Sentence examples for propositions form from inspiring English sources

So one is apparently forced to reject the assumption that propositions form one type, and hence to require that they ought to have various types, while logical products ought to have propositions of only one type as factors.

By analysis we reduce them to propositions which are as nearly as possible simple and precise, and we arrange them in deductive chains, in which a certain number of initial propositions form a logical guarantee for all the rest.

We know that it was alleged to show that these three propositions formed an inconsistent triad, but exactly how it did this remains uncertain.

Thus Heytesbury's analysis, according to which insolubles do signify otherwise than they normally do, cannot be applied to propositions formed in mental language.

Closely related to the idea of a valid inference form is that of a valid proposition form.

Then the condition stated above for the validity of the inference form "α, therefore β" amounts to saying that no instance of the proposition form "α and not-β" is true i.e., that every instance of the proposition form(7) Not both: α and not-β is true or that line (7), fully spelled out, of course, is a valid proposition form.

Such a wff is therefore a proposition form in the sense explained above and hence is valid if and only if all its instances express true propositions.

A proposition form is an expression of which the instances (produced as before by appropriate and uniform replacements for variables) are not inferences from several propositions to a conclusion but rather propositions taken individually, and a valid proposition form is one for which all of the instances are true propositions.

An expression of the form "the so-and-so" is called a definite description; and (ιx), known as a description operator, can be thought of as forming a name of an individual out of a proposition form.

If a wff of LPC is considered as a proposition form, instances of it are obtained by replacing all free variables in it by predicates or by names of individuals, as appropriate.

This fact is easily seen from the fact that α ⊃ β means the same as "not both: α and not-β"; for, as was noted above, whenever the latter is a valid proposition form, "α, therefore β" is a valid inference form.