### Glossary section:

theory
The process of forming a <A HREF="bword://set">set</A>, typically by <A HREF="bword://bind">bind</A>ing a <A HREF="bword://free variable">free variable</A> in a formula which expresses the <A HREF="bword://truth">truth</A> condition, for membership in the set, of the value denoted by the variable. <I>Comprehension</I> and <I>separation</I> are particular kinds of set abstraction. Abstraction to properties (predicates or propositional functions) is analogous.

(functional), 
Forming a function, typically by binding a free variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable. 

also
<A HREF="bword://abstract algebra">abstract algebra</A> <A HREF="bword://computer algebra">computer algebra</A> 

(logic), 
a proof which proceeds by analysis of the desired conclusion showing that it is derivable from accepted premises (from classical Greece). Such proofs are now sometimes known as a <I>backward</I> or <I>goal oriented</I> proofs.

(philosophy), 
expressing a relationship between concepts. A statement or proposition which lacks empirical content and is true in virtue of its meaning.

(philosophy), 
a kind of philosophy particularly concerned with logical or linguistic analysis (see: <A HREF="../history/his003.htm" CLASS=conref>Varieties of Philosophical Analysis</A>).

theory)
definable in second order arithmetic  

(philosophy), 
a paradox or contradiction  

posteriori
knowable or justifiable only on the basis of experience 

priori
knowable or justifiable prior to experience based on purely rational considerations 

also
<A HREF="bword://g delization">g&ouml;delization</A> 

method
a method of doing mathematics in which subject areas are presented and studied as axiomatic theories 

(computing), 
a semantics for a programming language given by defining axioms which permit reasoning about the effects of execution of the various parts of a program.