The Nature Of Truth

By Dennis J. Darland

June 1, 2007

Revised December 19, 2007

True_belief

We can define true_belief(S,t,R,a,b,c)

As simply S believes(R,a,b,c) at time t & R(a,b,c)

And false_belief(S,t,R,a,b,c)

As S believes(R,a,b,c) at time t & ~R(a,b,c)

True_proposition

We can define true_proposition(R,a,b,c)

As proposition(R,a,b,c) & R(a,b,c)

And define false_proposition(R,a,b,c)

As proposition(R,a,b,c) & ~R(a,b,c)

From the definition of proposition(R,a,b,c) and S believes R(a,b,c ) at time t

It follows from S believes R(a,b,c) at t that

S understands R(a,b,c) at t thus

Proposition(R,a,b,c)

And from that it follows

True_proposition(R,a,b,c ) or false_proposition(R,a,b,c)

Which answers, I think, Wittgenstein’s objection which paralyzed Russell.

See The Collected Papers of Bertrand Russell (vol 7), Theory of Knowledge, The 1913 Manuscript pp. xxvii-xxviii.

Question: Isn’t it likely that Russell's paralysis involves

the tension between 1) his need to have a relation occur as such, i.e.

as relating entities ,in order to have a meaningful proposition and not a

mere list and 2) his need to explain false belief without introducing

objective false propositions?

For consider (loves, Amy, Bob): if the relation

loves actually relates the entities Amy and Bob, then what the belief

asserts –that Amy loves Bob—is true, but if the relation does not relate the

entities—i.e. Amy doesn't love Bob—then there is nothing relating the

terms (which might as well be loves, loves, loves; or Bob, Bob, Bob),

hence no proposition the believer may be said to believe, i.e. either

there is no content or there is no false belief.

To be paralyzed over the status of the relation and

over the account of false belief is not to imply the instant rejection

of the (multiple relation) theory of belief, which Russell clings to,

admitting its weaknesses, until 1918.

Answer: I will explain what is a little different about my

analysis (my answer is a bit different than what Russell could have said,

because my analysis is a bit different!), which you may not have noticed.

The proposition R(a,b,c) will exist when

($S)($w)($x)($y)($z)($t) such that

·         & symbol_1r(S,t,w,R)

·         & symbol_0r(S,t,x,a)

·         & symbol_0r(S,t,y,b)

·         & symbol_0r(S,t,z,c)

·

·

Or on plain symbols:

(ES)(Ew)(Ex)(Ey)(Ez)(Et) such that

·         & symbol_1r(S,t,w,R)

·         & symbol+0r(S,t,x,a)

·         & symbol_0r(S,t,y,b)

·         & symbol_0r(S,t,z,c)

(this is implied by S believes R(a,b,c) at time t).

and also, if S believes it you will have that

belief_r(S,w,x,y,z,t). This belief_r relates the

symbols w,x,y & z in a way to indicate what fact would

hold if R(a,b,c).  So the fact, though it may not

exist, is indicated by the relations between the

symbols.  Also, if there are propositions, which are

never believed, which seems likely, then we must say

the belief-R is not needed, but that the logical-form

& symbol-R relations are then sufficient, themselves to

make such a proposition exist.  These existing would

imply a practice of using w,x,y & z to represent R,a,b

& c, and the logical form rf of relating them.

Symbolic relations can hold between tokens and

objects. (actually via a norm for tokens). There can

be many utterances of tokens of "cat" but one word

cat. The relations of the tokens to the word are

resemblance. The relation of the word to the object

is a practice.

There are really (at least) two types of symbolic

relations. One for relations (between symbols and

relations) and another between symbols and objects.

The when the symbols for a relation R and symbols for

objects a and b exist for Speaker S at Time t there is

a proposition R(a,b). We speak of a corresponding fact

if a stands in the relation R to b.