AI3:::Adaptive Information Mike Bergman on the semantic Web and structured Web 2017-11-15T06:00:32Z http://www.mkbergman.com/feed/atom/ WordPress Mike Bergman http://www.mkbergman.com <![CDATA[Hierarchies in Knowledge Representation]]> http://www.mkbergman.com/?p=2087 2017-11-15T06:00:32Z 2017-11-14T21:20:25Z

KBpediaSome Basic Use Cases from KBpedia

The human propensity to categorize is based on trying to make sense of the world. The act of categorization is based on how to group things together and how to relate those things and groups to one another. Categorization demands that we characterize or describe the things of the world using what we have termed attributes in order to find similarities [1]. Categorization may also be based on the relationships of things to external things [2]. No matter the method, the results of these categorizations tend to be hierarchical, reflective of what we see in the natural world. We see hierarchies in Nature based on bigger and more complex things being comprised of simpler things, based on fractals or cellular automata, or based on the evolutionary relationships of lifeforms. According to Annila and Kuismanen, “various evolutionary processes naturally emerge with hierarchical organization” [3]. Hierarchy, and its intimate relationship with categorization and categories, is thus fundamental to the why and how we can represent knowledge for computable means.

Depending on context, we can establish hierarchical relationships between types, classes or sets, with instances or individuals, with characteristics of those individuals, and between all of these concepts. There is potentially different terminology depending on context, and the terminology or syntax may also carry formal understanding of how we can process and compute these relationships. Nillson provides a general overview of these kinds of considerations with a useful set of references [4].

Types of Hierarchical Relationships

As early as 1997 Doyle noted in the first comprehensive study of KR languages, “Hierarchy is an important concept. It allows economy of description, economy of storage and manipulation of descriptions, economy of recognition, efficient planning strategies, and modularity in design.” He also noted that “hierarchy forms the backbone in many existing representation languages” [5].

The basic idea of a hierarchy is that some item (‘thing’) is subsidiary to another item. Categorization, expressed both through the categories themselves and the process of how one splits and grows categories, is a constant theme in knowledge representation. The idea of hierarchy is central to what is treated as a category or other such groupings and how those categories or groupings are tied together. A hierarchical relationship is shown diagrammatically in Figure 1 with A or B, the ‘things’, shown as nodes.

Direct Hierarchy

Figure 1: Direct Hierarchy

All this diagram is really saying is that A has some form of superior or superordinate relationship to B (or vice versa, that B is subordinate to A). This is a direct hierarchical relationship, but one of unknown character. Hierarchies can also relate more than two items:

Simple Hierarchy

Figure 2: Simple Hierarchy

In this case, the labels of the items may seem to indicate the hierarchical relationship, but relying on labels is wrong. For example, let’s take this relationship, where our intent is to show the mixed nature of primary and secondary colors [6]:

Multi-hierarchy

Figure 3: Multiple Hierarchy

Yet perhaps our intent was rather to provide a category for all colors to be lumped together, as instances of the concept ‘color’ shows here:

Extensional Hierarchy

Figure 4: Extensional Hierarchy

The point is not to focus on colors – which are, apparently, more complicated to model than first blush – but to understand that hierarchical relations are of many types and what one chooses about a relation carries with it logical implications, the logic determined by the semantics of the representation language chosen and how we represent it. For this clarity we need to explicitly define the nature of the hierarchical relationship. Here are some (vernacular) examples one might encounter:

A

subsumes

B

A

is more basic than

B

A

is a superClassOf

B

A

is more fundamental than

B

A

is broader than

B

A

includes

B

A

is more general

B

B

is-a

A

A

is parent of

B

A

has member

B

A

has an instance of

B

A

has attribute

B

A

has part

B

Table 1: Example Hierarchical Relationships

Again, though we have now labeled the relationships, which in a graph representation are the edges between the nodes, it is still unclear the populations to which these relations may apply and what their exact semantic relationships may be.

Table 2 shows the basic hierarchical relations that one might want to model, and whether the item resides in the universal categories of Charles Sanders Peirce of Firstness, Secondness or Thirdness, introduced in one of my previous articles [7]:

Firstness

Secondness

Thirdness

attribute

token (instance)

sibling

|

sibling

child

parent

|

parent

token

type

part

whole

|

whole

sub

super

|

sub

Table 2: Possible Pairwise (―) Hierarchical Relationships

Note that, depending on context, some of the items may reside in either Secondness or Thirdness (depending on whether the referent is a particular instance or a general). Also note the familial relationships shown: child-parent-grandparent and child-child relationships occur in actual families and as a way of talking about inheritance or relatedness relations. The idea of type or is-a is another prominent one in ontologies and knowledge graphs. Natural classes or kinds, for example, fall into the type-token relationship. Also note that mereological relationships, such as part-whole, may also leave open ambiguities. We also see certain pairs, such a sub-super, child-parent, or part-whole, need context to resolve the universal category relation.

Reliance on item labels alone for the edges and nodes, even for something as seemingly straightforward as color or pairwise relationships, does not give us sufficient information to determine how to evaluate the relationship nor how to properly organize. We thus see in knowledge representation that we need to express our relationships explicitly. Labels are merely assigned names that, alone, do not specify the logic to be applied, what populations are affected, or even the exact nature of the relationship. Without these basics, our knowledge graphs can not be computable. Yet well over 95% of the assignments in contemporary knowledge bases have this item-item character. We need interpretable relationships to describe the things that populate our domains of inquiry so as to categorize that world into bite-sized chunks.

Salthe categorizes hierarchies into two types: compositional hierarchies and subsumption hierarchies [8]. Mereological and part-whole hierarchies are compositional, as are entity-attribute. Subsumption hierarchies are ones of broader than, familial, or evolutionary. Cottam et al. believe hierarchies to be so basically important as to propose a model abstraction over all hierarchical types, including levels of abstraction [9]. These discussions of structure and organization are helpful to understand the epistemological bases underlying various kinds of hierarchy. We should also not neglect recursive hierarchies, such as fractals or cellular automata, which are also simple, repeated structures commonly found in Nature. Fortunately, Peirce’s universal categories provide a powerful and consistent basis for us to characterize these variations. When paired with logic and KR languages and “cutting Nature at its joints” [10], we end up with an expressive grammar for capturing all kinds of internal and external relations to other things.

So far we have learned that most relationships in contemporary knowledge bases are of a noun-noun or noun-adjective nature, which I have loosely lumped together as hierarchical relationships. These relationships span from attributes to instances (individuals) and classes [11] or types, with and between one another. We have further seen that labels either for the subjects (nodes) or for their relationships (edges) are an insufficient basis for computers (or us!) to reason over. We need to ground our relationships in specific semantics and logics in order for them to be unambiguous to reasoning machines.

Structures Arising from Hierarchies

Structure needs to be a tangible part of thinking about a new KR installation, since many analytic choices need to be supported by the knowledge artifact. Different kinds of structure are best for different tools or kinds of analysis. The types of relations chosen for the artifact affects its structural aspects. These structures can be as simple and small as a few members in a list, to the entire knowledge graph fully linked to its internal and external knowledge sources. Here are some of the prominent types of structures that may arise from connectedness and characterization hierarchies:

  • Lists — unordered members or instances, with or without gaps or duplicates, useful for bulk assignment purposes. Lists generally occur through a direct relation assignment (e.g., rdf:Bag)
  • Neural networks (graphs) — graph designs based on connections modeled on biological neurons, still in the earliest stages with respect to relations and KR formalisms [12]
  • Ontologies (graphs) — sometimes ontologies are treated as synonymous with knowledge graphs, but more often as a superset that may allow more control and semantic representation [13] Ontologies are a central design feature of KBpedia [14]
  • Parts-of-speech — a properly designed ontology has the potential to organize the vocabulary of the KR language itself into corresponding parts-of-speech, which greatly aids natural language processing
  • Sequences — ordered members or instances, with or without gaps or duplicates, useful for bulk assignment purposes. Sequences generally occur through a direct relation assignment (e.g., rdf:Seq)
  • Taxonomies (trees)— trees are subsumption hierarchies with single (instances may be assigned to only one class) or multiple (instances may be assigned to multiple classes or types) inheritance. The latter is the common scaffolding for most knowledge graphs
  • Typologies — are essentially multi-inheritance taxonomies, with the hierarchical organization of types as natural as possible. Natural types (classes or kinds) enable the greatest number of disjoint assertions to be made, leading to efficient processing and modular design. Typologies are a central design feature of KBpedia; see further [15].

Typically KR formalisms and their internal ontologies (taxonomy or graph structures) have a starting node or root, often called ‘thing’, ‘entity’ or the like. Close inspection of the choice of root may offer important insights. ‘Entity’, for example, is not compatible with a Peircean interpretation, since all entities are within Secondness.

KBpedia’s foundational structure is the subsumption hierarchy shown in the KBpedia Knowledge Ontology (KKO) — that is, KBpedia’s upper ontology — and its nodes derived from the universal categories. The terminal, or leaf, nodes in KKO each tie into typologies. All of the typologies are themselves composed of types, which are the hierarchical classification of natural kinds of instances as determined by shared attributes (though not necessarily the same values for those attributes). Most of the types in KBpedia are composed of entities, but attributes and relations also have aggregations of types.

Of course, choice of a KR formalism and what structures it allows must serve many purposes. Knowledge extension and maintenance, record design, querying, reasoning, graph analysis, logic and consistency tests, planning, hypothesis generation, question and answering, and subset selections for external analysis are properly the purview of the KR formalism and its knowledge graph. Yet other tasks such as machine learning, natural language processing, data wrangling, statistical and probabalistic analysis, search indexes, and other data- and algorithm-intensive applications are often best supported by dedicated external applications. The structures to support these kinds of applications, or the ability to export them, must be built into the KR installation, with explicit consideration for the data forms and streams useful to possible third-party applications.


[1] The most common analogous terms to attributes are properties or characteristics; in the OWL language used by KBpedia, attributes are assigned to instances (called individuals) via property (relation) declarations.
[2] The act of categorization may thus involve intrinsic factors or external relationships, with the corresponding logics being either intensional or extensional.
[3] Arto Annila and Esa Kuismanen. 2009. “Natural Hierarchy Emerges from Energy Dispersal”. Biosystems 95, 3: 227–233. https://doi.org/10.1016/j.biosystems.2008.10.008
[4] Jørgen Fischer Nilsson. 2006. “Ontological Constitutions for Classes and Properties”. In Conceptual Structures: Inspiration and Application (Lecture Notes in Computer Science), 35–53.
[5] Jon Doyle. 1977. Hierarchy in Knowledge Representations. MIT Artificial Intelligence Laboratory. Retrieved October 24, 2017 from http://dspace.mit.edu/handle/1721.1/41988
[6] The first and more standard 3-color scheme was first explicated by J W von Goethe (1749-1832). What is actually more commonly used in design is a 4-color scheme from Ewald Hering (1834-1918).
[7] Michael K. Bergman. 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness”. AI3:::Adaptive Information. Retrieved September 18, 2017 from http://www.mkbergman.com/1932/a-foundational-mindset-firstness-secondness-thirdness/
[8] Stanley Salthe. 2012. Hierarchical Structures. https://doi.org/10.1007/s10516-012-9185-0<
[9] Ron Cottam, Willy Ranson, and Roger Vounckx. 2016. “Hierarchy and the Nature of Information”. Information 7, 1: 1. https://doi.org/10.3390/info7010001
[10] Plato. “Phaedrus Dialog (page 265e)”. Perseus Digital Library. Retrieved November 11, 2017 from http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0174%3Atext%3DPhaedrus%3Apage%3D265
[11] In the OWL 2 language used by KBpedia, a class is any arbitrary collection of objects. A class may contain any number of instances (called individuals) or a class may be a subclass of another. Instances and subclasses may belong to none, one or more classes. Both extension and intension may be used to assign instances to classes.
[12] Adam Santoro, David Raposo, David G. T. Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap. 2017. “A Simple Neural Network Module for Relational Reasoning”. arXiv:1706.01427 [cs]. Retrieved November 1, 2017 from http://arxiv.org/abs/1706.01427
[13] RDF graphs are more akin to the first sense; OWL 2 graphs more to the latter.
[14] In the semantic Web space, “ontology” was the original term because of the interest to capture the nature or being (Greek ὄντως, or ontós) of the knowledge domain at hand. Because the word ‘ontology’ is a bit intimidating, a better variant has proven to be the knowledge graph (because all semantic ontologies take the structural form of a graph).
[15] Michael K. Bergman. 2016. “Rationales for Typology Designs in Knowledge Bases”. AI3:::Adaptive Information. Retrieved September 18, 2017 from http://www.mkbergman.com/1952/rationales-for-typology-designs-in-knowledge-bases/
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Mike Bergman http://www.mkbergman.com <![CDATA[How I Interpret C.S. Peirce]]> http://www.mkbergman.com/?p=2077 2017-09-20T22:55:36Z 2017-09-20T22:55:36Z

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Charles Sanders Peirce, approx. Age 60Another 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.
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Mike Bergman http://www.mkbergman.com <![CDATA[Pulse: KBpedia v 151 Released]]> http://www.mkbergman.com/?p=2075 2017-09-13T18:31:33Z 2017-09-13T18:31:33Z

AI3 Pulse

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.

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Mike Bergman http://www.mkbergman.com <![CDATA[How I Study C.S. Peirce]]> http://www.mkbergman.com/?p=2069 2017-11-05T16:35:54Z 2017-08-29T21:10:55Z

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Charles Sanders Peirce, Government ServiceA 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 Collected 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-assemble 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.
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