[lit-ideas] elliptic curves over the field of rational numbers are related to modular forms
- From: Adriano Palma <Palma@xxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Sun, 19 May 2013 08:53:41 +0000
perhaps you don't get it. I f what your friend, this mysterious wiki calls
conjecture if FLT it is not a conjecture.
it is a theorem,
I quote for your convenience a simple statement with the historical appendix of
what has been done.
\beg quote
the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture
and several related names) states that elliptic curves over the field of
rational numbers are related to modular forms. Andrew Wiles proved the
modularity theorem for semistable elliptic curves, which was enough to imply
Fermat's last theorem, and Christophe Breuil, Brian Conrad, Fred Diamond, and
Richard Taylor extended his techniques to prove the full modularity theorem in
2001.
\end quote
it is perhaps a good idea 12 years after the facts, to get said facts straight
rather than insisting in pouring idiocies on the readers.
________________________________________
From: lit-ideas-bounce@xxxxxxxxxxxxx [lit-ideas-bounce@xxxxxxxxxxxxx] on behalf
of Jlsperanza@xxxxxxx [Jlsperanza@xxxxxxx]
Sent: 19 May 2013 10:24
To: lit-ideas@xxxxxxxxxxxxx
Subject: [lit-ideas] Grice's Implicature (Was: Fermat's Conjecture)
We are discussing levels of approaching something as Fermat's conjecture (I
follow Wiki: "The expression 'conjecture' is sometimes used here"). One
thing is the particular experience involved in this particular person, called
Fermat. Another thing is the abstraction we may get from it: _what_ Fermat
conjectured. Similarly, we can follow Grice in distinguishing
implicature
implicatum
The implicature is the actual implying on the part of an utterer. The
'implicatum' is the content of the implicature, and which allows for this or
that abstraction.
---
--- Was Grice's Paradigm.
D. McEvoy was referring to a passage -- in Wikipedia -- on "downward
causation" that uses the term 'paradigm':
In a message dated 5/16/2013 8:51:03 A.M. UTC-02,
donalmcevoyuk@xxxxxxxxxxx writes:
"First, as to the comments in the other thread that crucially claim:-
"This is the current paradigm.
"Now, the opposite view is that everything starts with consciousness."
McEvoy comments: "The remarks on the current paradigm seem correct; the
key point being that, if we think a materialist or physicalist conception
encompasses reality, then it very hard to give human rationality or morality
any genuine status [as opposed to being epiphenomena, and illusory in terms
of their affects] - for it is very hard to see how human rationality or
morality can be explained in materialist or physicalist terms - they can only
be explained away. Popper is opposed to this "current paradigm" and among
the points he makes against it is that, as a programme for scientific
research, "materialism" has been overtaken by its own success ["Materialism
transcends itself"] as what the "materialist" programme in science has revealed
is that the explanation for matter takes us to forces and dark matter that
refute the original materialist idea that everything can explained in terms
of matter; but he also wants to defend against materialism or physicalism
as all-emcompassing of reality by bringing out that knowledge has World 3
and not mere World 1 status. Traditionally the opposite of materialism was
some form of idealism, and so we can understand it being claimed that, "Now,
the opposite view is that everything starts with consciousness." But this
is not the only alternative to materialism, as Popper shows: we may say
everything began with only a World 1 - and a World 1 that lacked many of the
chemical and biological levels that later emerged within it. But not only
has biological life emerged from what began as a universe devoid of
biological life, but what has emerged from World 1 are a World 2 and then a
World 3.
So we can get start from World 1 but, by way of emergence, get to World 2
and then to World 3."
Interesting. It is good to focus on 'paradigm', since it's a word that
should not ALWAYS be used. We of course follow Kuhn. And I'm glad to see the
phrase, "programme for scientific research" being used above, since this
Lakatosian expression is what we need. For 'paradigm' and 'programme for
scientific research' interact and they have to deal with serious issues as to
what counts as genuine evidence. Etc.
----- In this regard, perhaps 'consciousness' and 'paradigm' are used
rather liberally in the original quote, which was meant to illustrate the use of
'downward' versus 'upward' causation, anyway.
---- As for the Popperian view -- "the Three Poppers", I'm inclined to call
all this -- one may wonder if the 'rational reconstruction' -- the 'myth'
-- of a succession of World 1 --> World 1 + World 2 --> World 1 + World 2 +
World 3 -- is meant to be 'historical' -- or 'diachronical.
Similarly, Grice had argued that 'meaning' originates in pre-rational,
natural states. But he seems to see this as a 'rational reconstruction',
without a necessarily historic base (which would render his programme "not
philosophical").
----- As for 'consciousness', this was interestingly, the topic of R.
Paul's post (May 15):
"Do you mean that experience, or 'experience,' itself is (somehow)
irreducible (which makes no sense) to something else (such as numbers?)
or are you talking about qualia _as_ the irreducible (again, to what?)
elements, or features _of_ experience, e.g. the color or a certain
tulip, the aroma of coffee, the sound produced by striking a single key
of an out of tune piano?
Some philosophers, but not all, do talk about qualia: C. I. Lewis
(1929), who introduced the term, in its modern sense into philosophy,
and David Chalmers, who uses the notion (although he prefers other names
for it), in his discussions of the 'hard' and the 'easy' problems of
consciousness.
Chalmers original paper on the problem of consciousness is online at
<http://consc.net/papers/facing.html>
This site has links to twenty-six responses to Chalmers.
Do I change the subject? Then I change the subject. It would seem that
talking about 'experience' in some broad, elusive sense ('It was an
experience I'll never forget,' 'Snails don't experience existential
dread,' 'Those who lack the ability to see green, experience the world
in a different way from those who do have the ability')."
Well, apparently Popper is no big follower of 'consciousness' since he
makes the big point (as stressed by McEvoy) that UNconscious processes (such as
"I am sleeping now" -- cfr. Malcom, "I am dreaming now") are just as
constitutive of World 2 (as he calls this realm of irreducible stuff) as
Descartes's Cogito is ("I am thinking of a white Christmas").
R. Paul:
"Do you mean that experience, or 'experience,' itself is (somehow)
irreducible (which makes no sense) to something else (such as numbers?)
or are you talking about qualia _as_ the irreducible (again, to what?)
elements, or features _of_ experience, e.g. the color or a certain
tulip, the aroma of coffee, the sound produced by striking a single key
of an out of tune piano?"
I don't think Popper does use 'qualia'. But it seems that some experiences
are so particular that it would does not make sense to have abstractions
from them onto the world of Objectivated Spirit (as Hegel grandiosely calls
this), which is Popper's World 3. But R. Paul is apt in noticing how tricky
the grammar of 'reduce' can be -- note that to complicate things Popper
uses 'downward' and 'upward' causation and allows for all sorts of
'directionalities' as involved in stuff. So that an abstraction can be a
content of a
particular qualia -- and a particular qualia may get objective status.
R. Paul:
Some philosophers, but not all, do talk about qualia: C. I. Lewis
(1929), who introduced the term, in its modern sense into philosophy,
and David Chalmers, who uses the notion (although he prefers other names
for it), in his discussions of the 'hard' and the 'easy' problems of
consciousness.
Chalmers original paper on the problem of consciousness is online at
<http://consc.net/papers/facing.html>
This site has links to twenty-six responses to Chalmers.
Do I change the subject? Then I change the subject. It would seem that
talking about 'experience' in some broad, elusive sense ('It was an
experience I'll never forget,' 'Snails don't experience existential
dread,' 'Those who lack the ability to see green, experience the world
in a different way from those who do have the ability')."
Well, as I understand things, McEvoy related the use of 'all starts with
consciousness' (as being the alleged current paradigm) as a threat to
materialism. And McEvoy explains how Popper's view is NOT materialistic. One of
McEvoy's points: Matter cannot be explained in terms of matter, and Popper's
dualism (which I prefer to call 'trialism').
But it does seem apt to keep the adjective 'conscious' to hand when dealing
with experience, since the phrase 'unconscious experience' sounds slightly
otiose to me (cfr. Popper, "Fermat's conjecture, qua particular experience
in the consciousness of one French person called Fermat, is one thing:
_what_ he conjectured is yet another" -- cfr. "Grice's implicature" -- what
Grice implicated -- the implicatum -- and content of the implicature).
And so on.
Cheers,
Speranza
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