Sentence examples for preserves truth from inspiring English sources

Substitution of equi-designating signs preserves truth.

Whereas the classical consequence relation preserves truth in all logically possible worlds, nonmonotonic consequence relations preserve truth in all least abnormal worlds.

Plausibly, the first pattern reflects the default direction of valid replacement: removing a restriction preserves truth, except in special cases like those involving negation.

And for argument involving only factual propositions, the converse is also true: the same class of arguments necessarily preserves truth, necessarily preserves certainty and necessarily preserves probability in the sense of PPP.

That such an embedding $j V\to M$ is elementary means that $j$ preserves truth, i.e., for every formula $\varphi x_11,\ldots,x_n)$ of the language of set theory, and every $a_1,\ldots,a_n$, the sentence $\varphi a_11,\ldots,a_n)$ holds in $V$ if and only if $\varphi (j(a_1),\ldots,j(a_n))$ holds in $M$.

Hacking shows that, given certain background semantic assumptions (bivalence, valid inference preserves truth), any introduction and elimination rules meeting certain proof-theoretic conditions (subformula property, provability of elimination theorems for Cut, Identity, and Weakening) will uniquely determine a semantics for the constant they govern (Hacking 1979, 311 314).

SCIENCE has proved that memory does far better at fashioning simple, meaningful stories about one's childhood than objectively preserving truth in amber.

Moreover, even substituting co-designative terms for 'the earth' may not preserve truth.

So in special cases, adding a restriction to a general term like 'dog' can preserve truth.

Substituing other true sentences for 'the earth was spherical' will not necessarily preserve truth.

Thus, deductions preserve truth, and there aren't too many deductions.