Sentence examples for infinite conjunction from inspiring English sources

Since the language with an added truth predicate has only countably many formulas, not every infinite conjunction can be expressed by a different finite formula.

Because we mistakenly think that "an infinite conjunction" is similar to "an enormous conjunction," we erroneously reason that just as we cannot determine the truth-value of an enormous conjunction because we don't have enough time, we similarly cannot, due to human limitations, determine the truth-value of an infinite conjunction (or disjunction).

For the same reason, a finitary general proposition is not to be understood as an infinite conjunction but "only as a hypothetical judgment that comes to assert something when a numeral is given" (ibid).

The utility of a generalization like (56) is not so much that it eliminates the need to rely on an infinite conjunction, but that it is 'blind' (i.e., made under partial ignorance of what was said).

On the contrary, however, advocates of the deflationary theory (particularly those influenced by Ramsey) are at pains to point out that anyone who has the concept of truth in this sense is in possession of a very useful concept indeed; in particular, anyone who has this concept is in a position to form generalizations that would otherwise require logical devices of infinite conjunction.

It is plain that not all infinite conjunctions can be expressed because there are uncountably many (non-equivalent) infinite conjunctions over a countable language.

According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions.

But clearly, moving to languages in which infinite conjunctions and disjunctions are freely allowed, the restrictions would vanish.

Wittgenstein (1921) disapproves of universal facts; apparently, he wants to re-analyze universal generalizations as infinite conjunctions of their instances.

Field has addressed this issue, and he initially suggested that the mathematical fictionalist could use substitutional quantification to express these infinite conjunctions (Field 1984).

The formal work on axiomatic theories of truth has helped to specify exactly which infinite conjunctions can be expressed with a truth predicate.