What is truth?
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From: Adrian Ferent on 2 May 2010 08:45 Lao Tzu writes: Why are people starving? Because the rulers eat up the money in taxes. Therefore the people are starving. http://www.chebucto.ns.ca/Philosophy/Taichi/lao.html
From: Adrian Ferent on 5 May 2010 04:48 I and Darwin: Darwin studied the Evolution on animals. I studied the Evolution on people and here are the results(my books): 98% of population is at animal level; only 1 in 1300 people have a connection with God...
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 |