Sentence examples for proposition forms from inspiring English sources

As a formal system the propositional calculus is concerned with determining which formulas (compound proposition forms) are provable from the axioms.

Formal logic is concerned with proposition forms as well as with inference forms.

The study of proposition forms, however, cannot be similarly accommodated under the study of inference forms, and so for reasons of comprehensiveness it is usual to regard formal logic as the study of proposition forms.

Because a logician's handling of proposition forms is in many ways analogous to a mathematician's handling of numerical formulas, the systems he constructs are often called calculi.

The study of proposition forms can, in fact, be made to include that of inference forms in the following way: let the premises of any given inference form (taken together) be abbreviated by alpha and its conclusion by beta.

It also provides a method of deriving from these inference forms valid proposition forms, and in this way it is analogous to the derivation of theorems in an axiomatic system.

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.