Language and thought

[tinyp3nis]

I grouped all under "verbal" because sign languages are based on verbal languages

To them it's 100% visual, and that's my point. They don't care or even have to be aware how the language was developed in the first place. It doesn't matter.
All I'm saying it doesn't have to be verbal.

[Nubclear]

Re: Re: Re: Language and thought

Originally posted by JimmyCracksCorn


That explains alot...

That would be logical if I said "I dont think at all". Because I dont think in either words or pictures I can think many things every second without being lagged down.

Your comment simply proves your the opposite of myself

Edit: In fact, one could say its a form of human evolution

[Urban Ranger]

Originally posted by tinyp3nis
To them it's 100% visual, and that's my point. They don't care or even have to be aware how the language was developed in the first place. It doesn't matter.
All I'm saying it doesn't have to be verbal.

In one sense, all written languages are visual (unless you are blind), because you read written material through your eyes.

That doesn't matter, though, because your brain processes it through the language centre, not the imagery centre.

[tinyp3nis]

Do you accept the fact that people who have never heard a thing can use sing language?

[Ramo]

I disagree. Language must be verbal. Because a visual or mental "language" can only be private, thus cannot be used as a medium of communication.

If I "say" something "in my head," I'm not using a form of "language?" There's no internal communication in a human brain? As for visual languages, there is math, written variants of verbal languages, sign language, etc.

Proof by definition.

That's the only kind of proof there is.

[Ramo]

Regarding math and empiricism, the basic conventions i are often based in the empiricial world (base 10, etc.), but it's independent of the empirical world. A change in the empirical world (say, humans have 14 fingers in the future) doesn't necessitate a change in math.

There is no truth" in mathematical assertions. The conventions you use are totally arbitrary. If you define real numbers a different way, "obvious" mathematical assertions can suddenly become "nontruth." For instance, is the set of real numbers open? It's as good an answer to say yes as it is to say no. Of course, a number of mathematical theorems may be contingent upon the convention of the set of real numbers being open.

[Agathon]

Originally posted by Asher
I bet it's some childish dig at me since it's embarassing for you to be completely owned by an undergrad compsci student...

You sound like Saddam Hussein when he claims "victories".

If you'd only clarify your own statements instead of sulking, you might even convince me. Like this one:

The notation, and the ideas behind addition, are mathematics. There is no mathematical "system", it's just a fact of our world that if we have one object and we add another object, we have two objects.

Yes and that is why "1+1=2" is true. Not because we decided that it did or made up some convention. Whatever system we use to describe the fact doesn't change it at all - the world is supremely indifferent to our attempts to conceptualise it.

The systems we use to calculate this, the words we use to describe it, and the notation we use, are all man-made constructs. That's what mathematics is.

But that doesn't prove that all mathematical truth is conventional. All it states is the deeply unexciting thesis that we made up the symbolic system. Ordinary language and it's grammar are constructs in exactly this sense - we made them up - but not all meaningful statements made by said languages are made true or false by convention.

If this is supposed to be your killer claim then it's pretty f*cking useless.

Let's look at your claim again

The systems we use to calculate this, the words we use to describe it, and the notation we use, are all man-made constructs. [/quote].

What do the bolded words refer to if not the fact? They certainly don't refer to the conventions since they are spoken of in relation to it.

[Agathon]

Originally posted by Ramo
Regarding math and empiricism, the basic conventions i are often based in the empiricial world (base 10, etc.), but it's independent of the empirical world. A change in the empirical world (say, humans have 14 fingers in the future) doesn't necessitate a change in math.

There is no truth" in mathematical assertions. The conventions you use are totally arbitrary. If you define real numbers a different way, "obvious" mathematical assertions can suddenly become "nontruth." For instance, is the set of real numbers open? It's as good an answer to say yes as it is to say no. Of course, a number of mathematical theorems may be contingent upon the convention of the set of real numbers being open.

At last a reasonable post on the matter. See Asher this is what you need to do instead of BAMing like some two year old.

All I was claiming Ramo is that Asher hasn't made the case for mathematics being entirely a matter of convention. Whatever base we use is arbitrary, but it seems to me that the truth of simple mathematical propositions like "2+2=4" is explained by universalizable facts about the world rather than our conceptualisation - or at least that is the default common sense position which needs reasons against it. One could argue that mathematics is a priori, but that doesn't entail conventionalism without some more argument.

There are a number of possible explanations for mathematical truths: platonism (mathematical statements are about real entities); Aristotelianism (mathematical statements are about abstracted universals); conventionalism (mathematical statements aren't about anything and respond to arbitrary norms); or innateness (innate structures in the mind are the root of mathematical truth). And there's more.

I can think of compelling reasons for and against each of these, but I'm not sure that they'd help us with the Sapir-Whorf thesis.

[Agathon]

Originally posted by Ramo

If I "say" something "in my head," I'm not using a form of "language?" There's no internal communication in a human brain? As for visual languages, there is math, written variants of verbal languages, sign language, etc.

If you say something "in your head" is this to be taken literally or metaphorically, and is it even a referring expression like "something in the garden"?

[HershOstropoler]

Interesting question.

I consciously use english and german for specific purposes when thinking about legal issues. German is more precise and usually richer in describing complex ideas, maybe due to its notorious composita. English is often better at expressing broad ideas or concepts with some emotional content.

It's a bit stranger with economics. I learned the basics in german and sometimes lack the english words. On the specialised issue that I've dealt more with, I read most about it in english, and sometimes lack the german terms. I sometimes switch languages during one thought.

[Ramo]

All I was claiming Ramo is that Asher hasn't made the case for mathematics being entirely a matter of convention. Whatever base we use is arbitrary, but it seems to me that the truth of simple mathematical propositions like "2+2=4" is explained by universalizable facts about the world rather than our conceptualisation - or at least that is the default common sense position which needs reasons against it. One could argue that mathematics is a priori, but that doesn't entail conventionalism without some more argument.

If you have one pair of an apples and another pair of apples, and you bring them together and get 4 apples, this is an empirical, physical observation, and has no bearing on mathematical systems. If nature of reality were changed in such a way that if you bring two pairs of apples together, one apple disappears, this would not refute the idea that 2 + 2 = 4. The assertion that 2 + 2 = 4 is true only because the addition of real numbers is defined in a way such that 2 + 2 = 4.

You could make a case that certain mathematical concepts have been tied to the empirical world in the past, for instance the calculus of the infinitesimal or the Dirac delta function. But they have since been properly formalized - infinitesimal calculus by Riemann, Cauchy, et al. in the 19th century, the Dirac delta function relatively recently. Math is no longer dependent upon the physical world.

If you say something "in your head" is this to be taken literally or metaphorically, and is it even a referring expression like "something in the garden"?

Literally. By this, I mean communication between internal constructs your mind makes up.

[Asher]

Agathon: I'm confused, but not surprised, that you're still having trouble with this.

Mathematics is a system devised by man to describe and analyze natural phenomenon, that's why it's man-made.

I'm not sure why you require me to delve into 200 pages of philosophical bull**** when it's such a simple fact...

[Agathon]

Originally posted by Ramo

If you have one pair of an apples and another pair of apples, and you bring them together and get 4 apples, this is an empirical, physical observation, and has no bearing on mathematical systems. If nature of reality were changed in such a way that if you bring two pairs of apples together, one apple disappears, this would not refute the idea that 2 + 2 = 4. The assertion that 2 + 2 = 4 is true only because the addition of real numbers is defined in a way such that 2 + 2 = 4.

It perhaps has an epistemic bearing on the question of how we come to know such things are true and what the truth makers for mathematical propositions are. The latter is what I am worried about rather than the former.

I think your argument about the apples is invalid, if I brought two apples together and one disappeared we would no longer be talking about the same fact. All I need to get my realist argument going is that in the natural world there are real sets of things like "three apples" and that such a proposition would be true even if nobody existed. I'm arguing that simple mathematical statements of addition and so on have truth conditions that are independent of our conceptualising activities (i.e realist truth conditions). After all it seems dumb to say that the possibility of three apples existing is mind dependent (as it would be if all mathematical notions were conventional).

Whatever ontological moves one wants to make after this don't really bother me.

My main annoyance with conventionalism is that it is like other forms of conceptual relativism in that it is on the face of it impossible for us to deny that 2 and 2 is 4 and no compelling evidence to assume that the opposite would ever be intelligible to anyone. While there is nothing wrong with non-euclidean geometries I find the notion of counter-logics less than compelling. And moreover the attempts to assert conceptual relativism as a general thesis violates its own prohibitions.

You could make a case that certain mathematical concepts have been tied to the empirical world in the past, for instance the calculus of the infinitesimal or the Dirac delta function. But they have since been properly formalized - infinitesimal calculus by Riemann, Cauchy, et al. in the 19th century, the Dirac delta function relatively recently. Math is no longer dependent upon the physical world.

I'm not saying that all of it is thus far. And I'm not endorsing the claim that if it isn't absolute conventionalism is true. After all platonism about mathematical entities would do a better job of making sense of our intuition that some mathematical statements are true and others are false and would not make mathematical statements dependent on the physical world. That's roughly what I've been objecting to - the move straight to conventionalism without further argument. And it's one thing to say that mathematics is mind dependent but another to say that it is conventional all the way down.

In fact I'm inclined more to the Quinean view that there is nothing which isn't dependent on the physical world and that there are no a priori claims - partially because such things would be untranslatable (basically Davidson's objection to the Sapir-Whorf thesis) and partially because I've never seen a compelling account of a priori knowledge. If they are right then mathematics would be largely conventional but subject to empirical revision.

Literally. By this, I mean communication between internal constructs your mind makes up.

Not physically respectable entities are they? Why do you assume that when I say "I have an idea in my mind" that I'm referring to an actual object?

[Agathon]

Originally posted by Asher

Mathematics is a system devised by man to describe and analyze natural phenomenon, that's why it's man-made.

(A) Language is to a large degree a system devised by man to describe and analyze natural phenomenon, that's why it's man-made. ("to a large degree" is meant to exclude social uses of language: imperatives, avowals, etc.)

but from (A) by itself does not follow:

(B) Every sentence of every language has truth conditions which are conventional.

Inferring from A to B without some argument is committing a fallacy. That's my objection to your premature conventionalism, in a nutshell.


Anyway, I'm not the only person who's confused about the correct view of mathematics. I am in distinguished company.

Logicism: [Bertrand Russell, Gottlob Frege] The position that mathematics is reducible to pure logic (i.e., derived from logical concepts using deductive methods) -- mathematics is nothing but a part of logic.

Intuitionism: [L.E.J. Brouwer, Arend Heyting] The position that mathematics is the production of the human intellect. There is no mathematical existence independent of human thought. (see Constructivism and Finitism).

Formalism: [David Hilbert, Haskell B. Curry] The position that mathematics is a combinatorial game played with defined symbols (primitives of the language). In doing mathematics, we determine in a finitary combinatorial way to which combination of symbols the construction methods (proofs) lead.

Platonism: [Plato, Kurt Gödel, Pennelope Maddy] The position that abstract entities (e.g., numbers, sets, proofs, relations, functions) exist independently of human thought.

Nominalism: [John Burgess, Duns Scotus, Charles Chihara] The position that abstract entities (e.g., numbers, sets, proofs, relations, functions) do not exist independently of human thought.

Foundationalism: [Gottlob Frege, Bertrand Russell, L.E.J. Brouwer] The position that mathematics requires a foundation from which the rest of mathematics is developed.

Conventionalism: [W.V. Quine] The position that the truth of mathematical statements is purely conventional (presumable we could have had other conventions).

Finitism: [David Hilbert] The position that all meaningful mathematics must rely of methods that are finitary (i.e., the methods must come to an end after a finite amount of time).

Constructivism: [L.E.J. Brouwer, Immanuel Kant] The position that mathematics is a construct of the human mind.

Empiricism: [John Stuart Mill, Philip Kitcher] The position that mathematics is learned from empirical data -- we learn to count by collecting rocks and from there develop the abstract notion of number.

Structuralism: [BOURBAKI, Stewart Shapiro] AS BOURBAKI state, the position that "mathematics is a structure of abstract forms." In other words, mathematics is the study of structure and pattern.

Anti-Formalism: [Henri Poincare, Kurt Gödel] The position that no mechanistic, formal method can create all of mathematics, rather mathematics requires genuine creativity.

Logicism seems to me to be a dead duct since mathematics doesn't seem to be reducible to pure logic. I'd be closest to Quine (who is not a pure conventionalist - so this guy is wrong). But I don't know - the empiricist version looks like common sense.

And who would have thought that such a respected mathematician as Godel would be a f*cking platonist?

[Asher]

This thread makes me so sad.

To think, taxpayer's money goes into **** like this.