Bruno Marchal wrote: > > > On 05 Oct 2011, at 17:33, benjayk wrote: > >> >> >> meekerdb wrote: >>> >>> On 10/4/2011 1:44 PM, benjayk wrote: >>>> >>>> Bruno Marchal wrote: >>>>>> >>>>>> Bruno Marchal wrote: >>>>>>>> But then one 3-thing remains uncomputable, and undefined, >>>>>>>> namely the very foundation of computations. We can define >>>>>>>> computations in >>>>>>>> terms of numbers relations, and we can define number relations >>>>>>>> in >>>>>>>> terms of >>>>>>>> +,*,N. But what is N? It is 0 and all it's successors. But >>>>>>>> what is >>>>>>>> 0? What >>>>>>>> are successors? They have to remain undefined. If we define 0 >>>>>>>> as a >>>>>>>> natural >>>>>>>> number, natural number remains undefined. If we define 0 as >>>>>>>> having >>>>>>>> no >>>>>>>> successor, successor remains undefined. >>>>>>> All theories are build on unprovable axioms. Just all theories. >>>>>>> Most scientific theories assumes the numbers, also. >>>>>>> But this makes not them undefinable. 0 can be defined as the >>>>>>> least >>>>>>> natural numbers, and in all models this defines it precisely. >>>>>> But natural *numbers* just make sense relative to 0 and it's >>>>>> successors, >>>>>> because just these are the *numbers*. If you define 0 in terms of >>>>>> natural >>>>>> numbers, and "least" (which just makes sense relative to >>>>>> numbers), you >>>>>> defined them from something undefined. >>>>>> So I ask you: What are natural numbers without presupposing 0 >>>>>> and its >>>>>> successors? >>>>> This is a bit a technical question, which involves logic. With >>>>> enough >>>>> logic, 0 and s can be defined from the laws of addition and >>>>> multiplication. It is not really easy. >>>> It is not technical at all. If you can't even explain to me what the >>>> fundamental object of your theory is, your whole theory is >>>> meaningless to >>>> me. >>>> I'd be very interested in you attempt to explain addition and >>>> multplication >>>> without using numbers, though. >>> >>> It's easy. It's the way you explain it to children: Take those red >>> blocks over there and >>> ad them to the green blocks in this box. That's addition. Now >>> make all >>> possible >>> different pairs of one green block and one red block. That's >>> multiplication. >> OK. We don't have to use numbers per se, but notions of more and >> less of >> something. >> Anyway, we get the same problem in explaining what addition and >> multiplication are in the absence of any concrete thing of which >> there can >> be more or less, or measurements that can be compared in terms of >> more and >> less. >> >> >> meekerdb wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> But to get the comp point, you don't need to decide what numbers >>>>> are, >>>>> you need only to agree with or just assume some principle, like 0 >>>>> is >>>>> not a successor of any natural numbers, if x ≠ y then s(x) ≠ >>>>> s(y), >>>>> things like that. >>>> I agree that it is sometimes useful to assume this principle, just >>>> as it >>>> sometimes useful to assume that Harry Potter uses a wand. Just >>>> because we >>>> can usefully assume some things in some contexts, do not make them >>>> universal >>>> truth. >>>> So if you want it this way, 1+1=2 is not always true, because >>>> there might >>>> be >>>> other definition of natural numbers, were 1+1=&. >>> >>> It's always "true" in Platonia, where "true" just means satisfying >>> the >>> axioms. In real >>> life it's not always true because of things like: This business is so >>> small we just have >>> one owner and one employee and 1+1=1. >> Yeah, but it remains to be shown that platonia is more than just an >> idea. I >> haven't yet seen any evidence of that. >> Bruno seems to justify that by reductio ad absurdum of 1+1=2 being >> dependent >> on ourselves, so 1+1=2 has to be true objectively in Platonia. I >> don't buy >> that argument. If our mind (or an equivalent mind, say of another >> species >> with the same intellectual capbilites) isn't there isn't even any >> meaning to >> 1+1=2, because there is no way to interpret the meaning in it. > > Would you say that if the big bang is not observed then there is no > big bang? > Why would it be different for "1+1 = 2"? > Right, the big bang is the infinite power of observing itself, so without observing,... Well, there is no without observing.
Bruno Marchal wrote: > >> It only seems >> to us to be true independently because we defined it without explicit >> reference to anything outside of it. But this doesn't prove that it >> is true >> independently anymore than the fact that Harry Potter doesn't >> mention he is >> just a creation of the mind makes him exist independently of us >> eternally in >> Harry-Potter-land. > > This does not logically follows, and beyond this, it is obvious that > Harry-Potter land does exist in any "everything" type of theories. > Indeed with comp, or with other everything type of theories, the > problem is that such fantasy worlds might be too much probable, > contradicting the observations. The mere existence of them cannot be > used in a reductio ad absurdum. My point is just that AR is not plausible just because we have rigid definitions that we claim to be unchangeable. Bruno Marchal wrote: > > We don't know what reality is. We are searching. I don't think reality is primarily a "what". It is an "that". "What"s arise is reality. benjayk -- View this message in context: http://old.nabble.com/COMP-is-empty%28-%29-tp32569717p32614926.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 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.
