On 9/27/2011 5:28 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.Is there a "truth detector"?There can be truth detectors, in some sense we may be truth detectors, but us discoveryof 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 havethe word parity for the status of even or odd, for example, but I could not think ofsuch a word that conveys the same for true or false, which is why I used "the state ofbeing 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 makesthem values in the same sense of numbers.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 ornon-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 isyet another category of things.The relation ship might be as follows: if I tell you to multiply 1200 x 1800, you couldarrange 1800 rows of 1200 beans and count them all, or you could follow some simplerules of transformation applied to the labels '1200' and '1800' and have a shortcut tothe answer, without having to do all that 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.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 whereother forms of logic are more appropriate. For unambiguous propositions about numbers,do you agree with the law of the excluded middle?Jason

`I think this an assumption or another axiom. Consider the conjecture that every even`

`number can be written as the sum of two primes. Suppose there is no proof of this from`

`Peano's axioms, but we can't know that there is no proof; only that we can't find one.`

`Intuitively we think the conjecture must be true or false, but this is based on the idea`

`that if we tested all the evens we'd find it either true or false of each one. Yet`

`infinite testing is impossible. So if the conjecture is true but unprovable, then it's`

`undecidable.`

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