What is truth?
in [Math]
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From: rods on 7 May 2010 16:44 I somehow lost this good post about the subject. It pretty much give the options on how to deal with the subject. Some more comments inline ... On 26 abr, 14:37, Alan Meyer <amey...(a)yahoo.com> wrote: > troll wrote: > > > Gradually, I have started getting the idea that goodness > > has no real meaning at all. Entropy and information > > has a clear definition in physics and mathematics, but > > goodness is just a nice sounding word and no one > > can ever agree on what it actually means. > > > > Recently, however, I have started to wonder whether > > truth has any real meaning. Is there a mathematical > > or physical definition of truth, and if so what is it? > > > > I get the idea that I am missing something simple, > > but I am not sure what it is. What is the definition > > of truth in physics and mathematics? At least a > > very simple web search ends up getting choked > > with meaningless drivel from philosophers. > > Trolls so often pose interesting questions - even when they > really think that the answers are meaningless drivel. > > Here are three possible approaches to a definition of truth, as > near as I can recall from the not so meaningless education I > received in philosophy. I make my apologies in advance to those > who understand these theories deeply and can see all of the > gross simplifications or worse that I am introducing here. > > 1. Correspondence to reality. > > This is the most straightforward definition and unquestionably > the one that most people intend when they say that a statement > is true. > > If I say "It is raining" or "The dog is wet", those statements > are true if and only if, in fact, it is raining or the dog is > wet. > > Problems only arise with this view when we get away from > simple observational statements and start to talk about > values, or about models of reality, or about objects which > exist within a certain body of theory but which are not > directly observable - like subatomic particles or infinite > quantities or states of mind. > > The other two theories given below are attempts to handle > cases where we need to go beyond observational reality. > However I don't think either of them denies that true > statements are statements corresponding to reality, although > the "reality" in question is not always an observational one. > > 2. Coherence within a self-consistent theory. > > By "coherence" I mean that a statement to be evaluated is > found to be consistent in all respects with a larger and > self-consistent theoretical framework. > > This is the kind of "truth" that seems to make the most sense > when discussing mathematics. 7 + 9 = 16 coheres with the > theory of arithmetic. This also happens to correspond with > reality when we discuss 7 apples and 9 apples, but the > definition can be just as easily applied in theoretical > frameworks such as non-Euclidean geometry, n-dimensional > spaces, etc., where "correspondence to observational reality" > becomes problematical or impossible. > > The coherence theory is also valuable in everyday life. When > someone tells us he saw water flow uphill, or a ghost, or a > perpetual motion machine, or anything of the like, we normally > reject such statements without having to investigate them. > Such statements are inconsistent with a body of theory that > has so much history and so much weight of evidence behind it > that it would be a waste of time to investigate purported > exceptions. > > Sometimes that gets us in trouble. Very occasionally someone > discovers something that is inconsistent with a very widely > accepted and supported theory and further investigation shows > that there really is a problem with the theory that no one saw > before. But in spite of such exceptional cases, the > requirement for coherence saves us from error vastly more > often than it leads us into it. Here is where I think Godel's theory plays an important role. I read Godel as (please comment/correct me logic experts): a theory can't have a rules that garantee that some "truths" are true, because if we do that this theory is necessarily incoherent. Notice the "if and only if" on the quote: Quote from http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Second_incompleteness_theorem "For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent." So a truth must necessarily be a consequence of "something" and never the cause. If we just assume that "something" is true I am OK with that. But if we say that "something" is "experimentally" true I think this is somehow paradoxal. Because an experiment is something thought to prove the consistency of a theory. It just have a definitive meaning when it is a failure, because this means that the theory is wrong (at least partially). But if it is sucessufully it just means "so far so good". Rodrigo I > 3. Forming the basis of accurate predictions. > > When we say that "the dog is wet", we are implying that > certain experiences can be predicted. For example, if you > touch the dog, your hand will get wet. If you stand next to > the dog and the dog shakes himself, you will get splattered. > If the dog lies down on the carpet, there will be a wet spot. > And so on. > > If these observations are made but the predicted events do not > occur, then the original statement "the dog is wet", is false, > or at least not completely true (maybe his feet are wet but > not his fur.) > > Where this theory of truth becomes particularly valuable is in > discussing empirical objects or events that cannot be directly > observed, such as nuclear particles and forces. We can't see > an electron or an x-ray, but we can make predictions about > observations which, if they are in fact observed, give us > reason to assert that statements about the electron or x-ray > are true. > > This theory, proposed by the American philosophers Charles > Peirce, William James, and John Dewey, is called the > "pragmatic" or "instrumental" theory of truth. > > Alan
From: tadchem on 7 May 2010 18:14 On Apr 16, 7:18 am, troll <trolid...(a)go.com> wrote: > Gradually, I have started getting the idea that goodness > has no real meaning at all. "Goodness" is a morally relative term, defined by the user according to idiosyncratic concepts. > Entropy and information > has a clear definition in physics and mathematics, Two terms, two definitions... Generally physics and mathematics share definitions fairly well. > but > goodness is just a nice sounding word and no one > can ever agree on what it actually means. ....because everybody has their own idea what it is, like "god" > Recently, however, I have started to wonder whether > truth has any real meaning. Is there a mathematical > or physical definition of truth, and if so what is it? "Truth" is a context-dependent term. In philosophy (specifically epistemology) each 'philosopher' has their own individual concept of what 'truth' means, and generally they aren't even aware of the fact that they are 'comparing apples and oranges'. Mathematically 'truth' refers to a logical proposition that can be proven within the context of propositional calculus. Goedel did a lot of work with describing the limits of applicability of propositional logic. Physically 'truth' refers to an empirically testable proposition which has not yet failed an empirical test. Physics differs from mathematics in that the arbitration of truth requires an element that is independent of logic - empirical validation. > I get the idea that I am missing something simple, > but I am not sure what it is. What is the definition > of truth in physics and mathematics? At least a > very simple web search ends up getting choked > with meaningless drivel from philosophers. Caveat: don't accept anything said about 'physics' or 'truth' from a philosopher who fails to recognize that simple fact that 'science' is a *method* of investigating propositions to identify 'the truth', not an art or a body of lore. HTH Tom Davidson Richmond, VA
From: Aatu Koskensilta on 11 May 2010 09:21 rods <rodpinto(a)gmail.com> writes: > The way Tarski works this out is to use a pure semantic definition of > truth. Just what is it you take Tarski to be "working out"? > Godel's incompleteness theorem shows that if there is a theory, you > can have something that is true in this theory and not provable. But > something that cannot be proved is not an experimental truth. Why not? On the face of it there's nothing to relate the existence of formal derivations to truth of statements about experimental matters. Your invocation of G�del is entirely vacuous, pure waffle, of no substance whatever. > I think it is easier if we just assume that truth is something that > cannot be provable and a experimental truth is a tautology. This is pure nonsense. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 11 May 2010 09:22 Frederick Williams <frederick.williams2(a)tesco.net> writes: > The problem is: how does one classify truths as being empirical or > logical? It is a matter of arbitrary convention. More nonsense. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Frederick Williams on 11 May 2010 09:42
Aatu Koskensilta wrote: > > Frederick Williams <frederick.williams2(a)tesco.net> writes: > > > The problem is: how does one classify truths as being empirical or > > logical? It is a matter of arbitrary convention. > > More nonsense. Not at all. One's choice of logical constants will affect what logical truth is, and one's choice of logical constants is a matter of arbitrary convention. -- I can't go on, I'll go on. |