On 9/26/2011 7:56 PM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
On 9/26/2011 11:52 AM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
snip
Jason,
I really would like to understand how it is that the
truth valuation of a proposition is not dependent on our
knowledge of it can be used to affirm the meaning of the
referent of that proposition independent of us?
That sentence was hard to parse! If I understand it correctly,
you are asking how a truth, independent of our knowledge, can
confer meaning to something without us?
[SPK]
Essentially, yes.
Things unknown to anyone can have consequences which are
eventually do make a difference to beings which are aware of the
difference. A comet colliding with the Earth and hitting a pond
of unicellular organisms may have drastically altered the course
of evolution on our planet. That such a comet impact ocurred is
a fact which is either true or false, despite it being
independent of anyone's knowledge of it. Yet it has perceptable
results.
[SPK]
The web of causes and effects is an aspect of the material
universe. I am taking that concept into consideration.
Correspondingly, the existence of some mathematical truth (even
if not comprehended by anyone) can have effects for observers, in
fact, it might explain both the observers themselves and their
experiences.
[SPK]
Slow down! "existence of some mathematical truth"??? Do you
mean the truth value of some existing mathematical statement? That
is what I mean in my question by the phrase "truth valuation of a
proposition". Is a truth value something that exists or does not
exist?
I am not sure what you mean by "exists" in this case so let me say
this, the state of being true, or the state of being false, for the
proposition in question, was settled before a human made a
determination regarding that proposition.
[SPK]
Is the "state of being true" a physical state, like the "state of
having 10 units of momentum"? Is there a "truth detector"? Are you sure
that "state" and "true" are words that go together? AFAIK, true (or
false) are values, like numbers. In fact logics can have truth values
that range over any set of numbers. This puts truth valuations in the
same category as numbers. No?
How does the sentence "17 is prime is a true statement"
confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by
"meaning"? 17's primality is a fact of nature. The statement's
existence or non-existence, comprehension or non-comprehension
makes no difference to 17, only what you could say we humans have
discovered about 17.
[SPK]
Is the symbol 17 the same extant as the abstract number it
refers to?
No, as I mentioned to Brent in a post the other day, we ought not
confuse the label for the thing. Nor should we confuse our idea of a
thing for the thing itself.
[SPK]
OK, does not this imply that there are (at least) two separate
categories: Labels and Things? What relation might exist between these
categories?
Do you believe that symbols and what they represent are one and
the same thing???
No, we can apply some simple rules to the symbols in certain way to
learn things about the object in question.
[SPK]
What relation might exist between the "rules" of symbols and the
"rules" of things?
How does not the fact that many symbols can represent one and the
same extant disprove this hypothesis? Is the word "tree" have a
brownish trunk and greenish foliage? What about the case where
sets of symbols that have more than one possible referent?
Consider the word FORD. Does it have wheels and a motor? What is
the height of the water that one displaces when we might walk
across it? There is a categorical difference between an object and
its representations and the fact that one subobject of those
categories exists is not proof that a subobject in another
category has a given truth value. BTW, truth values are not
confined to {True, False}.
For well-defined propositions regarding the numbers I think the values
are confined to true or false.
Jason
--
[SPK]
Not in general, unless one is only going to allow only Boolean
logics to exist. There have been proven to exist logics that have truth
values that range over any set of numbers, not just {0,1}. Recall the
requirement for a mathematical structure to exist: Self-consistency.
Onward!
Stephen
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