Tag Archives: Mathematics

Higher Order Sign Relations • 1

Posted on August 1, 2012 by Jon Awbrey

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.  They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to … Continue reading →

Posted in C.S. Peirce, Higher Order Sign Relations, Inquiry, Inquiry Into Inquiry, Logic, Mathematics, Recursion, Reflection, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , | 8 Comments

Notes on the Foundations of Mathematics • 2

Posted on July 5, 2012 by Jon Awbrey

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 a long evolution in human thought, we shall … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Kaina Stoicheia, Logic, Mathematics, Semiotics | Tagged , , , , , | Leave a comment

Notes on the Foundations of Mathematics • 1

Posted on July 5, 2012 by Jon Awbrey

Re: Peirce List Discussions 2012 • (1) • (2) • (3) • (4) Cf: Previous Discussions 2005–2006 • (A) • (B) • (C) I will have to be off and on the internet for the next month or so, and … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Kaina Stoicheia, Logic, Mathematics, Semiotics | Tagged , , , , , | Leave a comment

Approaching Peirce

Posted on June 30, 2012 by Jon Awbrey

I gradually grow accustomed to the distinct possibility that there will always be different readings, and even divergent interpretations of Peirce’s writings. Some of that appears to be a two- or three-cultures issue — the readings that befit aesthetic, cultural, … Continue reading →

Posted in Anthem, Inquiry, Logic, Mathematics, Peirce, Science, Semiotics | Tagged , , , , , , | 2 Comments

C.S. Peirce • Of Triadic Being

Posted on June 14, 2012 by Jon Awbrey

Selection from C.S. Peirce, “Some Amazing Mazes, Fourth Curiosity” (c. 1909) Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them; and for the present purpose such an enumeration would … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, References, Relation Theory, Semiotics, Sources | Tagged , , , , , , , | 3 Comments

Definition and Determination • 8

Posted on June 13, 2012 by Jon Awbrey

Re: Peirce List • Jim Willgoose (1) (2) The most general meaning of “formal” is “concerned with form”, but the Latin “forma” can mean “beauty” in addition to “form”, so perhaps a normative “goodness of form” enters at this root. … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 9 Comments

Definition and Determination • 7

Posted on June 11, 2012 by Jon Awbrey

Peirce clearly set great store by his 1902 definition of logic as formal semiotic, whose principles he proposed to deduce by evident and rigorous mathematical reasoning from his triadic relational definition of a sign. It is from this definition, together … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 6 Comments

Definition and Determination • 6

Posted on June 6, 2012 by Jon Awbrey

Re: Peirce List • Gary Fuhrman (1) (2) The following two passages may help to clarify Peirce’s admittedly peculiar usage of “formal” in this context. C.S. Peirce • Objective Logic C.S. Peirce • Logic as Semiotic Re: Peirce List • … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 6 Comments

C.S. Peirce • Logic as Semiotic

Posted on June 4, 2012 by Jon Awbrey

Selection from C.S. Peirce, “Ground, Object, and Interpretant” (c. 1897) Logic, in its general sense, is, as I believe I have shown, only another name for semiotic (σημειωτική), the quasi-necessary, or formal, doctrine of signs.  By describing the doctrine as … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Peirce, References, Semiotics, Sources | Tagged , , , , , , , | 29 Comments

Definition and Determination • 5

Posted on June 2, 2012 by Jon Awbrey

Walking the line between phenomenology and mathematics, let us cast our eyes on the prize of defining logic.  Peirce defines logic as formal semiotic — and that in turn calls for a definition of sign. Here is a place where … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 7 Comments