Proposition 3.1 is applied in the proof of the following results.
If F ⩾ 0, then for any fixed λ ∈ [ λ k A, λ k + 1 A ), a linking with respect to E k ⊕ E k ⊥ can be constructed. Proposition 2.3 is applied again to get a nontrivial solution z ∗ satisfying C ℓ k + 1 ( Φ, z ∗ ) ≇ 0. (3.15).
If a propositional function is applied to a proposition of a particular order, then it yields a proposition of a higher order.
Then Proposition 3.8 in [18] is applied to get C 1 ≇ 0. (iv) In Theorem 1.3, the global condition ( F ∞ ± ) is somewhat abstract and has been used in [12].
That is to say, such theorists eschew propositions as reference-level entities: of course the word "proposition" may be, and sometimes is, applied to Fregean Thoughts at the level of sense, rather than Russellian propositions at the level of reference.
The gap between the two views is perhaps at its smallest when the Bayesian model is applied to the proposition describing the overlap, or hard core, of a Lakatosian research programme.
This truth-value, 'undetermined', is applied to contingent propositions regarding the future (McCall 1967, p. 64).
The expression "in itself" [an sich] is applied only to propositions and ideas, never to things or metaphysical objects such as the soul or God.
In ordinary conversation the word probability is applied not only to variable phenomena but also to propositions of uncertain veracity.
What does follow are two books of propositions that provide means for inferring forces from motions and motions from forces and a final book that illustrates how these propositions can be applied to the system of the world first to identify the forces governing motion in our planetary system and then to use them to differentiate between certain true and apparent motions of particular interest.
