Copyright (C) 2018 Dennis Joe Darland
NOTE: 1/15/2019 THIS SECTION NEEDS MUCH MORE WORK!!!!
NOTE: I am creating this page after much of the writing was done. I was not altogether consistent in my notation. I intended to go back and make revisions so it matches this page.
However, when I started to do so, it seemed to make understanding more difficult, at least in the earlier parts. I still plan to go through parts and make revisions. But, earlier on I had used, e.g. “idea_of_” etc. and names of objects, rather than the universals determining the events composing the objects. I am not revising all that. It makes understanding more difficult.
Names are within quotes, e.g. “Russell”
Ideas start with ‘i’ and end with ‘*’ (or 2 ‘*’ in case of an idea of an idea.’
Individuals (which I take to be events) are not normally named, but for illustrative purposes I will start with “ev_” (without quotes).
Universals of type 1 apply to individuals. They will be prefixed by “un_1_”. (without quotes).
Universals of type 2 apply to a mixture of individuals and universals of type 1. They will be prefixed by “un_2_” (without quotes).
Similarly for higher order universals.
P is a relation between a word and the idea of that word.
R is a relation between a idea of a word and an idea of an object.
E.g. “Russell” R iRussell*
S is a relation between an idea of a object and a object.
E.g. iRussell* S un_1_Russell
Where un_1_Russell applies to the events composing Russell.
S is also a relation between ideas of truth functions and those truth functions.
S is also a relation between idea iE* (there exists) and E
S is also a relation between ideas iu, iv, iw, ix, iy and iz for variables u, v, w, x, y and z.
| is the symbol for relative product. See PM *34.
We will consider whether there can be a relation T between a universal and a class.
E.g. un_1_Russell T ^x[un_1_Russell x]
L is symbol for necessity.
There is need for only one truth function. (nor or nand).
N is symbol for not.
C is symbol for material implication.
A is symbol for alternation.
Thus we have.
“E” R iE*
“|” R i|*
“L” R iL*
“N” R iN*’
“C” R iC*
“A” R iA*
And
iE* S E
i|* S |
iL” S L
iN* S N
iC* S C
iA* S A
“Russell” R|S un_1_Russell
“E” R|S E
“|” R|S |
“L” R|S L
“N” R|S N
“C” R|S C
“A” R|S A
There are also propositional attitudes: believing_private, desiring_private, etc.
I will only talk about believing_private (abbreviated BP)
They are relations between a person and ideas.
Ideas are usually specific for a person.
Thus BP(un_1_Russell,i_un_2_f,i_un_1_a)
Represents that Russell has the psychological relation of belief that a universal f applies to a universal a.
f might be intelligent.
a might be Whitehead.
It will be true if a has the universal f. f(a).
Or
un_2_f(un_1_a),
with the full notation.
Now this itself is a psychological state of Russell’s.
But Russell’s psychological states are not purely private.
He interacts with Whitehead and others who interact with Whitehead.
There is generally a consensus on the use of “intelligent” and “Whitehead”
“intelligent” R|S un_2_f
“Whitehead” R|S un_1_a
The intermediate term in the R|S could be quite different for different people.
Also the R’s and S’s would vary some from person to person.
People’s vocabularies and ideas vary.
Also we can only try to make our posits of the world as useful and consistent as possible, there is much we do not and can never know. The RHS of the S relation are posits.
I plan to write pages on my notation and definite descriptions and classes.
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