Icon, Likeness, Likely Story, Likelihood, Probability • 4

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

Lyle,

We are 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

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

We are what we repeatedly do… excellence, therefore, isn’t just an act, but a habit and life isn’t just a series of events, but an ongoing process of self-definition

— Aristotle

#Stoic #Stoicism #Aristotle

‘What are the most basic kinds of things that exist?’ https://philosophy.institute/metaphysics/aristotles-categories-western-metaphysics/

That is a bias question, as it presupposes existence which changes from what is to what is not, is its foundation. Is not a better question: What are the categories of causality, if it is the foundation of existence? It at least is not an ouroboros, but transcends such an absolute being by constituting the manifold of its dialectic principle. #philosophy #categories
#BiasQuestions #BetterQuestions #Aristotle #Socrates #DialecticPrinciple #existence #WhatIs #WhatIsNot #change

On Fear, and the Crossing

https://legawa.com/2026/06/09/on-fear-and-the-crossing/

On the Question of Self-Confidence: Whether to Build a Tower or to Become the Ground

https://legawa.com/2026/06/08/on-the-question-of-self-confidence-whether-to-build-a-tower-or-to-become-the-ground/

Join the Sacred Evolution of Humanity

#EudemoniaApp #Eudemonia #Eudaimonia #HumanFlourishing #Aristotle #Philosophy #AncientGreekPhilosophy

I'm trying out Aristotle and Lean Copilot for formalizing and proving theorems, and, so far, Aristotle feels way more powerful. Lean Copilot's suggestions aren't always right. Aristotle, on the other hand, can bring in previous lemmas, figure out missing hypotheses, and so on –besides, of course, finishing the proofs themselves.

Disclaimer: this is probably mostly down to the underlying model: Aristotle uses a specialized in-house model (within an agentic architecture), while Lean Copilot is using a more general-purpose one (and not a particularly strong one, at least in my setup... DeepSeek-R1, I think).

#lean #theoremproving #aristotle

#culture #science #religion #aristotle

https://scienceandculture.com/2026/05/designer-science-misrepresents-aristotle-and-ignores-church-history/?utm_source=flipboard&utm_medium=activitypub

Posted into FLIPBOARD EXCHANGE FEED 🗞️ @flipboard-exchange-feed-Econopass

“His Margites [ancient comedy by Homer] indeed provides an analogy: as are the Iliad and Odyssey to our tragedies, so is the Margites to our comedies"
Poetics, #Aristotle

Don’t rush out to buy this towering comedic masterpiece which Aristotle puts on a par with the Iliad and the Odyssey; the bookshop won’t have it. It’s almost entirely lost.
#philosophy

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi