Bruno Marchal wrote:
>
> On 30 Dec 2009, at 17:07, benjayk wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>
>>> They are. Numbers are primitive. The variable x and y represents
>>> excusively those numbers. Finite pieces of computation are speical
>>> numbers, like prime numbers. To be a (finite piece of a) computation
>>> is a property of number, a relation which has to be defined in term
>>> of
>>> addition and multiplication of numbers. To be a computation are
>>> emergent property (emerging from addition and multiplication).
>> Sorry, I just don't get it. Your theory necessarily presumes dreams
>> before
>> numbers, because for you numbers appear just in your dreams.
>
> Not at all. Comp presuppose some understanding of consciousness, but
> then, after the uda reasoning we can understand that for the ontology
> we need no mre than a theory like Robinson arithmetic. It does not
> presuppose dreams. Dreams will be defined in term of number relations
> (computations). I think you are confusing the level and the meta-level.
> Maxwell electromagnetism does not presuppose consciousness. And this
> has nothing to do that Maxwell presuppose consciousness in his
> colleagues when reading his paper, but that is an assumption at some
> metalevel, not in the theory.
OK; but nevertheless your theory becomes wrong, if you try to act like the
meta-level, the level the theory appears in, does not exist (like some
materialists say) or relies on some objects in your theory. But if your
saying "numbers give rise to conciousness" it seems to me your doing that,
even if you don't mean it. Maybe it is just a semantic issue.
For me it is undoubtable that the understanding of what numbers are (and I
obviously can not make sense out of "numbers" without there being an
understanding of it) can only come out of conciousness, so "numbers explain
(or give rise to) conciousness" is simply not graspable for me. It seems
like an empty statement unless you mean with conciousness "conciousness as
referred to in this theory", but this is not conciousness. It is the shadow
of (or the pointer to) conciousness in this theory.
Bruno Marchal wrote:
>
>> Additionally,
>> the notion of numbers relies on the notion of truth,
>
> Not at all.
OK, I shouldn't have written "notion". I rather meant numbers rely on there
being an understanding of what is *what I mean* with the word "truth" or
"meaning" or "sense".
Bruno Marchal wrote:
>
>> which is a notion that
>> fundamentally can't be defined, only known.
>
> This is not correct. Pean Arithmetic can define a notion of truth for
> any formula with a determinate length.
> Tarski theorem just forbid a
> general notion of truth to be defined in the theory, for formula with
> an finite but not fixed in advance length.
This is why I wrote "fundamentally". You can define truth in some context,
but not truth itself. Every definition presumes that there is truth/meaning
in what it defines.
Bruno Marchal wrote:
>
>> Without *experiencing* truth
>> there is no sense to numbers.
>
> I think you are confusing third person numbers, and the human first
> person experience of numbers.
I just don't get for "whom" there could be third person numbers? I think
third person objects are just objects shareable by different first person
viewpoints. But it always relies on there being a first person.
You write that you don't want to eliminate the person, but isn't saying
there are third person numbers apart from a first "person" (no human being
but conciousness) exactly this? To whom could you explain it if not to a
person that you already presume? Who could understand it?
Bruno Marchal wrote:
>
> Arithmetical realism is the explicit assumption that truth of the form
> "17 is a prime number" is not dependent of the existence of humans, or
> even of a physical universe.
I basically agree. But I don't think that it is even possible to
meaningfully propose that "17 is a prime number" is independent of
conciousness since you can't doubt (what I mean with the word) conciousness
and thus for every concious being (that is, every entity that is capable of
understanding something) everything is dependent on it.
Bruno Marchal wrote:
>
>> So there are numbers without there being
>> "dreaming"/experiencing first.
>
> I guess you meant "so there are no numbers ...".
> But this is not the theory I propose. I take Arithmetic as starting
> point. Dreaming/experiencing will be a property of numbers.
> It is really NUMBER => CONSCIOUSNESS => MATTER (=> HUMAN CONSCIOUSNESS
> => HUMAN NUMBER)
Right, I meant "so there are no numbers ...".
The problem for me is that you (in my mind) can't take arithmetics as a
starting point without taking you as a starting point. Of course you
understand that, but then it is confusing (or dishonest, but I absolutely
don't believe that of course;-)) to write "NUMBER => CONSCIOUSNESS =>
MATTER" because you can only mean "MY UNDOUBTABLE CONCIOUSNSS =>" (since
this is already clear on a meta-level apart from the theory it is, I think,
unecessary to write it) "NUMBERS => POINTER TO CONCIOUSNESS WITHIN THIS
THEORY => POINTER TO MATTER WITHIN THIS THEORY". You rather explain the
place of conciousness within your theory, not conciousness itself. Not
mentioning it is confusing IMO, even though it may be "obvious".
Bruno Marchal wrote:
>
>>
>> It seems to me that you call that "primitive", which relies already
>> on the
>> truths ("there are dreams/experiences") of which it gives emergence
>> to. Do
>> you see my problem with that?
>
> Not really. And it seems that your remark could apply to any theory.
> We have to agree on some starting point. The starting point I use is
> already used by almost all theories of nature and human.
Of course. But almost all theories of nature and human don't claim to
explain conciousness or matter. Even "fundamental" science like physics do
not (generally) claim to explain conciousness or matter in itself. And when
scientists claim to do, I am very critical, too.
Bruno Marchal wrote:
>
> You are
> confusing, I think, a statement like 2+3 = 5, and "I understand that
> 2+3 = 5". Those are very different. 2+3 = 5 points to what I understand
> about numbers and "I understand that 2+3 = 5" points to *that* I
> understand what it means that 2+3=5. This is indeed an important
> difference, but is it what you meant?
Bruno Marchal wrote:
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> But since you don't only assume mechanism, but
>>>> also conciousness (like all theories)
>>>
>>> Digitam mechanism (comp) assumes consciousness explicitly (cf the
>>> sense of the "yes doctor"). Most theories does not assume
>>> "consciousness". The word does not appear in the description of the
>>> theories.
>> I don't think it's necessary to write that you assume conciousness.
>> All
>> theories assume truth and still no one makes this implicit.
>
> By assumption, I mean the assumption present, concretely, in the
> theory. Not the meta-assumption needed to understand that humans can
> understand the theory.
OK, but still we should not forget that any theory is within a meta-level
that assumes certain things, and every theory inherits this assumption from
this meta-level (call it "reality" or even just "what I can't (really)
doubt").
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> and consensual reality (the dreams in
>>>> which the representations of numbers appear), I don't see how it
>>>> makes sense
>>>> to put numbers "before" conciousness and (perceived) reality.
>>>
>>> Well, it is a bit like "addition" comes before "being prime". You
>>> need
>>> addition in Robinson arithmetic to define what a prime number is.
>>> Then
>>> you need addition, and prime, before defining when a number represent
>>> a finite piece of computation. And you need that to eventually attach
>>> consciousness to computations. The "before" is logical, not temporal.
>> I need someone making sense of "addition in Robinson arithmetic"
>> before I
>> (logically) can refer to addition in Robinson arithmetic (or if you
>> want it
>> this way "I need the sense itself in 'addition in Robinson arithmetic'
>> before I can refer to addition in Robinson arithmetic").
>> It makes sense for me to say that we need numbers in order to link
>> conciousness to numbers, but that is already obvious. But you need
>> conciousness (the mysterious "senser" or "sensing") in order to make
>> sense
>> of anything, including numbers.
>
> Not in the theory. This would lead to an infinite regress.
OK, but your theory appears in your conciousness. Simply not stating this in
the theory doesn't remove the assumption from the theory, because the theory
is built upon the assumption (or rather knowledge) of conciousness.
Bruno Marchal wrote:
>
> Just open
> any book of math, you will not see any assumption on consciousness.
This would be rather ridiculous, since everybody "assumes" consciousness
either way... But nevertheless there is no sense in math without there being
sense in conciousness, so it is an implicit assumption.
Bruno Marchal wrote:
>
> This makes it possible to a machine to prove elementary addition to be
> correct. If we assume consciousness at that level, then we will not
> explain consciousness.
Does it make a difference whether we assume conciousness or not? After all
we already know conciousness to be true.
Bruno Marchal wrote:
>
>> Numbers just come before any *notion* of conciousness that is
>> reflected in
>> the numbers, but they can't come before conciousness itself.
>
> They can't come, in any sense. A number does not come. A number is
> even or odd, or little than an other number, etc.
I expressed myself badly. I meant "numbers are logically prior to etc...".
Bruno Marchal wrote:
>
> I use the number like a physicist or any scientist. You will not
> criticize Einstein's relativity, because he use numbers without
> mentioning consciousness. There is no reason to do this here.
But Einstein did not claim to explain conciousness.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>> But this is just insulting the machines, and nothing else.
>>>> My point is not to insult machines. A machine is identified by what
>>>> it does,
>>>> because feelings can not be uniquely linked with a machine.
>>>
>>> Why? We can, for all practical purpose, attach a mind to a machine.
>>> What we cannot do is to attach a machine to a mind, but "only" an
>>> infinity of machine to a mind.
>> How can we attach a mind to a machine? If you have the description
>> of a
>> machine, you know what it feels? You are a machine lover indeed ;).
>
>
> If I have a description of the machine, I still cannot *known* if it
> feels. But if the 3-description of the machine and its behavior, is
> enough similar to me, then I can believe, or guess, that it feelms
> something relatrively similar to me. This is what I do with *you*
> right now. Progress in neurophysiology could help to make me better
> guesses, but attributing consciousness to an other is always a sort of
> guess.
OK, did ignore your "for all practical purpose" somewhat. Sorry.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> Conciousness is already attached to an
>>>> infinity of machines and from our perspective we are at least
>>>> conciousness;
>>>> that which is always sure here and now. So every observer, just by
>>>> virtue of
>>>> observing *anything*, already feels the truth about an infinity of
>>>> machines.
>>>> But *are* we machines then? If we always are or "could be"
>>>> infinitely many
>>>> machines, if we always feel some truth about *every machine*, it is
>>>> not a
>>>> bit of an understatement to say we are a machine or even machines?
>>>
>>> You are right, and that is why sometimes I sum up the reversal by
>>> saying that
>>> 3-we being a 3-machine entails that the 1-we are not machine.
>>> There is a sense to say that first person, from the first person
>>> view,
>>> are not machine. This is already true for the third (and seventh and
>>> eigth) hypostases. the machine already tell us that they are not
>>> machine, from their point of view. But G*, the "theologian of the
>>> machine" knows that 1-we = 3-we. The machine cannot know that.
>> This is not clear for me. "3-we being a 3-machine entails that the 1-
>> we are
>> not machine.", but "1-we = 3-we"...? How could this possibly be?
>
> Yes, that is subtle. This is alas clear only at the AUDA level. We
> have that G* proves (1-we = 3-we), but G does not prove it. It means
> that the statement "(1-we = 3-we)" is true but not provable (like self-
> consistency). All those true but non provable statement belongs to the
> corona G* \ G. It is true (for the machine) but unprovable (by the
> machine). It is the sort of sentences that Gödel, Löb etc. have
> discovered.
OK, I still do not understand how this could be, but this is probably due
to:
Bruno Marchal wrote:
>
> My feeling is that you lack a bit of mathematical logic, which makes
> you confuse level of theories, and which makes you lack the important
> distinction between syntactical truth and semantical truth.
> Mathematical logic has such distinction as main subject matter,
> including results linking the two notions.
Your feeling is right indeed.
Bruno Marchal wrote:
>
>> It seems to
>> be possible only if it is wrong that 3-we is a machine, but assuming
>> it
>> leads to the right conclusion it is not a machine. But this would
>> mean COMP
>> is self-refuting.
>
> Not really. G does not prove 1 = 3. This does NOT mean that G proves
> NOT(1 = 3). You are confusing, I think: G does not prove p, with G
> proves NOT p. (~Bp is not equivalent with B~p)
If G does not prove NOT(1 = 3), why can we say that "3-we being a 3-machine
entails that the 1-we are not machine."?
Bruno Marchal wrote:
>
> I really suggest to you to buy the book by Mendelson on logic. It
> would provide you a big help.
Thanks for your tip. I probably won't read it anytime soon, though, because
I am tired of formalisms.;-)
I am more interested in what your words convey to someone interested in
fundamental questions, but not necessarily firm in logic. And I feel that
they may be a bit missleading then.
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