Re: A quote (and question) about intuitionism


On Nov 13, 8:23 am, Angus Rodgers <twir...@xxxxxxxxxxx> wrote:
|On Mon, 12 Nov 2007 23:35:13 -0800, Keith Ramsay
|<kram...@xxxxxxx> wrote:
|>One attempt as explaining the meaning of a sentence, for
|>example, is to say that knowing the meaning is the same as
|>knowing the set of conditions under which it would be true.
|>(I think many philosophers would dispute such a definition
|>in some way, but it is some approximation to the way that
|>"meaning" is understood in lots of philosophies.) In
|>constructivism, it's closer to say that knowing the meaning
|>of a sentence is knowing the conditions under which it can
|>be considered known. (Probably many constructivists would
|>dispute this definition in some way, but it's similarly
|>some approximation to the way "meaning" is understood by
|>them.)
|
|Known by whom?

It seems to me that really the ball is still in your
court, or at least it should be, as long as you are unable
to explain any better to me why I need to specify one
individual to serve as "the" subject, than to keep asking
who it is.

The point is, we can talk coherently about deeds done by
you, and deeds done by me, as (in some cases being) "doing
the same thing". There may be a sense in which they are
not _exactly_ the same thing, but it seems to me that
meanings of statements differ between people in just the
same way, and to the same extent. I don't see any way
around there being _some_ difference between "what a
statement means to me" and "what it means to you".

Consider the claim that there exists an even integer n>2
which is not the sum of two primes. According to a
constructivist, the meaning of this is related to having
an algorithm that would compute such an integer. To have
such an algorithm is what it takes to know that the claim
is true.

If you now ask, "known by whom?", it's as if you thought
that the conditions required for *your* having such an
algorithm and for *my* having such an algorithm were not
essentially the same thing. At this point what am I supposed
to do, except shrug in bafflement?

If you have a statement where, for some reason, the act of
your verifying it and the act of my verifying it are somehow
not comparable, then to that extent the statement is
subjective. Perhaps the claim that "Renoir's 'Boating Party'
is a work of genius" is subjective in this way.

In mathematics, we deal (almost?) exclusively with claims
which are intentionally kept objective. From a constructivist
point of view, we allow you to delegate any aspect of the
verification of a truth to someone else. I know that Fermat's
Last Theorem is true, not because I know the entire proof,
but because I know others have (collectively, at least,
though some individually in this case) known a proof.

|>Think about the claim that
|
|> (*) "there are statements that are true right now that
|> are not currently known to be true".
|
|>What does it mean? If you look at it from a constructivist
|>point of view, you understand its meaning as closely tied to
|>the kind of experience that (in some sense) justifies saying
|>it.
|
|Whose experience?

Anybody's. Whoever is saying it.

|I don't get the impression that you're defending solipsism!
|So, if you believe in the existence of conscious minds other
|than your own, aren't you already a realist? If so, what is
|the point of not also being realistic about other entities?

I'm sorry, but I just don't see that this holds water.
Why does belief in conscious minds other than my own
constitute "realism", in the sense that constructivism is
not "realism"?

|If you're going to argue for a theory which take subjectivity
|seriously, surely you are going to have to pay very serious
|attention to precisely who the "subject" is. How can you do
|that subjectively?

Thinking that a constructivist must somehow pick a subject
to be "the" subject seems a serious misconception to me.

Keith Ramsay
.

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