Peirce’s Triadic Thinking on Discovery and Design
It’s not obvious why C.S.Peirce’s triadic thinking has utility. The ordering of concepts in firstness, secondness, and thirdness explains how existing systems may have evolved. But existing systems exist in their thirdness, so their history does not lend to prediction.
The utility of triadic thinking is in design. This is because it tells you the first principles one needs to establish in one’s vocabulary.
Humans are naturally dyadic thinkers, and we traffic in analogy-making. But analogy-making has its limits in that it can’t discern first principles. It’s important to know what comes first so as to design new ways of thinking.
AGI is difficult because we don’t really know its first principles. Furthermore, the first principles of autonomy are not identical to the first principles of abstract thinking. This is despite symbol grounding, the frame problem, and abduction sharing much in common.
Triadic thinking is 7 dimensional. 3 concepts, 3 relationships, and the whole. This is at the limit of human cognition. We can only hold between 5–7 concepts simultaneously.
Dyadic thinking is much simpler because it’s 3 dimensional with 2 concepts and their relationship. Analogic thinking is also 3 dimensional: two relationships and their similarity.
A yet-to-be-invented superintelligence might have quadratic thinking. 7*4. That’s 28 dimensions. Coincidentally, the same number at Peirce’s 28 categorizations of signs. Peirce has another categorization that involves 66 categories!
Human explainability perhaps requires dyadic thinking. Thus an AI must at least frame its explanation by disentangling triadic or higher thinking into dyadic form. It’ll do so in a way that appears like an overlapping patchwork of dyadic expressions.
Human memory is dyadic. It travels a 2D path, and at various landmarks in that path is an object that can serve as a pointer to something relevant. We use symbols like we use landmarks. Landmarks that guide our thoughts in meaningful directions. Dyadic reactions are degenerate manifestations of triadic mediation, while a genuine triadic relation cannot be built up from multiple dyadic relations.
Calculus is a language that connects our intuition about linear shapes with that of curvature and change. Similarly, one cannot speak about cognition without semiotics. Semiotics is the language of meaning as calculus is the language of change.
C.S.Peirce divides all of science into discovery, review, and practicality. He divides the science of discovery into mathematics, philosophy, and idioscopy. Math he further divides into logic, discrete series, continua, and pseudo-continua. Where does semiotics fit?
Semiotics is under “logic”, where he defines 3 categories: speculative grammar, logical critic, and speculative rhetoric. What we know of logic today is under “logical critic”. The analysis of signs and their combination is under “speculative grammar.”
The usual use of the term “semiotics” is confined to the classification of signs into icons, indexes, and symbols. But Peirce had a much broader and deeper framework under speculative grammar. Furthermore, his “logical critic” includes not just logic (i.e., deduction) but also induction, and abduction.
Also, it’s important to note that Peirce’s categorizations are NOT orthogonal. Instead, they follow his triadic thinking. Hence the categorization has a firstness, secondness, and thirdness. Thus a symbol is a kind of index that is a kind of icon. Thus in the triadic categorization of logic under speculative grammar, logical critic, and speculative rhetoric. Deduction, induction and deduction (i.e., inferences) are dependent on speculative grammar (i.e., signs).
Logic is under mathematics and is considered a firstness. Mathematics is also a firstness under the science of discovery. Thus you cannot have any discovery absent “speculative grammar”.
The kind of taxonomy that Peirce proposed is unlike conventional taxonomies where siblings are disjoint. There’s always a triadic relationship about what must come first over the others. A firstness is a necessary condition. The entire triad is a sufficient condition.
Given Peirce’s taxonomy of the discovery as science, where do we place Deep Learning? Does its placing reveal its limitations and the kind of technologies that we must build to achieve AGI?
Deep Learning has its coordinates beginning at the top at continua. It involves a subset of speculative grammar (i.e., icons and indexes) and a subset of the logic critic (i.e., induction). Many aspects are clearly absent from becoming the ring to rule all rings.
But the trillion-dollar question is, are there alternative forms that reveal artificial intuition or artificial fluency behavior other than deep learning? Are there alternative ways of measuring iconicity outside of finite series of sums?