On 23 Feb 2011, at 17:37, benjayk wrote:

Bruno Marchal wrote:Bruno Marchal wrote:Brent Meeker-2 wrote:The easy way is to assume inconsistent descriptions are merelyanarbitrary combination of symbols that fail to describe something in particular andthus have only the "content" that every utterance has byvirtue ofbeing uttered: There exists ... (something).But we need utterances that *don't* entail existence.If we find something that doesn't entail existence, it stillentailsexistence because every utterance is proof that existence IS. We need only utterances that entail relative non-existence or that don't entail existence in a particular way in a particular context.You need some non relative absolute base to define relative existence.The absolute base is the undeniable reality of there beingexperience.But this one is not communicable. It does play a role in comp,though.But we can say "there is an undeniable reality of there beingexperience".Isn't this communicating that there is the undeniable reality ofthere beingexperience?

`OK. I was using communicating in the sense of a provable`

`communication. You cannot convince someone that you are conscious. If`

`he decides that you are a zombie, you might better run, probably, but`

`there is no way you could prove the contrary.`

We merely communicate something that everbody already fundamentallyknows.

That is correct also, I think.

Though some like to deny what they already know.

That is bad faith, and is common.

Bruno Marchal wrote:But it is not enough. usually people agree with the axiom of Peano Arithmetic, or the initial part of some set theory.But Peano Arithmetics is not a non relative absolute base. It isrelative tothe meaning we give it and to the existence of some reality. 1+1=2can haveinfinite meanings, that all are relative to our interpretation ("IfI layanother apple into the bowl with one apple in it there are twoapples" isone of them) and there being meaning in the first place.

`Hmm... Most people agrees on a standard meaning for the natural`

`numbers, like in the Fermat theorem, or any theorem or conjecture in`

`number theory, or when you are using numbers in computer science.`

`1+1 = 2 is true in all those interpretations, even if computer science`

`we use also some algebra where 1+1=0. That does not contradict that`

`the standard integer are all different from 0, except 0.`

Bruno Marchal wrote:Bruno Marchal wrote:Brent Meeker-2 wrote:So we can say things like, "Sherlock Holmes lived at 10 Baker Street" are true, even though Sherlock Holmes never existed.Whether Sherlock Holmes existed is not a trivial question. Hedidn'texist like me and you, but he did exist as an idea.Even if you met *a* Sherlock Holmes in Platonia, you have nocirteriato say it is the usual fictive person created by Conan Doyle, because, in Platonia, he is not created by Conan Doyle, ...In Platonia he is not created by Conan Doyle, which makes sense, given thepossible that other people use the same fictional character, so heisessentially discovered, not created. But I don't know what you want to imply with that.Just that fictionism, the idea that numbers are fiction of the same type as fictive personage from novels does not make sense, except to confuse matter.Well I didn't want to imply that. Fictionage personage usually referto somerelative manifestation of an idea, while numbers are a more generalandabstract notion.And if they are fiction, they are very prevalent fiction (not justamongpeople but among nature), which makes them basically non-fiction.

OK.

Bruno Marchal wrote:Bruno Marchal wrote:Brent Meeker-2 wrote:So they don't add anything to platonia because they merelyassertthe existence of existence, which leaves platonia as described by consistent theories.I think the paradox is a linguistic paradox and it posesreally noproblem.Ultimately all descriptions refer to an existing object, butsomeare too broad or "explosive" or vague to be of any (formal) use.I may describe a system that is equal to standard arithmeticsbutalso has 1=2 as an axiom. This makes it useless practically (or so I guess...) but it may still be interpreted in a way that it makes sense. 1=2 may mean thatthere is 1 object that is 2 two objects, so it simply assertstheexistence of the one number "two". 3=7 may mean that there are 3 objects that are 7 objects which might be interpreted as aserting the existence of (for example) 7*1, 7*2 and 7*3.The problem is not that there is no possible trueinterpretation of1=2;the problem is that in standard logic a falsity allows you toproveanything.Yes, so we can prove anything. This simply begs the question what the anything is. All sentences we derive from the inconsistency would mean the same (even though we don't know what exactly it is). We could just write "1=1" instead and we would have expressed the same, but in a way that is easier to make sense of.This is not problematic, it only makes the proofs in theinconsistensystem worthless (at least in a formal context were we assume classical logic).And it would make Platonia worthless. The "real", genuine, Platonia isalready close to be worthless due to the consistency ofinconsistencyfor machine. This already put quite a mess in Platonia. By allowing complete contradiction, you make it a trivial object.Why? When we contradict ourselves we may simply interpret this as a expression of the trivial truth of existence. This doesn't change Plantonia at all, because it exists either way.The whole point of Gödel's theorem is that M proves 0=1 is different from M proves provable('0=1'). The first implies the second, but the second does not implies the first. The difference between G and G* comes from this fact.If we know that something can be proven, how is it different fromtaking itto be proven?

`By incompleteness "provable(false) -> false" is not provable in the`

`system.`

I is true for the machine, but the machine cannot prove it.

The only difference I could see could be that "M proves provable('0=1')" means "provable in another system".

`No, by Gödel's construction it really means "provable by the system`

`itself". It is still third person reference, and the machine is not`

`necessarily aware that "she is that system". Later we can see she can`

`*never* be aware of that, but she might trust her doctor, and make`

`bet, etc.`

Bruno Marchal wrote:And why is inconsistency allowed for machine, but disallowed forotherobjects?Because if a machine proves "0=1", she will be in trouble, but if God or Platonia proves "0=1", then we are *all* in trouble.I thought we already established that 0=1 can have a clear meaning(equivalent to statements of the form 0*A+B=1*C+D in standardarithmetics),and so it poses no problem.

?

`I have no clue what you are saying here. If "0 = 1" means "I love`

`chocolate", then of course "0=1" might be true. Again, we use the`

`standard meaning. Natural numbers and finite sets and finite strings`

`have a common interpretation rich enough so that we can agree on a`

`little but powerful set of axioms. This is already less clear for the`

`notion of sets, although most mathematicians believe so. But for the`

`natural numbers, we do agree on those axioms, and their correspond to`

`what has been taught at school.`

`If some my student defend ideas like 0 = 1, I give them a 0/10, and I`

`reassure them that it is a good note because if 0 = 1, then 10 = 0. 10`

`= 1+1+1+1+1+1+1+1+1+1 = 0+0+0+0+0+ 0+0+0+0+0 = 0.`

My suggestion is that every statement has such an interpretation.Circleswith edges makes sense if we allow hyperreal numbers as numbers ofedges andlenght of edges, triangles with four sides may mean such a geometricobject:http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.pngand thatGod is omnipotent may mean anything.

`Logic has been invented for avoiding interpretations as much as`

`possible, and then for studying mathematically what can be`

`interpretations, and the relations (Galois connection) between formal`

`deduction and relations on interpretations. We force the`

`"propositions" which mean anything to be eliminated, for helping the`

`progress toward genuine truth and meaning.`

`We can say that first order logic does succeed in the interpretation`

`elimination, thanks to a theorem of completeness (not incompleteness)`

`by Gödel. A formula is a theorem IF and ONLY IF the formula is true in`

`all interpretations.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.