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From: tonyb on 16 Mar 2010 11:41
> > I'll ask the damn question again...if you claim that math is a language,
> > what are the verbs?
>
> I will answer the damn question again: not verbs, but predicates.
> Another, more general, name for mathematics, is, guess what, logic:

I don't think a language has to have any verbs in order to be
considered a language in the first place.

My understanding of Wittgenstein (??) is that we use language to point
to pre-existing learnt concepts; these are learnt through 'language
games' played as a child (see below); that concepts are essentially
abstracted experiences e.g. "give dad the blue block" is a compound of
many integrated language-games involving pointing at 'dad', 'block'
and holding one various lumps of wood in your hand etc... Language
then, is just like pointing at abstracted memories using symbols
(words and other things) and our shared experience allows us to convey
meaning.

If you hold with this definition of a language and then think about
how we learnt to count as children, you have the basis of mathematics.
I'm no an expert here (any ideas rabid_fan?) but I think Russell then
takes this 'definition' of counting as the starting point of formal
logic.

Then think about your early experiences of velocity, perhaps sitting
on a river-bank watching the water. You may have even spotted a guy in
a white-wig sitting near you, muttering something about fluxions. Good
language for rivers, that one.

(From Wikipedia: Wittgensten:)
The classic example of a language-game is the so-called "builder's
language" introduced in §2 of the Philosophical Investigations:
The language is meant to serve for communication between a builder A
and an assistant B. A is building with building-stones: there are
blocks, pillars, slabs and beams. B has to pass the stones, in the
order in which A needs them. For this purpose they use a language
consisting of the words "block", "pillar" "slab", "beam". A calls them
out; — B brings the stone which he has learnt to bring at such-and-
such a call.
Later "this" and "there" are added (with functions analogous to the
function these words have in natural language), and "a, b, c, d" as
numerals. An example of its use: builder A says "d — slab — there" and
points, and builder B counts four slabs, "a, b, c, d..." and moves
them to the place pointed to by A. The builder's language is an
activity into which is woven something we would recognize as language,
but in a simpler form. This language-game resembles the simple forms
of language taught to children, and Wittgenstein asks that we conceive
of it as "a complete primitive language" for a tribe of builders.
From: rabid_fan on 16 Mar 2010 13:46
On Tue, 16 Mar 2010 08:41:56 -0700, tonyb wrote:

>
> My understanding of Wittgenstein

Wittgenstein... wasn't he the protege of Russell, or vice versa?
In any case, they both typify the pristine Edwardian style which
attempts to reduce human intelligence into purely logical elements.

The human being is an animal, lest we forget, and the roots
of our intelligence are the roots of our biological nervous
system which is based in the crude yet absolutely fundamental
purpose of motility.

Indeed, simple gestures, or movements of various parts of the
body, can easily constitute a highly effective and universal
type of language.

Psychoanalysts were perhaps the first to introduce this view
of human thinking, and its associated language structures.

To be brief, environmental stimuli (both internal and external)
induce motor responses. In the human animal, these motor responses
can be suspended to a large extent by an inter-mediation structure
that we often vaguely refer to as the "mind." According to Freud,
the foremost contributor to psychoanalysis: "Thinking is trial-acting,
with the smallest quantities of cathexis [instinctual energy]."

But the elements of thought, according to Freud, are the memory
traces of word-images, originally acoustic, or word-remainders.
These may initially be considered similar to the "pre-existing learnt
concepts" that you mention, but the context of psychoanalysis is
vastly different from the ordered and logical psychic mileau which
is implied by your description and consequently they must be given
a different interpretation and significance.

How does mathematics (and also music) fit into the psychoanalytic
view? Suffice it to say that word-remainders are not the only grist
for the "trial-acting" mill.


(??) is that we use language to point
> to pre-existing learnt concepts; these are learnt through 'language
> games' played as a child (see below); that concepts are essentially
> abstracted experiences e.g. "give dad the blue block" is a compound of
> many integrated language-games involving pointing at 'dad', 'block' and
> holding one various lumps of wood in your hand etc... Language then, is
> just like pointing at abstracted memories using symbols (words and other
> things) and our shared experience allows us to convey meaning.
>
>
> Then think about your early experiences of velocity, perhaps sitting on
> a river-bank watching the water. You may have even spotted a guy in a
> white-wig sitting near you, muttering something about fluxions. Good
> language for rivers, that one.
>

Mathematics does not possess a single quality or characteristic.
The idea of a fluxion only applies to certain kinds of analysis.
The concept of a group, first formulated in the mid-nineteenth
century, is another type of basic entity in mathematics, and
quite distinct from the fluxion, or differential.

From: tonyb on 16 Mar 2010 15:14
On 16 Mar, 17:46, rabid_fan <r...(a)righthere.net> wrote:
> On Tue, 16 Mar 2010 08:41:56 -0700, tonyb wrote:
>
> > My understanding of Wittgenstein
>
> Wittgenstein... wasn't he the protege of Russell, or vice versa?
> In any case, they both typify the pristine Edwardian style which
> attempts to reduce human intelligence into purely logical elements.

I think your characterization of Russell as a modernist is correct.
But for Wittgenstein, I think you couldn't be more wrong; he really
marks the end of modernism and is seen (by some) as almost anti-
rationalist. Amongst other things, I think he is discussing the
impossibility of definition because of what a language really is, at
heart - he actually believed he had demonstrated the absolute end of
(the modernist project) of philosophy, certainly of philosophical
analysis! But I mentioned him mainly because the original thread was
about the role of mathematics as a language in stating certainty or
probability. In my interpretation, he makes a pretty clear description
(not analysis) of what a language is, hence the reference.

> The human being is an animal, lest we forget, and the roots
> of our intelligence are the roots of our biological nervous
> system which is based in the crude yet absolutely fundamental
> purpose of motility.
>
> Indeed, simple gestures, or movements of various parts of the
> body, can easily constitute a highly effective and universal
> type of language.

Yep. I completely agree.

> Psychoanalysts were perhaps the first to introduce this view
> of human thinking, and its associated language structures.

snip

> But the elements of thought, according to Freud, are the memory
> traces of word-images, originally acoustic, or word-remainders.
> These may initially be considered similar to the "pre-existing learnt
> concepts" that you mention, but the context of psychoanalysis is
> vastly different from the ordered and logical psychic mileau which
> is implied by your description and consequently they must be given
> a different interpretation and significance.

I don't agree. All these clever people are talking about the same
reality. W and F tell us what a language is; most people on this
thread agree that mathematics is a language. Why? W. tells us how we
actually do language - we learn meaning from context, through a series
of games (and yes, quite right - the motor system plays an important
part here.) I think Russell then uses a similar idea (not directly
taken from W.) to define counting - he describes the 'language
game' (in W's terms) that gives numerals their meaning - numbers are
the process of literally pointing at things with your finger and
counting, 1, 2, 3 - he analyses this language game extremely
carefully. From a series of analysed games he then attempts to form a
foundation for logic.

> How does mathematics (and also music) fit into the psychoanalytic
> view?  Suffice it to say that word-remainders are not the only grist
> for the "trial-acting" mill.

(Assuming your not being rhetorical) I think that Freud and W. are
both giving us a (perhaps similar) account of what language is, more
specifically how we attribute meaning. The relationship is that
mathematics and music both carry signification - they evoke meaning. I
have a feeling I'm not understanding the your point/question here

> (??) is that we use language to point
>
> > to pre-existing learnt concepts; these are learnt through 'language
> > games' played as a child (see below); that concepts are essentially
> > abstracted experiences e.g. "give dad the blue block" is a compound of
> > many integrated language-games involving pointing at 'dad', 'block' and
> > holding one various lumps of wood in your hand etc... Language then, is
> > just like pointing at abstracted memories using symbols (words and other
> > things) and our shared experience allows us to convey meaning.
>
> > Then think about your early experiences of velocity, perhaps sitting on
> > a river-bank watching the water. You may have even spotted a guy in a
> > white-wig sitting near you, muttering something about fluxions. Good
> > language for rivers, that one.
>
> Mathematics does not possess a single quality or characteristic.
> The idea of a fluxion only applies to certain kinds of analysis.
> The concept of a group, first formulated in the mid-nineteenth
> century, is another type of basic entity in mathematics, and
> quite distinct from the fluxion, or differential.

Absolutely! and as you point out, these are what W. would see as two
entirely distinct language games - they have completely different
purposes: one is for talking about counting and the properties of
things that make them similar; the other is for looking at change.
Both great languages - I'm not trying to unite them, I'm just saying
that Ws 'definition' of language looks to me like a model worth
pursuing when we are discussing the linguistic nature of the
mathematics (plural)
From: rabid_fan on 16 Mar 2010 16:29
On Tue, 16 Mar 2010 12:14:03 -0700, tonyb wrote:


> this language game extremely carefully. From a series of analysed games
> he then attempts to form a foundation for logic.

Which then completely blows up when Goedel and his incompleteness
enters the picture. Wittgenstein was forever opposed to this
indeterminacy introduced by Goedel. In reality, there can be
no overarching foundation, only ad hoc and disjointed fragments
generated to meet some utility or purpose.

>
> The relationship is that
> mathematics and music both carry signification - they evoke meaning.
>

Well, music is much closer to basal motility. It has no meaning
in the usual sense of the term. Music is a direct substitute
for motility, or, less awkwardly stated, music *is* motility.

In fact, thought itself, and hence meaning, is able to dissolve
completely into movement. This is the phenomenon of the dance --
dance in a very primordial sense involving an actual suspension
of consciousness.

In other words, there is no distinction between thought, meaning,
and motility.

The nervous system has evolved to control motility. There is no
other purpose. The question is therefore: how does thought and
meaning arise from this motility control structure? Thought and
meaning seem to be beyond physicality, and this apparent uniqueness
has beguiled philosophers throughout human history.

>
> have a feeling I'm not understanding the your point/question here
>

Well, it is difficult to be clear using only very few words. I am more
or less rambling do the unexpected turns of the topic.

There is much background material to introduce before a serious undertaking
of this subject can be begun.

From: Urion on 16 Mar 2010 16:39
Mathematics is a language but it is also an art, just like chess or a
painting is also an art.
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