Background to my Multiple Relative Product Theory of Belief

by Dennis J. Darland
November 8-19, 2022

This is a background for my theory. It does not exactly
represent Bertrand Russell's views at any time, but it
does represent, in my opinion, the best way to revise
his views.

Before there was intelligent life, there was a world - there were facts.
But truth is primarily a correspondence between belief and fact.
So before there was intelligent life there was no truth.
If there was rain was a fact, then there being rain or there not
being rain would also be a fact. But without beliefs there would be
no corresponding truths.
Likewise, if it were not a fact then it not being a fact would be a fact.
Any combination of disjunctions and negations of facts would also
be a fact or its negation would be a fact.
Likewise if F is a universal, and x is an a variable then (Ex)F(x) is a fact
in the case that some x instansiates F.

Next consider a, b, c, ... to be individuals.
F, G, H to be universals. 
Consider ia, ib, ic, ... to be ideas (in an intelligrent being) of a, b, and c
Consider iF, iG, iH to be ideas of universals
Also wa, wb, wc, ... to be words for those ideas of individuals
Also wF, wG, wH to be words for ideas of thos ideas of universals

(Note: Words and Ideas are also objects)

Now to truth. First truth of belief.

Letting S be the relation of an idea to the corresponding object.
and R be the relation of a word to the corresponding idea.

By thest simple conventions:

ia S a
and iF S F
In that case the belief of that intelligent being would be a relation
of the ideas iF and ia.
Say Bi(iF, ia)
This would be true in case F(a).

A sentence for that intelligent being would be:
Bw(wF, wa)
In that case the belief of the sentence of that intelligent being would
be a relation of the words wF and wa.

This would be true in case F(a).
Note in this case, by my conventions:
ia S a
iF S F
wa R ia
and
wF R iF

Or
wa R|S a
wF R|S F

Note, really the R and S relations depend upon the person (intelligent being)
and the time. The above in this respect a simplification.

I'm going to work out more details in regard to truth functions next.

For any facts 
F(a) G(a,b) etc

there will be facts (from PM *1.2)
F(a) v F(a) .>. F(a)     
G(a,b) v G(a,b) .>. G(a,b)

Similarly for PM *1.3-*1.6

But PM *1.1 and *1.7-1.72 are not facts. (In the same way.)
They
They represent ways intelligent beings have learned to
reason from facts to other facts.

PM's propositions are like my facts.

Consider *1.72
It is correct to reason that if iF(ia) is a relation of ideas then
iF(ia) iv iF(ia) .i>. if(ia) is relation of ideas.

So if
iF S F

ia S a

iv S v

i> S >

an intelligent being

can conclude from PM *1.2 that

F(a) v F(a) .>. F(a)

is a fact

because 

iF(ia) iv iF(ia) .i>. iF(ia) is relation of ideas.

and is a true thought.

In arriving at this conclusion the person draws an inference.
That is an action. It does not correspond to the conclusion.
although that the action occurs will itself be a fact.

Actions could also occur corresponding to false conclusions.
Logic describes how to make correct conclusions.
Psychology describes the making of actual conclusions (and other things).