmaticism,” The Monist, Vol. 16, No. 4 (October, 1906), pp. 492-546; see http://www.jstor.org/stable/27899680 [10] Charles S. Peirce, 1908. “The Ten Main Trichotomies of Signs,” in “Excerpts to Lady Welby”, in Charles S. Peirce, 1998. The Essential Peirce – Volume 2: Selected Philosophical Writings (1893-1913), edited by the Peirce Edition Project, Indiana University Press, June 1998, 624 pp., ISBN: 978-0-253-21190-3; also CP 8.363-365. [11] See his very useful ‘Analysis of the 76 definitions of the sign’ http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM (Accessed March 2016). [12] Tony Jappy, 2017. Peirce’s Twenty-Eight Classes of Signs and the Philosophy of Representation: Rhetoric, Interpretation and Hexadic Semiosis, Bloombury Press, London, 2017, 225 pp. See https://oapen.org/download?type=document&docid=625766. [13] Beverly Kent, 1987. Charles S. Peirce: Logic and the Classification of the Sciences, McGill-Queen’s University Press, Montreal, 258 pp. [14] Max H. Fisch, “Peirce’s Arisbe: The Greek Influence in his Later Philosophy,” in Peirce, Semiotic, and Pragmatism, p. 227   [15] Murray G. Murphey, 1993. The Development of Perice’s Philosophy. Hackett Publishing Company, Inc., Indianapolis. [16] Joseph Brent, 1998. Charles Sanders Peirce: A Life (2nd edition), Indiana University Press, Bloomington. [17] Kelly A. Parker, 1998. The Continuity of Peirce’s Thought. Vanderbilt University Press, Nashville. [18] Charles S. Peirce, 1867. “On a New List of Categories,” Proceedings of the American Academy of Arts and Sciences 7 (1868), 287–298. Presented, 14 May 1867. See CP 1.545-559. [19] M.K. Bergman, 2015. “‘Natural’ Classes in the Knowledge Web,” AI3:::Adaptive Information blog, July 13, 2015. [20] Peirce sets this forth as one of his conditions for determining a natural classification; see CP 1.224. [21] CP 1.355; also, Cosmogenic Philosophy, EP 1.297 [22] See CP 6.32-34 [23] This exact categorization was never used directly by Peirce (or so my investigations to date suggest). However, it is clear throughout his writings that he relates monads to Firstness, ‘particulars’ and ‘particularities’ to Secondness, and ‘generals or ‘generalities’ to Thirdness. Further, these terms are understood and used in other categorization schemes, such as those by Aristotle and Kant. We also see, by this chart, that Peirce himself employs many different terms for his universal categories. We have chosen these to be the three main categories in the KBpedia Knowledge Ontology for these reasons. See further CP 1.300-338. [24] CP 2.84-86; see also 2.146; it is NOT 1 –> 2 –> 3 present v hic et nunc ; CP 5.459-463 [25] CP 5.263 [26] CP 1.337 [27] CP 6.343-344 [28] CP 1.365 [29] CP 1.366; This is an example of what Peirce called ‘degenerate’ categories of the category. Degenerate means that it is a component of the category, but not sufficient as a concept in the 1o and 2o [30] CP 5.454 [31] CP 1.418-420 [32] CP 5.121 [33] CP 1.409 [34] CP 1.411 and CP 1.175 [35] CP 6.201-202; also called Tritism or Synechism (or “all that there is”) [36] CP 1.417-420 [37] CP 2.87-89; Peirce using his obscure labels in seeking exactitude [38] CP 4.537 [39] CP 1.555 and CP 2.418; the initial categories were actually bracketed by Being and Substance (5 categories total) [40] CP 1.393 [41] CP 1.398 [42] CP 6.302 [43] CP 6.302 [44] CP 1.378 [45] CP 7.551; thought is taken to be as equivalent to medisense [46] EP 1.260 [47] The analysis of the labels and relations is provided in these two articles: M.K. Bergman, 2017. “KBpedia Relations, Part III: A Three-Relations Model,” AI3:::Adaptive Information blog, May 24, 2017; and M.K. Bergman, 2017. “KBpedia Relations, Part IV: The Detailed Relations Hierarchy,” AI3:::Adaptive Information blog, June 27, 2017. [48] CP 1.537 [49] CP 5.283-284 [50] EP 1.261 [51] CP 6.18-20 [52] CP 7.348 [53] CP 7.528 cf [54] Peirce did not explicitly list these terms, but they can be readily and logically derived from CP 2.419-421. The idea of information being a product of depth (1o, intensionality) times breadth (2o, extensionality) is quite insightful [55] Though ‘general type’ is a common term for Thirdness in Peirce’s writings, he rarely used ‘attibute’ and preferred particulars to ‘individuals’. ‘Attributes’ and ‘individuals’ are now in modern usage, and clearly refer to 1o and 2o, respectively.We have chosen these two terms for use in the KBpedia Knowledge Ontology for these reasons. [56] Somewhat modified from CP 5.469 cf, with external and conceptual replacements supported by the senses of the accompany text [57] Taken from the analysis of Peirce documented in [47]; these are the terms chosen for use in terms for use in the KBpedia Knowledge Ontology [58] CP 1.339; ‘representation’ is also called a ‘sign’ [59] CP 1.191; can also be called ‘speculative grammar’ or ‘nature of signs’; in Jappy 2017 this is called ‘Sign-Object’, Table 1.2 A Synthesis of MSS R478 and R540, 1903 [60] CP 4.537 fn 3; called simply ‘Sign’ in Jappy 2017, Table 1.2 A Synthesis of MSS R478 and R540, 1903. [61] CP 1.370-371; can substitute ‘facts’ for ‘characters’ [62] CP 2.95, also CP 8.337; CSP also expresses ‘arguments’ as inferences or syllogisms [63] CP 5.475-6 [64] From Jappy 2017, Table 1.2 A Synthesis of MSS R478 and R540, 1903 [65] CP 8.366, with respect to the nature of dynamical objects [66] CP 8.366, with respect to the nature of dynamical objects [67] CP 2.325 [68] CP 1.293 [69] CP 4.57 [70] CP 1.369 [71] CP 3.457 [72] CP 2.98; in an earlier version, I listed ‘abduction’ as a Thirdness, but I was corrected on the Peirce-L mailing list. On the other hand, abduction is at the interface between Thirdness and Firstness, since it is the source of the possibilities that need to be considered for a given category. The dynamic nature of Peirce’s semiosis is part of the sign-making and -recognition process. [73] CP 1.191 [74] CP 1.239-242; the ‘special sciences’ include the physical (physics, chemistry, biology, astronomy, geognosy, and whatever may be like these sciences) and the psychical (psychology, linguistics, ethnology, sociology, history, etc.) sciences [75] CP 1.280-282 [76] CP 1.281 [77] CP 3.422; also, Forms of Rhemata (singular, dual or plural) [78] Mostly random notes teken from various Peirce writings. [79] Richard J Bernstein, 2010. The Pragmatic Turn, Polity Press, Malden, MA. 2010.

Pulse: KBpedia v 151 Released

AI3:::Adaptive Information (Mike Bergman) - Wed, 09/13/2017 - 18:31

KBpedia, a computable knowledge structure combining six major public knowledge bases, received a minor update today to version 1.51. This release makes some minor corrections and provides updated statistics. No material changes from version 1.50 released a month ago were made.

The KBpedia knowledge structure combines six (6) public knowledge bases – Wikipedia, Wikidata, OpenCyc, GeoNames, DBpedia and UMBEL – into an integrated whole. These core KBs are supplemented with mappings to more than a score of additional leading vocabularies. The entire KBpedia structure is computable, meaning it can be reasoned over and logically sliced-and-diced to produce training sets and reference standards for machine learning and data interoperability. KBpedia greatly reduces the time and effort traditionally required for knowledge-based artificial intelligence (KBAI) tasks. KBpedia was first released in October 2016, though it has been under active development for more than six years. KBpedia is sponsored by Cognonto Corporation.

How I Study C.S. Peirce

AI3:::Adaptive Information (Mike Bergman) - Tue, 08/29/2017 - 21:10

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A Man of Depth and Context Demands Many Perspectives

In my last article I explained some of the reasons why I study Charles Sanders Peirce as an authority on knowledge representation. Now, I would like to complement that piece by describing how I study Peirce. My approach has been gained after a decade of study of Peirce. It has taken me that long to assemble a relatively complete library of his writings and writings about him. I’m sure there are many ways to approach such study, but I would have personally enjoyed getting some tips when I was starting out.

I will cut to the quick chase first. In a comment to that last article, I was asked to recommend some starting resources for learning more about Peirce. I replied:

I actually have plans to lay out sources and how I read Peirce (“purse”) in a future article. But the quick version is: 1) start with the Charles Sanders Peirce article and category on Wikipedia; it is a remarkably good starting point; 2) then I would read The Essential Peirce, Vol 1, with attention to Nathan Houser’s great introduction; and 3) for a complete view, and one which offers (I believe) one of the fairest and well-reasoned views of Peirce, I really like Murphey’s The Development of Peirce’s Philosophy. There are many other useful sources and I don’t mean to slight them by not mentioning them here.

That is still the best summary, I think, about how to proceed. But now I’d like to complete my plan to provide additional advice and sources about how to study Peirce.

Begin with Wikipedia

My first recommendation to begin learning about Peirce is to start with Wikipedia. Wikipedia’s entry on Charles Sanders Peirce is actually quite good and rather complete. There is an entire category dedicated to Peirce on Wikipedia, with some 40 articles listed. I think the articles on semiosis, abductive reasoning, and pragmaticism are some of the better ones. Unfortunately, the article on Peirce’s universal categories is pretty weak. To compensate, however, the Peirce bibliography is a very good reference source.

Try an Early Introduction

Peirce is hardly easy to read, and most of what is written about him is also pretty dense. Though those seasoned in Peirce studies might find it covering standard ground, the 2013 Cornelis de Waal guide to Peirce [1] is possibly the most accessible introduction to Peirce and his contributions available. I find I no longer consult it for facts or details, but as an intro it is helpful and a relatively quick read. If this piques your interest, then it is probably worth your time to start exploring Peirce in more depth. I also like de Waal’s labeling of the”doctrine of the categories”.

Editorial Compilations of Peirce’s Writings

Of course, all of the material up to this point is others writing about Peirce, and not Peirce in his own words or form. The only way to find out what is in a house is to enter it, explore it, and poke into various corners. For this, it is necessary to read Peirce directly.

The earliest known compilation of Peirce’s writings was by Cohen in 1923 [2], nearly a decade after Peirce’s death, and is both a good intro and starting compilation. An even better starting compilation is that of Buchler [3]. However, I personally did not start with either or these, nor with de Waal, because my initial research discovered that searchable PDF versions of the first “complete” compilations of Peirce’s writings could be obtained for free online [4]. These Complete Papers have also been posted online, which is easier to read than the PDF versions, and can also be searched [see 5]. The problem with these sources, however, is that the editorial order of CP is not chronological, gaps exist because of the sources initially chosen, and the formatting and editorial decisions are not equal to later standards. The online version is better for learning and reading purposes, but the lack of editorial oversight hurts CP irrespective of format. However, DO get a local copy of the online PDF for your serious library shelf because it is an important way to be able to electronically search large portions of Peirce’s writings.

[There was a CD library at one time that provided even a broader, searchable coverage of Peirce’s writings, but that is unfortunately only now being maintained for prior purchasers [6]. If you ever see a copy available, it is perhaps worth looking if the price is reasonable.]

There are, of course, many different editor’s compilations of Peirce’s writings. In mathematics, you likely want to focus on the fantastic four-volume series from Eisele [7], which can often be found for free online. As a non-mathematician, I found Volume 4 to be the most useful. For my own interests in logic and knowledge representation, I have found Vol 1 of The Essential Peirce [8] to be the best single compilation of relevant writings. In fact, you can re-assembly the entire contents of EP (as it is abbreviated) from free, online PDFs (see further below), and I have, but that also means you lose the fantastic Nathan Houser introduction and the nice packaging and portability of an actual paperback book. There are, of course, many other compilations also available (see the various bibilography sources).

I almost uniformly find the introductions by the editors of these compilations to be some of the most useful insights about Peirce. The introductions often weave in relevant personal details to help evaluate Peirce as a person. The editors bring a perspective and context about Peirce’s accomplishments, since they are being offered from an external vantage. Under the category of editorial compilations, I especially like Nathan Houser’s introduction to EP. But, from different perspectives, I also think the intros by both Brent and Murphey (see below) helped in a similar way to make Peirce come more alive.

Comprehensive Studies

After this kind of a dive into Peirce’s own writings, again usefully supported by the editor’s intros, I find I want a big picture of Peirce, that covers his motivations, circumstances, discoveries and maturation. I suspect these are the hardest of the books about Peirce to write. It requires a breadth of familiarity and a deep understanding of (at least what the author thinks are) Peirce’s intentions. There also are wrinkles of this kind of approach, sometimes shading into only specific slices (such as religion [9]) or even further into specific academic perspectives.

The online Arisbe, the Peirce Gateway, lists some 210 books published on these kinds of topics since 1995 or so, with 114 published since 2006 alone. The site further lists 357 doctoral dissertions about Peirce, most in the last few decades. Note, many of these sources are not in English, since Peirce is studied worldwide, with a strong contingent from Latin America, especially Brazil and Colombia. The Arisbe site is helpful in that most entries are accompanied by at least a paragraph of description, and often with links to longer online excerpts. This is a good resource should specific topics pique your interest while studying Peirce.

Amongst the comprehensive studies covering the entirety of Peirce’s life work, I will mention two. The first is the book from Kelly Parker in 1998 [10] that focuses on Peirce’s emphasis on continuity (synechism). Parker writes well, is lucid, and has an excellent notes section. The second compilation, and one of my favorite Peirce reads, is the earlier 1993 book by Murphey [11] on the development of Peirce’s philosophy. Some other scholars, notably Hillary Putnam, have suggested that Murphey’s interpretations are often controversial. Murphey did, indeed, change some of his opinions of Peirce, especially with regard to continuity, in the second edition. But, I find Murphey’s analysis of the phases of Peirce’s developments to conform to my own sense. The latter section of his book is really excellent. I find it strange that many other general recommendations for Peirce readings tend to overlook this book. Perhaps a bit of this neglect came from Putnam’s early comments, but Murphey is one of the resources I most often consult.

When first learning about Peirce, it is striking how dominant semiosis and his theory of signs (and logic) pervade many of the resources. To be sure, these are important Peircean topics, but I find that it took me a while to probe beyond these topics into others I find even more fascinating. I have clearly focused on Peirce’s universal categories of Firstness, Secondness and Thirdness. But I have also been studying abductive reasoning, language grammars, the link between logic and mathematics, and how Peirce’s views dovetail into current topics in topology and category theory. With regard to these last topics, I recommend Fernando Zalamea [12]. Zalamea’s scholarship is quite advanced and perhaps is not a good starting point, but after some exposure to Peirce I like the synthetic view that Zalamea brings to the table. His scholarship clearly shows that Peirce continues to bring major insights to modern logic and mathematics.

Peirce Biographies

Louis Menand won a Pulitzer prize for his recounting of the birth of pragmatism in the US [13]. He told the story through the lens of the major participants in the Metaphysical Club, really more of an informal grouping of intellectuals. William James, Chauncey Wright, and Oliver Wendall Holmes figured prominently in that group, but none perhaps more so than Peirce. (Peirce and James were lifelong friends, but Wright was tremendously respected by Peirce for his insight and intellect and they were very close friends; Wright unfortunately died young at 45.) What is great about this book is that the movement to pragmatism is framed through the prism of slavery and abolition, the Civil War, and rapid intellectual and technological change. This is a really good read because it does such a marvelous job of placing Peirce into the context of his times, as well as providing equivalently fascinating looks at his very accomplished colleagues. However, this is not the single book to read if you want to probe deeply into Peirce’s theories and world view.

My favorite biography of Peirce, whose publication is a pretty astonishing story in its own right, is Brent’s life biography of C.S. Peirce [14]. Brent first began his biography of Peirce to answer the question of who invented the US philosophy of pragmatism, triggered by clues in a biography of Peirce’s friend, William James. He completed his dissertation in 1960 and intended to publish it, but ran into permission difficulties from Harvard, which was still acting poorly with regard to Peirce’s archival papers. Brent had to drop the project and moved on to other things. Then, in 1988, Thomas Sebeok, himself a then emerging-Peirce scholar, encountered a description of the dissertation in a footnote in another book. He was able to get the dissertation through interlibrary loan and finally read it in 1990. He was astonished with what he learned and the quality of the work, and set out to find Brent, whom he finally tracked down in Washington, DC. Through Sebeok’s catalyst, a publisher was found, Brent agreed to update his 30-year old dissertation, itself an effort of considerable labor, and the work was finally published in 1993. Brent provides an unvarnished and fair look at Peirce the person and shows great insight into his accomplishments and unique ways of thinking about the world. Brent tackled head on all of Peirce’s foibles and weaknesses as well. The resulting biography is a masterpiece, what Sebeok termed a “tragicomic thriller.” Brent himself came to believe “in philosophy [Peirce] was one of the most original thinkers and system builders of any time, and certainly the greatest philosopher the United States as ever seen.” Brent came to feel “deep affection” for his subject, despite those foibles and weaknesses.

The Brent biography is an incredibly intelligent treatment of an incredibly intelligent man. As might be expected from a work that began as a dissertation, it is thorough and well referenced. As might not be expected from a dissertation, it is really well written. Brent uses Peirce’s own “architectonic“, a term new to me then but studied by me now, a term drawn from Aristotle but modified by Kant and then Peirce, as a way of framing his own treatment. Brent is also attuned to shifts in Peirce’s thinking over time, a great boon to better understand the development of his theories. Since I believe Peirce will be studied for centuries, as with other great thinkers of humankind, Brent’s biography will be a must-include companion to Peirce’s own writings also over those centuries. As I note in the close to this article, Brent and Sebeok are but two of the hundreds of individuals that have made it their life’s work and passion to better understand Peirce, what he was trying to tell us, and to bring awareness of him to broader audiences.

There is also a fictionalized biography of Peirce’s mysterious second wife, Juliette, that has some voyeuristic interest, but is an unsuitable source for any reliable information about either Charles or Juliette [15].

The Academic Perspective

The bulk of commentary, of course, about Peirce may be found in the academic literature. I often find when studying Peirce that a new topic (or one that finally gets my attention) will arise that I want to learn more about. As with all such topics, I first consult Wikipedia for a starting article, if one exists, to get a bit of background and then some key links. But my real focus in such investigations centers on Google Scholar.

Google Scholar contains nearly 40,000 articles about or discussing Peirce, with the bulk, perhaps 70%, in English [16]. When searching Scholar, I always use “peirce” as one of my keywords and keep that search term in quotes (without the quotes, Scholar will also give you results from “pierce” since it seems to assume “peirce” is a misspelling). Since I am not affiliated with an academic institution and do not have ready access to interlibrary loan, I tend to focus on those articles that show a PDF link in the right column. (For articles of keen interest without such a link, I click on the ‘all xx versions’ link if it displays; occasionally, a PDF version will then show up.) I also tend to click off the citations and patents options to eliminate superfluous results for my purposes. If I really, really need the paper in full, I will also conduct a standard search using the last name of the author and the paper title in quotes as the query string. Sometimes PDFs may also be found on the standard Internet, independent of the academic sources indexed by Google Scholar. Or, I may ask a colleague to obtain the paper for me from interlibrary loan.

If I discover a paper of repeat interest, I save it. For papers of keen importance, I will also click the link ‘Cited by xx’ link on Scholar and do a secondary inspection of those to find other interesting papers that have cited the one of interest. This latter technique is particularly helpful when I’m not sure what all of the terms of art may be for my topic of interest, or if I want to trace how a topic has evolved. Inspecting multiple papers is one way to learn the terminology to improve query precision.

I have been following this approach to the academic literature on Peirce for nearly a decade. I keep all of my PDFs under a single root directory (Peirce). I add and expand folder sub-topics as needed. Prior to saving, I also tend to alter many of the Web URIs to a more descriptive label, since many PDFs are indexed under cryptic or numeric handles. This technique makes it easier to find articles later on my file system. After 10 years of following this approach, I now have about 650 papers in my local electronic Peirce library, organized into over 60 sub-topics. The PDFs currently take up about 500 MB of storage. Of course, when I am working on a given topic, I first consult and then add to this electronic library as I continue my research.

Web Sites About Peirce

This little guide to sources is obviously not the first such set of resources on the Web for Peirce. There are, in fact, dozens of useful ones I have found. I outline some of these in this section.

There are many writers whose Web sites tend to emphasize, if not exclusively focus upon, Peirce. I have often mentioned the influence of John Sowa in first getting me interested in Peirce, so his site (with query specific to Peirce) is a good one to include on your list. Sowa tends to focus on existential graphs, knowledge representation, logic and natural language understanding. A good source for Web writers on Peirce may also be found on the Arisbe site; check out the blogroll on the left column. Of course, I, too, write not infrequently about Peirce. You may obtain my Peirce articles under my blog’s Peirce category. There are perhaps another dozen or so who write often on Peirce.

In terms of broad electronic resources on Peirce, probably the best is Arisbe, noted already. (See here for the history of the term Arisbe as used by Peirce for his Pennsylvania home.) Two high-quality, online philosophy sites, the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy, are often good introductory resources when beginning to learn about a new topic. Many of their Peirce articles are written by one of the authoritative scholars for that subject area. A site which has not been updated since the early 2000s, but which has some unique and high-quality articles by outside experts, is the Digital Encyclopedia of Peirce. If you lack the electronic sources I noted above, a useful site to see some different uses of specific Peircean terms may be found on the Commens Web site. Besides the dictionary, there are some Peirce articles and a narrower (and higher quality) listing of academic articles than what Google Scholar provides.

Some tens of thousands of Peirce’s handwritten pages have not yet been transcribed for broad use. The Charles S. Peirce Project was established in 1976 to continue the mission of making Peirce’s writings available, started by the Collected Papers (CP) project [4] going back to the 1930s. The Project continues to produce a multi-volume chronological and critical edition of Peirce’s writings. Traditionally, this is expensive work in terms of vetting and cross-referencing manuscripts, all the while trying to maintain the highest editorial quality. Progress has been slow. More recently, efforts to broaden participation with crowdsourcing and more modern technology are attempting to speed up the release of Peirce’s written backlog [17] and make information digitally searchable. Note that the Project, like the Arisbe gateway, is managed by Indiana University, which has taken the lead role globally in many areas of Peirce resources and writings.

Peirce’s theory of semiosis began with three categories, which could be interpreted as six categories [by including what Peirce called the “degenerate” forms for Thirdness (2) and Secondness (1)], but then he expanded to 10, and after the turn of the 1900 century pushed for 28- and 66-category schema. These latter were some of the last substantive contributions made by Peirce to his semiotic theory, and were clearly in a state of flux with many changes in Peirce’s last notes. The extension of the sign categorization is exciting, however, and various attempts have been made to try to complete Peirce’s thinking or inductively argue for certain additions and schema. One of the funnest to work with is from Romanini’s Minute Semeiotic Web site. The 66-sign schema is reasonably argued, and the Web interface is cool (requires Flash).

A useful piece of information if you study Peirce further, given that so much of his writing appeared long ago or has been transcribed or compiled by editors, is how to decipher the citation schemes used. Good sources on Peirce citation standards are Wikipedia CSP abbreviations, the Robin catalog for citing papers and manuscripts, and the abbreviations listing in [1]. There is a Peirce Society, established in 1946, to encourage study of and communication about the work of Peirce and its ongoing influence. It has an annual meeting and conducts an annual essay competition.

Since first established by Joe Ransdall in 1993, there is a dedicated discussion list, Peirce-L, with often lively discussion. That link will allow you to search archives going back to 2011 and to subscribe to the list. The archives go back for years (I have not tried to retrieve from as far back as 1993!) and can be searched for (often) salient commentary on Peirce topics of interest. (Actually, if you have been on the list for some years, as I have, some topics keep returning like waves breaking on the shore.) Consult Arisbe for archives earlier than 2011. Most users are lurkers, but the list attendees are really good about answering questions or providing assistance. There is a similar mail list group in biosemiosis, another field that Peirce played no small role in helping to gestate.

A Man of Complexity, Unlikely to be Fully Plumbed

Though obviously many intellectual giants of history were recognized as such in their own times — Newton, Einstein, Darwin and Aristotle come to mind — all of us like the story of the genius unjustly ignored in his own lifetime [18]. In science, famous examples include Copernicus, Galileo, Wegener and Mendel. Charles Sanders Peirce fully belongs in this pantheon as well, a possible outcome I think he realized himself [19]. Ill, in poverty, and shunned by the establishment of his time, Peirce worked feverishly in his last years to get down on paper as much as he could, pretty much laboring alone and in obscurity. We are still plumbing these handwritten papers, gaining new insights and perspectives of what we think we know about Peirce’s philosophy and perspectives.

In the early days after Peirce’s death, it was his wife Juliette and his colleague Josiah Royce who saved his papers, unfortunately to a shaky initial trusteeship by Harvard. Royce died himself soon thereafter. It was a decade before the first editorial compilation of Peirce was published [2] and nearly twenty years until initial release of his (flawed) Collected Papers [4]. Meanwhile, largely lacking students to survive him nor a standard history of academic publications, others appropriated his discoveries and work with no or inadequate recognition. Notable names in mathematics and philosophy may have been guilty to one degree or another of these sins.

One of Peirce’s most famous admonitions is “there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.” (CP 1.135). Slowly at first, and then growing after publication of the Collected Papers, there has been a legion of researchers and academics who have labored to preserve, understand and explicate Peirce’s insights. Virtually every author and name mentioned in this article has played such a role, with hundreds more, some even more active than those cited, contributing their part to Peirce’s growing legacy. And the army keeps growing.

Yet, given Peirce’s own constant questioning and revision of his theories, plus the fragmented nature of the written record he left behind, I think it fair to assert that we will never come to fully understand Peirce’s “truth”. On the other hand, I also think we are only just beginning to understand how Peirce’s insights can continue to inform our understanding of the world and our own role in it.

Lastly, please do let me know if I missed what you think are some of the most noteworthy Peirce resources.

[1] Cornelis de Waal, 2013. Peirce: A Guide for the Perplexed, Bloomsbury Academic, London. [2] Morris R. Cohen, ed., 1923. Chance, Love, and Logic: Philosophical Essays. Harcourt, Brace and World, New York, NY. Reissued by Bison Books, University of Nebraska, 1998. [3] Justus Buchler, ed., 1940. Philosophical Writings of Peirce, Routledge and Kegan Paul Ltd., reissued by Dover Publications, New York NY, 1955. [4] See the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme used for these sources is commonly seen in Peirce scholarship, and is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [5] You can use a Google site search to search within the textlog.de site, even though it is in German and does not have its own search function, by using a query similar to the following: https://www.google.com/search?hl=en&as_q=peirce+abduction&as_sitesearch=www.textlog.de. Note, include ‘peirce’ in the request, because there are other philosopher papers on the textlog.de site. Also note this approach is tailored for English, with the example querying for “abduction”; replace your own search query in the query string. [6] InteLex, The Writings of Charles S. Peirce — A Chronological Edition. Electronic Edition. ISBN: 978-1-57085-015-8. See the InteLex site for an older listing. In 2011 InteLex shifted to an online model serving institutions, with the CDs no longer available. [7] C.S. Peirce, The New Elements of Mathematics by Charles S. Peirce, 4 volumes in 5, Carolyn Eisele, ed., Mouton Publishers, The Hague, Netherlands, 1976; these may be found online in PDF for download from uberty.org: Vol 1, Vol 2, Vol 3, and Vol 4. [8] Nathan Houser and Christian Kloesel, eds., 1992. The Essential Peirce, Vol (1867-1893), Indiana University Press, Bloomington, IN, [9] Michael Raposa, 1993. Peirce’s Philosophy of Religion. Indiana University Press, 180 pages [10] Kelly A. Parker, 1998. The Continuity of Peirce’s Thought. Vanderbilt University Press, Nashville, [11] Murray G. Murphey, 1993. The Development of Perice’s Philosophy. Hackett Publishing Company, Inc., Indianapolis. [12] Fernando Zalamea, 2012. Peirce’s Logic of Continuity: A Conceptual and Mathematical Approach, Docent Press, Boston, 182 pp. Short of purchasing a book to start, there are two useful papers online in PDF to cover the gist of this book, one mostly on existential graphs, the other somewhat longer with discussion of category theory. [13] Louis Menand, 2001. The Metaphysical Club: A Story of Ideas in America, Farrar, Straus and Giroux, New York, NY. [14] Joseph Brent, 1998. Charles Sanders Peirce: A Life (2nd edition), Indiana University Press, Bloomington. [15] Mina Samuals, 2006. The Queen of Cups, Unlimited Publishing LLC, Bloomington. [16] Here is an example query: https://scholar.google.com/scholar?q=”peirce”+abduction. Substitute your own topic keywords for ‘abduction’ in the example query string. [17] I could post the links here, but the editors in charge of these transcription efforts are naturally desirous to maintain quality and keep participation manageable. However, if you are seriously into Peirce, it is quite informative to contribute to the process. If you think you’d like to contribute, do some searching on transcribe and Peirce to find these projects on your own, or contact me directly for sources. [18] It is not only scientists, but writers, artists and musicians sometimes also do not achieve lasting fame until after their deaths. See https://www.google.com/search?q=genius+recognized+after+death. [19] I am helping to transcribe “Significs and Logic” (MS 641-642, 1909), a late, unpublished, handwritten manuscript, wherein Peirce states, “I am striving with all my might to set them [his analyses of the relations between semiotic and logic] in a book so that they may be critically examined; but whether my powers hold out for so great a task is dubious.” This sense of racing against the clock pervades his last writings.

Why I Study C.S. Peirce

AI3:::Adaptive Information (Mike Bergman) - Tue, 08/22/2017 - 03:52

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I Can Sum it Up in Six Words

I am not an armchair philosopher, nor one to seek out books and articles by “big thinkers”. I suppose I have the standard amount of curiosity about questions of metaphysics and cosmology, but I also have never set out to plumb these questions closely. I do not feel wayward or questing for cosmic truths. Yoga might be a good idea, but I don’t do it.

Yet, for now more than a decade, and with growing intensity and focus, I find I am studying and reading and learning as much as I can about the great 19th century American logician and polymath, Charles Sanders Peirce. I have to admit I surprise myself with the ongoing dedication I am applying to learn more about this unique scientist and philosopher, one whom I am coming to believe was one of the greatest thinkers in human history. So, it is rather natural I should ask myself: Why do I study this single individual so closely? Why, among all of the writers and thinkers across history, am I compelled to study this man?

While I can appreciate Peirce for his intellectual arrogance, a trait we share, I don’t think my attraction to Peirce is personal. He was born into privilege and was brought up among the intellectual elite in Cambridge. His father, Benjamin Peirce, was a professor at Harvard and one of the most prominent mathematicians of the early- to mid-1800s. Charles received a first-rate education, including much personal tutoring by his father, and was given preference and positions and sinecures at a young age probably unjustified by his early accomplishments. He was a dandy and an iconoclast, and also flaunted society’s conventions, living with his second wife prior to marriage and after being abandoned by his first wife. He was a prodigious writer and very hard worker over fifty years, but was cavalier, if not unethical, in his abuse of his positions and public funds. He was reportedly a user of morphine and cocaine, ostensibly for neuralgia, but with many of the hallmarks of a basic addict. He pursued his personal intellectual interests at the expense of his paid responsibilities. He created powerful enemies that ultimately kept him from securing a professorship at a leading university, which he and his family believed to be his birthright. He made poor decisions concerning money and finances, often disastrous ones, and died essentially penniless, with no fame and little notoriety. Yet he befriended and influenced many of the leading thinkers of his time, including William James, Josiah Royce, John Dewey and Oliver Wendell Holmes. After his death, Harvard was scandalous in how it (mis-) handled his donated papers and restricted access for many years to his unpublished writings, a continuation of the vendetta brought by Charles W. Eliot, the longstanding Harvard president. Peirce was routinely undercut by his supposed supporter and family friend, but actual enemy, Simon Newcomb. Yet, within a decade of his death, anthologies were published and his reputation and stature began to grow. The understanding of his insights and accomplishments continues to grow as his voluminous unpublished writings get released and are studied. Peirce’s reputation now is the highest it has ever been in the hundred years since his death, growing, and surely greatly exceeds whatever fame he saw during life.

Peirce did not view himself as a philosopher, but as a scientist and logician. His advances in mathematics, logic, the physical sciences, and the scientific method are legion. He was the first to develop a theory of signs (semiosis), is the acknowledged “father” of American pragmatism, developed diagrammatic ways to represent logic via existential graphs, and explicated a new kind of inference, abductive reasoning. He made contributions to linguistics, the categorization of the sciences, geodesy, and topology. His precise work on physical measures with pendulums and in chemistry led him to make advances in probability, statistics and instrumental errors. He was a realist and understood the limits to truth. His advances appear to be grounded in a relentless questioning of premises and a rigorous application of logic to the most basic questions. These quests led him to a fundamental cosmogony built around the irreducible and universal categories of Firstness, Secondness and Thirdness. More on that anon.

As my own blog explains, I was originally trained as an evolutionary biologist and population geneticist. Since my graduate days, I have replaced my focus on biological information with one based on digital information and computers. My passion has been on the role of information — biological or cultural — to confer adaptive advantage to deal with an uncertain future and as a means of generating economic wealth. My intuition — really, my basic belief — is that there are commonalities between biological and cultural information. I have been seeking insights on this intuition for more than four decades.

The first attraction to Peirce began with my professional interests in the semantic Web. My earliest exposure to the semantic Web kept drawing my attention to questions of symbolic knowledge representation (KR). Like the genetic language of DNA in biology, my thought has been that there must be better (more “truthful”) ways of representing knowledge and information in digital form. My sense has been that there must be better — as well as, of course, worse — ways to represent knowledge. My sense is that syntax or specific language is not the key, but that the basic building blocks of grammar and primitives hold that key. We further need a set of primitives well suited to natural language understanding, since so much of humanity’s cultural information is embodied in text. Structured data forms not able to represent natural language are not an appropriate starting point.

In the realm of knowledge representation and computer understanding of information, John Sowa‘s advocacy to study Peirce was the initial reason I began reading up on Peirce, starting about in 2006 [1]. Peirce’s semiosis and views on the symbolic nature of language and relation to meaning and representation struck a chord. Yet, despite many links and sources, studying Peirce is hard. This difficulty is partly the result of Peirce himself: in his quest for precision in terminology, Peirce has created his own vocabulary, sometimes jawbreaking, often with multiple terms that change over time for specific concepts. The difficulty is also due to the fragmented nature, even today, of Peirce’s writings. And, the difficulty also comes from the cacophony of voices and views about what Peirce did or intended to say. It literally takes years to tease out these various camps and personal advocacies sometimes admixed with Peirce’s own views.

However, now that we have released KBpedia, a major artifact in artificial intelligence and semantic technologies based on our (ongoing) understanding of Peirce’s insights, I wanted to reach back over my own decade of exploring Peirce to explain why I think his teachings are so relevant to these new fields. Given Peirce’s manifest accomplishments, others often point to very different things they find important in Peirce. That is fine. We all see and gain what we must from our information at hand. But in my context in regard to knowledge representation, here are the six reasons why I study Peirce.

Chance, Both Probable and Absolute

Peirce brings two remarkable insights about chance in his writings. The first insight, now somewhat prosaic but new for its time, was the importance of probability to many problems. The results, for many problems, are not absolute, but probable across a distribution of possible outcomes. To test these probabilities, it is essential to sample randomly, or by chance. Peirce was an early explicator about random sampling and statistics. Indeterminant problems are common, and an understanding of chance and probabilities is the only tractable way to assess them.

The second remarkable insight is more fundamental, and perhaps even more important. Peirce was an early supporter of Darwin’s theory of evolution and understood the role of variation. Peirce’s probability studies enabled him to see that our world was one of “surprising facts”. A completely random world would signal no variety, so that chance must be leading to variants that cause us to inspect and understand emerging properties. Chance is itself offering up variants, some which have the character of persistence because their strong tendencies have a probability to be reinforced. These forces of chance give our world the variety and diversity it possesses. These local variants are the opposite of general thermodynamic entropy. There are laws and habits that lead to regularities that both tend to perpetuate themselves as generalities, but also flash surprising variation that cause us to take stock and categorize and generalize anew. In Peirce’s cosmogony, these primitives of chance (Firstness), law (Secondness) and habit (Thirdness) can explain everything from the emergence of time and space, to the emergence of matter, life and then cognition. Though it is true that Thirdness (continuity) is the more synthesizing concept, the role of chance alone to drive this entire reality suggests its essential character. Note that Peirce often used the term tychism to refer to his ideas about chance and randomness [2].

The idea that chance alone could be the variant that led to the minute differences arising during the Big Bang, which is posited to have led to matter and its structure, or that self-perpetuating life could emerge from inanimate matter, or that forms of life would symbolically capture these variations via cognition and language, may all be seen as inevitable and unexpected events arising from chance. Perhaps most events have a cause, but the fundamental ones really result from chance. “Surprising facts” mean the world is unpredictable, and ultimately probabalistic. Achieving the limits, the 0s and 1s of Cartesian logic, is likely never achievable. Reality is shaded and nuanced.

When Peirce began putting forth these ideas, specifically in his Popular Science series in 1878 in “On the Nature” [3], these were radical ideas. At the time of these publications, science was still decades away from quantum mechanics and the Heisenberg uncertainty principal. And, even though Einstein (in) famously said that “God doesn’t play dice with the world,” [4] Einstein himself, and his unsettling of Newtownian physics, were still three decades away. This is but one, among many, examples where Peirce had insight and prescience well in advance of later supporting science.

The reason, Peirce would say and I would agree, is not that he was somehow miraculously able to see the future. But, through the rigorous application of logic, Peirce was able to see the requisite primitives of existence.

The Three Universal Categories

Not only at the most fundamental level, but actually, at almost all levels of understanding and logic, Peirce articulated a world view that was built around these universal categories of Firstness, Secondness and Thirdness. Peirce uses this triadic structure to describe language, signs, logic, relations, growth, emergence, science, truth, limits, meaning, community, and consensus-building. Though Peirce acknowledges natural classification systems, such as trees of life and dichotomous taxonomic keys, in most areas of ideas and concepts and metaphysics, he boils down his arguments into these three universal categories. He argues that each alone is necessary, each is irreducible, and all three are required to properly represent any information space.

I was first attracted to this schema because I was focused at the time on representing human language and its meaning. Only through context and perspective — Thirdness — may we hope to capture and understand the nuances of meaning. When I first saw this strength in Peirce’s world view, that (and his writings) led me to look at its applicability elsewhere. The first area where one most likely is to be exposed to Peirce’s triadic viewpoint is in his theory of signs (semiosis) consisting of the object, its sign or representation, and how it is interpreted (interpretant). This fundamental structure can be applied to signs themselves (icon – index – symbol) or to the very basis of logic (grammar – logics – methods). Indeed, as I discuss below, this same triadic viewpoint is what helps us think though how to organize our understanding of the world around us.

Too much of what we see today in so-called “upper ontologies” and the like are knowledge representation models that completely ignore the aspects of context and perspective. Most current upper ontologies — including BFO, Dolce, SUMO, Cyc, UFO — are grounded in some form of Cartesian dichotomy, the basis for argument between their proponents. But a Cartesian and nominalistic view is exactly what is wrong in these viewpoints. What makes for the meaning of context and perspective in any aspect of knowledge is gradation. Further, gradations need to move beyond shaded gray in a dichotomous spectrum of white and black, but to also include color, vibrancy, and nuance. Only Thirdness brings this factor.

The sheer ubiquity of Peirce’s universal categories often makes them seem invisible. We all can clearly see the folly of using dichotomous schema to model real phenomena, but we (that is, human systems) continue to pursue it without question. Our states and phenomena are not on and off, but are probable or graded, likely or nuanced, or often shaded. Yet we do not question why we continually apply a dichotomous schema to real world phenomena. Peirce did question such basic functions. It is not so much that he was a superhuman of intellect, but that he sussed out what we need to question in our premises, using sound logic to tease out insight and make questions simpler. This, and the universal categories, was Peirce’s secret sauce.

The Primacy of Logic

The reason these points are so important and fundamental to understanding Peirce is that his whole basis for reasoning was based on the primacy of logic. And, boy, does Peirce’s inspection of logic help bring clarity.

Peirce was totally familiar with the classic philosophers (Aristotle and Plato, and many others), the medieval scholastics (Duns Scotus), influential recent philosophers (Descartes and Kant) and new mathematics (Boole, Venn and DeMorgan). He explicated deductive and inductive reasoning in the clearest of ways, and corrected erroneous views of what constituted inductive reasoning. He most importantly recognized that, just as many problems are distributive in nature, so are many of the logical questions. For this, Peirce decomposed the basic syllogism of the Greek philosophers to articulate a third kind of inference, abductive reasoning. Abductive reasoning is the positing of possible premises that could lead to observed facts. Science calls them hypotheses.

So, for Peirce, logical tests needed to be clear, understood in terms of applicability and the meaning of results, and tested for logical rigor. For this later objective to be met, Peirce needed to explicate completely the basis, applicability and interpretation of deductive, inductive, and abductive logic. It is really this nugget at the core of Peirce and his approach that provides the understanding of how he generated his insights. As I understand it, Peirce’s primacy of logic is to be prosecuted like this: Every statement is to be decomposed into its fundamental premises. These premises are to be tested against all logical tests, including the implications resulting from inference. Anomalies or “surprising facts” should be singled out for attention and subjected to the pragmatic maxim (see below).

Of course, the idea of questioning premises is not so easy. It is not easy because many of us are queasy to really learn how insecure and inadequate we really are. It is not easy because ideas are like onions, and it is often hard to know how or via what perspective we should be peeling back the layers. It may not be easy because we know these things, but have our own agendas that we wish to shield from truthful inquiry. It is not easy because we all try to communicate, but do so imperfectly.

The clear thread through Peirce’s writings is the respect and attention given to the primacy of logic, but also the role of community in deciding belief and terminology. Though, as a normative science, logic is not the center root of Peirce’s categorization of science, he certainly bases all of his major arguments and insights on logic. And, those insights include ones about the role and principles of logic itself.

Truth is Testable and Fallible

Peirce was consistent in emphasizing that “truth” is not absolute; there is always a finite probability that we do not know actual “truth”. Any scientist spending much time on Peirce’s writings would quickly affirm that, in nature, Peirce is a scientist. His insights and attentions are grounded in science. His understandings of measurement and error and precision are those of a scientific practitioner.

Peirce’s time, as is our own now, was a time of great scientific advance and challenges to conventional understanding. During Peirce’s professional lifetime, advances were occurring in the understanding of waves and fields, the chemical periodic table, evolution, electricity, and thermodynamics and gases. Given this ferment, it is clear why Peirce’s world view supported the ideas of truth as a limit function, the potential fallibility of understood “truth”, and the fact that truth itself stood upon a gradation of certainty.

Yet, whether a product of his own times, or correct and prescient in his nature, I agree totally with the strong thread in Peirce’s writings that truth is itself a gradation. “Truth” is a limit function. The purpose of being and inquiry is the questioning of truth, but no matter what the information nor the logic, we will never have complete understanding. Knowledge is fundamentally an open world problem. Completeness of information and completeness of understanding are each, themselves, ideals. We strive for them, but we never can fully achieve them. While we may reach sufficient certitude to bring about belief, itself an essential motivator in this question, we will never absolutely achieve it. “Truth”, then, is ultimately (as a continuous limit function) unachievable. But, “belief”, which actually guides our actions, may be achieved.

Drilling down further on these questions shows that “truth” is fallible. This is NOT an excuse for saying there is no right, and no wrong. Rather, the fallibility of truth means that we can never have complete certitude about truth. We may have a preponderance of evidence that gives us belief, and therefore the basis for action, but none of this guarantees actual truth. I actually believe that most of the real circumstances of our needing to test truth with logic are actually probabalistic circumstances. Again, that is not saying that truth is relative, but that absolute truth is perhaps never absolutely found.

There is a Categorical Way to Think About the World

These Peircean ideas of the universal categories, applied against basic logical principals, and subject to the understanding about fallibility and the limits to truth, provide a basic set of methods of how to think about and categorize the world. Start with any subject domain.

We know the things, and therefore the characteristics, of the things that populate this domain. So, we first spend time enumerating and describing the features of the things in this domain. We’ll call this category of characteristics, Firstness. Then, we try to enumerate and organize the actual things in this domain. These, specifically, are the events and entities, that we can imagine or enumerate about this domain. This list of particulars, what we call Secondness, is surely always going to grow, so from an operational viewpoint we want easy update and modifiable input files for these items.

But the items in our domain also have generalities and shared aspects that help place those items into meaningful categories. These groupings, admittedly synthetic in one sense, are also real in another sense when the groupings make logical sense. These generalities are an expression of Thirdness. This categorization into Thirdness is actually fairly straightforward to do on simple logical grounds, but is more difficult when explanatory power is desired.

Nonetheless, when the “surprising fact” arises that causes us to question premises and regularities, we can apply this same categorization logic in order to assess the next level of subject specificity. Some logic activities are, indeed, processes, and are a combination of steps or states. But, now, we are in a mediating portion of our information space, likely again requiring new categorization. Peirce’s universal categories provide a powerful unifying force for organizing and categorizing knowledge domains.

We Must Make Practical Choices in Our Limited Time

In a probabalistic world, which it is, we see lines of evidence everywhere for inferring various aspects of the world, now and into the future. The truth is, as Peirce often makes clear, is that only the here and now is knowable; what might come next (into the future) is a probability. The stronger, or more definitive, means of inference, deduction and induction, can never apply to the future. I’m not sure Peirce understood that his formulation of abductive reasoning was the needed pathway here, but it is also true that abductive reasoning is the only path to new knowledge or novelty.

The future is not given. The future may be changed via action. Some future conditions are more favorable to me as an entity in the present than other future conditions. There is every reason to believe that active agents will pursue acts in the present to perpetuate their interests into the future.

The choice of next actions among many possible next actions has some pragmatic implications. One, not all alternatives may be tested simultaneously. Two, some alternatives are more likely to be instrumental than others. Three, any alternative has its own unique set of actions and steps. Peirce developed what he called the pragmatic maxim [5] as a way to sift through the myriad of possible explanations for things in order to select those with the most economy and likelihood of bearing fruit. The pragmatic maxim provides guidance to scientists as to what to study next, and how.

So, Why I Study Peirce

These points should make it clear that Peirce considered himself foremost as a scientist, who probes and questions premises with logic and purpose. Peirce’s critical attention and refinement of the scientific method places him in the top tier of philosophers of science. Peirce believed all questions lent themselves to scrutiny and logical analysis. Among the myriad of possibilities available to us for inquiry as scientists, Peirce’s methods help point to those options most likely to yield fruit within limited time and resources. The universal categories provide us with a constant and consistent framework for representing, analyzing and organizing knowledge.

As for the six words that help me understand Peirce’s writings, I offer: chance, universal, logic, fallible, categorical, and practical. These are topics I will turn to again as we continue to probe Peirce’s views on the world and knowledge.

[1] For Sowa’s writings, see https://www.google.com/search?as_q=%22peirce%22&as_sitesearch=jfsowa.com. For my own writings on Peirce to date, see http://www.mkbergman.com/category/c-s-peirce/. [2] See Philip Rose, 2013. “Another Guess at the Riddle: More Ado About Nothing,” Analecta Hermeneutica 4 (2013) and Philip Rose, 2016. “CS Peirce’s Cosmogonic Philiosophy of Emergent Evolution: Deriving Something from Nothing,” SCIO Revista de Filosofía Journal of Philosophy: 123-142, November 2016. [3] C.S. Peirce, 1878, “The Order of Nature“, Popular Science Monthly, v. 13, pp. 203–217 (June 1878). Reprinted (CLL 106-130), (CP 6.395-427), (EP 1:170-185). [4] See https://en.wikiquote.org/wiki/Albert_Einstein. [5] In Peirce’s own words, “It appears, then, that the rule for attaining the third grade of clearness of apprehension is as follows: Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.” (CP 5.402)

KBpedia v 150 Released

AI3:::Adaptive Information (Mike Bergman) - Thu, 08/17/2017 - 00:37
Sometimes These Releases Get Complicated

Well, I just completed a five-part article series on major changes to KBpedia that I have been writing over the past few months. Sometimes releases with their version increment numbers seem pretty artificial and don’t always reflect the real changes that were underfoot. Such is this case.

I am pleased to today release version 1.50 of KBpedia. Virtually no changes have occurred in this version with respect to size or scope in comparison to the last release, v 1.40 in February 2017. Rather, this current release is more of a story of consolidation and re-organization for what was already there. Still, these re-organizations feel like they have been pretty substantial, and what is being released today is the cleanest version ever. And, oh, by the way, KBpedia now has a complete predicate organizational schema. So, let’s look at some of these changes.

The Predicates Addition

The background to the five-part series on relations in KBpedia makes the point that most knowledge graphs focus on nouns and little attention has been given to properties or relations, especially as a classification of signs with key relevance to knowledge representation (KR). Actions, through exertions or perceptions, drive events that create cognition, categorizations and new knowledge. Yet we have a relatively poor KR vocabulary for handling relations of all types, be they attributes, external relations, or representations. Since actions drive the real changes in the world, understanding them and their relationships, plus a more rigorous means for identifying and extracting them, should also lead to better fact and relation extraction from unstructured data (text). This is essential for completing the integration of unstructured data with structured data.

The idea of categorizing predicates is not common in the knowledge representation space, but the writings and Logic of Relatives of Charles Sanders Peirce [1], among many of his other writings, help provide guidance for how to think about such matters. That is what we have been doing over the past three years of thinking specifically about properties (OWL sense) or predicates.

Theoretical ideas resulting from reading and study needed to be subjected to real data sources and their attributes as test beds for the theory. In these cases, theory always gives way to facts, so actual data representations, a key benefit from Wikidata, brings practical guidance to theoretical constructs.

Throughout, Peirce’s Logic of Relatives and other writings, particularly his three universal categories, proved invaluable for discerning and deciding edge cases. Broad categorization is relatively easy. The head-scratching always occurs at the interfaces, the margins, the transitions from one understood category to another. Yet this is also the area where the most insight and understanding occurs.

My own current choices have taken some years to gestate, and they may likely change still again. What I understand Peirce’s methodologies to be are not the limiting factor; rather, it is understanding the nature and attributes of whatever object is under scrutiny. It seems there is always something more to learn about anything.

The focus on verbs v nouns also transported me to better understand the nature of the event, action-reaction model. This process also helped bring understanding that events are particulars along with entities, which combined represent all of the real things in the present. (Particulars are a Secondness in terms of Peirce’s universal categories.)

Follow-ons from the Predicates Addition

The organization of relations into attributes (A:A), external relations (A:B) and representations (re:A) has resulted in the addition of about 66 properties to KBpedia, now expressed in this version 1.50. These properties, in turn, have been mapped to about 2500 Wikidata properties, representing more than 90 percent of the property occurrences within that knowledge base. Via one or more properties, this mapping now extends KBpedia’s coverage to about 30 million entities. Future efforts will extend this property coverage to some of the other major KBpedia knowledge bases, including the DBpedia ontology, schema. org and GeoNames. Look for these mappings in future releases.

The addition of these predicates also resulted in some fairly significant updates to the upper structure of KBpedia via the KBpedia Knowledge Ontology, or KKO. We not only added properties to KBpedia, but classed and categorized the predicates into the KKO node structure. This parallel treatment in both properties and classes is one classic technique for being able to reason over predicates [2]. More than 10% of the KKO knowledge graph was changed in version 1.50 to accommodate these changes.

Other Notable Changes

In the process of making these changes we noticed another flaw in the KBpedia knowledge graph, largely the result from earlier inheritances from OpenCyc. Namely, the existing subsumption structure often made direct subClassOf assertions to grandparents or greater. For example, a wasp may be a form of insect, which is a form of arthropod, which in turn is a form of animal. Yet, rather than let inference handle these connections, the original subsumption links might have assigned wasp directly as a sub-class of animal. Though this assertion is correct, it is confusing to mix lower level classes (such as wasps) with higher level ones such as birds, reptiles or mammals, which are more directly sub-classes of animals. We found and cleaned up about 8,000 mixed subsumption assignments in the earlier KBpedia. This clean-up leads to a much easier understood and streamlined hierarchical structure. We will continue to clean such unneeded assignments as they are discovered.

Another change was to add a further 2200 definitions to the existing entries. KBpedia still has an issue of missing definitions, with about one-quarter of the structure still lacking them. But, again, we made a 14% improvement in the coverage of definitions and altLabels in this most recent version. We are committed to working through and completing these assignments.

Where possible, we also added missing mappings to Wikipedia and Wikidata. About 76% of KBpedia now has mappings to Wikipedia. We are committed to raise this coverage to the theoretical limit of about 90%.

In the nearly six months since the last version 1.40 release, tens of thousands of changes have been made to KBpedia. We estimate the entire structure has been re-built from scratch more than 100 times in the interim, each time testing for logic and inconsistencies. The net result is a pretty clean structure from top to bottom, including refinements to all of the existing 80 or so typologies in the system, especially the 30 “core” ones. We believe the overall structure to be much cleaner and more readily understood than prior versions.

Besides these specific changes, we also decided to dedicate KBpedia to its own Web site. This independent identity is in keeping with our desire to establish KBpedia on its own, separate from our company Cognonto as the sponsor. We anticipate further changes along these lines for subsequent releases.

To Learn More

There is much documentation and an active knowledge graph on the KBpedia site. You can also run a demo showing how KBpedia information can inform a relatively simple tagger. The entire upper structure for KBpedia, KKO, is also available for download and inspection. I particularly recommend the separate demo version of KKO, which labels the major nodes according to the Peircean universal categories of Firstness, Secondness and Thirdness. Please note this separate demo version is for learning purposes only, and is not actually used in the online knowledge graph.

The Warmest of Notes About Fred

Another aspect of the changes to KBpedia over the past few months has been the unfortunate end to my business partnership with Fred Giasson. Fred and I have worked directly and constantly with one another for nearly the past decade. While we will continue to be partners in our open source efforts, our formal business relationship has come to an end. My work decade with Fred has been one of the most rewarding of my career. I have had the tremendous, great fortune to work with some of the best and most renowned developers of my time. Fred belongs in that pantheon, if not at the top of it. He is one of the most thoughtful, innovative and disciplined computer scientists of my experience.

Fred and I are three decades apart in age, and also have different native tongues. Fred now has two children and family needs that demand better stability and benefits and consistent income than our business years exhibited. With my own senior years closing in, I personally also want to do more writing and public service. Such are the natural tensions of life that cause highly successful partnerships to move in their own directions. I already miss my daily interactions with Fred. But I am happy to report he is in a stable position with great job satisfaction and prospects. I could not be happier for him and his family. I also know we will be working together for many years to come on our shared passions.

As part of this transition, I now own and run most of the test and build scripts that Fred developed during our joint business tenure. As a non-developer, it is a testament to Fred’s skills that it has been relatively straightforward for me to adopt and embrace his scripts. It is funny. We had worked together for years, but it is only now that I truly appreciate his unique skills and fantastic practices in creating code useful and maintainable by others. Kudos, my friend.

Such kinds of changes often engender other thoughts and changes. I will be sharing some of these with you in articles to come. For today, however, I am most thankful for being able to release version 1.50 of KBpedia. And, to say thanks and pay honor to a computer scientist of the first rank, Fred Giasson.

This series on KBpedia relations covers topics from background, to grammar, to design, and then to implications from explicitly representing relations in accordance to the principals put forth through the universal categories by Charles Sanders Peirce. Relations are an essential complement to entities and concepts in order to extract the maximum information from knowledge bases. This series is now completed with this release of KBpedia (v 150). [1] Charles Sanders Peirce, 1870. “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9 (1870), 317–378 (the “Logic of Relatives”). [2] Natasha Noy et al., editors, 2006. Defining N-ary Relations on the Semantic Web, W3C Working Group Note, 12 April 2006. See esp Pattern 1.

KBpedia Relations, Part V: The Updated KBpedia Grammar

AI3:::Adaptive Information (Mike Bergman) - Tue, 08/01/2017 - 03:13
Re-capping the Terminology for the Knowledge Graph

This last part on the updated KBpedia grammar is the final advance article on the knowledge graph prior to the release of version 1.50. In this article, I update and summarize the grammar at the heart of the ontology. I have written previously [1] on the role that Charles Sanders Peirce gave to what he called a speculative grammar, a Firstness in his triadic view of semiosis, or the logic of signs.  The basic idea of a speculative grammar is simple. What are the vocabulary and relationships that may be involved in the understanding of the question or concept at hand? What is the “grammar” for the question at hand that may help guide how to increase our understanding of it? What are the concepts and terms and relationships that populate our domain of inquiry? Of course, in our context, the domain of inquiry is the representation of knowledge in a knowledge graph useful to knowledge-based artificial intelligence, or KBAI.

Here is how Peirce in his own words placed speculative grammar in relation to his theory of logic [2]:

“All thought being performed by means of signs, logic may be regarded as the science of the general laws of signs. It has three branches: (1) Speculative Grammar, or the general theory of the nature and meanings of signs, whether they be icons, indices, or symbols; (2) Critic, which classifies arguments and determines the validity and degree of force of each kind; (3) Methodeutic, which studies the methods that ought to be pursued in the investigation, in the exposition, and in the application of truth.” (CP 2:260)

As I stated in an earlier article on a speculative grammar [1]:

“Effective use of knowledge bases (KBs) for artificial intelligence (AI) would benefit from a definition and organization of KB concepts and relationships specific to those AI purposes. Like any language, the construction of logical statements within KBAI (knowledge-based artificial intelligence) requires basic primitives for how to express these arguments. Just as in human language where we split our words into roughly nouns and verbs and modifiers and conjunctions of the same, we need a similar primitive vocabulary and basic rules of statement construction to actually begin this process. In all language variants, these basic building blocks are known as the grammar of the language. A well-considered grammar is the first step to being able to construct meaningful and coherent statements about our knowledge bases. The context for how to construct this meaningful grammar needs to be viewed through the lens of the KB’s purpose, which, in our specific case, is for artificial intelligence and machine learning.”

As Peirce says in his Logic of Relatives paper [3]:

“The fundamental principles of formal logic are not properly axioms, but definitions and divisions; and the only facts which it contains relate to the identity of the conceptions resulting from those processes with certain familiar ones.” (CP 3.149)

He goes on to say that the “. . . the woof and warp of a thought and all research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is of the essence of it.” (CP 2.220) An understanding of this language for KBpedia is essential to appreciate what the knowledge graph does and how to use it.

The Grammar Begins with the Universal Categories

The upper structure of KBpedia is captured by the KBpedia Knowledge Ontology. KKO is informed by the triadic logic and basic (“universal”) categories of C.S. Peirce. These same triadic universal categories are also the basis for Peirce’s semiosis, which both captures his views on the nature of logic and the basis of signs in representation and communication. These three universal constituents of Peirce’s trichotomy were in his view the most primitive or reduced manner by which to understand and categorize things, concepts and ideas. A key point for our purposes is that ‘threes’ are the fewest by which to model context and perspective, essential to capture the nature of knowledge [4].

Peirce’s trichotomy of the universal categories can be roughly summarized as:

  • Firstness [1ns] — these are possibilities or potentials, the basic forces or qualities that combine together or interact in various ways to enable the real things we perceive in the world, such as matter, life and ideas. These are the unrealized building blocks, or primitives, the essences or attributes or possible juxtapositions
  • Secondness [2ns] — these are the particular realized things or concepts in the world, what we can perceive, point to and describe. A particular is also known as an entity, event, instance or individual
  • Thirdness [3ns] — these are the laws, habits, regularities and continuities that may be generalized from particulars. All generals — what are also known as classes, kinds or types — belong to this category. The process of finding and deriving these generalities also leads to new insights or emergent properties, which continue to fuel knowledge discovery. Insights arising from Thirdness enable us to further explore and understand things, and is a driving force for further categorization.

The ideas of Firstness, Secondness and Thirdness in Peirce’s universal categories are not intended to be either sequential or additive. Rather, each interacts with the others in a triadic whole. Each alone is needed, and each is irreducible.

KKO begins with these three universal categories, all subsumed under the standard owl:Thing root node (a convention when using OWL). The first Firstness of KKO is called the Monad branch. This branch represents the qualities or potentials or possibilities that help define the actual individual things in the ontology, or Particulars, the real entities or events in the ontology. Monads are attributes and similar, such as colors or shapes; they do not exist independently except as concepts or ideas of themselves. They are only embodied when in relation to a specific instance. Particulars, or instances, are the second branch, which is the first Secondness. Particulars are the real individual things of the ontology. The largest branch in terms of nodes for KKO is the third one, the Generals (also called SuperTypes), wherein the general kinds, classes or types of the ontology are located. Generals are where generalizations (or categorizations) of individual things are made into types or classes. The idea of a man (as a representation of male humans) or the idea of a camera (as a representation of devices to capture an image) are generals. In Peircean terms, generals are as real as particulars, even though they are not instantiated into an individual thing. Generals are the largest category in terms of conceptual or classificatory richness in KKO.

Most layers of the the upper KKO are themselves split into threes, with the same ideas of Firstness, Secondness and Thirdness applied to the categories at each level. Categorization is itself a process grounded in these senses of the universal categories. Whenever an anomalous fact is discovered or the scale of a given category gets too large, it is time to create a new category with its own terminology (grammar), instances and generalities. It is through the application of this Peircean mindset that the breadth and scope of the knowledge graph may be grown.

Each level of the KKO may be labeled as to whether its given category is one of Firstness (1, or 1ns), Secondness (2, or 2ns), or Thirdness (3, or 3ns). We can here see the full upper structure of KKO, with its some 170 concepts, each one labeled as to which of the universal categories applies:

The Upper KBpedia Knowledge Ontology (KKO) Structure

Unfortunately, the graphing software used does not order the nodes by Firstness (1), Secondness (2) or Thirdness (3). (A demo version, viewable in Protege, is labeled such that this ordering is maintained; it will be made available upon KBpedia v 1.50’s release.)

The KKO structure enables us to capture the ideas of constituents and building blocks under the Monads; to place individual instances of entities and events under Particulars; and to generalize or find natural consistencies amongst kinds (or classes) under the Generals. There tends to be some conceptual parallelisms in this structure. The idea about a quality or relation may be placed as an abstract consideration under Monads; an embodied or instantiated quality or relation may be placed as an individual instance under Particulars; or a generalization (or “law”) about such qualities or relations may be placed under Generals. We can reason across all branches and levels of this structure, which means we can reason over things like colors and attributes and relations as easily as types. There is no object or concept, real or imaginary, historical or in the future, which can not be placed into this knowledge representation (KR) structure.

More than 85% of the classificatory structure of KBpedia resides in the generals, or types. These, in turn, are organized according to a set of typologies, or natural classification structures. (The tie-in points to these typologies are shown in the structure above, but the actual typology structures are not.) Unlike the KKO upper structure, each typology is not necessarily organized according to Peirce’s triadic logic. That is because once we come to organize and classify the real things in the world, we are dealing with objects of a more-or-less uniform character (such as animals or products or atomic elements). There are about 80 such typologies in the KBpedia structure, about 30 of which are deemed “core”, meaning they capture the bulk of the classificatory system. Another document presents these 30 “core” typologies in more detail.

The KKO structure in the figure above is quite different than the first versions of the KKO. As this article series has elaborated, our analysis and then additions of relations to KBpedia has resulted in quite a few changes. These relations, categorized as attributes (1ns), relations (2ns) and representations (3ns) are shown under the 2ns of the Predications branch under Generals. While properties for each of these categories are separately provided under object properties, data properties and annotation properties, they are provided here as class types so that we can reason over these different kinds of relations. 

Key Terminology within the Grammar

The complete terminology of the KBpedia ontology is provided through these concepts. However, some of these concepts are more key than others to important structural aspects of the ontology. Thus, besides the universal categories of Firstness, Secondness and Thirdness, here are some of those key concepts, split into three broad groups:

The first group relates to the predicates of the grammar, and includes these three main branches under the Predications node:

  • Attributes are the ways to characterize the entities or things within the knowledge base; while the attribute values and options may be quite complex, the relationship is monadic to the subject at hand. These are intensional properties of the subject
  • Relations are the way we describe connections between two or more things; relations are external-facing, between the subject and another entity or concept; relations set the extensional structure of the knowledge graph, and
  • Representations are icons, denotations, indexes and the metadata of the KB; these can not be inferenced over. But, they can be searched and language features can be processed in other ways.

This first group was the subject of Part III and Part IV in this series.

The second broad group are the individual instances within the ontology. Besides the monadic dyads (which are the reifications of the qualities in the ontology), the two main kinds of instances are:

  • Events are possibly nameable sequences of time, are described in some manner, can be referenced, and may be related to other time sequences or types, and
  • Entities are the basic, real things in our domain of interest; they are nameable things or ideas that have identity, are defined in some manner, can be referenced, and should be related to types; entities (by count) are the bulk of the overall knowledge base.

The understanding of events from a Peircean viewpoint also leads to a better understanding of actions, activities and processes. Events are a bona fide particular, being an expression of time, while entities, which can have tangible form, are a particular expression of space.

The last grouping relates to the terminology and organization of the Generals branch. Here the key concepts are:

  • Types are the hierarchical classification of natural kinds within all of the terms above
  • The Typology structure is not only a natural organization of natural classes, but it enables flexible interaction points with inferencing across its ‘accordion-like’ design (see further [5]).
Understanding the Release Through Its Grammar

When I first adopted this approach of using a speculative grammar, I wrote in part of its advantages [1]:

“In Peirce’s universal categories, Firstness is meant to capture the potentialities of the domain at hand, the speculative grammar; Secondness is meant to capture the particular facts or real things of the domain at hand, the critic; and Thirdness is meant to capture methods for discovering the generalities, laws or emergents within the domain, the methodeutic. This mindset can really be applied to any topic, from signs themselves to logic and to science. The “surprising fact” or new insight arising from Thirdness points to potentially new topics that may themselves become new targets for this logic of semiosis.

“Without the right concepts, terminology, or bounding — that is, the speculative grammar — it is clearly impossible to properly understand or compose the objects or Secondness that populate the domain at hand. Without the right language and concepts to capture the connections and implications of the domain at hand — again, part of its speculative grammar — it is not possible to discover the generalities or the “surprising fact” or Thirdness of the domain.

“The speculative grammar is thus needed to provide the right constructs for describing, analyzing, and reasoning over the given domain. Our logic and ability to understand the focus of our inquiry requires that we describe and characterize the domain of discourse in ways that are properly scoped and related. How well we bound, characterize and signify our problem domains — that is, the speculative grammar — directly relates to how well we can reason and inquire over that space. It very much matters how we describe, relate and define what we analyze and manipulate.

“Let’s take a couple of examples to illustrate this. First, imagine van Leeuwenhoek first discovering “animacules” under his early, advanced microscopes. New terms and concepts like flagella, cells, and vacuoles needed to be coined and systematized in order for further advances in microorganisms to be described. Or, second, imagine “action at a distance” phenomena such as magnetic repulsion or static electricity causing hair to stand on end. For centuries these phenomena were assumed to be caused by atomistic particles too small to see or discover. Only when Hertz was able to prove Maxwell‘s equations of electromagnetism hundreds of years later in the mid-1800s were the concepts and vocabulary of waves and fields sufficiently developed to begin to unravel electromagnetic theory in earnest. Progress required the right concepts and terminology.

“For Peirce, the triadic nature of the sign — and its relation between the sign, its object and its interpretant — was the speculative grammar breakthrough that then allowed him to better describe the process of signmaking and its role in the logic of inquiry and truth-testing (semiosis). Because he recognized it in his own work, Peirce understood a conceptual “grammar” appropriate to the inquiry at hand is essential to further discovery and validation.”

And then [6]:

“Peirce argues persuasively that how we perceive and communicate things requires this irreducible triadic structure. The symbolic nature of Thirdness means that communication and understanding is a continuous process of refinement, getting us closer to the truth, but never fully achieving it. Thirdness is a social and imprecise mode of communication and discovery, conducted by us and other agents separate from the things and phenomena being observed. Though it is a fallibilistic process, it is one that also lends itself to rigor and methods. The scientific method is a premier example of Thirdness in action.”

We are pleased that our next posting will be the announced release of KBpedia v 150.

This series on KBpedia relations covers topics from background, to grammar, to design, and then to implications from explicitly representing relations in accordance to the principals put forth through the universal categories by Charles Sanders Peirce. Relations are an essential complement to entities and concepts in order to extract the maximum information from knowledge bases. This series accompanies the next release of KBpedia (v 150), which includes the relations enhancements discussed. [1] See further M.K. Bergman, 2016. “A Speculative Grammar for Knowledge Bases“, AI3:::Adaptive Information blog, June 20, 2016. [2] See the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [3] This quote is drawn from Charles Sanders Peirce, 1870. “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9 (1870), 317–378 (the “Logic of Relatives”), using the same numbering as from [2]. [4] M.K. Bergman, 2016. “The Irreducible Truth of Threes,” AI3:::Adaptive Information blog, September 27, 2016. [5] M.K. Bergman, 2016. “Rationales for Typology Designs in Knowledge Bases,” AI3:::Adaptive Information blog, June 6, 2016. [6] M.K. Bergman, 2016. “Threes All the Way Down to Typologies,” AI3:::Adaptive Information blog, October 3, 2016.

KBpedia Relations, Part IV: The Detailed Relations Hierarchy

AI3:::Adaptive Information (Mike Bergman) - Tue, 06/27/2017 - 19:25

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Completing the Schema for the Relations Addition

In the previous part of this series I discussed the relations model that we are adding to the KBpedia knowledge structure for its upcoming version 1.50. This article continues that discussion by fleshing out the concept hierarchy for this relations addition. These changes are taking place within the upper structure of KBpedia, what we call the KBpedia Knowledge Ontology, or KKO. The addition of this relations model affects both the class hierarchy of KKO and its properties structure. Both aspects are discussed below.

The previous parts of this series introducing the new KBpedia v 150 provide the rationale for adding a relations or predications structure to KBpedia, as well as the rationale for grounding this structure in the universal categories and logic of relations developed by Charles Sanders Peirce. Let me expand on those arguments a bit further here.

Recall from the earlier parts in this discussion that we want to adopt a schema for relations because we are interested in assertions and propositions in our knowledge structures. As Peirce notes [1],”The unity to which the understanding reduces impressions is the unity of a proposition. This unity consists in the connection of the predicate with the subject; and, therefore, that which is implied in the copula, or the conception of being, is that which completes the work of conceptions of reducing the manifold to unity.” (CP 1.548). The previous part discussed the rationale for three main classes of relationship types and how they related to Peirce’s views on logic and the theory of signs (semiosis). It is now time to expand on those distinctions.

The Second Level of the Relations Hierarchy

At the top level, relations are defined in KBpedia as belonging to one of three main types: Attributes, which are how we describe and characterize individual things (using the shorthand of A:A); External Relations, which are how an individual thing may relate, interact or situate with regard to external things (using the shorthand of A:B); or Representations [3], which are how we may name or define, indicate or reference, or provide supporting information about an individual thing (using the shorthand of re:A). These three main categories capture every conceivable form of relation. Note that an individual thing may also include classes or types, as well as individuals. Through this means, we can talk about and refer to categories, concepts, classes or types when we need to consider them as things unto themselves.

These three main categories correspond to Peirce’s universal categories of Firstness, Secondness and Thirdness [2]. (Where appropriate, I also sometimes footnote some Peirce quotes relevant to the category at hand.) Using the same trichotomous approach to categorization [2], we can now expand these three main relational categories into a second level of nine categories:

Mid-level KBpedia Relations

For Attributes (A:A), the split is into these three categories:

  • Intrinsic — innate characteristics or essences of single entities or events (particulars). Example concepts include oneness, qualities, feelings, inherent, negation, is, has, intensional, naturalness, internal, innateness
  • Adjunctual — events that may occur to a single entities or events (particulars) that help characterize it. Example concepts include birth, death, marriage, events, accidents, surprises, happenings, extrinsic, adjunctual
  • Contextual — circumstances or placements of single entities or events (particulars) that help characterize it. Example concepts include space, time, continuity, contiguous, smooth, otherness, ratings, level, situational (w/ respect to A), sensible, contiguous, all placements thereto, derivative, classificatory, rankings.

For External Relations (A:B), the split is into these three categories:

  • Direct — a simple, direct relationship (no intermediaries) between two different objects (entities, events, or their types, considered as instances). Example concepts include is a, simple without parts, part of, members in types or classes, genealogical roles (parent, child, brother), identity, extensional
  • Copulative — relationships of combination, membership, quantity, action, or circumstance. Example concepts include accidental, real, place, time, situation, quantity, facets, aspects, conjunctive, one-to-many, many-to-one, sum of, contextual, verbs
  • Mediative — true, triadic external relations, such as “A gives B to C”; relationships of relevance, meaning or explanation – namely, thirdness – about subjects and types. Example concepts include concepts, generalities, similarity, genres, aspects, comparison, performance, thought, triadic, agreement/difference, placement in space/time (contiguity), conditional, reasoning, classification.

And, for Representations (re:A), the split is into these three categories:

  • Denotatives — icons or symbols that name or describe the subject. Example concepts include names, labels, images, descriptions, definitions, denotations, icons, designations, proper nouns
  • Indexes — indirect references or pointers that help situate or draw attention to the subject. Example concepts include URIs, identifiers, keys, indices, references, semes, propositions (w/o objects), codes, selections, directional, citations, pronouns [4]
  • Associatives — a situational and contextual assertion of proximity, affiliation or adjacency of the subject with regard to any contiguity. Example concepts include see also, lists, links (incoming + outgoing), associations, likenesses, resemblances [5].
The Third Level of the Relations Hierarchy

For the next level, we can continue with our process of categorization based on the universal categories applied to the nine categories listed above. Here is the schema that results from this approach:

Third Level of the KBpedia Relations Hierarchy

For the mid-level category of Intrinsics, the first of three categories under Attributes, here are the three subsidiary categorizations (representing the Firstness, Secondness and Thirdness, respectively):

  • Qualities — an internal characteristic or aspect of an object; collectively these define intensionally what kind of thing to which the object belongs, though that relationship is not intrinsic
  • Elementals — a contributing part of or integral input or aspect that adds to the understanding about the subject (A)
  • Configurations (forms) — forms or arrangements that are of the nature or perceivable of the subject (A).

For the mid-level category of Adjunctual, here are the three subsidiary categorizations:

  • Quantities — a characteristic of a subject (A) that is expressed as a number quantity
  • Eventuals — chance, accidental or planned occurrences that directly involve subject (A)
  • Extrinsics — external events or circumstances that directly involve subject (A) or help define the nature or reality of subject (A).

For the mid-level category of Contextual, here are the three subsidiary categorizations:

  • Situants — attributes or characteristics that help situate, or place in a locational context, the subject (A)
  • Ratings — an assigned value or characterization that orders subject (A) in relation to other subjects for a given attribute
  • Classifications — a characterization of subject (A) that involves evaluating subject (A) and providing a multi-factor typing, coding or value in relation to a given attribute or set of attributes.

For the mid-level category of Direct, the first of three categories under External Relations, here are the three subsidiary categorizations:

  • Equivalences — a simple, direct relatiionship between a subject (A) and an object (B) that asserts equalness or sameness
  • Parts — a simple, direct relationship where the object (B) is a part of or component of subject (A), including the idea of ‘whole’
  • Descendants — a simple, direct relationship where object (B) is a direct child or parent or subsumption (hyponym) or supersumption (hypernym) to subject (A).

For the mid-level category of Copulative, here are the three subsidiary categorizations:

  • Typings (is B) — this simple relation is for all of the is-a relations to types (B) for subject (A). Identities and common names fit into this category
  • ActionTypes — simple relations of energetics, perception or thought of subject (A) to some other object (B)
  • Conjoins — relations that involve the joining of a subject (A) to an object (B) via an intermediate object.

For the mid-level category of Mediative, here are the three subsidiary categorizations:

  • Comparisons — relations that compare, contrast or size up similarities or differences or overlaps between subject (A) and object (B)
  • Performances — relations of quantity or rank for how subject (A) performed in relation to object (B)
  • Circumstances — relations of subject (A) to external circumstances, situations or contexts.

For the mid-level category of Denotatives, the first of three categories under Representations, here are the three subsidiary categorizations:

  • Media — iconic images or sounds that invoke the identification with a given object or representation. Media in this sense draws attention to the object [6]
  • Labels — symbolic text strings that help to name or draw attention to a particular object
  • Descriptions — text strings that may be longer than labels and provide additional or contextual information or specify attributes about the object, beyond drawing attention.

For the mid-level category of Indexes, here are the three subsidiary categorizations:

  • Pointers — physical or symbolic indicators of a given thing and which draw attention to it
  • Identifiers — generally (unique) symbols or strings that provide a key to the given subject, often within some conventional scheme for generating and recognizing the token assigned
  • Codes — an assigned symbolic token or string that groups the object with similar items; the generation and interpretation of the token is (often) done in relation to an understood schema. Indexes are included in this category.

And, lastly, for the mid-level category of Associatives, here are the three subsidiary categorizations:

  • Lists — an aggregation, either ordered or unordered, of objects similar to one another with respect to given characters or types
  • Relateds (see also) — an indicator of some nature to other objects similar or related to the given object; the criteria and degree or strength of relationship between the items are indeterminate
  • Augments — an indicator to an external factor in relation to the object, which factor itself leads to still further explanations.

These categories, then, complete the three levels underneath the KBpedia Knowledge Ontology’s Predications branch (itself a Secondness under the basic Thirdness of Generals). We have established these as concepts within KKO such that we may reason over the ideas of these categories, and do other conceptual work with them. This conceptualization is helpful in order to consider the ideas of predicates and the relationships between them. However, for mapping properties from external sources, we need a parallel structure in terms of KKO properties.

An Analogous Structure for Properties

We thus created an analogous structure for properties within KBpedia. One useful addition that is forthcoming in the KBpedia v 1.50 release is a mapping of 2500 Wikidata properties to this property schema, which represents more than 95% of all property assignments to the 25 million+ entities within Wikidata. This is one of the first tangible expressions of the benefits of having a fully rational predicate structure within KBpedia.

Attributes, External Relations and Representations comprise OWL properties. In general, Attributes correspond to the OWL datatypes property; External Relations to the OWL object property; and Representations to the OWL annotation properties. These specific OWL terms are not used in our KKO grammar, however, because some attributes may be drawn from controlled vocabularies, such as colors or shapes, that can be represented as one of a list of attribute choices. In these cases, such attributes are defined as object properties. Nonetheless, the mappings of KKO’s grammar to existing OWL properties is quite close. In all cases, our mappings to external sources are done via the subPropertyOf relation in OWL.

Object and Data Properties

Because a given external non-annotation property (that is, all properties except Representations) may either refer to another object (IRI) or to a string or data value, we created parallel listings of object and datatype properties within KKO. Here is the listing for the object properties group as shown by a screen capture from Protégé:

A Matching KBpedia Object Properties Hierarchy

Note that Protégé lists its items alphabetically, rather than our preferred ordering of Firstness, Secondness and Thirdness. You also should note the parallelism to the concept hierarchy discussed above. Not shown is the similar datatype properties structure.

Annotation Properties

As noted, Representations correspond to annotation properties, and that listing is shown in this screen capture:

A Matching KBpedia Annotation Properties Hierarchy

In OWL2, annotations may be organized in a subPropertyOf manner, even though inferencing is not possible over this structure. The organization, though, is helpful to understand relationships (and they can independently be reasoned over with the matching concept structure) and may be used in search, SPARQL or external analytic scripts.

We also organize the SKOS and Dublin Core annotation properties used by KKO into the categorical structure of these Representations, as shown by the screen capture above. This organization helps elucidate the structure under the Representations branch using these commonly applied properties.

Some Caveats and Next Part

This completes the hierarchical specification of the Predications branch within KKO. These 39 categories (3 + 9 + 27), following the categorization approach suggested by Peirce’s universal categories, now complete our additions to this next version of KBpedia.

This addition has been under intense and active development for the past year, though it has been in the works for much longer than that. Over that time, the names of categories and, indeed, even the splits themselves, have changed frequently and evolved. Peirce’s Logic of Relatives [7], as one of the two main sources, is itself laid out in a dichotomous structure, though elsewhere in Peirce’s writings — as we showed in the previous parts — these are often expressed in Peirce’s more standard trichotomous structure. I am sure with use and more experience that we will see further refinements to the KBpedia relations schema as time goes on. Please do not be surprised if you see further changes.

We are now nearly complete with the advance material leading up the KBpedia v 1.50 release. We will have one next part in our series recapitulating the terminology and grammar for this new version. The announcement following that will finally release version 1.50.

This series on KBpedia relations covers topics from background, to grammar, to design, and then to implications from explicitly representing relations in accordance to the principals put forth through the universal categories by Charles Sanders Peirce. Relations are an essential complement to entities and concepts in order to extract the maximum information from knowledge bases. This series accompanies the next release of KBpedia (v 150), which includes the relations enhancements discussed. [1] Peirce citation schemes tend to use an abbreviation for source, followed by volume number using Arabic numerals followed by section number (such as CP 1.208) or page, depending on the source. For CP, see the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. [2] M.K. Bergman, 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness,” AI3:::Adaptive Information blog, March 21, 2016. [3] “I confine the word representation to the operation of a sign or its relation to the object for the interpreter of the representation.” (CP 1.540) “A very broad and important class of triadic characters [consists of] representations. A representation is that character of a thing by virtue of which, for the production of a certain mental effect, it may stand in place of another thing.” (CP 1.564) “as my analysis makes it to be, that a percept contains only two kinds of elements, those of firstness and those of secondness, then the great overshadowing point of difference is that the perceptual judgment professes to represent something, and thereby does represent something, whether truly or falsely. This is a very important difference, since the idea of representation is essentially what may be termed an element of “Thirdness,” that is, involves the idea of determining one thing to refer to another.” (CP 7.630) [4] “But it would be difficult if not impossible, to instance an absolutely pure index, or to find any sign absolutely devoid of the indexical quality. Psychologically, the action of indices depends upon association by contiguity, and not upon association by resemblance or upon intellectual operations.” (CP 2.306) “Indices may be distinguished from other signs, or representations, by three characteristic marks: first, that they have no significant resemblance to their objects; second, that they refer to individuals, single units, single collections of units, or single continua; third, that they direct the attention to their objects by blind compulsion. But it would be difficult if not impossible, to instance an absolutely pure index, or to find any sign absolutely devoid of the indexical quality. Psychologically, the action of indices depends upon association by contiguity, and not upon association by resemblance or upon intellectual operations.” (CP 2.306) [5] “Association is the only force which exists within the intellect, and whatever power of controlling the thoughts there may be can be exercised only by utilizing these forces; indeed, the power, and even the wish, to control ourselves can come about only by the action of the same principles. Still, the force of association in its native strength and wildness is seen best in persons whose understandings are so little developed that they can hardly be said to reason at all. Believing one thing puts it into their heads to believe in another thing; but they know not how they come by their beliefs, and can exercise no control over the inferential process. These unconscious and uncontrolled reasonings hardly merit that name; although they are very often truer than if they were regulated by an imperfect logic, showing in this the usual superiority of instinct over reason, and of practice over theory.” (CP 7.453) [6] “The only way of directly communicating an idea is by means of an icon; and every indirect method of communicating an idea must depend for its establishment upon the use of an icon. Hence, every assertion must contain an icon or set of icons, or else must contain signs whose meaning is only explicable by icons. The idea which the set of icons (or the equivalent of a set of icons)contained in an assertion signifies may be termed the predicate of the assertion.” (CP 2.278) [7] C.S. Peirce, 1897. “Logic of Relatives,” The Monist Vol VII, No 2, pp. 161-217. See https://ia801703.us.archive.org/12/items/jstor-27897407/27897407.pdf
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