Bruno Marchal wrote:
> Le 17-août-06, à 00:14, complexitystudies a écrit :
> I recall it is just the belief that the
> propositions of elementary arithmetic are independent of you. Do you
> sincerley belief that 37 could be a non prime number? Or that the
> square root of 2 can equal to a ratio of two integers?
> Or that if you run a program fortran it could neither stop nor not
> stop? (When all the default assumption are on, to evacuate contingent
> stopping of a machine implemented in some deep story)?
As 1Z has so nicely put, existence implies causal interaction.
Numbers cannot causally interact, therefore they do not exist,
save as thoughts in our brains.
Of course I do not believe that 37 could be a non prime number,
simply because what it means to be "prime" has been exactly
defined in arithmetic. I just say that these are thought constructs
with no independent existence (independent of human brains, not of a
concrete human brain).
You might say, that 37 was prime even in the Jurassic, but I say:
nobody had invented arithmetic yet, so it's about as true as the
fact that James Bond was played by Sean Connery was in the Jurassic.
I define a system:
1 + 1 = 2
2 + 1 = 1
1 + 2 = 1
That's all. Okay, it doesn't describe much and probably isn't very
useful, but other than that it is not inferior to peano arithmetic.
Does my system now exist mind-independtly for all eternity?
> I have not yet seen a book on human brain which does not presuppose the
> understanding of the natural numbers.
Of course, because it is a useful way to describe reality. But in our
brains, not numbers operate, but chemicals.
> Numbers are not symbol. Symbols can be used to talk about numbers, but
> they should not be confused with numbers.
You are right there of course. Symbols are only referents. What counts
is meaning. What I meant to say is that the meanings we assign to number
symbols exist only in our minds. Indeed, meaning _is_ only created by
interactions between an agent and an environment. With both of these,
no meaning. Indeed, in an mind-and-matter independent (=non existing
)universe, arithmetic would be about as meaningless as it gets.
> The notion of "same number" seems to have occur much before we
> discovered counting. Farmers have most probably learn to compare the
> size of the herds of sheep without counting, just by associating each
> sheep from one herd to the another. But this as nothing to do with the
> fact that sheeps were "countable" before humans learn to count it.
> Humans and brains learn to count countable things because they are
Not exactly. Animals and babies can distinguish up to 2-3 objects
(innate arithmetic, subitizing). The experiments with which this has
been ascertained are both fascinating and entertaining (google is your
This ability has an evolutionary advantage: it is necessary for higher
organisms to distinguish more or less abundant food sources or numbers
of predators. But this meaning this "countability", arises out of the
physical world, and is not independent of it.
> I think you are confusing the subject or object of math, and the human
> mathematical theories, which are just lantern putting a tiny light on
> the subject.
Indeed I am not. I am just saying that there is no independent subject
of math outside of human brains. Mathematics is the study of rules we
make up (axioms) and what follows of them (theorems).
If we pick our axioms wisely, we can even model some aspects of the
real, physical world with it.
> If numbers and their math was really invented, why should
> mathematicians hide some results, like Pythagoras with the
> irrationality of the square root of two, ... As David Deutsch says:
> math kicks back.
That is very easy: the Pythagoreans assumed axioms, and thought they
knew what would follow from them. Then, to their dismay, they found
out that also somewhat else followed from the axioms than they had
ideally envisioned, something that displeased their aesthetic sense.
Only human factors involved here,
no independent existence of math. It just shows how limited our thought
is, and that we do not even anticipate theorems that follow from our
axioms when they are rather simple.
>> Also, concepts like infinity are most definitely not universal
>> concepts "out there", but products of our mind.
> I doubt any mind could ever produce infinity.
But indeed, _only_ minds produce them, because, as you say, infinity
is a concept, and concepts exist only in minds.
In reality, there is no such thing as infinity. Even if space
would expand infinitely, this "infinity" would not exist as a thing
(except in the trivial *lol* sense as the universe exists), but would
be a concept for us humans to talk about it.
Concepts need not be precisely understood as to be concepts.
For example, consciousness is definitely not understood, but talked
about a lot.
How does the human mind create the concept of infinity:
Lakoff and Nunez have a nice metaphor:
Humans see repeated motion in nature, which seemingly does not end.
For instance, a vulture may appear in the sky, fly over us, and
disappear in the opposite direction. Combined with the concept
of iteration (if I can do something once, I can do it again),
this "motion without end" + "iteration" lead to the concept of
infinity. In reality, of course, the vulture has to land sometime,
and we also cannot indefinitely (energy limitations), so infinity
is a mental concept and not a physical existing thing.
I let you
> discover that, and feel free to ask questions if you have a problem
> with UDA.
Thank you, I will.
> It is really the point of the UDA. It shows that computationalism (the
> idea that I am a digitalizable machine) is incompatible with "weak
> materialism" (the idea that there is a primary stuff or matter or
> aristotelian substances).
Ok, I'll watch for this in UDA.
> But until now, comp leads only to weirdness, not contradiction. And
> then that weirdness seems to explain the quantum weirdness ...
> Intuitively and qualitatively (already by UDA), and then technically
> through the interview of some universal turing machine.
But wouldn't this universal turing machine need to be composed of
matter, and then the whole caboodle starts from the beginning?
Occam's Razor recommends materialism.
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