Re: Can mind be a computation if physics is fundamental?
On 06 Aug 2009, at 04:37, Colin Hales wrote: > Man this is a tin of worms! I have just done a 30 page detailed > refutation of computationalism. > It's going through peer review at the moment. > > The basic problem that most people fall foul of is the conflation of > 'physics-as-computation' with the type of computation that is being > carried out in a Turing machine (a standard computer). In the paper > I drew an artificial distinction between them. I called the former > NATURAL COMPUTATION (NC) and the latter ARTIFICIAL COMPUTATION (AC). > The idea is that if COMP is true then there is no distinction > between AC and NC. The distinction should fail. Why? COMP entails that physics cannot be described by a computation, but by an infinite sum of infinite histories. If you were correct, there would be no possible white rabbit. You are confusing comp (I am a machine) and constructive physics (the universe is a machine). > > > I found one an one only situation/place where AC and NC part > company. Call this situation X. > > If COMP is false in this one place X it is false as a general claim. > I also found 2 downstream (consequential) failures that ultimately > get their truth-basis from X, so they are a little weaker as formal > arguments against COMP. > > FACT: Humans make propositions that are fundamentally of an informal > nature. That is, the utterances of a human can be inconsistent and > form an fundamentally incomplete set (we don't 'know everything'). > The quintessential definition of a scientist is a 'correctable > liar'. When a hypothesis is uttered it has the status > indistinguishable of a lie. A lie presuppose the intention of communicating the false. > Humans can participate in the universe in ways which can > (apparently) violate any law of nature. Humans must be able to > 'violate' laws of nature in the process of accessing new/novel > formal systems to describe the unknown natural world. Look at the > world. It is not hard to see how humans exemplify an informal > system. All over the world are quite normal (non-pathologically > affected) humans with the same sensory systems and mental > capacities. Yet all manner of ignorance and fervently held > contradictory belief systems are ‘rationally’ adopted. > === > COMP fails when: > a) You assume COMP is true and build an artificial (AC/computer) > scientist and expect to be able to carry out authentic > original science on the a-priori unknownidentically to humans. > To do this you use a human-originated formal model (law of nature) > ts to do this your computer 'computes ts, you EMBODY the > computer in a suitable robotic form and then expect it to do science > like humans. If COMP is true then the human scientist and the robot > scientist should be indistinguishable. > > b) You then discover that it is a fundamental impossibility that > be able to debate/propose that COMP is a law of nature. > > c) Humans can debate/propose that COMP is a law of nature. > > BECAUSE: (b) <> (c) they are distinguishable. NC and AC are different > THEREFORE: ts cannot be the 'law of nature' for a scientist. > THEREFORE: COMP is false in the special case of (b) > THEREFORE: COMP is false as a general claim. > > (b) is not a claim of truth or falsehood. It is a claim that the > very idea of ever proposing COMP (= doubting that COMP is true) > is impossible. This is because it is a formal system trying, with a > fixed, formal set of rules (even self modifying according to yet > more rules) to construct statements that are the product of an > informal system (a human scientist). The very idea of this is a > contradiction in terms. The formal system is 100% deterministic, > unable to violate rules. When it encounters a liar it will be unable > to resolve what falsehood is being presented. It requires all > falsehoods to be a-priori known. Impossible. How can a formal system > encounter a world in which COMP is actually false? If it could, COMP > would be FALSE! If COMP is true then it can't. Humans are > informalergo we have some part of the natural world capable of > behaving informally=> GOTCHA! > > This argument is has very 'Godellian' structure. That was accidental. > > When you say 'physics is fundamental'. I don't actually known what > that means. > > What I can tell you is that to construct an authentic ARTIFICIAL > SCIENTIST (not a simulation, but an 'inorganic' scientist), you have > to replicate the real physics of cognition, not 'compute a model' of > the cognition or a 'compute a model of the physics underlying > cognition'. Then an artificial scientist is a scioentist in the same > sense that artificial light is light. > > R.I.P. COMP > > => Strong AI (a computer can be a mind) is false. > => Weak AI (A computer model of cognition can never be actual > cognition) is true. > > It's nice to finally
Re: Can mind be a computation if physics is fundamental?
Hi, it seems you start with the assumptions that an AI can't do science as humans... to conclude just that. Regards, Quentin 2009/8/6 Colin Hales : > Man this is a tin of worms! I have just done a 30 page detailed refutation > of computationalism. > It's going through peer review at the moment. > > The basic problem that most people fall foul of is the conflation of > 'physics-as-computation' with the type of computation that is being carried > out in a Turing machine (a standard computer). In the paper I drew an > artificial distinction between them. I called the former NATURAL COMPUTATION > (NC) and the latter ARTIFICIAL COMPUTATION (AC). The idea is that if COMP is > true then there is no distinction between AC and NC. The distinction should > fail. > > I found one an one only situation/place where AC and NC part company. Call > this situation X. > > If COMP is false in this one place X it is false as a general claim. I also > found 2 downstream (consequential) failures that ultimately get their > truth-basis from X, so they are a little weaker as formal arguments against > COMP. > > FACT: Humans make propositions that are fundamentally of an informal nature. > That is, the utterances of a human can be inconsistent and form an > fundamentally incomplete set (we don't 'know everything'). The > quintessential definition of a scientist is a 'correctable liar'. When a > hypothesis is uttered it has the status indistinguishable of a lie. Humans > can participate in the universe in ways which can (apparently) violate any > law of nature. Humans must be able to 'violate' laws of nature in the > process of accessing new/novel formal systems to describe the unknown > natural world. Look at the world. It is not hard to see how humans exemplify > an informal system. All over the world are quite normal (non-pathologically > affected) humans with the same sensory systems and mental capacities. Yet > all manner of ignorance and fervently held contradictory belief systems are > ‘rationally’ adopted. > === > COMP fails when: > a) You assume COMP is true and build an artificial (AC/computer) scientist > and expect to be able to carry out authentic original science on > the a-priori unknownidentically to humans. To do this you use a > human-originated formal model (law of nature) ts to do this your > computer 'computes ts, you EMBODY the computer in a suitable robotic form > and then expect it to do science like humans. If COMP is true then the human > scientist and the robot scientist should be indistinguishable. > > b) You then discover that it is a fundamental impossibility that be > able to debate/propose that COMP is a law of nature. > > c) Humans can debate/propose that COMP is a law of nature. > > BECAUSE: (b) <> (c) they are distinguishable. NC and AC are different > THEREFORE: ts cannot be the 'law of nature' for a scientist. > THEREFORE: COMP is false in the special case of (b) > THEREFORE: COMP is false as a general claim. > > (b) is not a claim of truth or falsehood. It is a claim that the very idea > of ever proposing COMP (= doubting that COMP is true) is impossible. > This is because it is a formal system trying, with a fixed, formal set of > rules (even self modifying according to yet more rules) to construct > statements that are the product of an informal system (a human scientist). > The very idea of this is a contradiction in terms. The formal system is 100% > deterministic, unable to violate rules. When it encounters a liar it will be > unable to resolve what falsehood is being presented. It requires all > falsehoods to be a-priori known. Impossible. How can a formal system > encounter a world in which COMP is actually false? If it could, COMP would > be FALSE! If COMP is true then it can't. Humans are informalergo we have > some part of the natural world capable of behaving informally=> GOTCHA! > > This argument is has very 'Godellian' structure. That was accidental. > > When you say 'physics is fundamental'. I don't actually known what that > means. > > What I can tell you is that to construct an authentic ARTIFICIAL SCIENTIST > (not a simulation, but an 'inorganic' scientist), you have to replicate the > real physics of cognition, not 'compute a model' of the cognition or a > 'compute a model of the physics underlying cognition'. Then an artificial > scientist is a scioentist in the same sense that artificial light is light. > > R.I.P. COMP > > => Strong AI (a computer can be a mind) is false. > => Weak AI (A computer model of cognition can never be actual cognition) is > true. > > It's nice to finally have at least one tiny little place (X) where the seeds > of clarity can be found. > > Cheers > colin hales > > > > > 1Z wrote: > > On 31 July, 22:39, David Nyman wrote: > > > I note that the recent posts by Peter Jones - aka the mysterious 1Z, > and the originator of the curiously useful 'real in the sense I am > real' or RITSIAR - occurred shortly after m
Re: Can mind be a computation if physics is fundamental?
Colin Hales wrote: > Man this is a tin of worms! I have just done a 30 page detailed > refutation of computationalism. > It's going through peer review at the moment. > > The basic problem that most people fall foul of is the conflation of > 'physics-as-computation' with the type of computation that is being > carried out in a Turing machine (a standard computer). In the paper I > drew an artificial distinction between them. I called the former NATURAL > COMPUTATION (NC) and the latter ARTIFICIAL COMPUTATION (AC). The idea is > that if COMP is true then there is no distinction between AC and NC. The > distinction should fail. > > I found one an one only situation/place where AC and NC part company. > Call this situation X. > > If COMP is false in this one place X it is false as a general claim. I > also found 2 downstream (consequential) failures that ultimately get > their truth-basis from X, so they are a little weaker as formal > arguments against COMP. > > *FACT*: Humans make propositions that are fundamentally of an informal > nature. That is, the utterances of a human can be inconsistent and form > an fundamentally incomplete set (we don't 'know everything'). The > quintessential definition of a scientist is a 'correctable liar'. When a > hypothesis is uttered it has the status indistinguishable of a lie. > Humans can participate in the universe in ways which can (apparently) > violate any law of nature. Humans must be able to 'violate' laws of > nature in the process of accessing new/novel formal systems to describe > the unknown natural world. Look at the world. It is not hard to see how > humans exemplify an informal system. All over the world are quite normal > (non-pathologically affected) humans with the same sensory systems and > mental capacities. Yet all manner of ignorance and fervently held > contradictory belief systems are ‘rationally’ adopted. > === > COMP fails when: > a) You assume COMP is true and build an artificial (AC/computer) > scientist and expect to be able to carry out authentic > original science on the a-priori unknownidentically to humans. To do > this you use a human-originated formal model (law of nature) ts to do > this your computer 'computes ts, you EMBODY the computer in a > suitable robotic form and then expect it to do science like humans. If > COMP is true then the human scientist and the robot scientist should be > indistinguishable. > > b) You then discover that it is a fundamental impossibility that be > able to debate/propose that COMP is a law of nature. > > c) Humans can debate/propose that COMP is a law of nature. > > BECAUSE: (b) <> (c) they are distinguishable. NC and AC are different > THEREFORE: ts cannot be the 'law of nature' for a scientist. > THEREFORE: COMP is false in the special case of (b) > THEREFORE: COMP is false as a general claim. > > (b) is not a claim of truth or falsehood. It is a claim that the very > idea of ever proposing COMP (= doubting that COMP is true) is > impossible. This is because it is a formal system trying, with a fixed, > formal set of rules (even self modifying according to yet more rules) to > construct statements that are the product of an informal system (a human > scientist). The very idea of this is a contradiction in terms. I don't see it. I can write a simple computer program that constructs statements which are a subset of those produced by humans (or any other system). Bruno's UD produces *all* such statements. So where's the contradiction? >The > formal system is 100% deterministic, unable to violate rules. When it > encounters a liar it will be unable to resolve what falsehood is being > presented. What does it mean to "resolve what falsehood is being presented"? >It requires all falsehoods to be a-priori known. Impossible. > How can a formal system encounter a world in which COMP is actually > false? If it could, COMP would be FALSE! If COMP is true then it can't. > Humans are informalergo we have some part of the natural world > capable of behaving informally=> GOTCHA! > > This argument is has very 'Godellian' structure. That was accidental. > > When you say 'physics is fundamental'. I don't actually known what that > means. > > What I can tell you is that to construct an authentic ARTIFICIAL > SCIENTIST (not a simulation, but an 'inorganic' scientist), you have to > *replicate the real physics of cognition, *not 'compute a model' of the > cognition or a 'compute a model of the physics underlying cognition'. > Then an artificial scientist is a scioentist in the same sense that > artificial light is light. But what is the "real physics of cognition"? Apprently you don't think it is neurons firing, since you refer to an 'inorganic' scientist. And artificial light is made of photons the same as sunlight or any other light. Brent > > R.I.P. COMP > > => Strong AI (a computer can be a mind) is f
Re: Can mind be a computation if physics is fundamental?
Man this is a tin of worms! I have just done a 30 page detailed refutation of computationalism. It's going through peer review at the moment. The basic problem that most people fall foul of is the conflation of 'physics-as-computation' with the type of computation that is being carried out in a Turing machine (a standard computer). In the paper I drew an artificial distinction between them. I called the former NATURAL COMPUTATION (NC) and the latter ARTIFICIAL COMPUTATION (AC). The idea is that if COMP is true then there is no distinction between AC and NC. The distinction should fail. I found one an one only situation/place where AC and NC part company. Call this situation X. If COMP is false in this one place X it is false as a general claim. I also found 2 downstream (consequential) failures that ultimately get their truth-basis from X, so they are a little weaker as formal arguments against COMP. *FACT*: Humans make propositions that are fundamentally of an informal nature. That is, the utterances of a human can be inconsistent and form an fundamentally incomplete set (we don't 'know everything'). The quintessential definition of a scientist is a 'correctable liar'. When a hypothesis is uttered it has the status indistinguishable of a lie. Humans can participate in the universe in ways which can (apparently) violate any law of nature. Humans must be able to 'violate' laws of nature in the process of accessing new/novel formal systems to describe the unknown natural world. Look at the world. It is not hard to see how humans exemplify an informal system. All over the world are quite normal (non-pathologically affected) humans with the same sensory systems and mental capacities. Yet all manner of ignorance and fervently held contradictory belief systems are 'rationally' adopted. === COMP fails when: a) You assume COMP is true and build an artificial (AC/computer) scientist and expect to be able to carry out authentic original science on the a-priori unknownidentically to humans. To do this you use a human-originated formal model (law of nature) ts to do this your computer 'computes ts, you EMBODY the computer in a suitable robotic form and then expect it to do science like humans. If COMP is true then the human scientist and the robot scientist should be indistinguishable. b) You then discover that it is a fundamental impossibility that be able to debate/propose that COMP is a law of nature. c) Humans can debate/propose that COMP is a law of nature. BECAUSE: (b) <> (c) they are distinguishable. NC and AC are different THEREFORE: ts cannot be the 'law of nature' for a scientist. THEREFORE: COMP is false in the special case of (b) THEREFORE: COMP is false as a general claim. (b) is not a claim of truth or falsehood. It is a claim that the very idea of ever proposing COMP (= doubting that COMP is true) is impossible. This is because it is a formal system trying, with a fixed, formal set of rules (even self modifying according to yet more rules) to construct statements that are the product of an informal system (a human scientist). The very idea of this is a contradiction in terms. The formal system is 100% deterministic, unable to violate rules. When it encounters a liar it will be unable to resolve what falsehood is being presented. It requires all falsehoods to be a-priori known. Impossible. How can a formal system encounter a world in which COMP is actually false? If it could, COMP would be FALSE! If COMP is true then it can't. Humans are informalergo we have some part of the natural world capable of behaving informally=> GOTCHA! This argument is has very 'Godellian' structure. That was accidental. When you say 'physics is fundamental'. I don't actually known what that means. What I can tell you is that to construct an authentic ARTIFICIAL SCIENTIST (not a simulation, but an 'inorganic' scientist), you have to *replicate the real physics of cognition, *not 'compute a model' of the cognition or a 'compute a model of the physics underlying cognition'. Then an artificial scientist is a scioentist in the same sense that artificial light is light. R.I.P. COMP => Strong AI (a computer can be a mind) is false. => Weak AI (A computer model of cognition can never be actual cognition) is true. It's nice to finally have at least one tiny little place (X) where the seeds of clarity can be found. Cheers colin hales 1Z wrote: > > On 31 July, 22:39, David Nyman wrote: > >> I note that the recent posts by Peter Jones - aka the mysterious 1Z, >> and the originator of the curiously useful 'real in the sense I am >> real' or RITSIAR - occurred shortly after my taking his name in vain. >> Hmm... >> >> Anyway, this signalled the resumption of a long-running debate about >> the validity of causal accounts of the first person based on a >> functional or computational rationale. I'm going to make an attempt >> to
Re: Can mind be a computation if physics is fundamental?
On 31 July, 22:39, David Nyman wrote: > I note that the recent posts by Peter Jones - aka the mysterious 1Z, > and the originator of the curiously useful 'real in the sense I am > real' or RITSIAR - occurred shortly after my taking his name in vain. > Hmm... > > Anyway, this signalled the resumption of a long-running debate about > the validity of causal accounts of the first person based on a > functional or computational rationale. I'm going to make an attempt > to annihilate this intuition in this thread, and hope to encourage > feedback specifically on this issue. You will recall that this is at > the heart of Bruno's requirement to base COMP - i.e. the explicitly > computational account of mind - on the the number realm, with physics > derived as an emergent from this. Step 8 of the UDA addresses these > issues in a very particular way. > > However, I've always felt that there's a more intuitively obvious and > just as devastating blow that can be dealt to functional or > computational notions based on physical entities and relations > conceived as ontologically foundational and singular (i.e. no dualism > please). So as not to be misunderstood (too quickly!) let me make it > clear at the outset that I'm addressing this to first person conscious > experience, not to third person descriptions of 'mentality' - so > eliminativists can stop reading at this point as there is nothing > further that requires explanation in their view (as odd as I trust > this sounds to you non-eliminativists out there). > > The argument runs as follows. To take what physics describes with > maximal seriousness - as standing for ontological reality - is just to > take its entities and causal relationships seriously to the same > extent. God knows, physicists have gone to enough trouble to define > these entities and relationships with the most precisely articulated > set of nomological-causal principles we possess. Consequently, taking > these with maximal seriousness entails abjuring other causal > principles as independently efficacious: i.e. showing how - or at > least being committed to the belief that - all higher order causal > principles somehow supervene on these fundamentals. Any other > position would be either obscurantist or incoherent for a physical > realist. > > Now I should say at this point that I'm not criticising this position, > I'm merely articulating it. It follows from the foregoing that > although we may speak in chemical, biological, physiological or > historical narratives, we believe that in principle at least these are > reducible to their physical bases. We also know that although we may > speak of cabbages and kings, weather, oceans, processes, computations > and untold myriads of equally 'emergent' phenomena, we still must > retain our commitment to their reducibility to their physical bases. > So of course, we can - and do - legitimately speak, in this way, of > physical computers as 'performing computations', but following the > foregoing principle we can see that actually this is just a convenient > shorthand for what is occurring in the physical substrates upon which > the notion of computation must - and of course does - rely for its > realisation in the world. > > To be more explicit: The notion of a 'program' or 'computation' - when > we place it under analysis - is a convenient shorthand for an ordered > set of first person concepts In what sense "first person"? Surely not in the sense that qualia are supposed to be mysteriously and incommunicably first-person. Presumably in the sense that something is only a computer when regarded as such, (like certain pieces of paper being money). But that is quite contentious. It is not enough to say "under analysis", one must actually analyse > which finds its way into the physical > account in the form of various matter-energy dispositions. The > macroscopic media for these are variously paper and ink, actions of > computer keyboards, patterns of voltages in computer circuitry, > illumination of pixels on screens, etc. All of these, of course, can > - and must - reduce to fundamental relations amongst physical > 'ultimates'. At some point after entering the physical causal nexus, > this chain of dispositions may re-enter the first person account > (don't ask me how - it's inessential to the argument) at which point > they may again be construed *by someone* in computational terms in a > first person context. But at no point is the 'computation' - qua > concept - in any way material (pun intended) to the physical account; > a fortiori, in no way can it - or need it - be ascribed causal > significance in terms of the physical account. After all, what could > this possibly mean? Are these spooky 'computational' relationships > 'reaching across' the energy-transfers of the computer circuitry and > changing their outcomes? Of course not. How could they? And why > would they need to? Everything's going along just fine by it
Re: The seven step series
Bruno, just to take off some mal-deserved feathers:
I think Theaetetus has two different 'e' sounds one after the other (anybody
can pronounce him better?) and in Hungarian we have them (' e ' like in
'have' and e' like in 'take') with a 3rd variation where the accent is not
applied: a closed and an open ' e ' sound (instrumental in dialects). So I
have no problem to pronounce the discussing gentleman as The'-etetus. Maybe
he called himself (?) Te-aythetos? Ask Plato you are close to him.
(And I always proudly thought that Hungarian - vs. English - has a simple
vowel-code in an unchanging uniform pronunciation...).
German proverb: "Fremdworter sind glucksache" (= foreign words are a matter
of luck). A friend added: you can NEVER know what they mean.
John
On Tue, Aug 4, 2009 at 11:06 AM, Bruno Marchal wrote:
> John,
>
> Thanks for those informations. I thought that the "æ" was just a french,
> if not an old french, usage.
> Note that when I wrote "Theatetus", it is just a mispelling. I tend to
> forget that second "e", but your remark will help me to remind it. Note that
> Miles Burnyeat, in his book " The Theaetetus of Plato, and Levett in his
> traduction wrote simply "Theaetetus". But in french too, more and more
> people forget to attach the "o" and "e" in words like oeuvre, or soeur
> (sister).
>
> Bruno
>
> On 04 Aug 2009, at 15:05, John Mikes wrote:
>
> Bruno and Mirek,
> concerning Theateticus vs. Theaeteticus:
> in my strange linguistic background I make a difference betwee ai and ae -
> the spelling in Greek and Latin of the name. As far as I know, nobody knows
> for sure how did the 'ancient' Greeks pronounce their ai - maybe as the flat
> 'e' like in German "lehr" while the 'e' pronounciation might have been
> clsoer to (between) 'make' and 'peck' - the reason why the Romans
> transcribed it by their *ONE letter* *"ae",* (lehr) and not as English
> would read: *'a'+'ee'*. The spelling you gave points to this latter. The
> Latin 'ae' is not TWO separate letters (a+e), it is a twin, as marked in the
> Wiki article
> ..."*Theætetus"... **and not Theaetetus *
> which looked strange to me from the beginning .
> *(I wonder if the e-mail reproduces the (ae) one sign? look up in Wiki's
> Theaetetus Dialogue (in the title with the wrong spelling) the 1st line
> brings the merged-together double 'æ'.) *
> ***
> *English spelling always does a job on classical words, the Greek 'oi' has
> been transcribed into Latin sometimes as 'oe' and pronounced as in "girl"
> (oeuvre) while many think it was a sound like what the pigs say: as "oy".
> then comes America, with it's Phoenix (pron: feenix) *
> I don't think the Romans were much better off, centuries after and a world
> apart from the ancient (classical for them) Greeks.
> And who knows today if the great orator was Tzitzero or Kikero to turn
> later into Tchitchero?
> ***
> *"The Old Man" did quite a job on us at the tower of Babel. *
> ***
> *[[ - I am enjoying your 'other' post where you spelled out my own
> vocabulary as indeed thinking functions as relations, lately not as a static
> description, but also the interchanging factor - ]]*
> **
> *John*
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >
>
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Re: The seven step series
Hi Mirek, On 05 Aug 2009, at 00:52, Mirek Dobsicek wrote: > I've ordered the dialogue from a second-hand book shop :-) The > Stanford > encyclopedia says > "Arguably, it is his (Plato) greatest work on anything." > So I'll give it a try :-) I love that book, and it is also my favorite piece of Plato. To be sure, I don't think it is needed to understand neither UDA nor AUDA, but it can help. > This is probably the key problem for me. I know next to nothing about > provability, the logic of provability, PA/ZF provers. > > I know that quite often you reference Boolos 1993 - The Logic of > Provability. I took a look at it at Google Books preview but ... there > is something missing in my education. From the beginning I am puzzled > with "Why?, what?". What a headache :-) You miss an introductory course on mathematical logic. Have you herad about Gödel's incompletness theorem. Boolos book explains the sequel. I thought that, after Hofstadter best selling book on Gödel's theorem (Gödel, Escher, Bach), it would be possible to talk on mathematical logic to the layman, like we can talk on physics to the layman. But I was wrong. Gödel's theorem is not yet part of the common knowledge, and when it is used by non mathematician, in general it is abused. >> x divides y if and only if it exists a number z such that y = x*z. > > I don't dare to correct your english but "there is/exists a > number ..." > is what I would write. Thanks. > > >>> Ad 3) If natural numbers and their relations are the only entities >>> which >>> do exist then me, you, everything is a recipe of a Turing-computable >>> number. >> >> No. Not at all. Sorry. Gosh, you will be very surprised if you follow >> the UDA-7. On the contrary. Arithmetical truth VASTLY extends the >> computable domain. Most relations between numbers are not Turing >> emulable. > > Aha! Then I really have a wrong mental picture of your work. I > understood to arithmetical realism along the lines of this quotation > from the Stanford article on realism: > > "According to a platonist about arithmetic, the truth of the > sentence '7 > is prime' entails the existence of an abstract object, the number 7. > This object is abstract because it has no spatial or temporal > location, > and is causally inert. A platonic realist about arithmetic will say > that > the number 7 exists and instantiates the property of being prime > independently of anyone's beliefs, linguistic practices, conceptual > schemes, and so on." That is quite correct. All mathematicians are realist about arithmetic, and most are realist about sets. But set realism is a much more stronger belief than arithmetical realism. Comp necessitates arithmetical realism if only to be able to state Church thesis. Theoretical computer scientist are realist, because they belief that all machine either stop or not stop. > > > So I thought that you essentially take > a) Numbers and their properties and relations exists. Yes, but some people put to much sense in "exists". It is the mathematical usual sense, like when you derive "there exists a prime number" from the statement "17 is a prime number". No need to invoke Plato Heaven, in the assumption. > > b) Now, since you don't assume existence of anything else => your > body, > your bike and coffee must emerge as patterns in the world of numbers. I am agnostic. I assume neither that something else exists nor that it does not exist, and then I prove from the assumption that we are turing emulable, that physics is no more the fundamental science. I prove that if we are machine then matter has to be an emerging epistemological concept, and physics is a branch of machine biology/ psychology/theology, or mathematical computer science. "b)" is obviously non valid. The fact that bike an coffee must emerge from numbers is really the conclusion of the whole UD reasoning. It is not because I don't assume them, it is because their independent existence is shown contradictory. I show that mechanism makes physicalism epistemologically inconsistent. Even if matter really exists, it cannot be used to justify our belief in matter. A slight application of Occam razor eliminates matter, at that stage. > > c) Taking the Church-Turing thesis, these patterns are Turing- > computable. Not at all. The world of number is provably not Turing-computable. Only a very tiny part of the world of number is computable. There is a whole branch of mathematical logic devoted to the study of the degree of non computability of the relations existing among the numbers. Church thesis asserts only that the *computable* patterns are Turing computable. It is just the assertion that Turing computability can be used to define computability. > > d) Definitely, the vast majority of all patterns is not Turing- > computable. I don't understand. > > > This is how I have thought about your working framework. Notice, > that I >
