Monthly Archives: February 2015

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 7

Posted on February 28, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §4. Classification of Relatives 225.   Individual relatives are of one or other of the two forms and simple relatives are negatives of one or other of these two forms. 226.   The … Continue reading →

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

Relations & Their Relatives • Discussion 1

Posted on February 27, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien The divisor of relation signified by is a dyadic relation on the set of positive integers and thus may be understood as a subset of the cartesian product   It is an example 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

Mathematical Demonstration and the Doctrine of Individuals • 2

Posted on February 23, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) In reference to the doctrine of individuals, two distinctions should be borne in mind.  The logical atom, or term not capable of logical division, must be one of which every predicate may … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 5 Comments

Mathematical Demonstration and the Doctrine of Individuals • 1

Posted on February 22, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) Demonstration of the sort called mathematical is founded on suppositions of particular cases.  The geometrician draws a figure;  the algebraist assumes a letter to signify a single quantity fulfilling the required conditions.  … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 4 Comments

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 , , , , , , , , , , , , , , , | 11 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 , , , , , , , | 8 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 , , , , , , , | 8 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 , , , , , , , | 8 Comments