Category Archives: Triadic Relations

Relations & Their Relatives • 3

Posted on February 18, 2015 by Jon Awbrey

Here are two ways of looking at the divisibility relation, a dyadic relation of fundamental importance in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers corresponding to the relative term, “divisor of”.  … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • 2

Posted on February 17, 2015 by Jon Awbrey

What is the relationship between “logical relatives” and “mathematical relations”?  The word relative used as a noun in logic is short for relative term — as such it refers to an item of language used to denote a formal object. … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 10 Comments

Relations & Their Relatives • 1

Posted on February 17, 2015 by Jon Awbrey

Sign relations are special cases of triadic relations in much the same way binary operations in mathematics are special cases of triadic relations.  It amounts to a minor complication that we participate in sign relations whenever we talk or think … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 6

Posted on February 16, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §2. Relatives (concl.) 222.   Instead of considering the system of a relative as consisting of non-relative individuals, we may conceive of it as consisting of relative individuals.  Thus, since we have But … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 5

Posted on February 15, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §2. Relatives (cont.) 221.   From the definition of a simple term given in the last section, it follows that every simple relative is the negative of an individual term.  But while in … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 4

Posted on February 12, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §2. Relatives (cont.) 220.   Every relative, like every term of singular reference, is general;  its definition describes a system in general terms;  and, as general, it may be conceived either as a logical … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 3

Posted on February 11, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §2. Relatives 218.   A relative is a term whose definition describes what sort of a system of objects that is whose first member (which is termed the relate) is denoted by the … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 9 Comments

Six Ways of Looking at a Triadic Relation ⌬ 1

Posted on February 4, 2015 by Jon Awbrey

A triadic relation and its converses form a set of triadic relations all together, six grammatically and rhetorically distinct ways of representing what is logically the same information.  Peirce illustrates the situation as follows, with six variations on the theme … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 11 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 2

Posted on February 3, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §1. Individual and Simple Terms (concl.) 216.   Just as in mathematics we speak of infinitesimals and infinites, which are fictitious limits of continuous quantity, and every statement involving these expressions has its … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 11 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 1

Posted on February 1, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives §1. Individual and Simple Terms 214.   Just as we had to begin the study of Logical Addition and Multiplication by considering and terms which might have been introduced under the Algebra of the … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 10 Comments