What is truth?
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From: Aatu Koskensilta on 23 Apr 2010 17:20 rods <rodpinto(a)gmail.com> writes: > Just to make it clear what I wanted to say. > I think that there is no such thing as a empirical truth. > I would call such a empirical truth as a tautology, in the end we are > always comparing things like 1=1. And this is a tautology. I'm afraid this isn't very clear at all. Putting that to one side, perhaps you could explain what these odd proclamations have to do with the incompleteness theorem? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Alan Meyer on 26 Apr 2010 13:37 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. 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: rods on 6 May 2010 07:27 On 23 abr, 18:20, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > rods <rodpi...(a)gmail.com> writes: > > Just to make it clear what I wanted to say. > > I think that there is no such thing as a empirical truth. > > I would call such a empirical truth as a tautology, in the end we are > > always comparing things like 1=1. And this is a tautology. > > I'm afraid this isn't very clear at all. Putting that to one side, > perhaps you could explain what these odd proclamations have to do with > the incompleteness theorem? 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 let's say a theory is consistent. I would prefer to use the word model instead of theory. Let's say a model is consistent. And let's say in this model we have something called "empirical truth". My model cannot include a "statement of its own consistency" because if it does so I can use Godel's Second Incompleteness Theorem to show that model is inconsistent. The way Tarski deals with this is to use a semantical approach. So instead of saying that there is an "experimental truth" that would lead to an inconsistent model we can just use "Truth". And it is not required to have a "statement of its own consistency" to prove that my "defined" is really "truth". But if you do this, does it mean that there is no such thing as "experimental truth" ? Not exactly, I just say that then we must have a very well defined of what is "experimental". The uncertainty principle can also be used in favor of this approach. I am not saying that there is no such thing as an "experimental truth", I am just saying that the experiments just show the consistency of the model. Rodrigo
From: rods on 6 May 2010 07:31 On 6 maio, 08:27, rods <rodpi...(a)gmail.com> wrote: > On 23 abr, 18:20, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > rods <rodpi...(a)gmail.com> writes: > > > Just to make it clear what I wanted to say. > > > I think that there is no such thing as a empirical truth. > > > I would call such a empirical truth as a tautology, in the end we are > > > always comparing things like 1=1. And this is a tautology. > > > I'm afraid this isn't very clear at all. Putting that to one side, > > perhaps you could explain what these odd proclamations have to do with > > the incompleteness theorem? > > Fromhttp://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#S... > > 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 let's say a theory is consistent. I would prefer to use the word > model instead of theory. > Let's say a model is consistent. And let's say in this model we have > something called "empirical truth". My model cannot include a > "statement of its own consistency" because if it does so I can use > Godel's Second Incompleteness Theorem to show that model is > inconsistent. > The way Tarski deals with this is to use a semantical approach. So > instead of saying that there is an "experimental truth" that would > lead to an inconsistent model we can just use "Truth". And it is not > required to have a "statement of its own consistency" > to prove that my "defined" is really "truth". I meant "And it is not required to have a "statement of its own consistency" to prove that my "truth" (or my "defined truth") is really "truth"." > But if you do this, does it mean that there is no such thing as > "experimental truth" ? Not exactly, I just say that then we must have > a very well defined of what is "experimental". > The uncertainty principle can also be used in favor of this approach. > I am not saying that there is no such thing as an "experimental > truth", I am just saying that the experiments just show the > consistency of the model. > > Rodrigo
From: Aatu Koskensilta on 6 May 2010 07:50
rods <rodpinto(a)gmail.com> writes: > So let's say a theory is consistent. I would prefer to use the word > model instead of theory. Your preferences are your business, but to say of a model, in the technical sense used in mathematical logic and relevant to the incompleteness theorems, that it is consistent or inconsistent makes no sense whatever. > Let's say a model is consistent. And let's say in this model we have > something called "empirical truth". This too makes no apparent sense. > My model cannot include a "statement of its own consistency" because > if it does so I can use Godel's Second Incompleteness Theorem to show > that model is inconsistent. Again, this is but confused waffle. In light of this I can only suggest it's a good idea to leave G�del out of it altogether; if you're for some reason interested in the actual content of the incompleteness theorems you will find a clear and sober exposition in Torkel Franz�n's excellent _G�del's Theorem -- an Incomplete Guide to its Use and Abuse_. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |