On Feb 21, 9:11 am, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 21 Feb 2011, at 13:26, benjayk wrote: > > > > Bruno Marchal wrote: > > >> On 20 Feb 2011, at 00:39, 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? > >>> 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). > > >>> 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". > > >> But what is two if 2 = 1. I can no more have clue of what you mean. > > Two is the successor of one. You obviously now what that means. > > > So keep this meaning and reconcile it with 2=1. > > You might get the meaning "two is the one (number) that is the > > succesor of > > one". Or "one (number) is the successor of two". In essence it > > expresses > > 2*...=1*... or 2*X=1*Y. > > And it might mean "the succesor of one number is the succesor of the > > succesor of one number". or 2+...=1+... or 2+X=1+Y. > > > The reason that it is not a good idea to define 2=1 is because it > > doesn't > > express something that can't be expressed in standard arithmetic, > > but it > > makes everything much more confusing and redundant. In mathematics > > we want > > to be precise as possible so it's good rule to always have to > > specifiy which > > quantity we talk about, so that we avoid talking about something - > > that is > > one thing - that is something - that is two things - but rather talk > > about > > one thing and two things directly; because it is already clear that > > two > > things are a thing. > > OK.
> > > > Bruno Marchal wrote: > > >> Now, just recall that "Platonia" is based on classical logic where > >> the > >> falsity f, or 0 = 1, entails all proposition. So if you insist to say > >> that 0 = 1, I will soon prove that you owe to me A billions of > >> dollars, and that you should prepare the check. > > You could prove that, but what is really meant by that is another > > question. > > It may simply mean "I want to play a joke on you". > > > All statements are open to interpretation, I don't think we can > > avoid that > > entirely. We are ususally more interested in the statements that are > > less > > vague, but vague or crazy statements are still valid on some level > > (even > > though often on an very boring, because trivial, level; like saying > > "S afs > > fdsLfs", which is just expressing that something exists). > > We formalize things, or make them as formal as possible, when we > search where we disagree, or when we want to find a mistake. The idea > of making things formal, like in first order logic, is to be able to > follow a derivation or an argument in a way which does not depend on > any interpretation, other than the procedural inference rule. > > > > > Bruno Marchal wrote: > > >>> 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. > > >> Logicians and mathematicians are more simple minded than that, and it > >> does not always help to be understood. > >> If you allow circles with edges, and triangles with four sides in > >> Platonia, we will loose any hope of understanding each other. > > I don't think we have "disallow" circles with edges, and triangles > > with four > > sides; it is enough if we keep in mind that it is useful to use > > words in a > > sense that is commonly understood. > > That is why I limit myself for the TOE to natural numbers and their > addition and multiplication. > The reason is that it is enough, by comp, and nobody (except perhaps > some philosophers) have any problem with that. > > Yes. A couple of questions from a philosophical point of view: Language gives meaning to the numbers as in their operations; functions, units of measurements (kilo, meter, ounce, kelvin etc.). Numbers alone may symbolize some fundamental describable matter and forces but a complete and coherent TOE should include elevated human consciousness beyond the primitive which in itself requires a relatively sophisticated language to give meaning to the numbers and their operations. Would not any TOE describing the universe appears to require human sophisticated language using referent nouns, (and conjunctions, adjectives and verbs etc.) to give meaning to the numbers and their functions and operations? You repeatedly refer to “addition and multiplication”. Is not multiplication repeated addition or is there another separate principle involved with multiplication? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. 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.