Sentence examples for propositions equivalent from inspiring English sources

(Copeland and Sylvan (1999) is a survey; see also Copeland and Proudfoot (1999b).) The literature on the computational theory of the mind contains numerous endorsements of propositions equivalent or similar to thesis M that are supported by nothing more than a nod toward Turing or Church (as is illustrated by a number of the quotations given earlier).

In some sense, we have a non-wellfounded definition, which is as problematic as a contradiction (a proposition equivalent to its negation).

On a so-called attributive use, a sentence of the form 'The F is G' is used to express a proposition equivalent to 'Whatever is uniquely F is G'.

The following propositions are equivalent.

Then the following propositions are equivalent.

The following propositions are equivalent: (i) is exponentially convex, (ii) is continuous and (3.6).

For an operator (H Irightarrow V), the following propositions are equivalent: (i) H is exponentially convex.

In the seventeenth century, some logicians were to treat singular propositions as equivalent to universal propositions, but, as Dorp's remarks suggest, medieval logicians preferred to class singular propositions with particular propositions.

Then the following propositions are equivalent: (1 the functionals, are linearly independent; (2 the functions, are linearly independent; (3).

Then the following propositions are equivalent: (a) the forward escaping sets are biholomorphic;   (b) (H_{1}=H_{2}).  . the forward escaping sets are biholomorphic; (H_{1}=H_{2}).

Let ψ : I → ℝ, the following propositions are equivalent: (i) ψ is exponentially convex on I.   (ii) ψ is continuous and ∑ i, j = 1 n ξ i ξ j ψ x i + x j 2 ≥ 0,  .