His Triadic Logic is the Mindset for Categorization
Many of us involved in semantic technologies or information science grapple with the question of categorization. How do we provide a coherent organization of the world that makes sense? Better still, how might we represent this coherent structure in a manner that informs how we can extend or grow our knowledge domains? Most problems of a practical nature require being able to combine information together so as to inform new knowledge. Categories that bring together (generalize) similar things are a key way to aid that.
Embracing semantic technologies means, among standards and other things, that the natural structural representation of domains is the graph. These are formally specified using either RDF or OWL. These ontologies have objects as nodes, and properties between those nodes as edges. I believe in this model, and have worked for at least a decade to promote its use. It is the model used by Google’s knowledge graph, for example.
Knowledge graphs that are upper ontologies typically have 80% to 85% of their nodes acting to group similar objects, mostly what could be axiomatized as ‘classes’ or ‘types’. This realization naturally shifts focus to, then, how are these groups formed? What are the bases to place multiple instances into a given class? Are types the same things as classes?
Knowledge, inherently open and dynamic, can only be used for artificial intelligence when it is represented by structures readable by machines. Digitally readable structures of knowledge and features are essential for machine learning, natural language understanding, or other AI functions. Indeed, were such structures able to be expressed in a mostly automatic way, the costs and efforts to perform AI and natural language processing and understanding functions (NLP and NLU) would be greatly lessened.
Open and dynamic also means that keeping the knowledge base current requires simple principles to educate and train those charged with keeping the structure up to date. Nothing is perfect, humans or AI. Discovery and truth only result from questioning and inspection. The entire knowledge graph is fallible and subject to growth and revision. Human editors — trained and capable — are essential to maintain the integrity of such structures, automation or AI not withstanding. Fundamentally, then, the challenge becomes how to think simply about grouping things and forming categories. Discovery of simplicity is hard without generalization and deep thought.
A Peircean View in Thirdness
Scholars of Charles Sanders Peirce (“purse”) (1839 – 1913) [1] all acknowledge how infused his writings on logic, semiosis, philosophy, and knowledge are with the idea of “threes”. His insights are perhaps most studied with respect to his semiosis of signs, with the triad formed by object, representation, and interpretation. But Peirce recognized many prior philosophers, particularly Kant and Hegel, had also made “threes” a cornerstone of their views. Peirce studied and wrote on what makes “threes” essential and irreducible. His generalization, or abstraction if you will, he called simply the Three Categories, and to reflect their fundamental nature, called each separately as Firstness, Secondness and Thirdness. In his writings over decades, he related or described this trichotomy in dozens of contexts [2].
Across his voluminous writings, which unfortunately are not all available since they are still being transcribed from tens of thousands of original handwritten notes, I glean from the available materials this understanding of his three categories from a knowledge representation standpoint:
- Firstness [1ns] — these are potentials, the basic qualities that may combine together or interact in various ways to enable the real things we perceive in the world. They are unexpressed potentialities, the substrate of the actual. These are the unrealized building blocks, or primitives, the essences or attributes or possible juxtapositions; indeed, “these” and “they” are misnomers because, once conceived, the elements of Firstness are no longer Firstness;
- Secondness [2ns] — these are the particular realized things or concepts in the world, what we can perceive, point to and describe (including the idea of Firstness, Thirdness, etc.) A particular is also known as an entity, 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, what Peirce called the “surprising fact.”
Understanding, inquiry and knowledge require this irreducible structure; connections, meaning and communication depend on all three components, standing in relation to one another and subject to interpretation by multiple agents (Peirce’s semiosis of signs). Contrast this Peircean view with traditional classification schemes, which have a dyadic or dichotomous nature and do not support such rich views of context and interpretation.
Peirce’s “surprising fact” is new knowledge that emerges from anomalies observed when attempting to generalize or to form habits. Abductive reasoning, a major contribution by Peirce, attempts to probe why the anomaly occurs. The possible hypotheses so formed constitute the Firstness or potentials of a new categorization (identification of particulars and generalization of the phenomena). The scientific method is grounded in this process and reflects the ideal of this approach (what Peirce called the “methodeutic”).
Peirce at a High Altitude
Significant terms we associate with knowledge and its discovery include open, dynamic, process, representation, signification, interpretation, logic, coherence, context, reality, and truth. These were all topics of Peirce’s deep inquiry and explained by him via his triadic world view. For example, Peirce believed in the real as having existence apart from the mind (a refutation of Descartes’ view). He believed there is truth, that it can be increasingly revealed by the scientific method and social consensus (agreement of signs), but current belief as to what is “truth” is fallible and can never be realized in the absolute (it is a limit function). There is always distance and different interpretation between the object, its representation, and its interpretation. But this same logic provides the explanation for the process of categorization, also grounded in Firstness, Secondness and Thirdness [2].
Of course, some Peircean scholars may rightfully see these explanations as a bit of a cartoon, and a possible injustice to his lifetime of work. For more than 100 years philosophers and logicians have tried to plumb Peirce’s insights and writings. This summary by no means captures many subtleties. But, if we ourselves generalize across Peirce’s writings and his application of the Three Categories, we can gain a mindset that, I submit, is both easily grasped and applied, the result of which is a logical, coherent approach to categorization and knowledge representation.
First, we decide the focus of the categorization effort. That may arise from one of three sources. We either are trying to organize a knowledge domain anew; we are splitting an existing category that has become too crowded and difficult to reason over; or we have found a “surprising fact” or are trying to plumb an anomaly. Any of these can trigger the categorization process (and, notice, they are in 1ns, 2ns and 3ns splits). The breadth or scope of the category is based on the domain and the basis of the categorization effort.
How to think about the new category and decide its structure comes from the triad:
- Firstness – the potential things, ideas, concepts, entities, forces, factors, events, whatever that potentially bear upon or have relevance to the category; think of it as the universe of thought that might be brought to bear for the new category of inquiry
- Secondness – the particular instances, real and imagined, that may populate the information space for the category, including the ideas of attributes and relations, which also need to be part of the Firstness
- Thirdness – the generals, types, regularities, patterns, or logical groupings that may arise from combinations of any of these factors. Similarities, “truth” and predictability help inform these groupings.
What constitutes the potentials, realized particulars, and generalizations that may be drawn from a query or investigation is contextual in nature. I outlined more of the categorization process in an earlier article [2].
Peirce’s triadic logic is a powerful mindset for how to think about and organize the things and ideas in our world. Peirce’s triadic logic and views on categorization are fractal in nature. We can apply this triadic logic to any level of information granularity. The graph structure arises from the connections amongst all of these 1ns, 2ns and 3ns factors.
We will be talking further how this 40,000 ft view of the Peircean mindset helps create practical knowledge graphs and ontological structures. We will also be showing an example suitable for knowledge-based artificial intelligence (KBAI). The exciting point is that we have found a simple grounding of three aspects that is logically sound and can be readily trained. We also will be showing how we can do so much more work against this kind of natural KBAI structure.
Stay tuned.
