Re: Icon, Likeness, Likely Story, Likelihood, Probability • 3
Re: Laws of Form • Lyle Anderson

Lyle,

We are here engaged in the wider context of which Peirce’s systems of graphs for propositional logic and Spencer Brown’s calculus of indications constitute a prominent corner, one might even say a “cantonical field”, but still just one corner of the larger picture, abstractly syntactic and formally deductive in character.

Over and above that niche the overarching edifice of Peirce’s Logic of Science, supported by the theory of signs and the theory of inquiry, must cover all three forms of inference — abductive, inductive, deductive — plus the bridge from qualitative logic to quantitative statistics.  That is the architecture of inquiry with which we’ll be occupied for quite some time.

Continuing from where I left off last time —

What intrigues me about the recently cited passages from Aristotle is the way he uses what we now regard as semiotic terms — icon, index, sign — to describe the elements and structures of logical syllogisms, including the modes of non‑demonstrative inference.

The roles of signs informing sign relations and the rules of inference guiding inquiries are subjects Peirce explored in depth.  Especially in the early years the subjects of signs and inquiry are so entwined in Peirce’s relevant lectures and papers that he passes from one to the other with little sense of discontinuity between the two.

Over the years, both in Peirce’s work and the community of researchers following after, there develops such an intense focus on the problem of classifying signs that the theory of signs takes on the character of a separate subject, detached from its natural connection to the theory of inquiry.

One of our tasks is to heal that rift and regain a sense of the original common root.

Resource

• Theme One Program • User Guide • Appendix A

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