Monthly Archives: February 2015

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

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 , , , , , , , , | 6 Comments

Relations & Their Relatives : 4

Re: Peirce List Discussion • Helmut Raulien The “divisor of” relation signified by is a dyadic relation on the set of positive integers so it can be understood as a subset of the cartesian product   It is an example … Continue reading

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Mathematical Demonstration & the Doctrine of Individuals • 2

Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149 93.   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 … Continue reading

Posted in C.S. Peirce, Deduction, Determination, Doctrine of Individuals, Foundations of Mathematics, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Peirce, Relation Theory | Tagged , , , , , , , , , , , | 3 Comments

Mathematical Demonstration & the Doctrine of Individuals • 1

Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149 92.   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 … Continue reading

Posted in C.S. Peirce, Deduction, Determination, Doctrine of Individuals, Foundations of Mathematics, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Peirce, Relation Theory | Tagged , , , , , , , , , , , | 3 Comments

Relations & Their Relatives : 3

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 that corresponds to the relative term, “divisor … Continue reading

Posted in C.S. Peirce, Denotation, Logic, Logic of Relatives, Mathematics, Number Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 4 Comments

Relations & Their Relatives : 2

It may help to clarify the relationship between logical relatives and mathematical relations.  The word relative as used in logic is short for relative term — as such it refers to an article of language that is used to denote … Continue reading

Posted in C.S. Peirce, Denotation, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , | 4 Comments

Relations & Their Relatives : 1

Sign relations are just special cases of triadic relations, in much the same way that binary operations in mathematics are special cases of triadic relations.  It does amount to a minor complication that we participate in sign relations whenever we … Continue reading

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

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 , , , , , , , | 4 Comments

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

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

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

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 , , , , , , , | 4 Comments