On 9/27/2011 8:28 AM, Jason Resch wrote:
On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
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"?
If the object under consideration is a physical object, you might be
able to say that. If the object under consideration is 17, I would
say no.
[SPK]
OK. So it is your belief that , in general, objects (of any
categorical type) have specific and definite properties absent the
specification of the means of observation? How do you explain the
existence of conjugate observables in QM?
Is there a "truth detector"?
There can be truth detectors, in some sense we may be truth detectors,
but us discovery of a truth is not what makes it true.
Are you sure that "state" and "true" are words that go together?
I am at a loss for an english word that conveys the status of true or
false. We have the word parity for the status of even or odd, for
example, but I could not think of such a word that conveys the same
for true or false, which is why I used "the state of being true or false".
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?
True and false can be represented by two different numbers, but I am
not sure that makes them values in the same sense of numbers.
[SPK]
I was mentioning the fact that logics with truth values that range
over different sets of values have been proven to exist. Logic is not
limited to truth values over {0,1}, only Boolean logics are so
restricted by their defining rules.
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?
Labels are a human invention to support communication of ideas, which
you might say is yet another category of things.
[SPK]
Interesting. We "invented" labels. So representations, in general,
are they inventions also?
The relation ship might be as follows: if I tell you to multiply 1200
x 1800, you could arrange 1800 rows of 1200 beans and count them all,
or you could follow some simple rules of transformation applied to the
labels '1200' and '1800' and have a shortcut to the answer, without
having to do all that counting.
[SPK]
Is counting a uniquely human activity? Could not the behavior of
any physical system that has some dynamic behavior (f. ex. not
restricted to a single point in its configuration/state/phase space) be
considered as a form of counting? Is measurement in general not a form
of counting?
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?
I think I covered this above.
[SPK]
Is this relation an invention or a fact that was discovered? Could
you elaborate on your thoughts of this relation. Does it have a general
form?
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.
Okay, there may be other subjects, besides number theory and
arithmetical truth where other forms of logic are more appropriate.
For unambiguous propositions about numbers, do you agree with the law
of the excluded middle?
[SPK]
For logics that have a form of excluded middle law, yes. But those
are not the only form of logic. Heyting logics, for example, are
different. Is it necessarily the case that a logic must contain the law
of excluded middle to be "unambiguous"? If the rules and axioms are well
formed and self-consistent, why is the LEM necessary? For example, there
are logics that have truth values over {-1, 0,1}. Are they necessarily
ambiguous because of this?
Onward!
Stephen
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