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Notes on the Foundations of Mathematics : 2
Selections from R.L. Wilder, Introduction to the Foundations of Mathematics I. The Axiomatic Method Since the axiomatic method as it is now understood and practiced by mathematicians is the result of...
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C.S. Peirce • New Elements (Καινὰ Στοιχεῖα) : 1
Selections from C.S. Peirce, “New Elements (Καινὰ Στοιχεῖα)” Editors’ Headnote from The Essential Peirce, Volume 2 MS 517. [First published in NEM 4:235–63. This document was most probably written in...
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Reading C.S. Peirce • New Elements (Καινὰ Στοιχεῖα) : 1
Re: Editors’ Headnote from The Essential Peirce, Volume 2 Gmane Archive Threads — New Elements (Kaina Stoicheia) • EP Editors’ Headnote New Elements (Kaina Stoicheia) • EP Editors’ Headnote •...
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C.S. Peirce • Logic of Number (MS 229)
Selections from C.S. Peirce, [Logic of Number] (MS 229) I printed a paper on the Logic of Number in 1866, and it was not made up out of the first thoughts that came into my head about it, by any means,...
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Infinite Uses → Finite Means
The idea that a language is based on a system of rules determining the interpretation of its infinitely many sentences is by no means novel. Well over a century ago, it was expressed with reasonable...
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¿Shifting Paradigms? • 1
Re: Dana Scott • Shifting Paradigms? 2014 Jul 28 This is very interesting to me, but not all my posts make it to the list, so I will spend a few days reflecting on it and post a comment on my blog,...
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¿Shifting Paradigms? • 2
Re: Timothy Chow • Shifting Paradigms? 2014 Jul 31 I can’t remember when I first started playing with Gödel codings of graph-theoretic structures, which arose in logical and computational settings, but...
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¿Shifting Paradigms? • 3
Re: Harvey Friedman • Good Math 2014 Aug 17 Speaking of mathematics in the context of “general intellectual activity” brings to mind Raymond Wilder’s take on “mathematics as a cultural system”. I would...
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¿Shifting Paradigms? • 4
Re: Harvey Friedman • Foundational Crisis? 2014 Aug 22 Shock and surprise are relative to a prior state of belief. The belief that mathematics reduces to logic, and that of a purely deductive sort...
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C.S. Peirce • Syllabus • Selection 1
Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903) An Outline Classification of the Sciences 180. This classification, which aims to base itself on the principal affinities of...
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C.S. Peirce • Syllabus • Selection 2
But round about the castle there began to grow a hedge of thorns, which every year became higher, and at last grew close up round the castle and all over it, so that there was nothing of it to be...
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Survey of Precursors Of Category Theory • 1
A few years ago I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to...
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Survey of Relation Theory • 1
In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention...
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Signs Of Signs • 1
Re: Michael Harris • Language About Language There is a language and a corresponding literature that approaches logic and mathematics as related species of communication and information gathering,...
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Signs Of Signs • 2
Re: Michael Harris • Language About Language I compared mathematics to a “consensual hallucination,” like virtual reality, and I continue to believe that the aim is to get (consensually) to the point...
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Signs Of Signs • 3
Re: Michael Harris • Language About Language And if we don’t, who puts us away? One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities. As...
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Signs Of Signs • 4
Re: Michael Harris • Language About Language But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and...
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Inquiry, Signs, Relations • 1
Re: Michael Harris • A Non-Logical Cognitive Phenomenon Human spontaneous non-demonstrative inference is not, overall, a logical process. Hypothesis formation involves the use of deductive rules, but...
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All Liar, No Paradox
A statement asserts that a statement is a statement that is false. The statement violates an axiom of logic, so it doesn’t really matter whether the ostensible statement the so-called liar, really is a...
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All Liar, No Paradox • Comment 1
A statement asserts that a statement is a statement that is false. The statement violates an axiom of logic, so it doesn’t really matter whether the ostensible statement the so-called liar, really is...
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