### Some articles on *logic, order logic, logics*:

BIT Predicate

... In mathematical

... In mathematical

**logic**, the BIT predicate, sometimes written BIT(i, j), is a predicate which tests whether the jth bit of the number i is 1, when i is written in binary ... We can also prove that the class FO + BIT, of first-**order logic**with the BIT predicate, is the same as the class FO + PLUS + TIMES, of first-**order logic**with addition and ...Stewart Shapiro - Publications - Papers

... the mathematician", Current Issues in

... the mathematician", Current Issues in

**Logic**/ Temas Actuales de Lógica ... The limits of**logic**", introduction to The limits of**logic**Second**order logic**and the Skolem paradox, The international research library of philosophy (see above), Dartmouth Publishing Company ... "The triumph of first**order logic**", Festschrift for Alonzo Church, University of Chicago Press, forthcoming ...Theory (mathematical Logic) - Theories Expressed in Formal Language Generally - Consistency and Completeness

... In a deductive system (such as first-

... In a deductive system (such as first-

**order logic**) that satisfies the principle of explosion, this is equivalent to requiring that there is no sentence φ such that both φ and its negation can be proven ... For first-**order logic**, the most important case, it follows from the completeness theorem that the two meanings coincide ... In other**logics**, such as second-**order logic**, there are syntactically consistent theories that are not satisfiable, such as ω-inconsistent theories ...Ancestral Relation - Discussion

... Principia Mathematica made repeated use of the ancestral, as does Quine's (1951) Mathematical

... Principia Mathematica made repeated use of the ancestral, as does Quine's (1951) Mathematical

**Logic**... noting that the ancestral relation cannot be defined in first-**order logic**, and following the resolution of Russell's paradox both Frege and Quine largely considered the use of ... In particular, Quine did not consider second-**order logic**to be "**logic**" at all, despite his reliance upon it for his 1951 book (which largely retells ...Logicus - Topics in Logic - Predicate Logic

... Predicate

... Predicate

**logic**is the generic term for symbolic formal systems such as first-**order logic**, second-**order logic**, many-sorted**logic**, and infinitary**logic**... Predicate**logic**provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language ... Aristotelian syllogistic**logic**specifies a small number of forms that the relevant part of the involved judgements may take ...### Famous quotes containing the words logic and/or order:

“The usefulness of madmen is famous: they demonstrate society’s *logic* flagrantly carried out down to its last scrimshaw scrap.”

—Cynthia Ozick (b. 1928)

“...I feel anxious for the fate of our monarchy, or democracy, or whatever is to take place. I soon get lost in a labyrinth of perplexities; but, whatever occurs, may justice and righteousness be the stability of our times, and *order* arise out of confusion. Great difficulties may be surmounted by patience and perseverance.”

—Abigail Adams (1744–1818)