Sentence examples for trivial necessary from inspiring English sources

We take advantage of the recursive and direct constructing method to show that in cases LS[9](2,4,v) the trivial necessary condition is also sufficient.

A set of trivial necessary conditions for the existence of an LS[N] t,k,v) is N|v−ik−i for i=0,…,t.

We take advantages of the recursive and direct constructing methods to show that in the case LS[9] 2, 5, v) the trivial necessary conditions are also sufficient.

As a result, we show that the trivial necessary conditions for the existence of LS[3](2,v,v) are sufficient for k⩽80.

Then, if expanded descriptivism is correct, a sentence like (6) should sound (to Fred at least) trivial, necessary, and analytic.

It should sound as trivial, necessary and analytic as "Bachelors are unmarried" or "Squares have four sides," at least to Fred.

All that it implies is that A and B do not differ in their non-trivial essential properties and hence that, although there may well be non-trivial necessary conditions for being A in any possible world, and non-trivial necessary conditions for being B in any possible world, there are no non-trivial necessary conditions for being A that are not also necessary conditions for being B, and vice versa.

But what positive reasons are there for holding that transworld identities require non-trivial necessary and sufficient conditions (non-trivial individual essences), if arguments that are based on the epistemological, security of reference, and intelligibility assumptions are abandoned?

(It is natural to suppose that Della Rocca thinks that essential properties are non-trivial necessary properties, so that he can say things like, "Essentialism is the view that some objects have some essential properties".

It might be replied that there are non-trivial necessary existential propositions in mathematics, such as 'There are infinitely many primes' which implies of course 'the number 7 exists'.

Even if we can understand the claim that there is some past time at which George Bush is a baby without being able to specify informative (non-trivial) necessary and sufficient conditions for the identity of the adult George Bush with some previously existing infant, it does not follow that there are no such necessary and sufficient conditions.