On Tue, Sep 27, 2011 at 8:02 AM, Stephen P. King <[email protected]>wrote:
> On 9/27/2011 8:28 AM, Jason Resch wrote: > > > > On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King <[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]>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]>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? > Yes I believe objects have properties even if unobserved. Do you really believe the cat is both alive and dead (in the same universe) until it is observed? > How do you explain the existence of conjugate observables in QM? > > If you are a CI proponent, you could say being in many places at once, or having many simultaneous states simultaneously is a property of objects in superposition. The Everettian might say a more simply that a property of a particle (or the universe) is that it obeys the Shrodinger equation. I assume your point is that an particle cannot have a definite momentum and position, but this is really a statement about observation (the observer cannot know both simultaneously), not the object (or many objects) under consideration. > > > > >> 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. > > I think Bruno addressed this very well. > > >> >> >> >>> >>> 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? > > Some representations are human inventions. > > > 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? > No, Elephants, and even fish have been shown to count. > 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? > I would say it is a form of progression, counting has too different a connotation I think. > Is measurement in general not a form of counting? > > > > I think it depends on what is being measured. I'm not sure where you are going with this. > > >> >> >> >>> 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? > Our system of decimal representation is in some sense an invention, but the fact that theorem building can be framed in terms of string/symbol manipulations is the fact on which that invention is based. The analogy is the Apollo rocket was an invention, but it depends on the foundation of physics discovered by Newton. > Could you elaborate on your thoughts of this relation. Does it have a > general form? > > Which relation? > > > >> >> >> >>> 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. > So you believe every unambiguous proposition regarding the numbers is either true or false. Even the ones we have not yet proved, like Goldbach's conjecture. If so we don't need to observe a proof or disproof of Goldbach's conjecture for it to be true or false. > 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? > I don't know enough about these logics to say. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
