On 9/27/2011 8:28 AM, Jason Resch wrote:



On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

    On 9/26/2011 7:56 PM, Jason Resch wrote:


    On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King
    <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

        On 9/26/2011 11:52 AM, Jason Resch wrote:


        On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King
        <stephe...@charter.net <mailto:stephe...@charter.net>> 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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