Indeed, one can recognize the explanatory power of a theory without taking it to be true.
Wallace notes, however, that the QPT and hence the explanatory need for many worlds may not be true of all or even most quantum algorithms, although Wallace takes it to be true of Shor's.
On the basis of considerations of this sort, Clitomachus argued that we should distinguish 'assenting' to an impression, in the Stoic sense of taking it to be true, from 'approving' an impression, in the sense of acting on it or accepting it as if it were true.
One suggestion is that faith is taking it to be true that there are grounds for the hope that love is supreme not simply in the sense that love constitutes the ideal of the supreme good, but in the sense that living in accordance with this ideal constitutes an ultimate salvation, fulfilment or consummation that is, in reality, victorious over all that may undermine it (in a word, over evil).
Some philosophers take it to be obvious that if something is true, there must be something that makes it true, a truth-maker.
Montaigne assimilates opinions, according to what appears to him as true, without taking it to be absolutely true.
If the proposition is analytic, as the ontological argument takes it to be, then the statement would be true only because of the meaning given to the words.
Thus for a propositional language it will take as its basis, a clause according to which an atom is true or false accordingly as the valuation maps it to 1 or to 0. In systems in which ∨ is a primitive constant, the clause corresponding to disjunction takes α ∨ β to be true if at least one of α, β is true, and takes it to be false otherwise.
I'm paraphrasing, but I've taken it to heart and I believe it to be true.
