Copyright (C) 2018 Dennis Joe Darland
Here P|R is a relation between words and ideas
and S is a relation between ideas and objects (objects including universals, and the logical entities not, or, existing, various variables, and necessity).
Now (See Principia Mathematica *32)
the possible relata of S are objects. [some objects may not be relata]
The possible referents of S are ideas of objects.
The possible relata of R are ideas of objects.
The possible referents of R are ideas of words. [some ideas may not be in R relation to a word as a referent]
The possible relata of P are ideas of words.
The possible referents of P are words.
This can be equivalently expressed in terms of domains and converse domains (PM *33).
Anyway (just as an attempt), lets suppose for any possible sentence (composed of words),
there is a possible relation of ideas where for each word in the sentence, there corresponds an idea in the RHS of an P|R relation to the word. (call that, for any sentence, a proposition)
and also suppose,
there is a possible relation of objects where for each idea in the proposition, there possibly corresponds an object in the RHS of an S relation to the idea. (call that for any proposition a fact) For true propositions, there will be such facts.
There may be facts, for which there is no such proposition. [consider Church–Turing Thesis]
Words and ideas are also objects, as is the belief_private universal.
Also, note there could be an idea say a, for which there is no object b, such that a S b.
And, similarly, in some other cases.
Return to Dennis Joe Darland