Quote: logic and mathematics are only concerned with the truth value of forms; i.e., that which remains unchanged when every constituent is changed

Quotation

The "form" of a proposition is that, in it, that remains unchanged when every constituent of the proposition is replaced by another. Thus "Socrates is earlier than Aristotle" has the same form as "Napoleon is greater than Wellington," though every constituent of the two propositions is different. We may thus lay down, as a necessary (though not sufficient) characteristic of logical or mathematical propositions that they are to be such as can be obtained from a proposition containing no variables ... by turning every constituent into a variable and asserting that the result is always true or sometimes true, or ..., or any variant of these forms. And another way of stating the same thing is to say that logic (or mathematics) is concerned only with forms, and is concerned with them only in the way of stating that they are always or sometimes true--with all the permutations of "always" and "sometimes" that may occur.   Google-1   Google-2

Published before 1923

Related Topics

Topic: mathematics as a formal system (30 items)