Copyright (C) 2018 Dennis Joe Darland
It seems likely that individuals (not individual people, rather individual entities) are events.
It would be rare that an event be named.
Events are mostly described.
There are likely a non-denumerable number of events so some cannot be described.
There are (the next type) universals applying to events.
Any particular person is specified by a universal.
There is also a relation belong-to-same-person for any two person time slices making up a person.
Any particular idea is specified by a universal.
Any particular word is specified by a universal.
These universals determine classes of events.
Almost any word is related via P | R | S to another universal.
P being the relation of a word to an idea of the word – for a person.
R being the relation of the idea of a word to the idea of an object.
S being the relation of a an idea of an object to a universal for a person.
T being the relation between a universal and its extension. (which can be defined as an incomplete symbol.)
None of P, R, S, nor T need be one-one, but all obey the intersubstituitivity of identicals.
So P|R|S is the relation between a word and its universal.
E.g. (“Russell” P|R iRussell) and (iRussell S Russell)
and
“Russell” P|R|S|T ^x[Russell x]
where
“Russell” is the word for iRussell
iRussell is the idea for Russell (for someone)
Russell is a universal for the events composing that person.
^x[Russell x] is the events composing Russell.
There would be many universals determining the same class ^x[Russell x]
Also there could be many ideas iw such that iw S Russell.
As different people have different ideas for the same word it is also true:
There could be many iw such that “Russell” P|R iw.
There could also be other words, e.g. “Bertie” for various such iw.
Also there could be other ideas ix such that “Russell” R ix, E.g. the famous Celtics basketball player.
Generally there will be agreement between people that “Russell” P|R|S|T ^x[Russell x]
This is because the word “Russell” and ^x[Russell x] are more objective.
The connection between them is created at some past time, by a christening act and is what is called a rigid designator. But although, at least in almost all cases, the original act of christening is the beginning of a causal chain resulting in the P|R|S|T relation for various people, the P, R, S, and T relations can themselves be different for different people. E.g. Russell may be known to some as the god son of John Stuart Mill, and others may known to some as the greatest logician since Aristotle. (Whether or not this is true.) Both these descriptions could result from different causal chains going back to the original christening. The classes are usually inferred equal from “Russell” P|R|S|T ^x[Russell x] and “Russell” P|R|S|T ^x[Russell2 x]. Our universals Russell and Russell2 are different, but learned from different causal chains hopefully starting from the same christening. We also have an idea of personal identity. From our experiences of the word “Russell” we infer this relation holds between members of ^x[Russell x] and members of ^x[Russell2 x] – we could be wrong – we do not know all these members. Also people’s understanding (P|R|S|T) of “Russell” is only the end product of these causal chains, which could vary from one possible world to another – so it is not such a “rigid” designator. Also, generally speaking, there is no reason that an act of christening could not vary between possible worlds – that is an artificial formal logical requirement.
Mostly we can only posit that often N EyEx N y P|R|S|T x
(I.e. some words stand for something).
We know that Ex N Ey y P|R|S x
There are there are things for which there are no words. (By the Church-Turing Thesis)
In the case of R
there is inter-substutuitivity for R
if
“A” P|R iA
“B” P|R iB
and iA = iB
then
“A” P|R iB
and
“B” P|R iA
and sometimes iA != iB even if A = B
for S
iA S A
iB S B
Now if A = B
iA S A
iA S B
iB S A
iB S B
But this means there are 2 ideas for only 1 universal, so I think this expected – but perhaps unusual. Perhaps that is a key to synonymy.
Usually for 2 ideas – I think there are 2 universals – even if their extension is the same.
Also one can have ^[A x] = ^x[B x]
even when A != B
But if ^x[A x] = ^x[B x]
then
A T ^x[B x]
and
B T ^x[A x]
But this can be true even when A != B
One would expect that there be many different A and B with the same extension.
Using iA for idea of A
and ^x[A x] for extension of A.
A being a universal.
And “A” for the word having the idea iA.
Using iB for idea of B
and ^x[B x] for extension of B.
B being a universal.
And “B” for the word having the idea iB.
Also Q is a person.
Then Q believes V(A).
=df
believes_private(Q,iV,iA)
S(iV,V)
S(iA,A).
Now there may be a B such that:
^x[Ax] = ^x[Bx]
but still A != B.
And hence Q believes N V(B)
=df
[N for negation]
believes_private(Q,iN,iV,iB)
S(iN,N)
S(iV,V)
S(iB,B).
Even though ^x[A x] = ^x[B x]
This does not permit substitution of B for A.
Because
believes_private(Q,iV,iA)
but not
believes_private(Q,iV,iB)
because
iA != iB
and A != B
even though
^x[A x] = ^x[B x]
I think we reason about universals – not extensions directly.
But our knowledge of universals – (including Ideas and Words) comes from extensions.
That knowledge differs from person to person.
We do not know what the extensions are.
We may believe two universals have the same extension. (Without knowing the extension).
E.g, on the Frege-Russell definition of number – two is the class of all couples, but we do not know what that is. We do not know every couple. But we can know 2 + 2 = 3 + 1.
We can prove it in math or logic.
Example where universal varies but class is the same:
An example might be, George believes some featherless bipeds are not human.
Here ^x[featherless biped x] = ^x[human x] (the classes are the same)
but ^featherless biped x != ^human x (these being the functions or universals – different)
It was Bertrand Russell’s great accomplishment in Principia Mathematica to explain the use of classes as incomplete symbols.
So there could be distinct universals with the same extension.
Also, from limited knowledge, one cannot know the universals differ.
So I think, since there are distinct universals (such as featherless biped and human), classes must be incomplete symbols.
NOTE: I proofread 12/22/2018 making points clearer, and correcting typos.
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