The symbol relation

My discussion of belief and opacity uses the notion of a symbol

See

http://dennisdarland.com/philosophy/naming.html

where I use

Symbol_2r(S,t,v,B,)

Symbol_1r(S,t,w,R)

Symbol_0r(S,t,x,a)

Here S is the subject – a person

- v,w and x are symbols

- B is a propositional attitude

- R is a triadic relation (but you can imagine other arities)

- a is the name of a object.

- t is the time

It may be that Symbol_r’s in the three cases are of different types, they may be taken as typically ambiguous as is commonly done in Principia Mathematica.The analysis of belief given may be correct with the right interpretation of Symbol_r relations without me being able to explain Symbol_r relations, but I will try to do so now. I will also have to say something about persons and relations and objects.

Process Philosophy

Events

Both Bertrand Russell and Alfred North Whitehead after Principia Mathematica went on to develop philosophies in which events were primary.

Later Whitehead used the terms actual entity and actual occasion. Whitehead’s work developed out of the work he started on what was supposed to be volume IV of Principia Mathematica .which was going to develop geometry. Events are basically just volumes of space-time. Whitehead invented extensive abstraction, adopted by Russell, to define points, lines, planes, etc out of events.

Persons

Also persons are defined in terms of events. They are pretty much the class of events inside the track that person occupies in space-time, but, at least Whitehead, used the (causal?) relation between such events in his definition, so not just any collection of events would be a person.

Relations

Relations hold either between one (a predicate) or more objects. Higher order relations can hold between lower order relations. Whitehead later calls relations eternal objects.

Objects

Objects in the usual sense are, like persons, classes of events. Different sorts of objects can be defined, physical objects, etc.

Symbols

Symbols are whatever stand in the Symbol_r relation to an object, i.e. the class of x such that Symbol_r(S,t,x,a) for some S,a,and t.
This relation is difficult to fully explain as it may take many forms. Wittgenstein took it to be picturing in the Tractatus-Logico-Philosophicus. Russell tried to define is causally in The Analysis of Mind. Whitehead discussed it in his little book, Symbolism. Quine tries to define it in Word and Object. The later Wittgenstein shows the many forms it can take. I think they are all pointing, at least at some of, the instances of the relation. (Of course none of them spoke of the Symbol_r relations, but they spoke of people using symbols to stand for objects at some time.)(Although the later Wittgenstein may have insisted this was too narrow.) I think the later Wittgenstein came closest here. The relation is established by a practice of using the symbol to stand for the object. The symbol’s meaning may depend on its context in a sentence (e.g. definite descriptions or classes which are incomplete symbols) or a larger context, such as knowing a common (at least mostly) language where Symbol_r(s,t,x,a) holds between, at least mostly, the same x’s and a’s for many s’s and t’s.

Variables

There are also the variable_0r, variable_1r and variable_2r relations. They represent a relationship (in conjunction with quantifiers) between something sort of like a symbol, but generalized – like ‘some’ or ‘all’. We have a different application of these than the other symbols so I am calling them ‘variables’ – not ‘symbols.’

An objection answered

It might be said, “You say Wittgenstein is right in saying ‘Meaning is use’, but you define persons, relations, objects, and symbols different than their common usage.” “Yes”, I say, but Wittgenstein said “for most purposes.” I think we can take, from our scientific knowledge, some symbols as more “real” – as corresponding to objects recognized by science, and see how the use of other words can be explained in terms of them. The use of the other words can be continued though not taken as real as the symbols used by science.