What is a proposition?

By Dennis J Darland

May 31, 2007

Revised December 19, 2007

A proposition can be defined (we will use the case of a triadic relation) as follows:

The proposition corresponding to the fact R(a,b,c) would be the relation

proposition(R,a,b,c) between R,a,b,and c such that

($S)($t) S understands R(a,b,c) at time t.

IN OTHER SYMBOLS

(ES)(Et) S understands R(a,b,c) at time t.

See http://dennisdarland.com/philosophy/understanding.html

This is not to say that the proposition is true. The proposition is true if a fact corresponds to the proposition. One can see from the proposition, what fact would have to hold for the proposition to be true, but the fact need not hold, for the proposition to exist. Also we could relax that the symbolic relations all hold for the same person. We could say

proposition(R,a,b,c) iff

($w)($S2)($t2)($x)($S3)($t3)($y) ($S4)($t4)($z)($S5)($t5)

· & symbol-R(S2,t2,w,R)

· & symbol-R(S3,t3,x,a)

· & symbol-R(S4,t4,y,b)

· & symbol-R(S5,t5,z,c)