Re: ROADMAP (SHORT)
[EMAIL PROTECTED] wrote: > Tom, thanks, you said it as I will try to spell it out interjected in your > reply. > John > - Original Message - > From: "Tom Caylor" <[EMAIL PROTECTED]> > To: "Everything List" > Sent: Monday, September 11, 2006 12:21 PM > Subject: Re: ROADMAP (SHORT) > > > > > > [EMAIL PROTECTED] wrote: > > > - Original Message - > > > From: "Tom Caylor" <[EMAIL PROTECTED]> > > > To: "Everything List" > > > Sent: Wednesday, September 06, 2006 3:23 PM > > > Subject: Re: ROADMAP (SHORT) > > > > > > > > > > > > You wrote: > > > What is the non-mathematical part of UDA? The part that uses Church > > > Thesis? When I hear "non-mathematical" I hear "non-rigor". Define > > > rigor that is non-mathematical. I guess if you do then you've been > > > mathematical about it. I don't understand. > > > > > > Tom > > > -- > > > Smart: whatever I may come up with, as a different type of "vigor" > > > (btw is this term well identified?) you will call it "math" - just a > > > different type. > > > John M > > > --~--~-~--~~~---~--~~ > > > > The root of the word "math" means learning, study, or science. Math is > > the effort to make things precise. So in my view applied math would be > > taking actual information and trying to make the science precise in > > order to further our learning and quest of the truth in the most > > efficient manner possible. > Applied math is a sore point for me. As long as I accept (theoretical) > "Math" as a language of logical thinking (IMO a one-plane one, but it is not > the point now) I cannot condone the APPLIED "math" version, (math) using > the results of Math for inrigorating (oops!) the imprecise model-values > (reductionist) 'science' is dealing with. > Precise it will be, right it won't, because it is based on a limited vue > within the boundaries of (topical) science observations. It makes the > imprecise value-system looking precise. > > > > I think that this is the concept that is > > captured by the term "rigor". But what's in a name? I call it "math" > > and I think that a good many people would agree, but others might call > > it something else, like "rigor". I think that it's an intuitive > > concept limited by our finite capabilities, as you so many times point > > out, John. > I did, indeed and am glad that someone noticed. Your term 'rigor' is pretty > wide, you call it 'math' (if not "Math") including all those qualia-domains > which are under discussion to be 'numbers(?) or not'. OK, I don't deny your > godfatherish right to call anything by any name, but then - please - tell me > what name to call the old "mathematical math"? (ie. churning conventional > numbers like 1,2,3) by? > > > > Tom > > > John That is called arithmetic. I don't really want to pursue a discussion on terminology, but thanks for your thoughts. --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
Tom, thanks, you said it as I will try to spell it out interjected in your reply. John - Original Message - From: "Tom Caylor" <[EMAIL PROTECTED]> To: "Everything List" Sent: Monday, September 11, 2006 12:21 PM Subject: Re: ROADMAP (SHORT) > > [EMAIL PROTECTED] wrote: > > - Original Message - > > From: "Tom Caylor" <[EMAIL PROTECTED]> > > To: "Everything List" > > Sent: Wednesday, September 06, 2006 3:23 PM > > Subject: Re: ROADMAP (SHORT) > > > > > > > > You wrote: > > What is the non-mathematical part of UDA? The part that uses Church > > Thesis? When I hear "non-mathematical" I hear "non-rigor". Define > > rigor that is non-mathematical. I guess if you do then you've been > > mathematical about it. I don't understand. > > > > Tom > > -- > > Smart: whatever I may come up with, as a different type of "vigor" > > (btw is this term well identified?) you will call it "math" - just a > > different type. > > John M > > --~--~-~--~~~---~--~~ > > The root of the word "math" means learning, study, or science. Math is > the effort to make things precise. So in my view applied math would be > taking actual information and trying to make the science precise in > order to further our learning and quest of the truth in the most > efficient manner possible. Applied math is a sore point for me. As long as I accept (theoretical) "Math" as a language of logical thinking (IMO a one-plane one, but it is not the point now) I cannot condone the APPLIED "math" version, (math) using the results of Math for inrigorating (oops!) the imprecise model-values (reductionist) 'science' is dealing with. Precise it will be, right it won't, because it is based on a limited vue within the boundaries of (topical) science observations. It makes the imprecise value-system looking precise. > > I think that this is the concept that is > captured by the term "rigor". But what's in a name? I call it "math" > and I think that a good many people would agree, but others might call > it something else, like "rigor". I think that it's an intuitive > concept limited by our finite capabilities, as you so many times point > out, John. I did, indeed and am glad that someone noticed. Your term 'rigor' is pretty wide, you call it 'math' (if not "Math") including all those qualia-domains which are under discussion to be 'numbers(?) or not'. OK, I don't deny your godfatherish right to call anything by any name, but then - please - tell me what name to call the old "mathematical math"? (ie. churning conventional numbers like 1,2,3) by? > > Tom > John --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
[EMAIL PROTECTED] wrote: > - Original Message - > From: "Tom Caylor" <[EMAIL PROTECTED]> > To: "Everything List" > Sent: Wednesday, September 06, 2006 3:23 PM > Subject: Re: ROADMAP (SHORT) > > > > You wrote: > What is the non-mathematical part of UDA? The part that uses Church > Thesis? When I hear "non-mathematical" I hear "non-rigor". Define > rigor that is non-mathematical. I guess if you do then you've been > mathematical about it. I don't understand. > > Tom > -- > Smart: whatever I may come up with, as a different type of "vigor" > (btw is this term well identified?) you will call it "math" - just a > different type. > John M > --~--~-~--~~~---~--~~ The root of the word "math" means learning, study, or science. Math is the effort to make things precise. So in my view applied math would be taking actual information and trying to make the science precise in order to further our learning and quest of the truth in the most efficient manner possible. I think that this is the concept that is captured by the term "rigor". But what's in a name? I call it "math" and I think that a good many people would agree, but others might call it something else, like "rigor". I think that it's an intuitive concept limited by our finite capabilities, as you so many times point out, John. Tom --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
Bruno Marchal wrote:
> Le 06-sept.-06, à 21:23, Tom Caylor a écrit :
>
> >
> > Bruno Marchal wrote:
> >> Le 16-août-06, à 18:36, Tom Caylor a écrit :
> >>
> >>> I noticed that you slipped in "infinity" ("infinite collection of
> >>> computations") into your roadmap (even the short roadmap). In the
> >>> "technical" posts, if I remember right, you said that at some point
> >>> we
> >>> were leaving the constructionist realm. But are you really talking
> >>> about infinity? It is easy to slip into invoking infinity and get
> >>> away
> >>> with it without being noticed. I think this is because we are used
> >>> to
> >>> it in mathematics. In fact, I want to point out that David Nyman
> >>> skipped over it, perhaps a case in point. But then you brought it up
> >>> again here with aleph_zero, and 2^aleph_zero, so it seems you are
> >>> really serious about it. I thought that infinities and singularities
> >>> are things that physicists have dedicated their lives to trying to
> >>> purge from the system (so far unsuccessfully ?) in order to approach
> >>> a
> >>> "true" theory of everything. Here you are invoking it from the
> >>> start.
> >>> No wonder you talk about faith.
> >>>
> >>> Even in the realm of pure mathematics, there are those of course who
> >>> think it is invalid to invoke infinity. Not to try to complicate
> >>> things, but I'm trying to make a point about how serious a matter
> >>> this
> >>> is. Have you heard about the feasible numbers of V. Sazanov, as
> >>> discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
> >>> we just have 2^N instantiations or computations, where N is a very
> >>> large number?
> >>
> >>
> >> I would say infinity is all what mathematics is about. Take any
> >> theorem
> >> in arithmetic, like any number is the sum of four square, or there is
> >> no pair of number having a ratio which squared gives two, etc.
> >> And I am not talking about analysis, or the use of complex analysis in
> >> number theory (cf zeta), or category theory (which relies on very high
> >> infinite) without posing any conceptual problem (no more than
> >> elsewhere).
> >
> > When you say infinity is what math is all about, I think this is the
> > same thing as I mean when I say that invariance is what math is all
> > about. But in actuality we find only local invariance, because of our
> > finiteness. You have said a similar thing recently about comp. But
> > here you seem to be talking about induction, concluding something about
> > *all* numbers. Why is this needed in comp? Is not your argument based
> > on Robinson's Q without induction?
>
>
> Robinson Arithmetic (Q or RA) is just the ontic theory. The
> epistemology is given by Q + the induction axioms, i.e. Peano
> Arithmetic.
> This fix the things. The SK combinators (cf my older post on this
> subject) gives a more informative ontology, but in the long run none of
> the ontic theories play a special role. With regard to the TOE search
> they are equivalent. Now, RA is not interviewed. It defines the UD if
> you want (RA is turing equivalent). But RA cannot generalize enough. We
> need PA for having the machinery to extract physics from the ontic RA.
>
So you are saying we need induction for epistemology. I will wait to
see more of the roadmap.
>
>
>
>
> >
> >> Even constructivist and intuitionist accept infinity, although
> >> sometimes under the form of potential infinity (which is all we need
> >> for G and G* and all third person point of view, but is not enough for
> >> having mathematical semantics, and then the first person (by UDA) is
> >> really linked to an actual infinity. But those, since axiomatic set
> >> theory does no more pose any interpretative problem.
> >> True, I heard about some ultrafinitist would would like to avoid
> >> infinity, but until now, they do have conceptual problem (like the
> >> fact
> >> that they need notion of fuzzy high numbers to avoid the fact that for
> >> each number has a successor. Imo, this is just philosophical play
> >> having no relation with both theory and practice in math.
> >>
> >>
> >>> The UDA is not precise enough for me, maybe because I'm a
> >>> mathematician?
> >>> I'm waiting for the interview, via the roadmap.
> >>
> >> UDA is a problem for mathematicians, sometimes indeed. The reason is
> >> that although it is a "proof", it is not a mathematical proof. And
> >> some
> >> mathematician have a problem with non mathematical proof. But UDA *is*
> >> the complete proof. I have already explain on this list (years ago)
> >> that although informal, it is rigorous. The first version of it were
> >> much more complex and technical, and it has taken years to suppress
> >> eventually any non strictly needed difficulties.
> >> I have even coined an expression "the 1004 fallacy" (alluding to Lewis
> >> Carroll), to describe argument using unnecessary rigor or abnormally
> >> precise term with respect to the reasoning.
> >> So please, don't hesitate to
Re: ROADMAP (SHORT)
Le 06-sept.-06, à 21:23, Tom Caylor a écrit :
>
> Bruno Marchal wrote:
>> Le 16-août-06, à 18:36, Tom Caylor a écrit :
>>
>>> I noticed that you slipped in "infinity" ("infinite collection of
>>> computations") into your roadmap (even the short roadmap). In the
>>> "technical" posts, if I remember right, you said that at some point
>>> we
>>> were leaving the constructionist realm. But are you really talking
>>> about infinity? It is easy to slip into invoking infinity and get
>>> away
>>> with it without being noticed. I think this is because we are used
>>> to
>>> it in mathematics. In fact, I want to point out that David Nyman
>>> skipped over it, perhaps a case in point. But then you brought it up
>>> again here with aleph_zero, and 2^aleph_zero, so it seems you are
>>> really serious about it. I thought that infinities and singularities
>>> are things that physicists have dedicated their lives to trying to
>>> purge from the system (so far unsuccessfully ?) in order to approach
>>> a
>>> "true" theory of everything. Here you are invoking it from the
>>> start.
>>> No wonder you talk about faith.
>>>
>>> Even in the realm of pure mathematics, there are those of course who
>>> think it is invalid to invoke infinity. Not to try to complicate
>>> things, but I'm trying to make a point about how serious a matter
>>> this
>>> is. Have you heard about the feasible numbers of V. Sazanov, as
>>> discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
>>> we just have 2^N instantiations or computations, where N is a very
>>> large number?
>>
>>
>> I would say infinity is all what mathematics is about. Take any
>> theorem
>> in arithmetic, like any number is the sum of four square, or there is
>> no pair of number having a ratio which squared gives two, etc.
>> And I am not talking about analysis, or the use of complex analysis in
>> number theory (cf zeta), or category theory (which relies on very high
>> infinite) without posing any conceptual problem (no more than
>> elsewhere).
>
> When you say infinity is what math is all about, I think this is the
> same thing as I mean when I say that invariance is what math is all
> about. But in actuality we find only local invariance, because of our
> finiteness. You have said a similar thing recently about comp. But
> here you seem to be talking about induction, concluding something about
> *all* numbers. Why is this needed in comp? Is not your argument based
> on Robinson's Q without induction?
Robinson Arithmetic (Q or RA) is just the ontic theory. The
epistemology is given by Q + the induction axioms, i.e. Peano
Arithmetic.
This fix the things. The SK combinators (cf my older post on this
subject) gives a more informative ontology, but in the long run none of
the ontic theories play a special role. With regard to the TOE search
they are equivalent. Now, RA is not interviewed. It defines the UD if
you want (RA is turing equivalent). But RA cannot generalize enough. We
need PA for having the machinery to extract physics from the ontic RA.
>
>> Even constructivist and intuitionist accept infinity, although
>> sometimes under the form of potential infinity (which is all we need
>> for G and G* and all third person point of view, but is not enough for
>> having mathematical semantics, and then the first person (by UDA) is
>> really linked to an actual infinity. But those, since axiomatic set
>> theory does no more pose any interpretative problem.
>> True, I heard about some ultrafinitist would would like to avoid
>> infinity, but until now, they do have conceptual problem (like the
>> fact
>> that they need notion of fuzzy high numbers to avoid the fact that for
>> each number has a successor. Imo, this is just philosophical play
>> having no relation with both theory and practice in math.
>>
>>
>>> The UDA is not precise enough for me, maybe because I'm a
>>> mathematician?
>>> I'm waiting for the interview, via the roadmap.
>>
>> UDA is a problem for mathematicians, sometimes indeed. The reason is
>> that although it is a "proof", it is not a mathematical proof. And
>> some
>> mathematician have a problem with non mathematical proof. But UDA *is*
>> the complete proof. I have already explain on this list (years ago)
>> that although informal, it is rigorous. The first version of it were
>> much more complex and technical, and it has taken years to suppress
>> eventually any non strictly needed difficulties.
>> I have even coined an expression "the 1004 fallacy" (alluding to Lewis
>> Carroll), to describe argument using unnecessary rigor or abnormally
>> precise term with respect to the reasoning.
>> So please, don't hesitate to tell me what is not precise enough for
>> you. Just recall UDA is not part of math. It is part of cognitive
>> science and physics, and computer science.
>> The lobian interview does not add one atom of rigor to the UDA, albeit
>> it adds constructive features so as to make possible an expl
Re: ROADMAP (SHORT)
Bruno Marchal wrote:
> Le 16-août-06, à 18:36, Tom Caylor a écrit :
>
> > I noticed that you slipped in "infinity" ("infinite collection of
> > computations") into your roadmap (even the short roadmap). In the
> > "technical" posts, if I remember right, you said that at some point we
> > were leaving the constructionist realm. But are you really talking
> > about infinity? It is easy to slip into invoking infinity and get away
> > with it without being noticed. I think this is because we are used to
> > it in mathematics. In fact, I want to point out that David Nyman
> > skipped over it, perhaps a case in point. But then you brought it up
> > again here with aleph_zero, and 2^aleph_zero, so it seems you are
> > really serious about it. I thought that infinities and singularities
> > are things that physicists have dedicated their lives to trying to
> > purge from the system (so far unsuccessfully ?) in order to approach a
> > "true" theory of everything. Here you are invoking it from the start.
> > No wonder you talk about faith.
> >
> > Even in the realm of pure mathematics, there are those of course who
> > think it is invalid to invoke infinity. Not to try to complicate
> > things, but I'm trying to make a point about how serious a matter this
> > is. Have you heard about the feasible numbers of V. Sazanov, as
> > discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
> > we just have 2^N instantiations or computations, where N is a very
> > large number?
>
>
> I would say infinity is all what mathematics is about. Take any theorem
> in arithmetic, like any number is the sum of four square, or there is
> no pair of number having a ratio which squared gives two, etc.
> And I am not talking about analysis, or the use of complex analysis in
> number theory (cf zeta), or category theory (which relies on very high
> infinite) without posing any conceptual problem (no more than
> elsewhere).
When you say infinity is what math is all about, I think this is the
same thing as I mean when I say that invariance is what math is all
about. But in actuality we find only local invariance, because of our
finiteness. You have said a similar thing recently about comp. But
here you seem to be talking about induction, concluding something about
*all* numbers. Why is this needed in comp? Is not your argument based
on Robinson's Q without induction?
> Even constructivist and intuitionist accept infinity, although
> sometimes under the form of potential infinity (which is all we need
> for G and G* and all third person point of view, but is not enough for
> having mathematical semantics, and then the first person (by UDA) is
> really linked to an actual infinity. But those, since axiomatic set
> theory does no more pose any interpretative problem.
> True, I heard about some ultrafinitist would would like to avoid
> infinity, but until now, they do have conceptual problem (like the fact
> that they need notion of fuzzy high numbers to avoid the fact that for
> each number has a successor. Imo, this is just philosophical play
> having no relation with both theory and practice in math.
>
>
> > The UDA is not precise enough for me, maybe because I'm a
> > mathematician?
> > I'm waiting for the interview, via the roadmap.
>
> UDA is a problem for mathematicians, sometimes indeed. The reason is
> that although it is a "proof", it is not a mathematical proof. And some
> mathematician have a problem with non mathematical proof. But UDA *is*
> the complete proof. I have already explain on this list (years ago)
> that although informal, it is rigorous. The first version of it were
> much more complex and technical, and it has taken years to suppress
> eventually any non strictly needed difficulties.
> I have even coined an expression "the 1004 fallacy" (alluding to Lewis
> Carroll), to describe argument using unnecessary rigor or abnormally
> precise term with respect to the reasoning.
> So please, don't hesitate to tell me what is not precise enough for
> you. Just recall UDA is not part of math. It is part of cognitive
> science and physics, and computer science.
> The lobian interview does not add one atom of rigor to the UDA, albeit
> it adds constructive features so as to make possible an explicit
> derivation of the "physical laws" (and more because it attached the
> quanta to extended qualia). Now I extract only the logic of the certain
> propositions and I show that it has already it has a strong quantum
> perfume, enough to get an "arithmetical quantum logic, and then the
> rest gives mathematical conjectures. (One has been recently solved by a
> young mathematician).
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
What is the non-mathematical part of UDA? The part that uses Church
Thesis? When I hear "non-mathematical" I hear "non-rigor". Define
rigor that is non-mathematical. I guess if you do then you've been
mathematical about it. I don't understand.
Tom
--~--~-~--~~-
Re: ROADMAP (SHORT)
Le 16-août-06, à 18:04, David Nyman a écrit : > > Bruno Marchal wrote: > >> The self-reference logics are born from the goal of escaping circular >> difficulties. > > I think here I may have experienced a 'blinding flash' in terms of your > project. If, as I've said, I begin from self-reference - 'indexical > David', then I have asserted my 'necessary' point of origin. Yes but this "necessity" will appear to be a first person necessity, and as such is not communicable, and even not capturable by the self-reference logic. Note that the fact that that necessity is first person explains probably why you want to take the first person as primitive at the start. Unfortunately, as Godel as seen as early as 1933, the self-reference logic does not capture, neither the knower (the first person) nor the its necessity. So, curiously enough (without doubt) formal provability capture only "opinion" or "belief" (we lack Bp -> p, with B = formal proof). But that is what makes the Theaetetical definition of knowledge (true belief, or true proof, or true justified opinion) working in this aera, and leading then to a notion of (unameable) first person. We will come back. Of course, the more you will be precise, the more I can criticize you by comparing what you say with what G and G* says. That's normal. > From this > point of origin, I can interview myself (and entity-analogs simulated > or modeled within myself) and consequently discover the statements that > express my beliefs, the truth of which I can then evaluate in terms of > my theology. This theology will derive its consistency from provable > theorems, its relevance from generative and explanatory power (e.g. > with respect to both 'physical' and 'appearance' povs) and its ultimate > validity from faith in the number realm and the operations derived from > it. So, in performing such a process I undertake a personal voyage > through indexical reality, and never leave it, but there is no > tautological circularity since it's a genuinely empirical exploration > of the prior unknown, and what I discover could be totally surprising. > > Is grandma anywhere in the right area? Very very close indeed. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
Le 16-août-06, à 18:36, Tom Caylor a écrit :
> I noticed that you slipped in "infinity" ("infinite collection of
> computations") into your roadmap (even the short roadmap). In the
> "technical" posts, if I remember right, you said that at some point we
> were leaving the constructionist realm. But are you really talking
> about infinity? It is easy to slip into invoking infinity and get away
> with it without being noticed. I think this is because we are used to
> it in mathematics. In fact, I want to point out that David Nyman
> skipped over it, perhaps a case in point. But then you brought it up
> again here with aleph_zero, and 2^aleph_zero, so it seems you are
> really serious about it. I thought that infinities and singularities
> are things that physicists have dedicated their lives to trying to
> purge from the system (so far unsuccessfully ?) in order to approach a
> "true" theory of everything. Here you are invoking it from the start.
> No wonder you talk about faith.
>
> Even in the realm of pure mathematics, there are those of course who
> think it is invalid to invoke infinity. Not to try to complicate
> things, but I'm trying to make a point about how serious a matter this
> is. Have you heard about the feasible numbers of V. Sazanov, as
> discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
> we just have 2^N instantiations or computations, where N is a very
> large number?
I would say infinity is all what mathematics is about. Take any theorem
in arithmetic, like any number is the sum of four square, or there is
no pair of number having a ratio which squared gives two, etc.
And I am not talking about analysis, or the use of complex analysis in
number theory (cf zeta), or category theory (which relies on very high
infinite) without posing any conceptual problem (no more than
elsewhere).
Even constructivist and intuitionist accept infinity, although
sometimes under the form of potential infinity (which is all we need
for G and G* and all third person point of view, but is not enough for
having mathematical semantics, and then the first person (by UDA) is
really linked to an actual infinity. But those, since axiomatic set
theory does no more pose any interpretative problem.
True, I heard about some ultrafinitist would would like to avoid
infinity, but until now, they do have conceptual problem (like the fact
that they need notion of fuzzy high numbers to avoid the fact that for
each number has a successor. Imo, this is just philosophical play
having no relation with both theory and practice in math.
> The UDA is not precise enough for me, maybe because I'm a
> mathematician?
> I'm waiting for the interview, via the roadmap.
UDA is a problem for mathematicians, sometimes indeed. The reason is
that although it is a "proof", it is not a mathematical proof. And some
mathematician have a problem with non mathematical proof. But UDA *is*
the complete proof. I have already explain on this list (years ago)
that although informal, it is rigorous. The first version of it were
much more complex and technical, and it has taken years to suppress
eventually any non strictly needed difficulties.
I have even coined an expression "the 1004 fallacy" (alluding to Lewis
Carroll), to describe argument using unnecessary rigor or abnormally
precise term with respect to the reasoning.
So please, don't hesitate to tell me what is not precise enough for
you. Just recall UDA is not part of math. It is part of cognitive
science and physics, and computer science.
The lobian interview does not add one atom of rigor to the UDA, albeit
it adds constructive features so as to make possible an explicit
derivation of the "physical laws" (and more because it attached the
quanta to extended qualia). Now I extract only the logic of the certain
propositions and I show that it has already it has a strong quantum
perfume, enough to get an "arithmetical quantum logic, and then the
rest gives mathematical conjectures. (One has been recently solved by a
young mathematician).
Bruno
http://iridia.ulb.ac.be/~marchal/
--~--~-~--~~~---~--~~
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-~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
Bruno Marchal wrote: > The self-reference logics are born from the goal of escaping circular > difficulties. I think here I may have experienced a 'blinding flash' in terms of your project. If, as I've said, I begin from self-reference - 'indexical David', then I have asserted my 'necessary' point of origin. From this point of origin, I can interview myself (and entity-analogs simulated or modeled within myself) and consequently discover the statements that express my beliefs, the truth of which I can then evaluate in terms of my theology. This theology will derive its consistency from provable theorems, its relevance from generative and explanatory power (e.g. with respect to both 'physical' and 'appearance' povs) and its ultimate validity from faith in the number realm and the operations derived from it. So, in performing such a process I undertake a personal voyage through indexical reality, and never leave it, but there is no tautological circularity since it's a genuinely empirical exploration of the prior unknown, and what I discover could be totally surprising. Is grandma anywhere in the right area? David > Hi David, > > > Le 16-août-06, à 02:51, David Nyman a écrit : > > > > > Good to see this. First off some grandmotherly-ish questions: > > > >> 1) The computationalist hypothesis (comp), > >> > >> This is the hypothesis that "I am a digital machine" in the > >> quasi-operational sense that I can survive through an artificial > >> digital body/brain. I make it precise by adding Church thesis and some > >> amount of Arithmetical Realism (without which those terms are > >> ambiguous). > >> To be sure this is what Peter D. Jones called "standard > >> computationallism". > > > > I need to ask you to make this more precise for me. When I say I *am* a > > digital machine, what is my instantiation? IOW, am 'I' just the *idea* > > of a dmc for the purposes of a gedanken experiment, or am I to conceive > > of myself as equivalent to a collection of bits under certain > > operations, instantiated - well, how? > > > Well, for a "comp practitioners", saying "yes to the doctor" is not a > thought experiment. > I will try to explain at some point why we cannot really know what is > our instantiation, and that is why the "yes doctor" needs some act of > faith, and also why comp guaranties the right to say NO to the doctor > (either because you feel he is proposing a substitution level which is > too high, or because you just doubt comp, etc.). Eventually you will > see we have always 2^aleph_zero "instantiations". > > > > > > > > You may be going to tell me that > > this is irrelevant, or as you say a little further on: > > > >> From a strictly logical point of view this is not a proof that > >> "matter" > >> does not exist. Only that "primitive matter" is devoid of any > >> explanatory purposes, both for the physical (quanta) and psychological > >> (qualia) appearances (once comp is assumed of course). > > > > Ignoring for the moment the risk of circularity in the foregoing logic, > > > The self-reference logics are born from the goal of escaping circular > difficulties. > > > > > I'm not insisting on 'matter' here. Rather, in the same spirit as my > > 'pressing' you on the number realm, if I claim 'I am indexical > > dmc-David', I thereby assert my *necessary* indexical existence. > > > OK. This will be true (G*) but non communicable (G). Strictly speaking > you are saying something true, but if you present it as a "scientific" > fact or just a third person describable fact then you are in danger (of > inconsistency). > > > > > > If my > > instantiation is a collection of bits, then equivalently I am asserting > > the necessary indexical existence of this collection of bits. Is this > > supposed to reside in the 'directly revealed' Pythagorean realm with > > number etc and consequently is it a matter of faith? > > > Yes. > > > > > I just want to > > know if it is a case of 'yes monseigneur' before we get to 'yes > > doctor'. > > > That's the point, and that is why, to remain scientist at this point, > we must accept we are doing "theology". It is just modesty! With comp, > doctors are sort of "modern monseigneur". By "modern" here I mean no > consistent comp doctor will pretend to *know* the truth in these > matters. > > > > > > >> B does capture a notion of self-reference, but it is really a third > >> person form of self-reference. It is the same as the one given by your > >> contemplation of your own body or any correct third person description > >> of yourself, like the encoding proposed by the doctor, in case he is > >> lucky. > > > > Now we come to the 'encoding proposed by the doctor'. I hope he's > > lucky, BTW, it's a good characteristic in a doctor (this is grandma > > remember). > > > Indeed. Medicine is already quasi computationalist without saying. > > > > > Do we have a theory of the correct encoding of a third > > person description, or is this an idealisation? Penrose would claim, of > >
Re: ROADMAP (SHORT)
Bruno Marchal wrote:
> Hi David,
>
>
> Le 16-août-06, à 02:51, David Nyman a écrit :
>
>
>
> > Good to see this. First off some grandmotherly-ish questions:
> >
> >> 1) The computationalist hypothesis (comp),
> >>
> >> This is the hypothesis that "I am a digital machine" in the
> >> quasi-operational sense that I can survive through an artificial
> >> digital body/brain. I make it precise by adding Church thesis and some
> >> amount of Arithmetical Realism (without which those terms are
> >> ambiguous).
> >> To be sure this is what Peter D. Jones called "standard
> >> computationallism".
> >
> > I need to ask you to make this more precise for me. When I say I *am* a
> > digital machine, what is my instantiation? IOW, am 'I' just the *idea*
> > of a dmc for the purposes of a gedanken experiment, or am I to conceive
> > of myself as equivalent to a collection of bits under certain
> > operations, instantiated - well, how?
>
>
> Well, for a "comp practitioners", saying "yes to the doctor" is not a
> thought experiment.
> I will try to explain at some point why we cannot really know what is
> our instantiation, and that is why the "yes doctor" needs some act of
> faith, and also why comp guaranties the right to say NO to the doctor
> (either because you feel he is proposing a substitution level which is
> too high, or because you just doubt comp, etc.). Eventually you will
> see we have always 2^aleph_zero "instantiations".
>
>
Bruno,
I noticed that you slipped in "infinity" ("infinite collection of
computations") into your roadmap (even the short roadmap). In the
"technical" posts, if I remember right, you said that at some point we
were leaving the constructionist realm. But are you really talking
about infinity? It is easy to slip into invoking infinity and get away
with it without being noticed. I think this is because we are used to
it in mathematics. In fact, I want to point out that David Nyman
skipped over it, perhaps a case in point. But then you brought it up
again here with aleph_zero, and 2^aleph_zero, so it seems you are
really serious about it. I thought that infinities and singularities
are things that physicists have dedicated their lives to trying to
purge from the system (so far unsuccessfully ?) in order to approach a
"true" theory of everything. Here you are invoking it from the start.
No wonder you talk about faith.
Even in the realm of pure mathematics, there are those of course who
think it is invalid to invoke infinity. Not to try to complicate
things, but I'm trying to make a point about how serious a matter this
is. Have you heard about the feasible numbers of V. Sazanov, as
discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
we just have 2^N instantiations or computations, where N is a very
large number?
Tom
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Re: ROADMAP (SHORT)
Hi David, Le 16-août-06, à 02:51, David Nyman a écrit : > Good to see this. First off some grandmotherly-ish questions: > >> 1) The computationalist hypothesis (comp), >> >> This is the hypothesis that "I am a digital machine" in the >> quasi-operational sense that I can survive through an artificial >> digital body/brain. I make it precise by adding Church thesis and some >> amount of Arithmetical Realism (without which those terms are >> ambiguous). >> To be sure this is what Peter D. Jones called "standard >> computationallism". > > I need to ask you to make this more precise for me. When I say I *am* a > digital machine, what is my instantiation? IOW, am 'I' just the *idea* > of a dmc for the purposes of a gedanken experiment, or am I to conceive > of myself as equivalent to a collection of bits under certain > operations, instantiated - well, how? Well, for a "comp practitioners", saying "yes to the doctor" is not a thought experiment. I will try to explain at some point why we cannot really know what is our instantiation, and that is why the "yes doctor" needs some act of faith, and also why comp guaranties the right to say NO to the doctor (either because you feel he is proposing a substitution level which is too high, or because you just doubt comp, etc.). Eventually you will see we have always 2^aleph_zero "instantiations". > You may be going to tell me that > this is irrelevant, or as you say a little further on: > >> From a strictly logical point of view this is not a proof that >> "matter" >> does not exist. Only that "primitive matter" is devoid of any >> explanatory purposes, both for the physical (quanta) and psychological >> (qualia) appearances (once comp is assumed of course). > > Ignoring for the moment the risk of circularity in the foregoing logic, The self-reference logics are born from the goal of escaping circular difficulties. > I'm not insisting on 'matter' here. Rather, in the same spirit as my > 'pressing' you on the number realm, if I claim 'I am indexical > dmc-David', I thereby assert my *necessary* indexical existence. OK. This will be true (G*) but non communicable (G). Strictly speaking you are saying something true, but if you present it as a "scientific" fact or just a third person describable fact then you are in danger (of inconsistency). > If my > instantiation is a collection of bits, then equivalently I am asserting > the necessary indexical existence of this collection of bits. Is this > supposed to reside in the 'directly revealed' Pythagorean realm with > number etc and consequently is it a matter of faith? Yes. > I just want to > know if it is a case of 'yes monseigneur' before we get to 'yes > doctor'. That's the point, and that is why, to remain scientist at this point, we must accept we are doing "theology". It is just modesty! With comp, doctors are sort of "modern monseigneur". By "modern" here I mean no consistent comp doctor will pretend to *know* the truth in these matters. > >> B does capture a notion of self-reference, but it is really a third >> person form of self-reference. It is the same as the one given by your >> contemplation of your own body or any correct third person description >> of yourself, like the encoding proposed by the doctor, in case he is >> lucky. > > Now we come to the 'encoding proposed by the doctor'. I hope he's > lucky, BTW, it's a good characteristic in a doctor (this is grandma > remember). Indeed. Medicine is already quasi computationalist without saying. > Do we have a theory of the correct encoding of a third > person description, or is this an idealisation? Penrose would claim, of > course, that it is impossible for any such decription to be > instantiated in a digital computer, and his argument derives largely > from the putative direct contact of the brain with the Platonic/ > Pythagorean realm of number, which instantiates his 'non-computable' > procedures. But is your claim that a correct digital 3rd-person > description can indeed be achieved if the level of digital > 'substitution' instantiates non-computability, as Penrose claims for > the brain/ Pythagorean dyad? And if so what is that substitution level, > and what is that instantiation (in the sense previously requested)? Comp makes it impossible to know the level for sure. We can bet on it, and be lucky. If Penrose is right, then comp is just false. Note that Hammerof (who has worked together with Penrose at some time) eventually accept the idea that the brain is mechanical, albeit quantum mechanical (this makes him remaining under the comp hyp because quantum computer are Turing-emulable). > > What a curious and ignorant grandmother! > >> Basically a theology for a machine M is just the whole truth about >> machine M. This is not normative, nobody pretend knowing such truth. > >> Plotinus' ONE, or "GOD", or "GOOD" or its "big unnameable" ... is >> (arithmetical, analytical) truth. A theore
Re: ROADMAP (SHORT)
Bruno Marchal wrote: Hi Bruno Good to see this. First off some grandmotherly-ish questions: > 1) The computationalist hypothesis (comp), > > This is the hypothesis that "I am a digital machine" in the > quasi-operational sense that I can survive through an artificial > digital body/brain. I make it precise by adding Church thesis and some > amount of Arithmetical Realism (without which those terms are > ambiguous). > To be sure this is what Peter D. Jones called "standard > computationallism". I need to ask you to make this more precise for me. When I say I *am* a digital machine, what is my instantiation? IOW, am 'I' just the *idea* of a dmc for the purposes of a gedanken experiment, or am I to conceive of myself as equivalent to a collection of bits under certain operations, instantiated - well, how? You may be going to tell me that this is irrelevant, or as you say a little further on: > From a strictly logical point of view this is not a proof that "matter" > does not exist. Only that "primitive matter" is devoid of any > explanatory purposes, both for the physical (quanta) and psychological > (qualia) appearances (once comp is assumed of course). Ignoring for the moment the risk of circularity in the foregoing logic, I'm not insisting on 'matter' here. Rather, in the same spirit as my 'pressing' you on the number realm, if I claim 'I am indexical dmc-David', I thereby assert my *necessary* indexical existence. If my instantiation is a collection of bits, then equivalently I am asserting the necessary indexical existence of this collection of bits. Is this supposed to reside in the 'directly revealed' Pythagorean realm with number etc and consequently is it a matter of faith? I just want to know if it is a case of 'yes monseigneur' before we get to 'yes doctor'. > B does capture a notion of self-reference, but it is really a third > person form of self-reference. It is the same as the one given by your > contemplation of your own body or any correct third person description > of yourself, like the encoding proposed by the doctor, in case he is > lucky. Now we come to the 'encoding proposed by the doctor'. I hope he's lucky, BTW, it's a good characteristic in a doctor (this is grandma remember). Do we have a theory of the correct encoding of a third person description, or is this an idealisation? Penrose would claim, of course, that it is impossible for any such decription to be instantiated in a digital computer, and his argument derives largely from the putative direct contact of the brain with the Platonic/ Pythagorean realm of number, which instantiates his 'non-computable' procedures. But is your claim that a correct digital 3rd-person description can indeed be achieved if the level of digital 'substitution' instantiates non-computability, as Penrose claims for the brain/ Pythagorean dyad? And if so what is that substitution level, and what is that instantiation (in the sense previously requested)? What a curious and ignorant grandmother! > Basically a theology for a machine M is just the whole truth about > machine M. This is not normative, nobody pretend knowing such truth. > Plotinus' ONE, or "GOD", or "GOOD" or its "big unnameable" ... is > (arithmetical, analytical) truth. A theorem by Tarski can justified > what this notion is already not nameable by any correct (arithmetical > or analytical) machine. Now such truth does not depend on the machine, > still less from machine representation, and thus is a zero-person > notion. From this I will qualify as "divine" anything related to truth, > and as terrestrial, anything related to "provable by the machine". So here we arrive at the theology, and I think I finally see what you intend by a zero-person notion - i.e. one that does not depend on instantiation in persons, but I'm not yet convinced of the 'reality' of this. I hope to be able to stop pressing you on this 'indexical instantiation' mystery, so if the above are simply the articles of faith for this 'as if' belief system, then I'll stop questioning them for the duration of the experiment. > Meanwhile you could try to guess where qualia and quanta appear. > (I will see too if this table survives the electronic voyage ...) Hmm... Well, I guess I would expect qualia to be 'sensible', and quanta to be 'intelligible', but then I wouldn't know that quanta were intelligible until they were sensible as qualia. So if you mean 'appear' as in 'appears from the pov of indexical dmc-David', I guess it would have to be 'sensible matter' for both. But grandma grows weary.. G > Hi, > > > 1) The computationalist hypothesis (comp), > > This is the hypothesis that "I am a digital machine" in the > quasi-operational sense that I can survive through an artificial > digital body/brain. I make it precise by adding Church thesis and some > amount of Arithmetical Realism (without which those terms are > ambiguous). > To be sure this is what Peter D. Jones called "standard > computationallis
ROADMAP (SHORT)
Hi, 1) The computationalist hypothesis (comp), This is the hypothesis that "I am a digital machine" in the quasi-operational sense that I can survive through an artificial digital body/brain. I make it precise by adding Church thesis and some amount of Arithmetical Realism (without which those terms are ambiguous). To be sure this is what Peter D. Jones called "standard computationallism". Let us call momentarily "Pythagorean comp" the thesis that there is only numbers and that all the rest emerge through numbers dream (including possible sharable dreams); where dreams will be, thanks to comp, captured by infinite collection of computations as seen from some first person perspective. Then ... 2) The Universal Dovetailer argumentation (UDA) ... then the Universal Dovetailer Argumentation (UDA) is literally a proof that Standard computationalism implies Pythagorean computationalism. From a strictly logical point of view this is not a proof that "matter" does not exist. Only that "primitive matter" is devoid of any explanatory purposes, both for the physical (quanta) and psychological (qualia) appearances (once comp is assumed of course). The UDA needs only a passive understanding of Church Thesis (to make sense of the *universal* dovetailing). 3) The lobian interview and the rise of the arithmetical "plotinian" hypostases, or n-person perspectives. The difference between the UDA and the lobian interview is that in the UDA, *you* are interviewed. *you* are asked to implicate yourself a little bit; but in the lobian interview, instead of interviewing humans, I directly interview a "self-referentially correct" and sufficiently "rich" universal machine (which I call lobian for short). Computer science + mathematical logic makes such an enterprise possible. We can indeed study what a correct (by definition) machine is able to prove and guess about itself, in some third person way, and that's how the other notion of person will appear (cannot not appear). Let us abbreviate "the machine asserts "2+3=5"" by B(2+3=5). B is for Godel's Beweisbar notion of "formally provable". If "p" denotes any proposition which we can translate in the machine's language, we write Bp for "the machine asserts p". For a classical mathematician, or an arithmetical platonist, there is no problem with *deciding* to limit the interview to correct machine (independently that we will see that no correct machine can know it is a correct machine). To say that the machine is correct amounts to say that whatever the machine asserts, it is true. So Bp -> p, when instantiated, is always true. But now, by the incompleteness phenomena, although Bp -> p is always true, it happens that no correct machine can prove for any p that Bp -> p. For some p, Bp -> p is true, but not provable by the machine. The simplest case is when p is some constant falsity, noted f, like "0 = 1" for example, or like "p & ~p". In that case Bp -> p is Bf -> f, and this is equivalent (cf propositional truth table) to ~Bf, which is a self-consistency assertion not provable by the correct machine (by Godel's second incompleteness theorem). Due to this, "Bp" does not capture a notion of knoowledge, for which "Bp->p" should be not only true but known. B does capture a notion of self-reference, but it is really a third person form of self-reference. It is the same as the one given by your contemplation of your own body or any correct third person description of yourself, like the encoding proposed by the doctor, in case he is lucky. This means that "Bp & p", although equivalent with "Bp", cannot be proved equivalent by the machine. This means that the logic of "Bp & p" will be a different logic than the one of "Bp & p". Now Theaetetus has proposed to define "knowledge" by such a "true justified opinion", and I propose to define the logic of machine (perfect) knowledge by Bp & p. This remains even more true for other "epistemological nuances" arising from incompleteness, like the future probabilty or credibility (not provability!) notions, which I will capture by Bp & Dp and Bp & Dp & p, where Dp abbreviates, as usual (cf my older post) ~B~p (the non provability of the negation of p). Now, note this: I said "Bp & p" is equivalent to "Bp", but the machine cannot prove that equivalence. So the proposition "(Bp & p) <-> Bp" is an example of true (on the machine) but unprovable (by the machine) proposition. So, concerning the correct machine we talk about, we must distinguish the provable propositions and the true but unprovable propositions. Thanks to Solovay, the logic of the provable proposition is captured by a modal logic often named G, and the logic of the true proposition is captured by a vaster logic named G*. The corona G* minus G gives a logic of the true but non provable statements. I think I have enough to give you a sketch of the hypostases. I will use Plotinian greek neoplatonist vocabul
