What is truth?
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From: rods on 6 May 2010 09:18 On 6 maio, 08:50, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > rods <rodpi...(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 Gödel 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 Franzén's excellent > _Gödel's Theorem -- an Incomplete Guide to its Use and Abuse_. > Thanks for the reference. I think that you don't understand Tarski concept of truth. Maybe if you read something about it my point will be more clear. My argument is very simple. And you are refuting it just saying: > 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. So are you saying that a model being consistent or inconsistent is no relevant to the incompleteness theorems? This sounds like nonsense to me. Rodrigo
From: Aatu Koskensilta on 6 May 2010 09:26 rods <rodpinto(a)gmail.com> writes: > Thanks for the reference. I think that you don't understand Tarski > concept of truth. My understanding, however lacking, of such matters is entirely irrelevant. > So are you saying that a model being consistent or inconsistent is no > relevant to the incompleteness theorems? What I said was that in mathematical logic it simply makes no sense to say that a model is or is not consistent. This is an elementary point which you can easily check for yourself by looking up the relevant definitions in any standard text. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: bert on 6 May 2010 09:31 On May 6, 9:18 am, rods <rodpi...(a)gmail.com> wrote: > On 6 maio, 08:50, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > > > rods <rodpi...(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 Gödel 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 Franzén's excellent > > _Gödel's Theorem -- an Incomplete Guide to its Use and Abuse_. > > Thanks for the reference. I think that you don't understand Tarski > concept of truth. > Maybe if you read something about it my point will be more clear. > My argument is very simple. And you are refuting it just saying: > > > 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. > > So are you saying that a model being consistent or inconsistent is no > relevant to the incompleteness theorems? > This sounds like nonsense to me. > > Rodrigo- Hide quoted text - > > - Show quoted text - Truth is reality Bible is not reality. Gods are not reality.Humankind's quest is to find reality. Not easy for us for universe has so many misteries. Best we not forget that the universe created inteligent life so it can see itself Trebert
From: rods on 6 May 2010 09:36 On 6 maio, 10:26, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > rods <rodpi...(a)gmail.com> writes: > > Thanks for the reference. I think that you don't understand Tarski > > concept of truth. > > My understanding, however lacking, of such matters is entirely > irrelevant. > > > So are you saying that a model being consistent or inconsistent is no > > relevant to the incompleteness theorems? > > What I said was that in mathematical logic it simply makes no sense to > say that a model is or is not consistent. This is an elementary point > which you can easily check for yourself by looking up the relevant > definitions in any standard text. OK. So I think that we at least agree on our disagreement. Rodrigo
From: Jesse F. Hughes on 6 May 2010 09:39
rods <rodpinto(a)gmail.com> writes: > Thanks for the reference. I think that you don't understand Tarski > concept of truth. > Maybe if you read something about it my point will be more clear. > My argument is very simple. And you are refuting it just saying: > >> 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. > > So are you saying that a model being consistent or inconsistent is no > relevant to the incompleteness theorems? > This sounds like nonsense to me. He's saying that the claim "The model is consistent" is literally nonsense. Theories are consistent or not. Consistency is not a term that applies to models. It's really that simple. -- "I liked the world a lot better over ten years ago. I believed in a lot more things. Hell, most people believed in a lot more things. Back then the United States was still, well, known as most people used to know the United States." -- James S. Harris in a nostalgic mood |