Term
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Definition
| "not the process of reasoning but the rules for correct reasoning." |
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Term
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Definition
| An argument consists of a finite sequence of sentences, called premises, together with another sentence, the conclusion, which the premises are taken to support. |
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Term
| deductively valid argument |
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Definition
| An argument is deductively valid if and only if its conclusion is true whenever (in any possible circumstance) its premises are all true. |
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Term
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Definition
| An argument is sound iff (1) it is valid and (2) all its premises are true. |
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Term
| A set of sentences IMPLIES a given sentence just in case... |
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Definition
| ...the truth of that sentence is guaranteed by the truth of all the members of the set. |
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Term
| A sentence A IMPLIES another, B, iff... |
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Definition
| ...A's truth guarantees B's truth. |
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Term
| A sentence A is EQUIVALENT to a sentence B iff.. |
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Definition
| ...A and B always agree in truth value. |
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Term
| A sentence is CONTINGENT iff... |
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Definition
| ...it is possible for it to be true and possible for it be false. |
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Term
| A sentence is VALID (or tautologous, or logically true) iff... |
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Definition
| ...it is true in every possible circumstance. |
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Term
| A sentence is CONTRADICTORY iff... |
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Definition
| ...it is impossible for it to be true. |
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Term
| A sentence is SATISFIABLE iff... |
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Definition
| ...it is not contradictory. |
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Term
| A set of sentences is CONTRADICTORY iff... |
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Definition
| ...it is impossible for all its members to be true. A set is SATISFIABLE otherwise. |
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Term
| One sentence is a COMPONENT of another if... |
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Definition
| (a)it is a proper part of that sentence, and (b) replacing it with another sentence yields something meaningful. |
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Term
| A sentence is COMPOUND (or molecular) if... |
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Definition
| ...it has components. It is SIMPLE (or atomic) if it does not. |
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Term
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Definition
| ...is a word or phrase that forms a single, compound sentence from N component sentences. |
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Term
| A connective is TRUTH-FUNCTIONAL iff... |
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Definition
| ...the truth values of the component statements the connective joins always completely determine the truth value of the compound statement formed by the connective. |
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Term
| An N-ARY TRUTH FUNCTION... |
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Definition
| ...is a function taking N truth values as inputs and producing a truth value as output. |
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Term
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Definition
| Transforms the truth value of the component sentence into its opposite. An English connective that has this effect is the logical particle not. |
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Term
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Definition
Is true just in case both its components--called conjuncts--are true. Equivalent English expressions: and, both...and, but, though, although |
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Term
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Definition
Is true just in case either of its components--called disjuncts--is true. Equivalent English expressions: or, either...or, unless |
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Term
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Definition
composed of two components: the antecedent and the consequent. A conditional is true just in case it does not have a true antecedent and a false consequent. Equivalent English expressions (roughly): B if A, if A then B, A only if B, B so long as A |
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Term
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Definition
Biconditionals are true just in case their components agree in truth value. Equivalent English expressions: iff, when and only when, is a necessary condition for, just in case |
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