On Feb 9, 3:57 pm, Jason Resch <[email protected]> wrote: > 1Z, > > How do you define existence?
1. I am real 2. Anything I can interact with is real 3. Anything that provides a good explanation of 1&2 is probably real >For something to exist must it be something > you can see and feel, or would you say it has to be something that can be > studied objectively? Would you agree that for something to have objective > properties, it must exist? Clearly there are things humans have discovered > which we can't see or feel, but we think they exist because we see their > effects: wind, dark matter, black holes, etc. Or theories suggest their > existence: extra-solar life, strings, and so on. Sure. But I don't need to posit numbers, etc, as having any kind of causal or even nomological significance. They aren't required by (3). (And, contra the "indispensability argument", numbers aren't *posited* by science, just used). > I would argue that mathematical objects exist because this universe's > existence does not make sense in isolation. Imagine you were in a > windowless bathroom. Should you doubt the existence of the rest of the > world because you cannot see it, or would there be clues to support the > existence of things outside that room? The finely tuned physical constants, > laws, dimensions, etc. of this universe suggest that this universe is one of > many, perhaps one among all possible structures. Just as we see the affects > of wind and know it exists, one can look at the fine tuning of this universe > and believe in the existence of all possible structures. Every such > structure is a mathematical entity. If you doubt the existence of > mathematical objects, how do you explain fine tuning? > (http://en.wikipedia.org/wiki/Fine-tuned_Universe) > > Jason > > On Mon, Feb 7, 2011 at 4:55 PM, 1Z <[email protected]> wrote: > > > On Feb 7, 4:06 pm, Bruno Marchal <[email protected]> wrote: > > > On 06 Feb 2011, at 22:20, 1Z wrote: > > > > >>> On Feb 5, 7:43 pm, Bruno Marchal <[email protected]> wrote: > > > > >>>> Computationalism needs Church thesis which needs AR (Arithmetical > > > >>>> Realism). > > > > >>> Nope, just AT (arithmetic truth). > > > > >> Actually, comp needs only, for the ontology, the quite tiny complete > > > >> Sigma_1 truth. > > > > > As I have stated many times, it doesn;t matter in the least > > > > how many or few immaterial objects you attribute existence to. > > > > It's like saying pixies exist, but only a few > > > > What? > > > It is always better to make a theory precise. > > > The theory that some precise number of pixies exist is just > > as wrong as the theory that some indeterminate number exists. > > > Mathematical anti realists hold that *no* mathematical > > objects exist. And they still accept CT and all the rest. > > > > >> Please don't put metaphysics where there is only > > > >> religion > > > > > Believing in what is not proven is religion. I can > > > > argue for anti realism. > > > > I argue in favor of nothing. > > > You argue that some subset of mathematics has immaterial existence. > > > >That's philosophy. You force me to be > > > explicit on this; I do science. I am a logician, and I show that > > > rational agent believing in comp believe that ... etc. I don't know > > > about the truth. > > > > >> (saying yes to the admittedly betting doctor). > > > > > Saying yes to the doctor will not guarantee your > > > > immaterial existence if there is no immaterial existence. > > > > But there is immaterial existence. > > > To be fair, that's an unargued claim, not an argument. > > > > I recall you that I say in the > > > ontological context that something exist if Ex (bla-bla-bla x) is true > > > in the standard model of arithmetic. > > > Utterly wrong. In the *mathematical* context something > > exists if there is a true backwards-E statement asserting > > it, but the whole point of anti realism is that that is merely > > game playing and does NOT imply RITSIAR ontological existence. > > > >I use the standard meaning of > > > existence of numbers, etc. > > > As I have told you many times, there is no standard meaning. > > >http://en.wikipedia.org/wiki/Philosophy_of_mathematics > > > > > AR/Platonism is a separate assumption to yes Dr. > > > > I have drop out AR. You need AR (in which everyone believes except the > > > ultrafinitists and the bad faith philosophers) to understand the term > > > "digital" used by the doctor. > > > No you don't. Mathematical anti realists can understand "digital > > computer" > > > > > <And with comp, > > > >> it is math, indeed, even (full, above Sigma_1 arithmetic. > > > >> Arithmetical realism is what you need to apply the excluded middle in > > > >> computer science and in arithmetic. > > > > > The excluded middle is a much of a formal rule as > > > > anthing else. Formalists can apply it, so it is compatible > > > > with anti realism. > > > > The theory admits a formal study. You don't act like a formalist at > > > all. The term "Formalism" makes not an atom of sense without > > > arithmetical realism. > > > Formalism is a major variety kind of anti realism. > > > > In philosophy arithmetical realism is the weaker > > > of all possible realism, except again for the ultrafinitists. > > > The weakest kind is NONE WHATSOEVER....no pixies. Zip. Nada. > > > > If you are formalist and anti realist on the numbers you are in > > > contradiction, > > > What contradiction? > > > > or, once and for all, just replace numbers by the > > > following formal expression 0, s(0), s(s(0)), etc. + the axioms I just > > > sent to Andrew, etc. > > > Yep. Formalism says you have rules, and you manipulate them > > and certain things seem to move around a change, and we > > call those sets and numbers....and they don't really exist. > > When you switch off your PC there is no more Supermario, > > and when you stop doing maths there are no more numbers. > > > > AUDA provides more than a formalism, > > > I don;t mean "a formalism"=" a mechanisable system for applying rules" > > > I mean "formalism"="the claim that mathematics is a game played > > according to > > various sets of rules and is not 'about' any real entity". > > > I have pointed out the distinction to you many times > > > >it provides an arithmetisation, > > > which is a *weakening* of formalism, made possible by AR. Gödel > > > already exploited this. > > > > >> To understand the fundamental > > > >> consequences of Church thesis you need to accept that some program > > > >> computes function despite we have no means to know if it is total or > > > >> partial, or that a program will stop or not. > > > > > And I can accept that by positing LEM as a formal rule. I don;t > > > > have to posit an immaterial Plato's heaven > > > > I make clear that the immaterial Plato Heaven for the machine is just > > > the truth of arithmletical proposition. > > > Truth is not existence. > > > >It is an non arithmetical > > > notion, union of the entire Kleene-Mostowki arithmetical hierarchy, > > > and well know non controversal mathematical object in the field of > > > logic. > > > Sighh.to anti-realists, all immaterial existence is controversial > > > > I use the "immaterial Plato heaven" terminology, either as poetical > > > shortcut, > > > Well, it isn;t material since matter is some sort of iluusion within > > it, according to you > > > > or as a point in the arithmetical representation of some > > > term in Plotinus theory. > > > I explained this already to you, but you keep adding metaphysical > > > stuff which don't exist. > > > It's metaphyscial already. I exist , and you say I am a programme > > that is not running on a physcial platform. That adds up to > > a statement about existence. You are making a statement > > about me, so you are making a statement about existence. > > > You conclusion is ontological, so it either comes from > > an ontological premise or it is a non sequitur. > > > > >> Only ultrafinitist denies AR. > > > > > Wrong. Anti realists deny it. I have pointed this out many > > > > times. You think the only debate is about the minimal > > > > set of mathematical objects, and that is not the only debate. Anti > > > > realists > > > > can accept a maximal set of objects, with the proviso that their > > > > existence is fictive and not real existence > > > > I am agnostic on all notion of existence. > > > > All, except my own > > > consciousness here and now. > > > You keep insisting that some subset of arithmetic exists!!!! > > > > I suggest a theory, and derive > > > consequences in that theory. > > > > >> AR+, the idea that we don't need more than AR, in this setting, is a > > > >> consequence of the math. From 'outside' the tiny effective universal > > > >> sigma_1 complete set is enough. from inside, even mathematicalism is > > > >> not enough (it is more 'theologicalism'). > > > > >>> The ontological status of > > > >>> mathematical > > > >>> objects is a area of contention in metaphysics, and not > > > >>> straightforwardly > > > >>> proven by mathematics itself. > > > > >> With comp, you don't need more than the part on which almost > > > >> everybody > > > >> agrees: arithmetical realism. > > > > > Anti realists do not agee on the real existence of any > > > > part. There are no pixies at all, not just a few pixies. > > > > If you believe in prime numbers, > > > I don't. No pixies means no pixies. > > > > and if you are patient and good > > > willing, I can explain that there are all universal numbers, and why > > > assuming comp that's enough and that's necessary to solve the white > > > rabbit problem. And that postulating physical laws miss the > > > epistemological existence of the qualia. > > > The basic ontology is not important. If you take less than a universal > > > system (like numbers, combinators, ...) you don't have enough for > > > comp, if you take more you miss the qualia. > > > > No problem with a formalist interpretation of all this. Actually S4Grz > > > formalize at the meta-level what the machine can uderstand to be non > > > formalisable (like consciousness). > > > > >> The engineers, the scientists, most > > > >> philosophers. > > > >> Except for Thorgny Tholerus I never met an ultrafinitist. You don't > > > >> have to decide if numbers are idea of the mind or sort of angel in > > > >> Plato Heaven. With comp the very idea of number will itself be a > > > >> number, a sort of second order number, relative to universes > > > >> (universal numbers). > > > > > ULtrafinitism has nothing to do with it. For formalists > > > > no number exists. They have no prejudice about any kind, > > > > If comp is false > > ... > > read more » -- 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.
