Re: Choice sequences, intuition, etc
- From: Keith Ramsay <kramsay@xxxxxxx>
- Date: Wed, 5 Nov 2008 19:04:59 -0800 (PST)
On Oct 29, 9:54 pm, Bill Taylor <w.tay...@xxxxxxxxxxxxxxxxxxxxx>
wrote:
|Keith Ramsay <kram...@xxxxxxx> wrote:
|>| and emphasizes that the essential point of intuitionism involves
|>| *knowledge* about what is the case, as opposed to the orthodox
|>| concern with merely what IS the case.
|
|> I'm not sure why it is that you feel so comfortable with
|> this sort of pronouncement, given how little you seem
|> willing to explain where it's coming from.
|
|HUH!? It was explained in the very section above your excerpt!
|I must assume you overlooked this.
You do not *need* to assume that.
|Here it is again.
|
|
|
|But I'm sure it's the case. Consider their interpretation of the
|disjunctive connective - it says "either there is a construction
|for p or there is one for q AND WE KNOW which it is".
|Almost every book has such a phrase. Similar for the existential
|quantifier: "there exists such a number and WE KNOW what it is,
|or can constructively FIND IT OUT".
|
|Knowledge is clearly involved right at the root.
|<<<<<
|
|Surely this is a full explanation of "where it's coming from"?
Your comment falls far short of demonstrating what the
"essential point of intuitionism involves", or with what
intuitionism and classical mathematics are "concerned". Is
it possible that you're just confused form with motivation
here? You exhibit a remark which mentions a concept, and
seem to conclude based on it that that concept is somehow
more essentially the point, that it is of more direct concern to
the person making that definition.
|> See, you're so confident, you don't even feel the need to
|> keep it as a tentative impression. No, you think you know,
|> clearly enough that failing to agree can well be described
|> as "failing to admit". But why? You just seem quite glib.
|
|This seems a very edgy remark, veering toward the purely
|personal, which is surely unwarranted by what I wrote,
|and a surprise coming from the usually diplomatic Ramsay.
Perhaps it just doesn't seem to you like you're making
guesses as you go, which is a little disconcerting to me.
I try to prod you away from being glib about it, and you
are so convinced, you reassert the glibness here.
I suppose it's pointless to feel frustration at this; it's
not as though I had any reason to expect things to be
different.
Try to imagine that you are someone who is deeply concerned
with the well-being of another. You speak of this person's
state of health, whether they are in comfort, whether they
have peace of mind, whether they are safe, whether they can
enjoy the satisfaction of exercising their faculties, and
so on at length. Now imagine that after having made this
kind of extended expression of concern, someone who hasn't
considered all this sort of issue tells you, "Well obviously
your concern, unlike mine, isn't so much with this person's
true well-being, but with the mere state of their body and
brain. I, on the other hand, care primarily about this person's
'true self'."
|But in any event, from a constructivist PoV, it's not so much
|an ADMISSION, as a CLAIM! So they have no reason to be
|upset. It's just that it's a claim requently invoked,
|(as I observed above), but rarely stated outright.
|Strange, no?
For some flavors of constructivist, which I'd say are ones
that I'd consider the most natural, the reason why they'd
refrain from making such a claim is that they wouldn't
consider it true.
I'm not sure what your reason was for disagreeing with my
earlier remarks about Bishop unless perhaps we were just
talking past each other. But as I was saying then, Bishop's
approach had an abiding interest in the content of
mathematical statements. Dare we call that a quest for the
truth of the matter? I would.
|> If you want to distinguish between "concern" for truth and
|> "concern" for knowledge, you need to say something about
|> how concern for what's "merely" true is expressed, aside
|> from attempting to gain knowledge about it.
|
|Well for one thing, Daryl has made an excellent response to this;
|but for another, I'm surprised to see such a question from such
|an expert.
I was stating this as a minimal requirement for
distinguishing concern for truths from a concern for
provable results, and we only sort of halfway made that
distinction.
|Surely the whole tenor of (orthodox) math logic
|since Godel, has been to show how math statements are themselves
|examples of *strictly defined* objects of mathematical study.
|So the use/mention distinction here is superbly illustrated by
|this object/procedure distinction of math statements. Here I am
|just expanding on Daryl's point; but why I should be required
|to explain all this, which we all know, is a puzzle.
|
|-- Baffled Bill
One reason why I wanted for more of an elaboration from
your end is that I'd like to confirm that rational
discourse is able to address such questions.
Presumably you've heard of Kuhn's _The Structure of
Scientific Revolutions_. I'm afraid I haven't read it, but
it's been the source of a lot of thinking in the philosophy
of science. He wrote about this infamous notion of the
"paradigm shift". Kuhn apparently thought in a much less
radical way than a lot of his admirers do, but a number of
them have taken paradigm shifts as being such radical
changes in point of view, that it's very nearly impossible
for a person thinking from the point of view of one
paradigm to discuss rationally with a person thinking from
the point of view of another paradigm. Of course there are
a lot of variations on this theme, too many for me to sum
up briefly, but I hope I've conveyed the gist of it.
This idea that communication between paradigms is nearly
impossible has always seemed to me to be a rather overly
pessimistic view of the prospects of rational discussion to
bridge the differences between people. On the other hand,
there are times when it seems as though something like this
kind of barrier may be present between people who've
adopted a "classical" frame of mind and people who've
adopted a "constructivist" frame of mind.
So, I'd really like to find that it is possible, somehow,
for an issue like what counts as concern for what actually
is the case, and what counts as concern for what can be
proven to be the case, to be understood in a way that
doesn't require you to have learned how to adopt a
constructivist frame of mind. But if the nature of the
issue seems totally obvious, I'm not sure what we are left
to say except that it seems that way to you because you are
in a "classical" frame of mind whereas for a person in a
"constructive" frame of mind it seems completely different.
Keith Ramsay
.
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