# equivalence

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## equivalence

[i′kwiv·ə·ləns]
(mapping)
In an equal-area map projection, the property of having the ratio between areas on the map the same as the ratio between corresponding areas on the earth's surface.
(mathematics)
A logic operator having the property that if P, Q, R, etc., are statements, then the equivalence of P, Q, R, etc., is true if and only if all statements are true or all statements are false.
References in periodicals archive ?
I believe that the identity claim, like the biconditional principle it grounds, is a moral or evaluative claim.
This procedure is to be used when the general fact in need of explanation cannot be explained on the basis of the fact that some property is analyzable partly in terms of truth, but can be formulated by a sentence in prenex normal form in which the primary connective of the embedded open sentence is either the material conditional or material biconditional. The procedure is as follows.
In light of these and other examples, I concluded in Beyond Rigidity that Kripke's claims about theoretical identity sentences involving natural kind terms should be seen as encompassing cases in which the terms are used to form predicates, and the identity sentences are represented as universally quantified conditionals or biconditionals. The important point to emphasize here is that the predicate is hotter than is not even weakly essentialist, since one object can be hotter than another in one circumstance, without this being so in all possible circumstances in which the two exist.
So it would seem that we can link tensed truth predicates of sentences truth predicates of statements via a set of equivalences but the predicate will be uniformly tensed across the biconditional. The threatened problem is that this makes it difficult to see how it is we develop an account of the tensed truth predicates.
In effect, [alpha] ] [beta] is now defined, enthymematically, as ([alpha] [conjunction] R) [Mathematical Expression Omitted].(12) Condition (a) is satisfied since the enthymematic biconditional now follows simply from the straight one; and, Everett (1994) claims, so is condition (b).
As we saw, the commitment of his sample sentence, "a is F", is read off from the right hand side of the biconditional of Quine's semantic theory: "a is F" is true if and only if there exists an x such that "a" designates x and "F" applies to x.
This, however, suggests that the fact that these utterances express a common thought is connected with their each being partially rationalized by a single biconditional expectation--a biconditional sustaining two inferences by detachment.
The semantic indeterminacy of the sentence on the righthand side of the Tarski biconditional is exactly matched by an indeterminacy of context affecting the indexical truth-predicate on the lefthand side.
For the cognitive equivalence of "'Snow is white' is true" and "Snow is white" will lead to the (more or less indefeasible) acceptance of the biconditional "'Snow is white' is true iff snow is white"; and a natural way to put this (more or less indefeasible) acceptance is to say "'Snow is white' has the truth conditions that snow is white".
For any statement P we may formulate what he calls a "provisoed biconditional" (1988, p.
But any theory that delivers that last biconditional must record not merely the generic sense of the English word "I" - that is to say, the fact that any utterance of "I" designates its utterrer - but also the specific contextual fact that the utterer of u was Lauben.
Kiesewetter (The Normativity of Rationality, 162) explicitly proposes principles concerning rational belief and rational intention that capture something close to the left-to-right direction of the biconditional RB, even if presented in terms of support by decisive rather than sufficient reasons (this difference will not affect the essence of the arguments below).

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