Category Archives: Boole

¿Shifting Paradigms? • 5

Re: Peter Cameron • Infinity and Foundation We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style.  A number of thinkers have … Continue reading

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | 2 Comments

Survey of Animated Logical Graphs • 1

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s 1870 “Logic Of Relatives” • Comment 9.4

Boole rationalized the properties of what we now call boolean multiplication, roughly equivalent to logical conjunction, in terms of the laws that apply to selective operations. Peirce, in his turn, taking a very significant step of analysis that has seldom … Continue reading

Posted in Boole, Boolean Algebra, Boolean Functions, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , , | 1 Comment

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

Posted in Boole, Boolean Algebra, Boolean Functions, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , , | 2 Comments

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

Posted in Boole, Boolean Algebra, Boolean Functions, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , , | 2 Comments

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

Posted in Boole, Boolean Algebra, Boolean Functions, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , , | 1 Comment

Indicator Functions : 1

Re: Who Invented Boolean Functions? One of the things that 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 — in Peirce’s case a … Continue reading

Posted in Boole, Boolean Functions, Euler, Indicator Functions, John Venn, Logic, Peirce, Propositional Calculus, Venn Diagrams | Tagged , , , , , , , , | Leave a comment