On 10/25/2018 9:18 AM, Bruno Marchal wrote:
On 24 Oct 2018, at 03:22, Brent Meeker <[email protected]> wrote:
On 10/23/2018 9:23 AM, Bruno Marchal wrote:
On 23 Oct 2018, at 04:30, Brent Meeker <[email protected]> wrote:
On 10/22/2018 6:54 AM, Bruno Marchal wrote:
The mathematical reality has noting to do with languages, except that languages
are needed if machine/people want to share the results of their exploration.
So how do you prove theorems without a language?
Of course, proving a theorem requires a theory, and a language. I was saying
(see the quote) that the *arithmetical reality* does not require a language.
The arithmetical reality does not require a language more than dinosaurs needed
the word “dinosaur” to exist. The prime character of 17 does not need a
mathematician to assert it, or to think about.
To prove a theorem requires a theory, which requires a language. We can only
ope that our theory is in relation with truth, but the truth of 17 is prime,
assuming it true, does not need a proof to be true. A proof is neither
necessary, nor sufficient. The arithmetical reality is independent of the
big-bang. It is more plausible than an event like the big-bang requires some
part of the arithmetical reality.
But you are basing our shared reality in what is provable,
Absolutely not. I mean no more than any scientist, and I make clear my
hypotheses.theory, without have ever claim any truth, like any sane scientist
do. I am more exorcist: I base our shared reality on a mix of theory and
experiences.
A theory is better identify with a being or a set of belief. I say that a
machine believes A if the machine asserts A. I limit myself to what
self-referentially correct machine can say, and not say, ...
But don't you identify "machine believes A" with "machine can prove A"?
which is therefore dependent on having language. Right?
The reality itself does not depends on the language, even if the language will
be itself a part of the reality.
Not the reality, but the proof depends on language.
Brent
We need lanaguage to communicate about reality, including languages. We are
ourselves words, written in the biochemical languages, and particles are words
of some wort too. Now, the more a theory is lade independent of the language,
or the even the theories,, the more is has a chance to be deep, and to help
avoiding geographical prejudice on what is real or not.
Bruno
Brent
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