Re: Orthography supporting sound changes?

On 12 Jan 2006 12:07:04 -0800, Seán O'Leathlóbhair
<jwlawler@xxxxxxxxx> wrote in
<news:1137096424.678559.206940@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
in sci.lang:

> Brian M. Scott wrote:

>> On 12 Jan 2006 04:40:54 -0800, Seán O'Leathlóbhair
>> <jwlawler@xxxxxxxxx> wrote in
>> <news:1137069654.532020.152110@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
>> in sci.lang:

>>> Brian M. Scott wrote:

>>>> On 12 Jan 2006 02:25:27 -0800, Seán O'Leathlóbhair
>>>> <jwlawler@xxxxxxxxx> wrote in
>>>> <news:1137061526.982634.167620@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
>>>> in sci.lang:

>> [...]

>>>>> Also, it is hard to draw a clear line between maths and
>>>>> physics.

>>>> Actually, it isn't. The separation is very clear, despite
>>>> the fact that much mathematics was inspired by physical
>>>> questions and, conversely, much mathematics is used in
>>>> physics. The existence of non-Euclidean geometries, for
>>>> instance, is a purely mathematical result; that some of them
>>>> are useful in describing the spacetime in which we exist is
>>>> a matter for physicists.

>>> Non-Euclidean geometries have as much chance of being
>>> "real" as Euclidean ones. They are both, at times,
>>> useful models of real things. How real either is, is a
>>> difficult philosophical question.

>> But I'm not talking about 'real'. They exist in the usual
>> mathematical sense, independent of any possible application
>> as models of reality.

> So why did you introduce non-Euclidean geometry? I
> presumed that as a contrast with "real" Euclidean
> geometry.

Of course not! How can you possibly reconcile such a
presumption with 'THAT SOME OF THEM ARE USEFUL IN DESCRIBING
THE SPACETIME IN WHICH WE EXIST is a matter for physicists'
[emphasis added]. The whole point is that their existence
in the mathematical sense has nothing to do with the
physical world or with physics, even though they happen to
be of some value in describing the physical world. The
separation between non-Euclidean geometries as mathematical
constructs and non-Euclidean geometries as parts of physical
theories is perfectly clear.

> If it is just an example of maths that was not inspired by
> physics then it has plenty of company.

It was not so intended. It was *obviously* not so intended.
What inspired the study of non-Euclidean obviously has
nothing to do with the point that I was making.

[...]

>>>>> Physics is surely the archetypal science. How about
>>>>> statements such as "You cannot travel faster than light"?

>>>>> OK, a physicist's "cannot happen" is a bit weaker than a
>>>>> mathematician's but it is still a strong statement.

>>>> It isn't the same kind of statement at all. The
>>>> mathematician's 'cannot happen' refers to a logical
>>>> impossibility within a well-defined abstract system. The
>>>> physicist's 'cannot happen' by no means has the force of a
>>>> logical impossibility.

>>> The physicist's statement is nonetheless a strong
>>> statement and if a physicist said: "X cannot happen . .
>>> .", I would expect him to be prepared to justify his
>>> assertion. That is what I see as common between the
>>> mathematician's "cannot happen" and the physicist's
>>> "cannot happen".

>> Strength is not the point. The point is that the two have
>> completely different logical status. And the expectation
>> that the speaker be prepared to justify the claim seems to
>> me wholly irrelevant.

> The strength is my point. The only reason I introduced
> this topic was to explain that in some disciplines,
> justification is likely to be expected for statements
> such as "cannot happen" and "does not happen".

No, you introduced *mathematics* as an example of a
*science* whose practitioners 'frequently study why things
don't happen'. The entire discussion since then has
concerned the error in classifying mathematics as a science
in this context, which in turn -- as Colin said at the start
-- stems from the qualitative difference between a
mathematician's 'does not occur' and a scientist's.

[...]

>>> Of course, the justification is likely to take a different
>>> form but the justification of "cannot exceed the speed of
>>> light" is more mathematical than experimental.

>> 'In a universe in which conditions C_1, ..., C_n are true,
>> one cannot exceed the speed of light' can probably be cast
>> as a mathematical result; 'one cannot exceed the speed of
>> light' is in no sense a mathematical result.

> So why do physicists say that we cannot exceed the speed
> of light? Have they tested it in fast spaceships? I see
> it that observations suggested a model (special
> relativity), mathematical analysis of the model made many
> predictions including the speed limit, some of these
> predictions were tested and the results were in good
> concordance with the theory, hence the belief in the
> other not yet tested predictions.

That is entirely consistent with what I just said. IN THE
MODEL you can't exceed the speed of light; that's a
mathematical result. The claim that you cannot exceed the
speed of light IN THE REAL WORLD is obviously NOT a
mathematical result: it's a claim that the model is an
accurate representation of the real world in this respect.

[...]

> Was Newton a mathematician or a physicist? He was both.
> Was his calculus maths or physics? It is taught in maths
> today but where would modern physics be without it?

So what? That obviously has nothing to do with the
essential difference between the mathematician's 'cannot
occur' and the scientist's.

[...]

Brian
.

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