Tag Archives: Boole

Peirce’s 1870 “Logic Of Relatives” • Comment 9.3

An idempotent element in an algebraic system is one that obeys the idempotent law, that is, it satisfies the equation Under most circumstances it is usual to write this as If the algebraic system in question falls under the additional … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 9.2

In setting up his discussion of selective operations and their corresponding selective symbols, Boole writes the following: The operation which we really perform is one of selection according to a prescribed principle or idea.  To what faculties of the mind … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 9.1

Let us backtrack a few years and consider how George Boole explained his twin conceptions of selective operations and selective symbols. Let us then suppose that the universe of our discourse is the actual universe, so that words are to … Continue reading

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Indicator Functions • 1

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? One of the things it helps to understand about 19th Century mathematicians, and those who built the bridge to the 20th, is that they were capable of high abstraction … Continue reading

Posted in Abstraction, Boole, Boolean Functions, C.S. Peirce, Category Theory, Characteristic Functions, Euler, Indicator Functions, John Venn, Logic, Mathematics, Peirce, Propositional Calculus, Set Theory, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , | Leave a comment

I Wonder, Wonder Who

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? The question recalls recent discussions of discovery and invention in the mathematical field, bringing back to mind questions I’ve wondered about for as long as I can remember. Speaking … Continue reading

Posted in Anamnesis, Aristotle, Boole, Boolean Functions, C.S. Peirce, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment