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But taking propositions to be truthbearers will not be to every truthmaker theorist's liking.
Yet consistency (and deductive closure, which is implicit in taking propositions rather than sentences as the objects of belief) have been regarded as the minimal requirements on a belief set ever since Hintikka (1961).
Contradictory negation is not a one-place operator taking propositions into propositions, but rather a mode of predication, a way of combining subjects with predicates: a given predicate can be either affirmed or denied of a given subject.
The idea is rather that, as evidence-sensitive believers, we don't merely want to believe significant truths; rather, we want to have good grounds for taking propositions to be true, and to base our belief on those grounds (Feldman 2000; though again see David 2001).
Taking Propositions 4.1 and E into account together with the doubling condition for v with respect to the second variable we see that the operator J α 1 S α 2 is bounded from L dec, r p ( w, G 1 ) to L q ( v, G 2 ) if and only if the conditions (vi) and (vii) are satisfied.
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Taking Proposition 4 into account, we conclude that T u = u, that is, u is a fixed point of T. □.
(This is sometimes expressed by saying that variables range over propositions, or that they take propositions as their values).
All PC operators take propositions as their arguments, and the result of applying them is also in each case a proposition.
Versions of this view vary both according to which properties they take propositions to be, and what they take propositions to be properties of.
It has thus far been assumed that intuitions always take propositions as their objects.
As we see clearly in Russell (1903), for instance, he takes propositions to have constituents.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com