Bruno Marchal wrote: > > > On 20 Feb 2011, at 13:13, benjayk wrote: > >> >> >> Brent Meeker-2 wrote: >>> >>> On 2/19/2011 3:39 PM, benjayk wrote: >>>> >>>> Bruno Marchal wrote: >>>> >>>>> >>>>>> Isn't it enough to say everything that we *could* describe >>>>>> in mathematics exists "in platonia"? >>>>>> >>>>> The problem is that we can describe much more things than the one >>>>> we >>>>> are able to show consistent, so if you allow what we could describe >>>>> you take too much. If you define Platonia by all consistent things, >>>>> you get something inconsistent due to paradox similar to Russell >>>>> paradox or St-Thomas paradox with omniscience and omnipotence. >>>>> >>>> Why can inconsistent descriptions not refer to an existing object? >>>> >>> >>> Because an inconsistent description implies everything, whether the >>> object described exists or not. From "Sherlock Holmes is a detective >>> and is not a detective." anything at all follows. >> I think it is perfectly fine when something implies everything. For >> me it >> makes very much sense to think of everything as everything existing. >> The distinction something existant / something non-existant is a >> relative >> one, in the absolute sense existence is all there is - and it includes >> relative non-existence (for example Santa Claus exists, but has >> relative >> non-existence in the set of things that manifests in a consistent and >> predictable way to many observers). >> >> Aso, it emerges naturally from seemingly consistent logic that >> everything >> exists (see Curry's paradox). > > Curry "paradox" was a real contradiction, Curry put his theory in the > trash the day he sees the contradiction, and begun some other less > ambitious theory (the illetive theory of combinators). OK, but this doesn't change the rest of the rest of the argument. Also, the Curry paradox is still there in natural language, which seems capable of making useful statements even though the Curry paradox entails the truth of every statement in natural language.
Bruno Marchal wrote: > >> >> >> Brent Meeker-2 wrote: >>> >>>> The easy way is to assume inconsistent descriptions are merely an >>>> arbitrary >>>> combination of symbols that fail to describe something in >>>> particular and >>>> thus have only the "content" that every utterance has by virtue of >>>> being >>>> uttered: There exists ... (something). >>>> >>> >>> But we need utterances that *don't* entail existence. >> >> If we find something that doesn't entail existence, it still entails >> existence 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 being experience. 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. He didn't >> exist >> like me and you, but he did exist as an idea. > > > Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria > to 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 the possible that other people use the same fictional character, so he is essentially discovered, not created. But I don't know what you want to imply with that. Bruno Marchal wrote: > >> >> >> Brent Meeker-2 wrote: >>> >>>> So they don't add anything to platonia because they merely assert >>>> the >>>> existence of existence, which leaves platonia as described by >>>> consistent >>>> theories. >>>> >>>> I think the paradox is a linguistic paradox and it poses really no >>>> problem. >>>> Ultimately all descriptions refer to an existing object, but some >>>> are too >>>> broad or "explosive" or vague to be of any (formal) use. >>>> >>>> I may describe a system that is equal to standard arithmetics but >>>> also >>>> 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 that >>>> there is 1 object that is 2 two objects, so it simply asserts the >>>> existence >>>> 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 true interpretation of >>> 1=2; >>> the problem is that in standard logic a falsity allows you to prove >>> anything. >> 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 the inconsisten >> system >> worthless (at least in a formal context were we assume classical >> logic). > > And it would make Platonia worthless. The "real", genuine, Platonia is > already close to be worthless due to the consistency of inconsistency > for 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. And why is inconsistency allowed for machine, but disallowed for other objects? -- View this message in context: http://old.nabble.com/Platonia-tp30955253p30978461.html Sent from the Everything List mailing list archive at Nabble.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
