Re: Choice sequence lessons.

Dec 17, 5:05 am, Herman Jurjus <hjur...@xxxxxxxxx> wrote:

OK, I'm still behind on the "three-languages" posting,
(it turns out I'm busier than I expected to be right now!), so this
response is somewhat out of order, but hey! - this is Usenet.

But before I go on, I would like once again, to re-state my
standard RANT here, which Keith Ramsay, Darryl McCullough,
and others have chided me for, but which I stick to anyway.

Oh, i will not chide you for that.

Good-oh! It's nice to find someone from the dark side who
is sympathetic to this cause!

Some of my best friends are of the same opinions.

But would you want your daughter to marry one?
.....................

This [ANY rather than ALL] is exactly the point, indeed.

Excellent. It seems we are in full agreement on one thing, then.

i don't understand ... that you didn't pick that up from my story.

Stupidity, Herman, stupidity! Sometimes I wonder how I ever
managed to learn any math at all! And perhaps the ingrainedness
of orthodox (existential) thinking runs far deeper than we both
might have suspected. Maybe this is a point that proselytisers
such as yourself have still not fully taken on board?
It seems there is always massive trouble with this ingrainedness.
That's why I feel you(all) must take stronger steps to phrase
things in an existentially acceptable way; (while OC not warping
the essential nature of your content!) A heavy task.

Ok; apparently i have to work on my writing skills.

Rather, your empathetic skills.

About point b): yup; you got it - that's it.

Good-oh.

(I could expound on it a bit further, but that will perhaps
muddy the water too much.)

I hope my response to your followup on this was acceptable?

About point a), i'm not sure that i understand you.

This all comes from my trying to see things in an "existential"
way. I see it my way, you yours, but we can still come to
an agreement, I'm sure, even though we use different language.

The existential (orthodox) view is a very "static" one, and
the intuitionist view is a very "dynamic" one. The very idea
of choice sequences is one of dynamic change, volatility, as
you put it earlier. I remain hopeful that it *can* be adequately
expressed in existential language. One of my math-phil friends
once observed that although he was extremely sympathetic to
constructivist views, he HAD to part company with them when
they insisted on an essential *temporality* in math. That things
could be true now when they weren't true 200 years ago.
He, and I, and most orthodox mathies, find this idea extremely
repulsive, philosophically speaking, even anti-mathematical;
but there is no reason (I hope) that this opposition in math
philosophy should lead to a failure of "operational" understanding.
That's why I'm persisting with trying to find out what choice
sequences "really are", when the temporality of existence is
spirited away, as it has been with traditional computability.

The notion of choice sequence is too subtle to be
represented by a mere set of elements.

Very much so! The dynamic aspect is being emphasized.
Your task is to expound it, and mine is to re-cast your
exposition into temporality-free language.

That is why I spoke of "sequence SYSTEMS". I envisage these
as being like black boxes, *which have a pre-ordained aspect*,
(as I recall maybe even you agreed to - repeating the same
operations from the start should give the same results);
but black boxes which MAY vary according to what input is
fed into them, as per your game semantics. This is very
similar to the standard idea of a function, where the same
input must give the same output every time, even though
the innards of the box are left unrestricted - maybe a formula,
maybe a machine, maybe a look-up table. But whereas standard
math stops there, intuitionist math goes on to extend the idea
to allowing the inputs to depend on the quantifiers in some way.
I don't see any irresolvable conflict here, do you?

That said, for me, the notion of a choice sequence is
as directly intuitive and clear as the intuitive picture
of the sequence of natural numbers 0, 1, 2, ...

Certainly not to me, yet. And I doubt it will ever be clear
in the way it is to you. But there's no reson that it can't
become clear in an existential way, a black-box way, I hope.
So I must continue to beg your indulgence to let me keep talking
in existential terms, even if you think I'm missing the point -
I simply *cannot* bring myself to think of math in dynamic terms.
Other than modelling dynamism by static concepts, OC, as is
the case in the calculus of motion and in computability.

the latter paragraph shows a level of 'disagreement of philosophy'

Indeed so, but as I said, it needn't be fatal.

we would probably also have if we both spoke about something
uncontroversial like 1 + 1 = 2.

If there *were* one (which I doubt), it would be more immediately
resolvable. Linguistic preferences seldom make any operational
differences. The minimal-constructivist has long since found
this to be the case.

So bye for now, till I've read the 3-language post again.

-- Beetling-off Bill
.

Relevant Pages

  • Re: "Shared" procedure division code
    ... >>>The response could vary here, depending on your answer to the question. ... structures readily available to render its use unnecessary - then ... question is treated as an ALTER and should be structured out of existence. ... 'What are the suppositions and logic you employed in reaching this ...
    (comp.lang.cobol)
  • Re: Landis Hearing Closed
    ... My initial response was regarding your suggesting that organizations ... COUNTRY and decided that the evidence wasn't complete enough to warrant any ... UCI should be up on criminal charges and not just sued out of existence. ... Faberge eggs are elegant but I prefer Faberge bacon. ...
    (rec.bicycles.racing)
  • Re: Security Guard - God Guided Me And Protected Me
    ... answer than science or an answer because science cannot answer. ... We were kind of piling on John there for awhile so it is probably a breath of fresh air to find out that on other topics, you, Rita and I would probably disagree and John might possibly agree with one of us. ... but a response to the question of existence when framed ...
    (soc.retirement)
  • Re: Just how does magic work?
    ... Because of the seeming existence of constances like pi I ... >> things that we've yet to discover I guess there ... But I think it can be argued that math is created. ...
    (alt.fan.harry-potter)
  • Re: Fractional Transforms
    ... X = Y. Of course this doesn't quite rule out the existence ... "Understanding Godel isn't about following his formal proof. ... Thanks for the response - from both you and Robert. ...
    (sci.math)
Quantcast