Mathematics as a language
Aatu Koskensilta
Everyone has their pet peeves. One of mine is the oft peddled assertion
that mathematics is a language. The claim is of course nonsense taken
literally; it makes no sense to imagine a translation of Frank Herbert's
_Dune_ into mathematics, or a toddler learning mathematics as their
first language. Mathematics has its specialized notation and jargon, but
so do art history, botany, masonry, comparative literature, and so
on. So just what is the actual content of this notion, that mathematics
is a language?
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Bart Goddard
news:878w1uq...@dialatheia.truth.invalid:
> So just what is the actual content of this notion, that mathematics
> is a language?
>
Probably the fact that, like an ordinary language, mathematics
can be used to express certain kinds of thoughts. There are
some things I want to communicate to others which are best
said in English, but others which are best expressed in
equations or mathematical relations.
--
Cheerfully resisting change since 1959.
Aatu Koskensilta
> Probably the fact that, like an ordinary language, mathematics can be
> used to express certain kinds of thoughts. There are some things I
> want to communicate to others which are best said in English, but
> others which are best expressed in equations or mathematical
> relations.
Mathematical English is still English. If I want to relate to someone
particularly juicy linguistic tidbits I'll probably use linguistic
notation and jargon. Banalities like this don't usually inspire anyone
to observe that linguistics is a language. We need a better explanation
of the mathematics as a language metaphor.
Charlie-Boo
Probably the most common mistake people make in trying to formalize
something that is well-understood informally is to define the wrong
level of abstraction. A book title: Mathematics, the study of
Patterns. Doen't that also apply to, you know, seimstresses?
Why wouldn't physics be a language if math is a language (with that
mindset)?
Language is what we use to communicate with other people, animals or
machines. If you only want to communicate mathematical ideas, then by
definition you will use only a subset of English: "for all", "times",
"plus". Such a small subset, let us take advantage of that fact and
use short symbols for our primitives. And even go outside of natural
language symbols.
In the final analyzis, what you can say in English is the same as what
you can say in predicate calculus (FOL).
The real distinction is languages which can represent the complement
of everything they can represent, and those that can represent
themeselves. The weirdest part is, every langauge is (a subset of)
one or the other! And no language is both due to simple
diagonalization.
C-B
On Oct 19, 9:36 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
Aatu Koskensilta
> In the final analyzis, what you can say in English is the same as what
> you can say in predicate calculus (FOL).
We can't in any apparent sense say anything "in predicate calculus".
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, dar�ber muss man schweigen"
Bart Goddard
> Mathematical English is still English.
You're not following. If I want to express the relationship
between two vectors, I write down a matrix. It expresses
cleanly and exactly what I'm thinking, and it's the right
sort of "word" for doing that sort of thinking. Yes, I could
express it in English, but that would be imprecise, unweildy,
and wouldn't lend itself to further thought.
Language, besides being a means of communication, is also
a tool for thinking. If we're pushing algebraic symbols
around trying to discover some relationship amongst them,
then we're not pushing them around according to the rules
of English, but according to the rules of algebra.
Daryl McCullough
for that?
--
Daryl McCullough
Ithaca, NY
Charlie-Boo
> Charlie-Boo <shymath...@gmail.com> writes:
> > In the final analyzis, what you can say in English is the same as what
> > you can say in predicate calculus (FOL).
>
> We can't in any apparent sense say anything "in predicate calculus".
Then how can sentences be true or not?
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
Charlie-Boo
wrote:
That's called propositional calculus.
C-B
James Dolan
aatu koskensilta <aatu.kos...@uta.fi> wrote:
|Everyone has their pet peeves. One of mine is the oft peddled
|assertion that mathematics is a language.
it doesn't bother me too much except when it's said to be _just_ a
language.
|The claim is of course nonsense taken literally; it makes no sense to
|imagine a translation of Frank Herbert's _Dune_ into mathematics, or
|a toddler learning mathematics as their first language. Mathematics
|has its specialized notation and jargon, but so do art history,
|botany, masonry, comparative literature, and so on. So just what is
|the actual content of this notion, that mathematics is a language?
it has to do with the relationship between mathematics and certain
other activities, especially physics. the specialized notation and
jargon of art history probably isn't used too much by anyone but art
historians, but some of the specialized notation and jargon of
mathematics is intensively used by physicists (often in a peculiar
dialect, of course). for many of them it really is "just a language"
as far as they know, and out of ignorance or parochialism they may
believe or say (carelessly or more deliberately) that it's "just a
language" in general.
in understanding this phenomenon it may help to consider other
examples of roughly the same pattern, as for example:
category theory : algebraic geometry : math ::
math : physics : science
--
Charlie-Boo
> in article <878w1uqp8e....@dialatheia.truth.invalid>,
astrology
> --
>
> jdo...@math.ucr.edu
Henry
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
> --
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Mathematics can be used to convey meaning between those who understand
it. It has vocabulary, syntax and symbols, and even oddities (so
6-3-2 is usually 1 not 5, but 2^3^2 is usually 512 not 64).
I can't read Finnish, but I can understand most of the middle part on
logarithmic identities of http://fi.wikipedia.org/wiki/Logaritmi based
on the initial definition of the function "log_a", because it uses
mathematics to communicate.
Tronscend
"Aatu Koskensilta" <aatu.kos...@uta.fi> skrev i melding
news:878w1uq...@dialatheia.truth.invalid...
>
> Everyone has their pet peeves. One of mine is the oft peddled > assertion
/Moved up:/ So just what is the actual content of this notion,
> that mathematics is a language?
Well, first of all, it is a metaphor, an analogy. Of course math is not, as
you say, a language in the everyday sense, yet it displays a lot of traits
that it has in common with language: it uses signs, it has a syntax, and the
signs stand for concepts; i.e., it has a semantic. Since math is something
that is "done", I guess it also has its pragmatics.
> Mathematics has its specialized notation and jargon, but so do > art
> history, botany, masonry, comparative literature, and so on.
I'd say that the difference here is that many of the concepts are purely
abstract, they have no counterpart "in the real world", unlike disciplines
which deal mainly with concepts under which we usually subsume physical
objects.
T
"Alles, was sich aussprechen l��t, l��t sich klar aussprechen".
David C. Ullrich
<aatu.kos...@uta.fi> wrote:
>Bart Goddard <godd...@netscape.net> writes:
>
>> Probably the fact that, like an ordinary language, mathematics can be
>> used to express certain kinds of thoughts. There are some things I
>> want to communicate to others which are best said in English, but
>> others which are best expressed in equations or mathematical
>> relations.
>
>Mathematical English is still English. If I want to relate to someone
>particularly juicy linguistic tidbits I'll probably use linguistic
>notation and jargon. Banalities like this don't usually inspire anyone
>to observe that linguistics is a language. We need a better explanation
>of the mathematics as a language metaphor.
It's not clear to me what you want: An explanation of why it's
valid to call mathematics a language or an explanation of why
people do in fact call it that?
Robert Israel
> I want to know how to order chicken and rice. Do I need quantifiers
> for that?
I think you need advanced bistromathics.
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
MoeBlee
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language.
I'm going to have to agree on that one. Granted, that we can take
"mathematics is a language" in a broad enough sense that we get the
drift, but I don't see that it contributes much to our understanding.
MoeBlee
Herman Jurjus
>
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language.
Would it make sense to translate Dune into C++?
Don't you regard C++ as a language?
> Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
Perhaps the point of uttering 'mathematics is a language' is not so much
to say what mathematics -is-, but to say what it is -not-.
Disciplines like economics, physics or biology could be regarded as
languages, too, in a way: each has developed its own vocabulary, so to
say, a collection of terms that call forth standard associations when
used. Or perhaps better: a collection of notions by which certain parts
or aspects of reality are observed and classified.
But in contrast with these 'languages' (or 'idioms' if that's clearer),
mathematics is a language 'without a cause', i.e. without a
subject-matter - there is a sense in which it's just a vocabulary - just
a collection of notions, terms, standard results and associations, plus
thinking habits.
The way I understand it, the statement is close to Tim Chow's pet peeve
that mathematics is characterized not by its subject matter but by its
precision, or Sazonov's pet peeve that mathematics is all about formalizing.
Hope this makes some sense (because I should know better than to post at
such a late hour).
--
Cheers,
Herman Jurjus
Herman Jurjus
> On 10/19/2010 3:36 PM, Aatu Koskensilta wrote:
>>
>> Everyone has their pet peeves. One of mine is the oft peddled assertion
>> that mathematics is a language. The claim is of course nonsense taken
>> literally; it makes no sense to imagine a translation of Frank Herbert's
>> _Dune_ into mathematics, or a toddler learning mathematics as their
>> first language.
>
> Would it make sense to translate Dune into C++?
> Don't you regard C++ as a language?
>
>> Mathematics has its specialized notation and jargon, but
>> so do art history, botany, masonry, comparative literature, and so
>> on. So just what is the actual content of this notion, that mathematics
>> is a language?
>
> Perhaps the point of uttering 'mathematics is a language' is not so much
> to say what mathematics -is-, but to say what it is -not-.
>
> Disciplines like economics, physics or biology could be regarded as
> languages, too, in a way: each has developed its own vocabulary, so to
> say, a collection of terms that call forth standard associations when
> used. Or perhaps better: a collection of notions by which certain parts
> or aspects of reality are observed and classified.
>
> But in contrast with these 'languages' (or 'idioms' if that's clearer),
> mathematics is a language 'without a cause', i.e. without a
> subject-matter
Perhaps I should rather have said 'without any restriction on its
subject matter'.
--
Cheers,
Herman Jurjus
MoeBlee
> On 10/19/2010 3:36 PM, Aatu Koskensilta wrote:
> > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > that mathematics is a language. The claim is of course nonsense taken
> > literally; it makes no sense to imagine a translation of Frank Herbert's
> > _Dune_ into mathematics, or a toddler learning mathematics as their
> > first language.
>
> Would it make sense to translate Dune into C++?
> Don't you regard C++ as a language?
No, but there may be translations between C++ and other formal
languages.
That is unlike some general activity, field of study such as
mathematics. Mathematics is a field of study. It doesn't seem to me
that calling mathematics a 'language' adds to an explanation of
anything.
MoeBlee
Dan Christensen
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
How I see it: All languages include a vocabulary and grammar to form
statements of some kind. Mathematics includes a language -- the
language of sets, a specialized vocabulary and grammar for writing
statements about sets of objects in the abstract. Mathematics is more
than a language, however. It also includes a well-defined list of
rules for deriving statements expressed in this language from other
such statements. I find it convenient to distinguish these two aspects
of mathematics.
Dan
Download my DC Proof software at http://www.dcproof.com
scaaahu
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
> --
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
IMO, mathematics is a language, at least a subset of human language.
When someone writes down a sentence, "Let G be a group."
After reading this sentence,
An average person tends to ask, a group of what? group of people?
A math person wants to know, what group? abelian group?
Notice that I used the word "subset" in the first line
because I want to communicate this to the math community.
So, you get my point?
Gerry Myerson
Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
I don't know, but it has a first-rate proponent, Galileo:
"Philosophy is written in that great book which ever lies before our
eyes � I mean the universe � but we cannot understand it if we do not
first learn the language and grasp the symbols, in which it is written.
This book is written in the mathematical language, and the symbols are
triangles, circles and other geometrical figures, without whose help it
is impossible to comprehend a single word of it; without which one
wanders in vain through a dark labyrinth."
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
herbzet
Herman Jurjus wrote:
> Aatu Koskensilta wrote:
> >
> > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > that mathematics is a language. The claim is of course nonsense taken
> > literally; it makes no sense to imagine a translation of Frank Herbert's
> > _Dune_ into mathematics, or a toddler learning mathematics as their
> > first language.
>
> Would it make sense to translate Dune into C++?
> Don't you regard C++ as a language?
Beat me to it! I was gonna ask if Aatu's peeve extended
to computer "languages".
[...]
> The way I understand it, the statement is close to Tim Chow's pet peeve
> that mathematics is characterized not by its subject matter but by its
> precision
Does he really think that too?! Herbzet's aphorism (which he hopes will catch
on and give him a certain immortality): Drain ordinary language of ambiguity,
and what's left is mathematics.
--
hz
BGB / cr88192
"Herman Jurjus" <hjm...@hetnet.nl> wrote in message
news:i9l443$lnc$1...@news.eternal-september.org...
> On 10/19/2010 3:36 PM, Aatu Koskensilta wrote:
>>
>> Everyone has their pet peeves. One of mine is the oft peddled assertion
>> that mathematics is a language. The claim is of course nonsense taken
>> literally; it makes no sense to imagine a translation of Frank Herbert's
>> _Dune_ into mathematics, or a toddler learning mathematics as their
>> first language.
>
> Would it make sense to translate Dune into C++?
> Don't you regard C++ as a language?
>
Dune can be translated into C++ and then displayed back to the user in the
form of a 3D animated movie...
all the dialogue can be put in string literals, since these are a common
feature between languages (the English qoutation and the C / C++ / Java /
... string literal...).
>> Mathematics has its specialized notation and jargon, but
>> so do art history, botany, masonry, comparative literature, and so
>> on. So just what is the actual content of this notion, that mathematics
>> is a language?
>
> Perhaps the point of uttering 'mathematics is a language' is not so much
> to say what mathematics -is-, but to say what it is -not-.
>
> Disciplines like economics, physics or biology could be regarded as
> languages, too, in a way: each has developed its own vocabulary, so to
> say, a collection of terms that call forth standard associations when
> used. Or perhaps better: a collection of notions by which certain parts or
> aspects of reality are observed and classified.
>
> But in contrast with these 'languages' (or 'idioms' if that's clearer),
> mathematics is a language 'without a cause', i.e. without a
> subject-matter - there is a sense in which it's just a vocabulary - just a
> collection of notions, terms, standard results and associations, plus
> thinking habits.
>
> The way I understand it, the statement is close to Tim Chow's pet peeve
> that mathematics is characterized not by its subject matter but by its
> precision, or Sazonov's pet peeve that mathematics is all about
> formalizing.
>
> Hope this makes some sense (because I should know better than to post at
> such a late hour).
>
precision and formalizing: yep...
or mathematics is all about mysterious armies of people mysteriously like
either Mr. Data or Q...
all the Mr. Data clones wandering around being like "I have no emotions, I
understand nothing not stated in terms of arcane formalisms, and regard the
dictionary as a collection of jokes..." and being led around by some number
of Mr. Q's all like "I am far too intelligent to relate to the likes of mere
mortals, bow before me as I stroke my ego in your face...".
having more than a few people like this in a room is itself a surreal
experience, and in a way, almost indescribably awkward / annoying.
nevermind the crap storm that ensues as soon as anyone mentions quaternions.
I am just a programmer, and hence see the world a little differently it
seems, a world where "make it work" and "get it done" are some of the higher
ideals, where crufts and kludges, trial and error, ... are the name of the
game, and the ability to find an elegant hack or workaround may be a thing
of beauty...
but, one may find through a harsh experience, that even though math and
programming may seem similar, there is a harsh and barren desert between
them.
but, in a way, it is not so much about the topics themselves, but the people
behind them, of patterns and cultures.
it is like, there are many interconnecting patterns and associations:
between interests and beliefs;
between beliefs, preferences in clothing, preferences in musical styles;
...
much like how religious belief apparently equates to conservative dress
styles and a preference for country-western, and people believing that being
an atheist or agnostic automatically means they are more intelligent (by
default) than another person who holds religious belief.
and, where one is left to realize that they really are alone, by combining
preferences that just don't go together within the larger culture (that
seemingly nowhere is there anyone exactly like oneself).
the apparent oddity of a person who both likes programming and has religious
belief, and who dresses casually and likes goth, techno, and industrial. and
who spends a lot of the time geeking-out despite having totally not giving a
crap back in highschool (watch as I sit around in the back of the room and
ignore everything going on, but at least usually bothering to show up...),
and who thinks that being smart or stupid is largely immaterial anyways.
and then one can't find any females one can get along with as apparently
culture is split in several different directions and there is no one around
who there is much chance of getting along with.
all this itself is apparently a much greater irony it would seem.
well, ok, I totally wandered off topic here...
maybe just pretend the topic is ranting and pet peeves.
MoeBlee
> Herman Jurjus wrote:
> > Aatu Koskensilta wrote:
>
> > > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > > that mathematics is a language. The claim is of course nonsense taken
> > > literally; it makes no sense to imagine a translation of Frank Herbert's
> > > _Dune_ into mathematics, or a toddler learning mathematics as their
> > > first language.
>
> > Would it make sense to translate Dune into C++?
> > Don't you regard C++ as a language?
>
> Beat me to it! I was gonna ask if Aatu's peeve extended
> to computer "languages".
That is off target. Aatu didn't say that formal langauges aren't
languages. He said that mathematics is not itself a language.
> Drain ordinary language of ambiguity,
> and what's left is mathematics.
But there is also mathematics that is not drained of ambiguity
(otherwise all work that came before perfect formalization would not
be mathematics). Draining of ambiguity may be (in your view) a
sufficient condition for mathematics, but it is not a necessary one.
I like Bernay's quote that mathematics is the phenomenology of
abstract structures.
MoeBlee
Tim Golden BandTech.com
wrote:
> In article <878w1uqp8e....@dialatheia.truth.invalid>,
Very nice quote.
Isn't it also true that Aatu's assumption that one culture's language
can be expressed in another culture's language is not completely
valid? A person who reads an original Chinese text might not feel so
good about an english translation, and multiple translations will
vary. Worst of all is the dictionary's self referential means of
definition, which casts doubt on language beyond actual physical
mappings. The human languages are dubious at some level, and
mathematics too. The issue of a basis is nearby, and then axiomatic
construction as well. The human mind somehow learns language from a
blank slate, and this is a condition of mimicry, for it will only
learn the languages presented to it. This blessed curse could be
leveraged much more by exposing the youth to advanced concepts at an
early age, rather than pushing them through such an orderly system.
There is no reason that a young person should not be exposed to all
sorts of things that they might come to understand better at a later
age, for the familiarity that they were given of them at a younger
age. An argument that we don't want our children to be too bright
might come up here, and there is plenty of conflict of interest to go
around there. What if a student knows more than their teacher? The
whole system is doomed to hold them back. Their language is
restricted, for if they begin to answer in a language that their
teacher does not speak, then they will fail. If they find fault with
what they are taught then they will fail. It is a glitch that cannot
be avoided. I can't wait to see what the curious youth of this day
come up with, for their access to knowledge far beyond their teacher's
is excellent.
- Tim
MoeBlee
wrote:
> On Oct 20, 1:05 am, Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email>
> wrote:
>
>
>
>
>
> > In article <878w1uqp8e....@dialatheia.truth.invalid>,
> > Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
>
> > > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > > that mathematics is a language. The claim is of course nonsense taken
> > > literally; it makes no sense to imagine a translation of Frank Herbert's
> > > _Dune_ into mathematics, or a toddler learning mathematics as their
> > > first language. Mathematics has its specialized notation and jargon, but
> > > so do art history, botany, masonry, comparative literature, and so
> > > on. So just what is the actual content of this notion, that mathematics
> > > is a language?
>
> > I don't know, but it has a first-rate proponent, Galileo:
>
> > "Philosophy is written in that great book which ever lies before our
> > eyes ‹ I mean the universe ‹ but we cannot understand it if we do not
> > first learn the language and grasp the symbols, in which it is written.
> > This book is written in the mathematical language, and the symbols are
> > triangles, circles and other geometrical figures, without whose help it
> > is impossible to comprehend a single word of it; without which one
> > wanders in vain through a dark labyrinth."
Notice in that quote that there is a difference between, on the one
hand, "mathematics" and, on the other hand, "mathematical language" or
"the language in which [mathematics] is written". Maybe Galileo says
elsewhere that mathematics is a language, but not in that particular
quote.
I don't why people keep passing over this difference. Yes, there are
formal mathematical languages, and yes there is, for example, informal
mathematical English. But those are languages used to express
mathematics (mathematical ideas and practices), which is not itself a
language, except in a very loose metaphorical sense, and that
metaphorical sense does very ltitle for our understanding.
> Isn't it also true that Aatu's assumption that one culture's language
> can be expressed in another culture's language is not completely
> valid? A person who reads an original Chinese text might not feel so
> good about an english translation, and multiple translations will
> vary.
Okay, so there is not a perfect analogy in Aatu's examples. That's
aside the point. Mathematics itself is no kind of langauge that can
even be quite imperfectly "translated". Mathematics is a field of
study (and also, say, a "nexus" of ideas, an intellecual concern, a
history of practices, etc.). If mathematics is a language, then
virtually any field of study is a language. But saying, for example,
that "biology is a language" hardly adds to our understanding of
anything.
MoeBlee
Alan Smaill
Good point;
I do think though that the Galileo quote has the sense of
what people intend when saying things like "mathematics is
the language of science" -- even if Galileo says it better.
Incidentally, it seems to me more common to say that
"maths is the language of X", rather than "maths is a language"
tout court.
math.ucsd.edu/about/brochure/math_brochure.pdf
--
Alan Smaill
Bill Taylor
> I don't know, but it has a first-rate proponent, Galileo:
>
> "Philosophy is written in that great book which ever lies before our
> eyes ‹ I mean the universe ‹ but we cannot understand it if we do not
> first learn the language and grasp the symbols, in which it is written.
> This book is written in the mathematical language, and the symbols are
> triangles, circles and other geometrical figures, without whose help it
> is impossible to comprehend a single word of it; without which one
> wanders in vain through a dark labyrinth."
Yes, nice quote.
And possibly close to what Pythagoras might have said before him!
Indeed, I think it (yet another!) historical injustice that
"Platonism"
is named after Plato - it seems to me that it would have been
much fairer to call this type of thoroughgoing abstract
mathematical realism as "Pythagorianism".
(Then we could also shorten it today, to Pythonism....)
-- Balanced Bill
Frederick Williams
>
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
I, too, don't like the claim that mathematics is a language, but if it
were one, one would certainly have to add 'with a consequence relation
on it'.
May I ask you a question? Is it the case that of every two languages
(in the everyday sense) tone can be translated into the other?
--
Needle, nardle, noo.
Frederick Williams
> In the final analyzis, what you can say in English is the same as what
> you can say in predicate calculus (FOL).
If that's your final analysis, then you didn't analyse for very long.
--
Needle, nardle, noo.
Frederick Williams
>
> On Oct 19, 10:33 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> > Charlie-Boo <shymath...@gmail.com> writes:
> > > In the final analyzis, what you can say in English is the same as what
> > > you can say in predicate calculus (FOL).
> >
> > We can't in any apparent sense say anything "in predicate calculus".
>
> Then how can sentences be true or not?
By saying something about something. The language of predicate calculus
isn't about anything.
--
Needle, nardle, noo.
Frederick Williams
>
> Would it make sense to translate Dune into C++?
Easily done: put the text into a comment.
> Don't you regard C++ as a language?
--
Needle, nardle, noo.
Peter Webb
Jan Burse
>
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
krrrk krrrk ahh ahh -- Flipper(*) doing math.
Bye
(*)
They call him Flipper, Flipper, faster than lightning,
No-one you see, is smarter than he,
And we know Flipper lives in a world full of wonder,
Flying there under, under the sea!
scaaahu
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, dar ber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
First, please allow me to retract my earlier post that claims
mathematics
is a language. I was wrong.
I believe, the notion that "mathematics is a language" means:
Mathematics is a school of thoughts presented by the language of
mathematics,
such as predicate calculus, specialized notation, jargon and human
languages.
This notion is different from that mathematics is a language iff Java
is a language.
Java is a language which can be used to present mathematical thoughts
and other
thoughts as well, such as an application embedded in a cell phone. We
can argue that
a cell phone app is also a kind of mathematics because it's an
algorithm. Then we
are entering into a larger extent of the debate, is everything
mathematics?
Aatu Koskensilta
> It's not clear to me what you want: An explanation of why it's valid
> to call mathematics a language or an explanation of why people do in
> fact call it that?
Well, most likely people call mathematics a language because they find
this image intellectually appealing in some way. What I'm wondering
about is what exactly this metaphor is intended to convey.
To answer a question asked elsewhere in this thread, I'll happily
agree that C++ is a computer language. We may make good use of the
language metaphor in case of computer languages: we speak of dialects of
LISP, of idiomatic Haskell or Python, of someone's Scala style, and so
on. Analogously, it might well make perfect sense to describe a
formalism for recursive functions, partial differential equations,
commutative diagrams, a language. But mathematics is not such a
formalism. It is a field of study, a body of knowledge, methods,
concepts, ideas, techniques, associated with which we find various
formalisms, specialized notation, specialized jargon, and so on.
--
Aatu Koskensilta (aatu.kos...@uta.fi)
Aatu Koskensilta
> Mathematics is more than a language, however. It also includes a
> well-defined list of rules for deriving statements expressed in this
> language from other such statements.
No it doesn't. You seem to be describing a formal system of some sort.
Aatu Koskensilta
> Isn't it also true that Aatu's assumption that one culture's language
> can be expressed in another culture's language is not completely
> valid?
Where have I relied on this assumption?
Aatu Koskensilta
> Incidentally, it seems to me more common to say that "maths is the
> language of X", rather than "maths is a language" tout court.
>
> math.ucsd.edu/about/brochure/math_brochure.pdf
I don't have any objection to "mathematics is the language of X". What
is meant is usually relatively clear, that in X we make use of
mathematical notation, terminology, concepts, and so on, that, in
effect, X is a mathematical discipline.
Aatu Koskensilta
> May I ask you a question? Is it the case that of every two languages
> (in the everyday sense) tone can be translated into the other?
This is, to an extent, an empirical question and I'm no expert in
linguistics. I would find it very surprising if there were some concept
expressible in English, say, that was simply impossible to express in
this or that language. Certainly I'm sure that, perhaps with long-winded
explanations, anything I could say in English I could say in
Finnish. Puns, connotation, allusion, style, register, and so on, would
of necessity be lost in many cases. It rather depends on what we
understand by translation.
Aatu Koskensilta
> Mathematics is a language iff Java is a language
Java is a programming language, with formally defined syntax and
informally defined semantics. What sort of language is mathematics?
amzoti
> Everyone has their pet peeves. One of mine is the oft peddled assertion
> that mathematics is a language. The claim is of course nonsense taken
> literally; it makes no sense to imagine a translation of Frank Herbert's
> _Dune_ into mathematics, or a toddler learning mathematics as their
> first language. Mathematics has its specialized notation and jargon, but
> so do art history, botany, masonry, comparative literature, and so
> on. So just what is the actual content of this notion, that mathematics
> is a language?
>
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Definition: http://www.wordiq.com/language
1. http://www.wordiq.com/definition/Language (see bottom of page and
link below)
Charlie-Boo
> Bart Goddard <goddar...@netscape.net> writes:
> > Probably the fact that, like an ordinary language, mathematics can be
> > used to express certain kinds of thoughts. There are some things I
> > want to communicate to others which are best said in English, but
> > others which are best expressed in equations or mathematical
> > relations.
>
> Mathematical English is still English. If I want to relate to someone
> particularly juicy linguistic tidbits I'll probably use linguistic
> notation and jargon. Banalities like this don't usually inspire anyone
> to observe that linguistics is a language. We need a better explanation
> of the mathematics as a language metaphor.
They're trying to tell you that math is different from the other
sciences. And that boils down to, what is math? And whatever that
distinction is, they are equating that with the notion that it is a
language. That is the leap of faith.
Once you define math, you can address the question. You haven't.
C-B
Charlie-Boo
> Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote innews:874ociq...@dialatheia.truth.invalid:
>
> > Mathematical English is still English.
>
> between two vectors, I write down a matrix. It expresses
> cleanly and exactly what I'm thinking, and it's the right
> sort of "word" for doing that sort of thinking. Yes, I could
> express it in English, but that would be imprecise, unweildy,
> and wouldn't lend itself to further thought.
You're distancing yourself too much from English. It is all defined
in English. You can use different formats for displaying your
language, but like the Turing Machine that takes in a pair (TM,input)
as input, it all can be expressed as a string.
> Language, besides being a means of communication, is also
> a tool for thinking. If we're pushing algebraic symbols
> around trying to discover some relationship amongst them,
> then we're not pushing them around according to the rules
> of English, but according to the rules of algebra.
Yes you are pushing them around according to the rules of English.
English = WFF.
True English = WFF that follows the rules of algebra.
1+2=3+4 ; "The sum of one and two equals the sum of three and four." =
correct English.
1 + = + 423 : "One plus equals plus four two three." = incorrect
English.
C-B
> --
> Cheerfully resisting change since 1959.
Charlie-Boo
> On 19 Oct, 14:36, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
>
> > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > that mathematics is a language. The claim is of course nonsense taken
> > literally; it makes no sense to imagine a translation of Frank Herbert's
> > _Dune_ into mathematics, or a toddler learning mathematics as their
> > first language. Mathematics has its specialized notation and jargon, but
> > so do art history, botany, masonry, comparative literature, and so
> > on. So just what is the actual content of this notion, that mathematics
> > is a language?
>
> > Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> > "Wovon man nicht sprechen kann, darüber muss man schweigen"
> > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
>
> it. It has vocabulary, syntax and symbols, and even oddities (so
> 6-3-2 is usually 1 not 5, but 2^3^2 is usually 512 not 64).
>
> I can't read Finnish, but I can understand most of the middle part on
> logarithmic identities ofhttp://fi.wikipedia.org/wiki/Logaritmibased
> on the initial definition of the function "log_a", because it uses
> mathematics to communicate.
What you are fighting over is the next level of abstraction
(understanding) and I've already done that.
How can we define a set?
1. Program that accepts or enumerates it.
2. Wff that is true iff its variable is in the set.
3. English sentence that is true iff its pronoun is in the set.
4. Logic and wff that is provable iff its variable is in the set.
1=4. 2=3.
Systems 1 and 4 define the r.e. sets. Systems 2 and 3 define the
expressible sets.
Every system is one or the other. I note that in 1=4 the system
defines the set that is the relation between its set definition and
element of that set. I call them SELF because the system contains
itself. There is a Univeral Turing Machine. There is a wff W(x) that
is provable iff x is the number of a sentence that is provable.
Systems 2 and 3 define the complement of every set they define. We
can add the negation symbol ~ to any wff to express its complement. I
call these systems NOTX for historical reasons.
Any 2-place relation gives a system of defining sets.
P(set,element). The system is either SELF or NOTX.
English and Predicate Calculus based on truth are NOTX. Computers and
Predicate Calculus based on provabiliy are SELF.
People speak in NOTX. Robots speak in SELF.
Godel prove SELF and NOTX are different. The ultimate abstraction of
Godel's results is,
"Man and machine speak different languages."
A1. SELF / SELF : Definition of SELF.
R1. P / NOTX => ~P / NOTX : Definition of NOTX.
A2. - ~P / P : Diagonalization
Thm. - SELF , NOTX: SELF does not equal NOTX (Godel)
1. SELF , NOTX : Assume SELF equals NOTX.
2. SELF / SELF : A1
3. NOTX / NOTX : Substitute 1: SELF => NOTX in 2
4. ~NOTX / NOTX : R1: 3
5. - ~NOTX / NOTX : A2: P => NOTX
6. FALSE 4 + 5
qed
C-B
Marshall
> "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> writes:
> > Mathematics is a language iff Java is a language
>
> Java is a programming language, with formally defined syntax and
> informally defined semantics. What sort of language is mathematics?
Nicely put.
Java has a specification document. Does math? :-)
Marshall
Charlie-Boo
> "Aatu Koskensilta" <aatu.koskensi...@uta.fi> skrev i meldingnews:878w1uq...@dialatheia.truth.invalid...
>
> > Everyone has their pet peeves. One of mine is the oft peddled > assertion
>
> /Moved up:/ So just what is the actual content of this notion,
>
> > that mathematics is a language?
>
> you say, a language in the everyday sense, yet it displays a lot of traits
> that it has in common with language: it uses signs, it has a syntax, and the
> signs stand for concepts; i.e., it has a semantic. Since math is something
> that is "done", I guess it also has its pragmatics.
>
> > Mathematics has its specialized notation and jargon, but so do > art
> > history, botany, masonry, comparative literature, and so on.
>
> abstract, they have no counterpart "in the real world", unlike disciplines
> which deal mainly with concepts under which we usually subsume physical
> objects.
You're getting close.
1. You can't predict everything. (You can't answer "Will your next
answer be NO?")
2. Science is that which you can predict.
3. Math is the science that does not use any input. (We don't use our
5 senses to do math.)
Every other branch of science uses our 5 senses to create the
primitive facts, the axioms.
This is what mathematics really is and nobody realizes it. They have
debated "What is mathematics?" since day 1. This is the answer.
C-B
> T
>
> "Alles, was sich aussprechen l t, l t sich klar aussprechen".
Charlie-Boo
wrote:
If it's in Predicate Calculus, the English author simply translates
"^" into "and" etc. to express it.
If it's in English, the Predicate Calculus author just defines any
primitive values or relations to express it.
They are both NOTX and are equal. As Turing Machines and axiomatic
systems are SELF and equal. And that's all there is, NOTX and SELF.
What system of defining sets is not SELF or NOTX?
Every language is a system for defining sets. "It is blue." defines
the set of blue things. "My pen is blue." is a sentence, a zero-place
relation.
C-B
Charlie-Boo
wrote:
It's about its universal set. Predicate Calculus sentences are true
or false, making statements about things.
C-B
> --
> Needle, nardle, noo.
Charlie-Boo
> David C. Ullrich <ullr...@math.okstate.edu> writes:
>
> > It's not clear to me what you want: An explanation of why it's valid
> > to call mathematics a language or an explanation of why people do in
> > fact call it that?
>
> Well, most likely people call mathematics a language because they find
> this image intellectually appealing in some way. What I'm wondering
> about is what exactly this metaphor is intended to convey.
>
> To answer a question asked elsewhere in this thread, I'll happily
> agree that C++ is a computer language. We may make good use of the
> language metaphor in case of computer languages: we speak of dialects of
> LISP, of idiomatic Haskell or Python, of someone's Scala style, and so
> on. Analogously, it might well make perfect sense to describe a
> formalism for recursive functions, partial differential equations,
> commutative diagrams, a language. But mathematics is not such a
> formalism. It is a field of study, a body of knowledge, methods,
> concepts, ideas, techniques, associated with which we find various
> formalisms, specialized notation, specialized jargon, and so on.
Don't try to make the essence of mathematics too complicated. That's
the mistake everyone makes. And I always say, if that complex
definition is accurate, then what do all of its subsets and variations
define? If you define a primitive with a complex definition, these
subsets will define things more primitive and that is not what you
want - you are already at the most primitive level.
Primitive things need only simple definitions. ZF is nonsense. Frege
needed to add only about 1 axiom to take care of Russell. Just as in
the Theory of Computation we need only 1 axiom to prove sets non-r.e.
It's call "reducing to the halting problem" but actually we reduce to
the fact that the set of programs that don't halt yes on themselves is
not r.e., the diagonalization of the set of programs and inputs that
halt yes.
A recent FOM post said that Math is characterized by a certain
equation of 5 degrees. Those guys just miss it entirely.
C-B
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
VK
> You're distancing yourself too much from English. It is all defined
> in English. You can use different formats for displaying your
> language, but like the Turing Machine that takes in a pair (TM,input)
> as input, it all can be expressed as a string.
I'd like to see someone having translated "The Raven" by Edgar Allan
Poe into the math language :-) Same applies to JavaScript or C++
languages. There are natural languages. There are formal languages.
Math language is a formal language:
http://en.wikipedia.org/wiki/Formal_language
with all benefits and limitations it implies.
Charlie-Boo
> Dan Christensen <Dan_Christen...@sympatico.ca> writes:
> > Mathematics is more than a language, however. It also includes a
> > well-defined list of rules for deriving statements expressed in this
> > language from other such statements.
>
> No it doesn't. You seem to be describing a formal system of some sort.
The notion of a formal system of course is just a formalization or
generalization of mathematics, separating the syntax from the
semantics and saying that math is one syntax. Programming languages
take it to the hilt.
C-B
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
Charlie-Boo
> Frederick Williams <freddywilli...@btinternet.com> writes:
> > May I ask you a question? Is it the case that of every two languages
> > (in the everyday sense) tone can be translated into the other?
>
> This is, to an extent, an empirical question and I'm no expert in
> linguistics. I would find it very surprising if there were some concept
> expressible in English, say, that was simply impossible to express in
> this or that language. Certainly I'm sure that, perhaps with long-winded
> explanations, anything I could say in English I could say in
> Finnish. Puns, connotation, allusion, style, register, and so on, would
> of necessity be lost in many cases. It rather depends on what we
> understand by translation.
English = Predicate Calculus using truth = any natural language = a
system of defining sets that can define the complement of any set it
can define. I call it NOTX.
Computers = Predicate Calculus using proof = a system of defining sets
that can define the system itself, i.e., it can define the set that is
the relation between its set definitions and the elements of the set
defined. I call it SELF.
Program Synthesis is the translation of a set from a NOTX definition
into a SELF definition. They have argued for decades over what
constitutes a valid input to a program synthesis system. As they have
all failed to produce one, they rely on input that is SELF (i.e. a
program written in a new language) and translate it to another
programming language and call it Program Synthesis. Only NOTX systems
of set representation are valid input.
Godel's 1st Theorem is that SELF does not equal NOTX.
C-B
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
Charlie-Boo
> On Oct 19, 6:36 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
>
> > Everyone has their pet peeves. One of mine is the oft peddled assertion
> > that mathematics is a language. The claim is of course nonsense taken
> > literally; it makes no sense to imagine a translation of Frank Herbert's
> > _Dune_ into mathematics, or a toddler learning mathematics as their
> > first language. Mathematics has its specialized notation and jargon, but
> > so do art history, botany, masonry, comparative literature, and so
> > on. So just what is the actual content of this notion, that mathematics
> > is a language?
>
> > --
> > Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> > "Wovon man nicht sprechen kann, dar ber muss man schweigen"
> > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
>
> Definition:http://www.wordiq.com/language
A language is an enumeration of sets. A programming language is an
enumeration of r.e. sets.
C-B
> 1.http://www.wordiq.com/definition/Language(see bottom of page and
> link below)
>
> 2.http://www.wordiq.com/definition/Formal_language
MoeBlee
> Frege
> needed to add only about 1 axiom to take care of Russell.
No, his logic is monotonic. How many thousands of times has it been
explained that you can't add an axiom to an inconsistent system to
make it consistent?
MoeBlee
MoeBlee
> Math language is a formal language:
You just said math LANGUAGE is a formal language. (1) Mathematics is
expressed in both formal and informal languages. (2) More importantly
for the question of this thread, it's not at issue that mathematical
languages are languages, but rather whether mathematics ITSELF is a
language.
Sheesh, this has been answered over and over again in this thread.
Yes, there are mathematical languages but that doesn't entail that
mathematics itself is a language.
There are special notation systems even for things such as baseball.
The scorecard system is a language for baseball. That doesn't entail
that baseball itself is a language.
MoeBlee
Charlie-Boo
English is as formal as you want. You can do all the math in the
world in natural langauge only. Whether you write "1+1=2" or "One
plus one equals two.", you have the same system.
The real distinction between languages is whether they can represent
themselves and whether they can represent the complement of every set
they can represent.
A language is an enumeration of sets.
C-B
Charlie-Boo
His system is not inconsistent. There is no property of not applying
to yourself as a property - just as there is no set of sets that are
not elements of themselves. Set = Property. Naive set theory is
valid. Frege only needed to add the axiom that there is no Russell
set.
I have axiomatized about 6 branches of theoretical computer science.
In every case, a single axiom takes care of diagionalization. In
Theory of Computation it means "is not re". In Set Theory it means
"is not a set". But in every case it is the incompleteness created by
diagonalization.
C-B
Charlie-Boo
It sure the fuck is. Anytime you communicate you use a language. You
have a relation between syntax and semantics. The set of all possible
syntaxes (the first component) is the language.
C-B
> MoeBlee
VK
> You just said math LANGUAGE is a formal language. (1) Mathematics is
> expressed in both formal and informal languages. (2) More importantly
> for the question of this thread, it's not at issue that mathematical
> languages are languages, but rather whether mathematics ITSELF is a
> language.
I am not clear by what do you mean saying "whether mathematics ITSELF
is a language". Mathematics itself is a science, just like any other.
To express and to comprehend any acquired knowledge of this science in
a full and unambiguous way the formal mathematical language is
created.
> Sheesh, this has been answered over and over again in this thread.
Sorry if I overlooked it.
> Yes, there are mathematical languages but that doesn't entail that
> mathematics itself is a language.
There are no "mathematical languages", there is the formal
mathematical language and one can use either part of it for the
current purposes. The mathematics itself of course is a language.
> There are special notation systems even for things such as baseball.
> The scorecard system is a language for baseball. That doesn't entail
> that baseball itself is a language.
Definitely not, it is a sport game.
What is actually the purpose of such long discussion on "2+2 makes 4"?
OP or someone else claimed it to be 5?
VK
> The mathematics itself of course is a language.
The mathematics itself of course is NOT a language.
MoeBlee
> On Oct 24, 1:14 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Oct 24, 11:53 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > Frege
> > > needed to add only about 1 axiom to take care of Russell.
>
> > No, his logic is monotonic. How many thousands of times has it been
> > explained that you can't add an axiom to an inconsistent system to
> > make it consistent?
> His system is not inconsistent. There is no property of not applying
> to yourself as a property - just as there is no set of sets that are
> not elements of themselves. Set = Property. Naive set theory is
> valid. Frege only needed to add the axiom that there is no Russell
> set.
And the system proves that there is such a Russell "set" ('set' being
the extension of the predicate, or whatever specific terminology we
apply). You don't eliminate a theorem by simply taking as an axiom the
negation of a theorem.
You seem not to understand what montonicity is in logic.
MoeBlee
MoeBlee
> On Oct 24, 1:18 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > There are special notation systems even for things such as baseball.
> > The scorecard system is a language for baseball. That doesn't entail
> > that baseball itself is a language.
>
> It sure the fuck is.
Oh, okay, baseball is a language. Silly me, I thought it was an
athletic game with attendant institutions, history, and lore.
MoeBlee
MoeBlee
> MoeBlee wrote:
> > You just said math LANGUAGE is a formal language. (1) Mathematics is
> > expressed in both formal and informal languages. (2) More importantly
> > for the question of this thread, it's not at issue that mathematical
> > languages are languages, but rather whether mathematics ITSELF is a
> > language.
>
> I am not clear by what do you mean saying "whether mathematics ITSELF
> is a language". Mathematics itself is a science, just like any other.
> To express and to comprehend any acquired knowledge of this science in
> a full and unambiguous way the formal mathematical language is
> created.
Okay, then mathematics is a science and then there is a language used
to express that science. The thing expressed by the langauge is not
(usually) the language itself, right? Mathematics is a science, not a
language; and the language to express that science is a language.
That's not clear?
However, there is not just one formal mathematical language. And
mathematics is expressed not only in formal languages.
> > Yes, there are mathematical languages but that doesn't entail that
> > mathematics itself is a language.
>
> There are no "mathematical languages",
Sure there are. The language of PA, the language of ZFC, the language
of IST, et. al are mathematical languages.
> there is the formal
> mathematical language
There are many formal mathematical languages.
> and one can use either part of it for the
> current purposes. The mathematics itself of course is a language.
I give up.
> > There are special notation systems even for things such as baseball.
> > The scorecard system is a language for baseball. That doesn't entail
> > that baseball itself is a language.
>
> Definitely not, it is a sport game.
Right. And mathematics is not a language, but rather it is a field of
study (a science, if you wish).
MoeBlee
MoeBlee
Exactly.
MoeBlee
Tronscend
"Charlie-Boo" <shyma...@gmail.com> skrev i melding
news:251484ba-ecbd-4fe6...@t8g2000yqk.googlegroups.com...
On Oct 19, 12:04 pm, "Tronscend" <tronf...@frizurf.no> wrote:
> "Aatu Koskensilta" <aatu.koskensi...@uta.fi> skrev i
> meldingnews:878w1uq...@dialatheia.truth.invalid...
>
>You're getting close.
>1. You can't predict everything. (You can't answer "Will your next answer
>be NO?")
>2. Science is that which you can predict.
A very original way of formulating it ...
Do you mean "science is about what can be predicted,
because it deals in classes of events that are determined
by causes whose description can be captured in natural laws..."
or something like that? Then we agree, for the "natural philosophy" value of
"science".
>3. Math is the science that does not use any input. (We don't use our 5
>senses to do math.)
>Every other branch of science uses our 5 senses to create the
>primitive facts, the axioms.
Not quite. Math is one of several formal sciences (
http://en.wikipedia.org/wiki/Formal_science ).
>This is what mathematics really is and nobody realizes it. They >have
>debated "What is mathematics?" since day 1. This is the answer.
Well, you are 131 year behind Frege, who said it first.
T
Bart Goddard
84f9ea...@a36g2000yqc.googlegroups.com:
> You're distancing yourself too much from English. It is all defined
> in English.
No, it's not. You can talk about what you're doing in English,
but math follows it's own syntax. When you do math, you're
not following the rules of English grammar, you're following
the rules of mathematical reasoning.
Charlie-Boo
> There are special notation systems even for things such as
baseball.
Wow, there are even notational systems for things that use bats and
balls? But wait. These little 1's and 0's I see running through my
computer's memories look like . . . a bunch of bats and balls.
Tronscend
On Oct 24, 1:18 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> On Oct 24, 11:55 am, VK <schools_r...@yahoo.com> wrote:
>
> Anytime you communicate you use a language.
In the majority of cases, when you use a language, you communicate (although
there are plenty of folks who manage to avoid it).
But one can well communicate without using language.
We also communicate with signs, symbols, images, gestures etc.
T
MoeBlee
> On Oct 24, 12:37 pm, VK <schools_r...@yahoo.com> wrote:
> > The mathematics itself of course is a language.
>
> I give up.
Scratch that, since the poster made a subsequent correction:
"The mathematics itself of course is NOT a language." [caps in
original]
MoeBlee
Charlie-Boo
> On Oct 24, 12:28 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > On Oct 24, 1:14 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > > On Oct 24, 11:53 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > Frege
> > > > needed to add only about 1 axiom to take care of Russell.
>
> > > No, his logic is monotonic. How many thousands of times has it been
> > > explained that you can't add an axiom to an inconsistent system to
> > > make it consistent?
> > His system is not inconsistent. There is no property of not applying
> > to yourself as a property - just as there is no set of sets that are
> > not elements of themselves. Set = Property. Naive set theory is
> > valid. Frege only needed to add the axiom that there is no Russell
> > set.
>
> And the system proves that there is such a Russell "set"
No it doesn't. Give the proof.
Diagonalization refutes that the purported proof exists, not that the
system is inconsistent.
You will see this clearly only when you formalize the proof. Then you
will see:
There is no property of a set not containing itself.
There is no property of a property not applying to oneself.
There is no set of sets that do not contain themselves.
There is no set of properties that do not apply to themselves.
Axiom 1: -~P/P Diagonalization
All of the dozens of proofs that I have posted end with Axiom 1,
within the negative branches of cs (what is impossible.)
You are trying to refute P/PROP => P/SE (all properties are sets)
But you start with the premise ~SE/PROP (not being an element of
itself is a property)
However PROP,SE (properties and sets are the same thing)
So ~SE/PROP => ~SE/SE but -~SE/SE (Axiom 1) (There is no property of
not being an element of oneself.)
Contradiction in your premise.
The fundamental lacking in conventional wisdom is having a variable
for the base being used. They have a kludge definition for each case:
recursively enumerable, representable, expressible, defines a set.
(Then another kludge for each set declared to have the property.) It
HAS to be a variable to represent certain types of proofs. And it
also allows you to prove things at a higher level of abstraction -
each proof applies to all bases.
The amount of proof man will know is not limited by incompleteness.
That is not the limiting factor. The limiting factor is the total
amount of complexity one can undertsand at one time. If the system is
at a higher level of abstraction, it is an order of magnitude shorter
and simpler, so you understand an order of magnitude more proofs.
(The drawback is that it represents only certain proofs. So you
design the system so that it represents the proofs you want, and take
what you find.)
(That is why there is debate over the "real" significance of Godel's
results.)
> ('set' being
> the extension of the predicate, or whatever specific terminology we
> apply). You don't eliminate a theorem by simply taking as an axiom the
> negation of a theorem.
>
> You seem not to understand what montonicity is in logic.
No, you are stuck in the kindergarten of inbred professors.
C-B
> MoeBlee
Charlie-Boo
Oops I thought you meant the scoring isn't a language.
IT'S EASY. Math is the science that doesn't use our 5 senses. So
there are no animals or planets or photons to observe. People think
of science X which uses your senses to observe Y as being a deductions
about Y, so it is Y (animals, photons, etc.) and the rules that are
used to PREDICT Y.
Math is the science for which there is no Y. It is about rules in
general.
Math is the generalization of all of science. It is the highest level
after all of the things particular to individual branches are stripped
out.
ATTA WAKE UP!
C-B
> MoeBlee
MoeBlee
> On Oct 24, 1:42 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Oct 24, 12:28 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > On Oct 24, 1:14 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > > > On Oct 24, 11:53 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > > Frege
> > > > > needed to add only about 1 axiom to take care of Russell.
>
> > > > No, his logic is monotonic. How many thousands of times has it been
> > > > explained that you can't add an axiom to an inconsistent system to
> > > > make it consistent?
> > > His system is not inconsistent. There is no property of not applying
> > > to yourself as a property - just as there is no set of sets that are
> > > not elements of themselves. Set = Property. Naive set theory is
> > > valid. Frege only needed to add the axiom that there is no Russell
> > > set.
>
> > And the system proves that there is such a Russell "set"
>
> No it doesn't. Give the proof.
No, I'd rather not waste my time re-typing Russell's letter to Frege,
which can be found in many an anthology on the subject and which I
would guess is synopsized in many an Internet article.
As to the rest of your post, most of it not quoted here, it seems more
to do with your own personal ideas and notation than with Frege's
actual system.
> Axiom 1: -~P/P Diagonalization
Uh huh, and the language in which that axiom is stated is _______ ?
> > You seem not to understand what montonicity is in logic.
>
> No, you are stuck in the kindergarten of inbred professors.
Puerile comments like that one won't help you understand what
montonicity of logic is.
MoeBlee
Charlie-Boo
> Hi there,
>
> "Charlie-Boo" <shymath...@gmail.com> skrev i meldingnews:251484ba-ecbd-4fe6...@t8g2000yqk.googlegroups.com...
> On Oct 19, 12:04 pm, "Tronscend" <tronf...@frizurf.no> wrote:
>
> > "Aatu Koskensilta" <aatu.koskensi...@uta.fi> skrev i
> > meldingnews:878w1uq...@dialatheia.truth.invalid...
>
> >You're getting close.
> >1. You can't predict everything. (You can't answer "Will your next answer
> >be NO?")
> >2. Science is that which you can predict.
>
> A very original way of formulating it ...
> Do you mean "science is about what can be predicted,
> because
No "because". By definition. "Science" is just the term we use when
we refer to what is predictable. Thinking about HOW we predict is
another level of abstraction. That is the mistake that makes it hard
for people to understand what science is. They talk about the
different kinds of rules, but they are unlimited and in a sense
unrelated to science itself. In our particular universe we have
certain kinds of rules of science. Gravity attracts instead of
repels.
The intutive appeal to things of science is that we "understand"
them. But the fundamental distinction is predictability. From that
comes controlability, explainability etc. which people use as their
faulty definition.
> it deals in classes of events that are determined
> by causes whose description can be captured in natural laws..."
> or something like that?
No. Those are properties of this universe. Science is more general
than that. It is what we can predict in whatever universe we are in.
The fact that there is a maximum speed and that gravity attracts are
properties of this universe and not to be confused with the nature of
science itself.
>Then we agree, for the "natural philosophy" value of
> "science".
>
> >3. Math is the science that does not use any input. (We don't use our 5
> >senses to do math.)
> >Every other branch of science uses our 5 senses to create the
> >primitive facts, the axioms.
>
> Not quite. Math is one of several formal sciences (http://en.wikipedia.org/wiki/Formal_science).
It says "A formal science is a branch of knowledge that is concerned
with formal systems, for instance, logic, mathematics, systems theory,
computer science, information theory, decision theory, statistics."
Those are all branches of math. It started, it seems, when people
said Logic is not part of mathematics. How sad.
> >This is what mathematics really is and nobody realizes it. They >have
> >debated "What is mathematics?" since day 1. This is the answer.
>
> Well, you are 131 year behind Frege, who said it first.
What did he say first? Quote and reference?
When did Frege say that math is the science that doesn't use our 5
senses?
The belief that thinkers of the distant past can provide the ideas
needed today is absurd. They had the distinct disadvantage of lacking
the knowledge that we have developed and also in not having stripped
away the details we have as innovators have abstracted ideas to their
essence and worked at higher levels of abstraction.
C-B
> T
Charlie-Boo
> Charlie-Boo <shymath...@gmail.com> wrote in news:a99136d2-ed48-4ce1-b902-
> 84f9eaff1...@a36g2000yqc.googlegroups.com:
>
> > You're distancing yourself too much from English. It is all defined
> > in English.
>
> No, it's not. You can talk about what you're doing in English,
> but math follows it's own syntax.
So does French.
> When you do math, you're
> not following the rules of English grammar, you're following
> the rules of mathematical reasoning.
Interesting distinction but you need a little collaborative brain-
storming. :)
You're talking about English sentences vs gibberish, and now true
sentences vs false ones.
The parallel is there. Don't deny it - exploit it.
C-B
Charlie-Boo
> "Charlie-Boo" <shymath...@gmail.com> skrev i meldingnews:b35baf38-e483-4659...@e14g2000yqe.googlegroups.com...
> On Oct 24, 1:18 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Oct 24, 11:55 am, VK <schools_r...@yahoo.com> wrote:
>
> > Anytime you communicate you use a language.
>
> In the majority of cases, when you use a language, you communicate (although
> there are plenty of folks who manage to avoid it).
> But one can well communicate without using language.
> We also communicate with signs, symbols, images, gestures etc.
What did Charlie Brown use to say - "AAAAAAAAAYYYYYYYYYYYYY!!!!!!!!!"?
C-B
> T
Charlie-Boo
> On Oct 24, 6:43 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
>
>
>
>
> > On Oct 24, 1:42 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > > On Oct 24, 12:28 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > On Oct 24, 1:14 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > > > > On Oct 24, 11:53 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > > > Frege
> > > > > > needed to add only about 1 axiom to take care of Russell.
>
> > > > > No, his logic is monotonic. How many thousands of times has it been
> > > > > explained that you can't add an axiom to an inconsistent system to
> > > > > make it consistent?
> > > > His system is not inconsistent. There is no property of not applying
> > > > to yourself as a property - just as there is no set of sets that are
> > > > not elements of themselves. Set = Property. Naive set theory is
> > > > valid. Frege only needed to add the axiom that there is no Russell
> > > > set.
>
> > > And the system proves that there is such a Russell "set"
>
> > No it doesn't. Give the proof.
>
> No, I'd rather not waste my time re-typing Russell's letter to Frege,
You offer no proof. That is not mathematics.
Your personality flaw interferes with whatever mathematical abilities
you may have.
It's easy: Frege said every property is a set and there is a property
of not being an element of oneself, so not every property is a set.
But the mistake is that there is no property of not being an element
of oneself, just as there is no set of things not an element of
itself.
Property = Set. It is silly to try to develop an asymmetry between
two vague words like this.
The added axiom would expose the flaw in the proof so the mistaken
proof would not be allowed.
ALL ZF IS DOING IS LOOKING FOR WHICH WFFS ARE SETS AND WHICH WFFS ARE
NOT SETS.
In Theory of Computation we do the same but for RECURSIVELY ENUMERABLE
SETS.
1. You give axioms of what is r.e. e.g. the universal set or proof or
running a program.
2. You give rules for creating more r.e. sets.
3. You give 1 rule for what is not r.e.: the set of programs that do
not halt yes on themselves.
4. Proofs create r.e. sets using 1+2.
5. Proofs create non-r.e. sets using 2+3 and the rule of reducing to a
falsehood.
The same can be done with Set Theory.
1. AAA is a set.
2. If BBB and CCC are sets then DDD is a set.
3. There is no set of sets that don't contain themselves.
4. Therefore EEE is a set.
5. Therefore FFF is not a set (otherwise using rules (2), (3) would be
violated.)
The Theory of Computation reduces problems to the halting problem. It
really is reducing to the set of programs that do not halt yes on
themselves.
Set Theory needs to reduce to the Russell Set.
> which can be found in many an anthology on the subject and which I
> would guess is synopsized in many an Internet article.
>
> As to the rest of your post, most of it not quoted here, it seems more
> to do with your own personal ideas and notation than with Frege's
> actual system.
>
> > Axiom 1: -~P/P Diagonalization
>
> Uh huh, and the language in which that axiom is stated is _______ ?
CBL (a simple extension to FOL and the notion of characterizing sets)
> > > You seem not to understand what montonicity is in logic.
>
> > No, you are stuck in the kindergarten of inbred professors.
>
> Puerile comments like that one won't help you understand what
> montonicity of logic is.
They will help you understand what cronyism in cs publishing does.
Don't quote trivialities.
C-B
> MoeBlee- Hide quoted text -
>
> - Show quoted text -
scaaahu
> there are no animals or planets or photons to observe. People think
> of science X which uses your senses to observe Y as being a deductions
> about Y, so it is Y (animals, photons, etc.) and the rules that are
> used to PREDICT Y.
>
I beg to differ.
By your saying, Math is philosophy.
When you see one finger of your right hand and another
of left hand, your observation tells you 1+1=2. This is
the foundation of math. Math cannot be deviated from
reality too much. Otherwise you are studying philosophy.
William Elliot
Have you ever tried swearing in mathematics?
Gerry Myerson
Bart Goddard <godd...@netscape.net> wrote:
When you write "math follows it's own syntax,"
you're not following the rules of English grammar.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
scaaahu
> Have you ever tried swearing in mathematics?
If the question was directed to me, the answer is yes.
I am a retired software engineer. In the past year or
so, I have studied Lallement's Semigroups and com-
binatorial applications and D&F's Abstract Algebra.
D&F's book is so easy to tear apart, I already used
a whole roll of 3M tape to fix it. So, not only I swore
in math, but also I sweated.
I personally believe math needs to be useful and for real.
Transfer Principle
I post here because I want to comment on issues mentioned by
MoeBlee and VK in other threads, but this is the only thread
in which both MoeBlee and VK are active.
In another thread, I accused MoeBlee of being "dogmatic," and
he likewise called me "dogmatic." I wish to quote VK from
another thread to help determine who the dogmatist really is.
Here are the comments about dogmatism given by VK:
> > [Classical analysis, in which statements like 0.999...=1 hold]
> > is not an illogical meaninglessness, it is a mathematical _dogma_.
> > Just like the statements "the unity of Father, Son, and Holy Spirit as
> > three persons in one Godhead" or "God, existing as three persons, but
> > as one being" are meaningful to ones and a complete nonsense to
> > others. Among the first ones, as in any religion, there is a narrow
> > group of believers who truly "bellyfeel" the dogma and the mass of
> > people who just learned it by heart and learned to burn out
> > heretics :-)
[emphasis mine]
So VK makes clear what he considers to be dogma, and he even compares
it to the doctrine of the Holy Trinity, thus extending the religious
analogy that I made earlier, and which MoeBlee criticized.
Which posters does VK consider to be dogmatic? As it turns out, the
poster whom VK singles out is Virgil:
> > In this group IMHO the only "bellyfeel" is Virgil. When he fights for
> > Cantor, aleph etc., I see a real passion and the desire not only to
> > defeat the opponent, but to bring him/her back to the Only Church so
> > to save yet another soul :-)
> > Others are just sad monkeys most of the time. I don't feel any real
> > understanding behind their screaming, just argumentum ad nauseam of
> > chunks of holly texts they got in the seminary... sorry... in the
> > university :-)
"Only Church"? LOL!
> > 0.(9) = 1 (The limit of the infinite sequence 0.(9) is equal to 1) is
> > part of the _dogmatic_ set of a good part of the modern math (but not
> > all of it). It is important to note "the _dogmatic_ set", not "the
> > axiomatic set". The _dogma_ has nothing to do with an axiom, so it is no
> > way something "considered to be either self-evident, or subject to
> > necessary decision".
[emphasis mine]
So MoeBlee criticized my religious analogy, but I'm hardly the first
or
only poster who believes that ZFC is like a religion. Indeed, earlier
I
attributed the religious analogy to Herc, but I stumbled upon a thread
from 2006 in which Han de Bruijn made a similar analogy -- and
naturally
MoeBlee criticized HdB in 2006 as well.
HdB, Herc, VM, and myself -- the number of posters who considers
theories
to be like religions is slowly but surely growing. Gee, I wonder why
that
could be?
> > Long discussions can be found about Cantor, sets, diagonal argument
> > etc. See for instance:
[link snipped]
> > The practicality of such discussions is close to zero, just like if a
> > Catholic priest and a Judaism priest decided to prove who's God is
> > better by using nothing but strictly logical arguments. :-)
Similarly, one can't prove whose _theory_ is better by using nothing
but
strictly logical arguments, either.
MoeBlee
> On Oct 24, 7:21 pm, "Tronscend" <tronf...@frizurf.no> wrote:
>
> > "Charlie-Boo" <shymath...@gmail.com> skrev i meldingnews:b35baf38-e483-4659...@e14g2000yqe.googlegroups.com...
> > On Oct 24, 1:18 pm, MoeBlee <jazzm...@hotmail.com> wrote:
[...]
No, I didn't write the sentence below. Your post has both you and me
on the same quoted level (I don't know how far back the error goes,
whether originated in your posts or not)..
> > > Anytime you communicate you use a language.
MoeBlee
MoeBlee
> On Oct 24, 7:59 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > No, I'd rather not waste my time re-typing Russell's letter to Frege,
>
> You offer no proof. That is not mathematics.
Part of communication about mathematics is referring people to widely
available original sources.
> Your personality flaw interferes with whatever mathematical abilities
> you may have.
What you just said is not mathematics, and it's a stupid remark too.
> It's easy: Frege said every property is a set of not being an element of oneself,
I highly doubt that. Please quote exactly what remark of Frege you
have in mind.
> > > Axiom 1: -~P/P Diagonalization
>
> > Uh huh, and the language in which that axiom is stated is _______ ?
>
> CBL (a simple extension to FOL and the notion of characterizing sets)
There are many first order languages. What EXACTLY is your language
CBL?
MoeBlee
MoeBlee
> So MoeBlee criticized my religious analogy, but I'm hardly the first
> or
> only poster who believes that ZFC is like a religion.
So? There are MILLIONS of people who believe all kinds of ridiculous
things.
> Indeed, earlier
> I
> attributed the religious analogy to Herc, but I stumbled upon a thread
> from 2006 in which Han de Bruijn made a similar analogy -- and
> naturally
> MoeBlee criticized HdB in 2006 as well.
>
> HdB, Herc, VM, and myself -- the number of posters who considers
> theories
> to be like religions is slowly but surely growing. Gee, I wonder why
> that
> could be?
It could be for many reasons. Are you suggesting that the reason is
that you're correct? Surely you're not claiming that the fact that
some people share your belief is reason to conclude that your belief
is correct?
MoeBlee
MoeBlee
I've given rebuttals to the claim that set theory is "religion" or
even substantially like religion, etc.
You've not refuted my rebuttals.
MoeBlee
Charlie-Boo
> > IT'S EASY. Math is the science that doesn't use our 5 senses. So
> > there are no animals or planets or photons to observe. People think
> > of science X which uses your senses to observe Y as being a deductions
> > about Y, so it is Y (animals, photons, etc.) and the rules that are
> > used to PREDICT Y.
>
> Other texts snipped.
>
> I beg to differ.
>
> By your saying, Math is philosophy.
You mean philosophy is math? Philosophy does use the real world as
its starting point. If man enjoyed complete peace, justice and
harmony, we wouldn't be debating what is good and just.
> When you see one finger of your right hand and another
> of left hand, your observation tells you 1+1=2. This is
> the foundation of math. Math cannot be deviated from
> reality too much. Otherwise you are studying philosophy.
You may have something there. Math abstracts all branches of science
and doesn't need to refer to the real world from which they derived
their rules. But math relies on the other branches of science which
got their rules from reality.
C-B
Charlie-Boo
> Have you ever tried swearing in mathematics?
That's pretty common, actually. Have you ever heard a mathematician
find a flaw in his 20 page proof?
C-B
Charlie-Boo
> On Oct 24, 7:54 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > On Oct 24, 7:59 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > > No, I'd rather not waste my time re-typing Russell's letter to Frege,
>
> > You offer no proof. That is not mathematics.
>
> Part of communication about mathematics is referring people to widely
> available original sources.
>
> > Your personality flaw interferes with whatever mathematical abilities
> > you may have.
>
> What you just said is not mathematics, and it's a stupid remark too.
>
> > It's easy: Frege said every property is a set of not being an element of oneself,
>
> I highly doubt that. Please quote exactly what remark of Frege you
> have in mind.
I did but you misquoted me. Above I said: "It's easy: Frege said
every property is a set and there is a property
of not being an element of oneself, so not every property is a set."
The problem is there is no property of not being an element of
oneself. The source of the problem is his premise, not the system in
which the premise occurs.
> > > > Axiom 1: -~P/P Diagonalization
>
> > > Uh huh, and the language in which that axiom is stated is _______ ?
>
> > CBL (a simple extension to FOL and the notion of characterizing sets)
>
> There are many first order languages. What EXACTLY is your language
> CBL?
FOL + operators # / and / + interpreting free variables I J K . . . as
input and x y . . . as output, so FOL wffs can represent processes.
C-B
> MoeBlee
Charlie-Boo
> On Oct 24, 10:34 pm, Transfer Principle <lwal...@lausd.net> wrote:
>
> > So MoeBlee criticized my religious analogy, but I'm hardly the first
> > or
> > only poster who believes that ZFC is like a religion.
>
> So? There are MILLIONS of people who believe all kinds of ridiculous
> things.
1/4 of the American people think Obama is a Muslim. Almost 1/2 think
Saddam Heussein planned the 9/11 attack.
> > Indeed, earlier
> > I
> > attributed the religious analogy to Herc, but I stumbled upon a thread
> > from 2006 in which Han de Bruijn made a similar analogy -- and
> > naturally
> > MoeBlee criticized HdB in 2006 as well.
>
> > HdB, Herc, VM, and myself -- the number of posters who considers
> > theories
> > to be like religions is slowly but surely growing. Gee, I wonder why
> > that
> > could be?
>
> It could be for many reasons. Are you suggesting that the reason is
> that you're correct? Surely you're not claiming that the fact that
> some people share your belief is reason to conclude that your belief
> is correct?
A mathematician is someone who favors truth over feeling good. The
rest of the people are vice-versa.
C-B
> MoeBlee
Charlie-Boo
> P.S.
>
> I've given rebuttals to the claim that set theory is "religion" or
> even substantially like religion, etc.
>
> You've not refuted my rebuttals.
I think you want him to kiss your rebuttal.
C-B
> MoeBlee
>
> On Oct 24, 11:01 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
>
>
> > On Oct 24, 10:34 pm, Transfer Principle <lwal...@lausd.net> wrote:
>
> > > So MoeBlee criticized my religious analogy, but I'm hardly the first
> > > or
> > > only poster who believes that ZFC is like a religion.
>
> > So? There are MILLIONS of people who believe all kinds of ridiculous
> > things.
>
> > > Indeed, earlier
> > > I
> > > attributed the religious analogy to Herc, but I stumbled upon a thread
> > > from 2006 in which Han de Bruijn made a similar analogy -- and
> > > naturally
> > > MoeBlee criticized HdB in 2006 as well.
>
> > > HdB, Herc, VM, and myself -- the number of posters who considers
> > > theories
> > > to be like religions is slowly but surely growing. Gee, I wonder why
> > > that
> > > could be?
>
> > It could be for many reasons. Are you suggesting that the reason is
> > that you're correct? Surely you're not claiming that the fact that
> > some people share your belief is reason to conclude that your belief
> > is correct?
>
Jack Campin - bogus address
> Frege said every property is a set
No he didn't.
-----------------------------------------------------------------------------
e m a i l : j a c k @ c a m p i n . m e . u k
Jack Campin, 11 Third Street, Newtongrange, Midlothian EH22 4PU, Scotland
mobile: 07800 739 557 <http://www.campin.me.uk> Twitter: JackCampin
William Elliot
Solve for u, d/u(m + b) = a + s^2.
Herman Jurjus
> David C. Ullrich<ull...@math.okstate.edu> writes:
>
>> It's not clear to me what you want: An explanation of why it's valid
>> to call mathematics a language or an explanation of why people do in
>> fact call it that?
>
> Well, most likely people call mathematics a language because they find
> this image intellectually appealing in some way. What I'm wondering
> about is what exactly this metaphor is intended to convey.
>
> To answer a question asked elsewhere in this thread, I'll happily
> agree that C++ is a computer language. We may make good use of the
> language metaphor in case of computer languages: we speak of dialects of
> LISP, of idiomatic Haskell or Python, of someone's Scala style, and so
> on. Analogously, it might well make perfect sense to describe a
> formalism for recursive functions, partial differential equations,
> commutative diagrams, a language. But mathematics is not such a
> formalism. It is a field of study, a body of knowledge, methods,
> concepts, ideas, techniques, associated with which we find various
> formalisms, specialized notation, specialized jargon, and so on.
A large part of what students must learn is how to 'translate' their
intuitions (for example geometrical intuitions) into notions involving
groups, topological spaces, continuous maps, matrices, rings, field
extensions, complex functions, etc.
This does not yet involve a formal language in the above sense, but it
is a collection of notions and it requires effort to learn how to use
it. It's like learning a language. Actually it /equals/ learning a
language: namely the mathematicians' standard jargon.
--
Cheers,
Herman Jurjus
Herman Jurjus
> David C. Ullrich<ull...@math.okstate.edu> writes:
>
>> It's not clear to me what you want: An explanation of why it's valid
>> to call mathematics a language or an explanation of why people do in
>> fact call it that?
>
> Well, most likely people call mathematics a language because they find
> this image intellectually appealing in some way. What I'm wondering
> about is what exactly this metaphor is intended to convey.
>
> To answer a question asked elsewhere in this thread, I'll happily
> agree that C++ is a computer language. We may make good use of the
> language metaphor in case of computer languages: we speak of dialects of
> LISP, of idiomatic Haskell or Python, of someone's Scala style, and so
> on. Analogously, it might well make perfect sense to describe a
> formalism for recursive functions, partial differential equations,
> commutative diagrams, a language. But mathematics is not such a
> formalism. It is a field of study, a body of knowledge, methods,
> concepts, ideas, techniques, associated with which we find various
> formalisms, specialized notation, specialized jargon, and so on.
Right. Let's distinguish:
1) formal languages used in mathematics (such as FOL, ZFC, PA, etc.)
2) the 'language of mathematics'
(A considerable part of what young students must learn is: how to use
notions like 'set', 'function', 'group', 'ring', 'equation', 'Hilbert
space', 'cohomology', 'functor', etc. etc., and how to 'translate'
intuitions into this jargon and back.)
3) mathematics 'itself', i.e. as a 'body of knowledge'
I take it that we're only interested in 3) and in what sense 3) 'is a
language'.
Consider fields like biology, economics, physics.
These involve:
a) vocabulary (set of notions, plus standard associations)
b) a subject matter (the part of reality or the aspect(s) of reality
that is being studied)
c) some claims ('theories') about the subject matter / real world
When people say 'mathematics is a language', then (I think) they mean:
mathematics is like biology, economics, or physics, except that
- it doesn't have a (specific) subject matter attached
- it doesn't make claims about the real world
It only is/has jargon.
Does this make sense to anybody, or am I spouting nonsense?
--
Cheers,
Herman Jurjus
Charlie-Boo
<bo...@purr.demon.co.uk> wrote:
Why did he add an addendum to his book as a result of receiving a
letter from Russell?
C-B
> -----------------------------------------------------------------------------
MoeBlee
> On Oct 24, 11:56 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > On Oct 24, 7:54 pm, Charlie-Boo <shymath...@gmail.com> wrote:
> > > On Oct 24, 7:59 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > > It's easy: Frege said every property is a set of not being an element of oneself,
> > I highly doubt that. Please quote exactly what remark of Frege you
> > have in mind.
>
> I did but you misquoted me.
I didn't misquote you. I copied the text directly from your post.
> Above I said: "It's easy: Frege said
> every property is a set and there is a property
> of not being an element of oneself, so not every property is a set."
You also said what I quoted.
Now, where in Frege's specification of his system, did Frege say any
of this?
> The problem is there is no property of not being an element of
> oneself. The source of the problem is his premise, not the system in
> which the premise occurs.
The system includes the problematic axiom. Just read the letters
between Russell and Frege.
> FOL + operators # / and / +
So '#/' and '/+' are 1-place function symbols or 2-place function
symbols or what?
> interpreting free variables I J K . . . as
> input and x y . . . as output, so FOL wffs can represent processes.
Only you can say that means in terms of a first order language.
MoeBlee
MoeBlee
> 1/4 of the American people think Obama is a Muslim.
The poll I heard about had approximately 1/5 thinking Obama is a
Muslim.
MoeBlee
David R Tribble
>> 1/4 of the American people think Obama is a Muslim.
>
MoeBlee wrote:
> The poll I heard about had approximately 1/5 thinking Obama is a Muslim.
Most polls show that 1/2 of everyone is below average.