17-03-2003 10:39									#91
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quote: 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.

	17-03-2003 10:47									#92
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quote: 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

	17-03-2003 10:52									#93
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quote: 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.

	17-03-2003 10:59									#94
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Do you accept the fact that people who have never heard a thing can use sing language?

	17-03-2003 11:41									#95
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quote: 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.

quote: Proof by definition.

That's the only kind of proof there is.

	17-03-2003 11:55									#96
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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.

	18-03-2003 00:06									#97
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quote: 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:

quote: 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.

quote: 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.

	18-03-2003 00:19									#98
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quote: 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.

	18-03-2003 00:21									#99
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quote: 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"?

	18-03-2003 00:36									#100
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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.

	18-03-2003 02:02									#101
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quote: 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.

quote: 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.

	18-03-2003 02:09									#102
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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 bullshit when it's such a simple fact...

	18-03-2003 03:18									#103
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quote: 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.

quote: 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.

quote: 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?

	18-03-2003 03:26									#104
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quote: 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.

quote: 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?

	18-03-2003 03:32									#105
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This thread makes me so sad.

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

	18-03-2003 04:03									#106
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First of all: honestly, I have nothing against either you Asher or Agathon, but...

You clog too many threads with these long bickering matches you two have. If you want to bicker, make a thread called "the Asher and Agathon show", and go at it there. You can reach 500 posts, then start II and II and so forth..OK?

Now, back to the issue:

I must agree with Ramo on the issue of mathemitics simply being a different language form instead of some seperate thing. If, for example would we have calculus? And the "invention" of 0: was it the discovery of something? or simply the creation of a new term?

I also do think some thoughs obviously come up in some languages and not others..if not I think the transfer of words accross languages would be far less, if everyone had a word for the one concept that came up first. For example, schadenfreude..would such a notion ever have come up in English?

	18-03-2003 04:12									#107
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quote: Originally posted by GePap First of all: honestly, I have nothing against either you Asher or Agathon, but... You clog too many threads with these long bickering matches you two have. If you want to bicker, make a thread called "the Asher and Agathon show", and go at it there. You can reach 500 posts, then start II and II and so forth..OK? Now, back to the issue: I must agree with Ramo on the issue of mathemitics simply being a different language form instead of some seperate thing. If, for example would we have calculus? And the "invention" of 0: was it the discovery of something? or simply the creation of a new term? I also do think some thoughs obviously come up in some languages and not others..if not I think the transfer of words accross languages would be far less, if everyone had a word for the one concept that came up first. For example, schadenfreude..would such a notion ever have come up in English?

I have no desire to bicker with Asher at all. He follows me around the forum making snide comments about things that he doesn't appear to have a good grasp of and then refuses to answer when pressed. All in all it's got pretty boring.

Anyway, back on topic:

Do you think there is such a thing as an untranslatable language?

	18-03-2003 09:29									#108
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In what concerns mathematics, I have not read the whole discussion (too long), but IMHO Agathon is right.

	18-03-2003 09:40									#109
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quote: Originally posted by Ramo There is no truth" in mathematical assertions. The conventions you use are totally arbitrary.

Not completely arbitrary. For example, the system of axioms you choose should be noncontradictory.

	18-03-2003 09:48									#110
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You done much philosophy V? From your other posts you sound reasonably clued up.

	18-03-2003 09:50									#111
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quote: Originally posted by Asher Mathematics and stuff like physics are constructs created by man to help understand natural phenomenon.

So if mathematics "helps understand" natural phenomena, this means that it corresponds to something real in the real world. What is what you are arguing about, Asher?

quote: You don't seem to understand what mathematics is in the first place. You should realize that mathematics are rules and theorems based upon what we observe to be the case, not the actual cases themselves.

What is 'Asher'? Is it a person or a name of a person?

	18-03-2003 09:50									#112
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quote: Originally posted by The Vagabond In what concerns mathematics, I have not read the whole discussion (too long), but IMHO Agathon is right.

How is it right?
By the very definition of mathematics, it's man-made.

Agathon doesn't grasp the difference between mathematics and the actual phenonemon that occur that mathematics measure.

In very typical philosophical style, he tried to make the discussion so incredibly complex and longwinded when it's a simple matter. He didn't know what the word meant, when confronted with a definition he scoffed and mentioned some laughable excuse about OED not know anything about truth values.

	18-03-2003 09:51									#113
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quote: Originally posted by The Vagabond So if mathematics "helps understand" natural phenomena, this means that it corresponds to something real in the real world. What is what you are arguing about, Asher?

"Correspond" != "equal to"...

Mathematics is the study of the natural phenomenon that Agathon and you are mistaking for "mathematics". Mathematics is the STUDY of that phenomenon, not the phenomenon itself.

That's a very important distinction.

quote: What is 'Asher'? Is it a person or a name of a person?

Asher is the name, there are probably hundreds of thousands of people named Asher.

Not to mention it's not even my name.

Good question, helps illustrate my point.

	18-03-2003 09:55									#114
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quote: Originally posted by Agathon You done much philosophy V? From your other posts you sound reasonably clued up.

Well, just a regular Soviet course of philosophy. I am not a connoisseur of philosophy. I just happen to have sincere respect for it.

	18-03-2003 10:06									#115
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quote: Originally posted by Asher "Correspond" != "equal to"... Mathematics is the study of the natural phenomenon that Agathon and you are mistaking for "mathematics". Mathematics is the STUDY of that phenomenon, not the phenomenon itself. That's a very important distinction.

Of course it is just the description of the phenomenon, not the phenomenon itself.

What you're incorrect about is that mathematics is just a man-made system of conventions and has nothing to do with the truth about the real world.

	18-03-2003 10:24									#116
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quote: Originally posted by The Vagabond Of course it is just the description of the phenomenon, not the phenomenon itself. What you're incorrect about is that mathematics is just a man-made system of conventions and has nothing to do with the truth about the real world.

I've never said anything about the truth of the real world. Agathon went on a weird tangent about that and I've ignored it since it's irrelevant.

Mathematics is a man-made system, since man made it to help us understand how the world works. It "corresponds" to natural events because that's what it's designed to do.

It's a man-made system, regardless of truth values it has...

Philosophers have a really bad tendancy to obfuscate things beyond belief...

	18-03-2003 10:35									#117
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quote: 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.

1. What is "epistemic?"
2. The only truth maker for a mathematical proposition is that it isn't contradictory (with itself or generally accepted work).

quote: 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.

Would you mind explaining this? I think I can see where you're going (you can never have a pair of apples in the first place), but I'm not sure how you reach the conclusion of invalidity of my argument. What do you mean by "no longer talking about the same fact?"

quote: 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).

1. Did you mean to say four apples instead of three?
2. I really don't follow your argument, at all. No offense, but this sounds like a lot of bullshit to me.

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

I have no clue what you mean when you use words like "ontological." I've never taken a philosophy class except logic.

quote: 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.

I think that 2+2=4 is possible to deny. Maybe because I've taken too much math.

quote: And moreover the attempts to assert conceptual relativism as a general thesis violates its own prohibitions.

Ah, but it doesn't. The idea of conceptual relativism (unless it's some obscure term that isn't what it sounds like it should be) relies upon the same assumption that almost all math/philosophy relies upon, the equivalence of validity and non-contradiction. In fact, it follows directly from this assumption.

quote: 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.

Platonism is silly, IMO. What is the meaning of the existence of an abstract "entity" like a group outside the context of minds of sentient beings?

quote: 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.

What's the distinction between mind-dependent and conventional?

quote: In fact I'm inclined more to the Quinean view that there is nothing which isn't dependent on the physical world

Is an assertion like "A is true" dependent upon the physical world? If so, how?

quote: and that there are no a priori claims

I would agree with that.

quote: 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?

If the idea isn't in your mind, where is it? The idea isn't some box labelled "idea," but a bunch of neurons acting in a certain manner creating what's considered an idea.

	18-03-2003 10:36									#118
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quote: Originally posted by Asher Mathematics is a man-made system, since man made it to help us understand how the world works. It "corresponds" to natural events because that's what it's designed to do. It's a man-made system, regardless of truth values it has...

Certainly it is a man-made system, just as all other sciences.
But would you agree that it describes certain truth of the real world?

	18-03-2003 10:38									#119
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quote: Originally posted by The Vagabond Certainly it is a man-made system, just as all other sciences.

Thank you, this is what the argument was about.
Agathon tried (unsuccessfully) to argue the other way through smoke and mirrors.

quote: But would you agree that it describes certain truth of the real world?

Sure, why not. It describes certain truths in our world. No problem there.

	18-03-2003 10:43									#120
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quote: Mathematics is the study of the natural phenomenon that Agathon and you are mistaking for "mathematics". Mathematics is the STUDY of that phenomenon, not the phenomenon itself. That's a very important distinction.

Mathematics is a tool through which one studies natural phenomenon. Science is the study of natural phenomenon. There's plenty of math that's totally abstract and has virtually no connection with the physical world.

quote: Not completely arbitrary. For example, the system of axioms you choose should be noncontradictory.

Well yes, all generally accepted math is based on noncontradiction.

Of course, you could come up with a mathematical system that isn't based on noncontradiction. It's just that such a system wouldn't be particularly useful.