On Feb 9, 3:57 pm, Jason Resch <jasonre...@gmail.com> wrote:
> 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
even nomological significance. They aren't required by (3).
(And, contra the "indispensability argument", numbers aren't *posited*
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?
> On Mon, Feb 7, 2011 at 4:55 PM, 1Z <peterdjo...@yahoo.com> wrote:
> > On Feb 7, 4:06 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> > > On 06 Feb 2011, at 22:20, 1Z wrote:
> > > >>> On Feb 5, 7:43 pm, Bruno Marchal <marc...@ulb.ac.be> 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.
> > > > 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 »
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