17-03-2003 04:32									#31
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First answer this: If mathematics is not man-made construct, and someone makes an argument saying the same thing, couldn't they argue that the C programming language isn't a man-made construct?

filosofy...

And please don't talk to me about **** like the "law of non-contradiction"...

	17-03-2003 04:33									#32
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quote: And surely if no human beings existed two apples plus two apples would still be four apples and not five - even though there was nobody around to observe this stupendous fact.

Surely, but surely you also realize that mathematics is just the method of observing that phenomenon?

filosofy...

	17-03-2003 04:34									#33
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quote: Originally posted by Paul Hanson I always had the impression that we used to use Base 12 at some point in the past. The fact that a clock has 12 hours rather than 10, and that we say "eleven" and "twelve" rather than "oneteen" and "twoteen", for example.

If I recall correctly, the Babylonians used a non base-10 number system. I don't know if it was base-60 (and hence the sixty seconds and sixty minutes) or base-12, but I do think that it had an impact on our measure of time for some strange reason.

It wasn't a very good link, and I can't claim to have been impressed by the argument, but it's as sound a theory as any. I think I remember reading a book about the history of zero, and it had a break down of Mesopotamian number systems. It wasn't where I heard the time theory though, that was from some high school teacher.

In short, it's likely that there was a base-12 in the past. Wasn't the old pound/shilling/pence system base-12? And old English units of measure are more or less binary (e.g. 8 fluid ounces in a cup, 16 in a pint, 32 in a quart, 128 in a gallon)

	17-03-2003 04:36									#34
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Base 12 is AKA "DuoDecimal".

http://www.psinvention.com/zoetic/base12.htm

quote: Twelve was used as a basic group of things. The group of twelve was then multiplied by other numbers to get bigger numbers. One example being the Great Hundred of Northern Europe which was 120 units (10 x 12). The group of twelve could also be divided into equal groups by many numbers due to its many factors (numbers that can be divided into a number without a remainder). The Roman Duodecimal fractions consisted in fractions of only those factors of 12. (twelfths, sixths, fourths, thirds and halves). Base 12 was used not as a formalized place value, but rather as a grouping value that combined with other values to a larger grouping value. For example 10 twelves are 120 or the Great Hundred. The Cycle of Cathay for China represents the combination of a cycle of 10 and a cycle of 12 which results in a cycle of 120. Also 5 twelves are 60 which was a highly developed numbering system thousands of years ago. see base 60 The use of 12 as a grouping value can be seen as arising from its many divisors, which would let someone who had 1 dozen or group of something to divide it up easily. The use of 12 as a grouping value may also be related to the observation that there are approximately 12 months (moons) in year. Many cultures observed 12 zodiacal formations in the stars as the year progressed.

	17-03-2003 04:37									#35
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quote: Originally posted by Paul Hanson I always had the impression that we used to use Base 12 at some point in the past. The fact that a clock has 12 hours rather than 10, and that we say "eleven" and "twelve" rather than "oneteen" and "twoteen", for example.

Certainly for measures, perhaps because 12 is easy to divide. Inch and ounce both meant "a twelfth part" originally, and were subdivisions of the foot and pound respectively.

	17-03-2003 04:40									#36
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Thanks Asher, I didn't really feel like looking anything up on that.

	17-03-2003 04:43									#37
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I pity the nations that don't use metric system. I hope Canada is not one of them.
Anyway, somebody should make a system with a odd base number. 7 or 13 would be nice. Is there one already? And is this thread still on topic?

	17-03-2003 04:44									#38
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Canada uses the metric system.

	17-03-2003 04:51									#39
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A few words translated from thoughts on the matter. It is obvious that however we do think, it is something that has been with us since before we were homo sapiens sapiens. Homo erectus seemed to have many of the tools we enjoy, including a rich language capability. Thus it seems that for at least a million years our cognitive capabilities and rich language have evolved together. Is there thought without language? It depends on your definition of thought, for me the answer is certainly. Would our thoughts be very profound without language? Probably not. Puting aside the question of whether those of us who sometimes think without the languages we use to communicate to others are in fact communicating internally with another language of our own devising, we gain so much from the work of those that came before us. We do not have to reinvent the wheel because we can store immense amounts of information verbally as a community. Add printed or written texts and we can communicate with one another across generations with relatively little information loss. IMO though language and thought are two distinct things, in humans the two are so layered together that removing one would obliterate or nearly obliterate the other.

	17-03-2003 04:55									#40
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A thought only "means" something in the context of a language. The language doesn't have to be verbal. It can be visual or even mental. By this, I mean that I'm generalizing the idea of language as expression of thought. Without "language," there is no expression of thought. Furthermore, if you constrain language in certain respects, expression of though is similarly constrained. For instance, the "language" of tensor analysis, allows you to properly express the thought of gravity. If your languages have no concept of freedom, or in other words, the lack of constraint, you cannot express the thought of the lack of constraint. Furthermore, you can't use freedom as the lack of constraint as an axiom on which to come up with more complex thought. You can't fight for a generalized idea of freedom if you've never dealt with the concept.

I'm doing a paper on precisely this topic right now, in fact. Wycliffe and the Lollards supplied the English peasants a vocabulary of a more generalized version of freedom, even if he was primarily dealing with the struggle between the lay aristocracy and the Church, but the English peasantry picked up on this vocabulary and ran with it in 1381.

Speaking of Orwell, this might interest some of y'all:
http://www.resort.com/~prime8/Orwell/patee.html

	17-03-2003 05:03									#41
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quote: I always had the impression that we used to use Base 12 at some point in the past. The fact that a clock has 12 hours rather than 10, and that we say "eleven" and "twelve" rather than "oneteen" and "twoteen", for example.

Base 12 was probably initially based on the number of finger parts in a hand (excluding the thumb).

Interestingly enough, base 60 of Sumeria (60 seconds in an minute, 60 minutes in an hour, 360 degrees in a a circle) is probably a combination of base 12 and base 5 (which is due to the number of fingers in a hand).

	17-03-2003 05:24									#42
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quote: Originally posted by Ramo Base 12 was probably initially based on the number of finger parts in a hand (excluding the thumb). Interestingly enough, base 60 of Sumeria (60 seconds in an minute, 60 minutes in an hour, 360 degrees in a a circle) is probably a combination of base 12 and base 5 (which is due to the number of fingers in a hand).

Spread your right hand, and then, using each of the fingers of your left hand (including the thumb), touch each segment of your right hand fingers (excluding the thumb).

It counts to 60.

	17-03-2003 07:19									#43
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quote: Originally posted by Asher Surely, but surely you also realize that mathematics is just the method of observing that phenomenon?

Duh - lame. If it is observed that 2+2=4, that's your contention that mathematics is a human creation gone out of the window - since the fact remains the same independent of human thought. There are other problems too.

If mathematics is wholly conventional then it has no empirical basis.

	17-03-2003 07:21									#44
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Mathematics and stuff like physics are constructs created by man to help understand natural phenomenon.

I'm not sure why you don't understand that...

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.

If that makes sense anyway.

filosofy...

PS: I'm still completely amazed by your lack of general insightfulness and debate skills as a philosophy professor.

	17-03-2003 07:34									#45
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quote: Originally posted by Asher First answer this: If mathematics is not man-made construct, and someone makes an argument saying the same thing, couldn't they argue that the C programming language isn't a man-made construct?.

Easily done. The C programming language is wholly conventional, that is the standard of getting things right (constructing "grammatically correct" statements in the language) is based on a set of rules laid down by a human being or beings (like the rules of chess).

The mathematical statement 2+2=4 does indeed have a standard of grammatical correctness that is conventional (that is I have to use the right signs in the correct order to convey what I mean to another using a shared convention like Hindu Arabic numerals). But it also has the property of being true, of being in correspondence with the way the world is.

Statements in programming languages don't have such truth values.

Take another example: the game of chess has rules of correct play which are wholly conventional. But who would ask whether the move "Pawn to Rook 3" is true or false? We would ask whether it was allowed or not, but not whether it was true or false.

Now you could mount an argument that mathematical statements didn't have truth values, but you would need more than your superficial comparison.

	17-03-2003 07:37									#46
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quote: Originally posted by Asher Mathematics and stuff like physics are constructs created by man to help understand natural phenomenon. I'm not sure why you don't understand that...

I'd like to believe it, but I can't.

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.

Based on what we observe to be the case. That's not wholly conventional. Point proven.

quote: If that makes sense anyway.

Not really.

quote: PS: I'm still completely amazed by your lack of general insightfulness and debate skills as a philosophy professor.

Really, I'm still amazed by your lack of ability to respond to a point with anything other than assertion.

	17-03-2003 07:42									#47
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I can't explain it to someone who is incapable of understanding.

I make "assertions*", you make "bullshit".

* Assertions meaning observations based on fact, rather than random philosophical pondering

	17-03-2003 07:45									#48
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quote: Originally posted by Asher PS: I'm still completely amazed by your lack of general insightfulness and debate skills as a philosophy professor.

Actually this is pretty lame on your part. In the "philosophy" thread you were adamant that it was useless even though it was pointed out to you the uses of philosophy in cognitive science, logic, political theory, medical ethics, and the history of philosophy as a part of the study of history.

Your response was just to deny that these were useful or could come up with things that would be useful in the future, even though you have no knowledge of any of these subjects.

Then again in your daft "Republic of Alberta" thread, you couldn't answer the simple objection that it would be undemocratic for Alberta to separate when it didn't have the constitutional right to do so. I asked you the same question numerous times which you never answered properly.

I admit I have no debate skills as far as scoring cheap points using beliefs I picked up from talk radio. But they are worthless to me.

	17-03-2003 07:46									#49
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quote: Originally posted by Agathon Easily done. The C programming language is wholly conventional, that is the standard of getting things right (constructing "grammatically correct" statements in the language) is based on a set of rules laid down by a human being or beings (like the rules of chess).

ie, mathematics?

quote: The mathematical statement 2+2=4 does indeed have a standard of grammatical correctness that is conventional (that is I have to use the right signs in the correct order to convey what I mean to another using a shared convention like Hindu Arabic numerals). But it also has the property of being true, of being in correspondence with the way the world is. Statements in programming languages don't have such truth values.

Actually, they do...

Programming languages are a way to describe observations, exactly like mathematics. You seem to think mathematics is some magical subsystem of the universe -- that's not what we're talking about. We're talking about mathematics as mathematics, a set of rules and theorems governing observations around us.

quote: Take another example: the game of chess has rules of correct play which are wholly conventional. But who would ask whether the move "Pawn to Rook 3" is true or false? We would ask whether it was allowed or not, but not whether it was true or false.

How is this at all a relevant example?

	17-03-2003 07:50									#50
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quote: Originally posted by Agathon Actually this is pretty lame on your part. In the "philosophy" thread you were adamant that it was useless

as a university discipline. Please read, and comprehend that, I'm a bit tired of having to correct you constantly.

quote: Your response was just to deny that these were useful or could come up with things that would be useful in the future, even though you have no knowledge of any of these subjects.

You still don't even understand my argument. The argument was philosophy was totally useless as a university discipline, and you set up strawmen constantly (and still do now) to try to "win".

quote: Then again in your daft "Republic of Alberta" thread, you couldn't answer the simple objection that it would be undemocratic for Alberta to separate when it didn't have the constitutional right to do so. I asked you the same question numerous times which you never answered properly.

"undemocratic" to separate? Biggest bullshit statement I've heard from you in a while.
"illegal" to separate, yes. But if an entire ****ing region votes overwhelmingly to separate, I'd doubt it'd be "undemocratic" to do so.

	17-03-2003 07:50									#51
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quote: Originally posted by Asher I can't explain it to someone who is incapable of understanding. I make "assertions*", you make "bullshit". * Assertions meaning observations based on fact, rather than random philosophical pondering

What do you mean by "based"? Do you mean that we see 2 groups of 2 several times and infer that 2+2=4 or we notice a sort of general fact (I've never observed such a thing)?

In either case mathematics is not wholly conventional. The symbolism we use to express mathematical statements is conventional but the truths they express are not. I see you happily avoided my explanation of why mathematics is different from C.


Now Now - there's no need to be abusive because you posted without thinking.

	17-03-2003 07:53									#52
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quote: Originally posted by Agathon What do you mean by "based"? Do you mean that we see 2 groups of 2 several times and infer that 2+2=4 or we notice a sort of general fact (I've never observed such a thing)?

What the hell? Where do you get this stuff?
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.

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.

quote: In either case mathematics is not wholly conventional. The symbolism we use to express mathematical statements is conventional but the truths they express are not.

Again, you should figure out what mathematics is.

quote: I see you happily avoided my explanation of why mathematics is different from C.

No I didn't. Try reading the entire thread.

quote: Now Now - there's no need to be abusive because you posted without thinking.

The problem with you, and most "philosophy majors", is you over-think. Like in this case, you are overlooking the simple observational fact of what mathematics is.

Mathematics is entirely a 100% human-made construct to help us better understand natural phenomenon. For whatever reason, you seem to equate mathematics TO that natural phenomenon. It is not.

Recognize the distinction, please.

	17-03-2003 07:55									#53
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quote: Originally posted by Asher Programming languages are a way to describe observations, exactly like mathematics. You seem to think mathematics is some magical subsystem of the universe -- that's not what we're talking about. We're talking about mathematics as mathematics, a set of rules and theorems governing observations around us.

And what observations do they describe? I wasn't aware that an instruction is an observation. I don't know enough about C to comment, the only computer language I ever used was BASIC back in the early 80s.

In any case if the language is to describe things then its statements are true or false depending on whether they correspond to the facts. If they report the facts correcty the statements are not conventional any more than the fact that there's a glass on my desk is a matter of convention.

I don't care what "we're" talking about. I'm talking about the simple fact that 2+2=4 independently of my thinking about it or anyone elses thinking about it.

	17-03-2003 07:58									#54
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quote: Originally posted by Agathon And what observations do they describe?

Same things mathematics can, and more.

quote: I wasn't aware that an instruction is an observation.

Ah, well let me help you then. Simple example:

code:
if((2+2) == 4) printf(2+2 = 4);

This is the observation 2 + 2 = 4...

quote: I don't care what "we're" talking about. I'm talking about the simple fact that 2+2=4 independently of my thinking about it or anyone elses thinking about it.

Ah, here we go.
A simple semantic problem, the root of ALL philosophical discussions.

You don't comprehend that mathematics is more than simple arithmetic, it seems.

	17-03-2003 08:01									#55
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quote: Originally posted by Asher as a university discipline. Please read, and comprehend that, I'm a bit tired of having to correct you constantly.

Since amateur philosophy is generally pretty useless that seems to me to get it round the wrong way.

quote: You still don't even understand my argument. The argument was philosophy was totally useless as a university discipline, and you set up strawmen constantly (and still do now) to try to "win".

What argument? You BAMed. I've pointed out to you the myriad ways in which philosophy contributes and you just dismiss them out of hand. As for within the university - go and open up any social science book and likely as not you will find philosophical ideas being applied.

quote: "undemocratic" to separate? Biggest bullshit statement I've heard from you in a while. "illegal" to separate, yes. But if an entire ****ing region votes overwhelmingly to separate, I'd doubt it'd be "undemocratic" to do so.

And if a group of people didn't like the law and voted to secede financlally and legally from the country that wouldn't be undemocratic? I'll point it out again. If people can secede when they like there is no point to democracy, because one of the reasons we have a democracy is so that majority opinion prevails. If people just seceded when they didn't like the law the system would become a farce.

Come on Asher, you can do better than this.

	17-03-2003 08:05									#56
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quote: Originally posted by Agathon What argument? You BAMed. I've pointed out to you the myriad ways in which philosophy contributes and you just dismiss them out of hand.

Because they were ridiculous, like attributing any philosopher who ever thought of an idea 1500 years ago that a modern scientist actually was able to prove. You BAMed about that -- insisting that the philosopher was essential there.

It's silly. And that's why I dismissed them, there's so many philosophers spewing so much bullshit that one of them is bound to be right occasionally.

And even so, no one came even close to proving that you need to study philosophy to be a philosopher. Why can't a mathematician be a philosopher, why does he need to take university level philosophy courses? You and whoever else gleefully defended philosophy avoided those issues constantly, probably because you know philosophy is a ridiculous discipline and anyone in any faculty can be a philosopher...

quote: And if a group of people didn't like the law and voted to secede financlally and legally from the country that wouldn't be undemocratic? I'll point it out again. If people can secede when they like there is no point to democracy, because one of the reasons we have a democracy is so that majority opinion prevails. If people just seceded when they didn't like the law the system would become a farce. Come on Asher, you can do better than this.

That is some screwed up logic.

Maybe you have difficulty understanding the concept of being democratic, as well.

If an entire region votes that they'd be better off leaving a country, it's not undemocratic for them to leave. It WOULD be undemocratic to FORCE them to stay so you could milk them for their oil money, for instance.

	17-03-2003 08:09									#57
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quote: Originally posted by Asher Same things mathematics can, and more....

OH I see... hardly the killer argument is it? So it's just a fancy way of saying 2+2=4. All you've done is change the symbolism. I can do that:

"zwei und zwei ist fier"

I never said that the symbolism wasn't conventional (in fact I said that it was) but the fact it expresses is not conventional - especially not if it is based on observation.

If I am a moral relativist like you, I could say that "murder is wrong" expresses a convention rather than a fact since there are no objective moral values. "Murder is wrong" is not true because it doesn't correspond to a fact - like "Water always boils at 100 degrees at sea level" does. Are you saying that 2+2=4 is like "murder is wrong"?

I wouldn't - I think 2+2=4 is true.

quote: You don't comprehend that mathematics is more than simple arithmetic, it seems.

I comprehend that that is a reasonable position one might take after thinking about it. But that doesn't prove your position since you claimed that 2+2=4 is based on observation (while not saying what you mean by "based") and since 2+2=4 is a mathematical truth your case that mathematics is conventional collapses. It might be partly or mostly convetional, but that's not what you said.

	17-03-2003 08:18									#58
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quote: Originally posted by Agathon OH I see... hardly the killer argument is it? So it's just a fancy way of saying 2+2=4. All you've done is change the symbolism. I can do that: "zwei und zwei ist fier"

Was this another attempt to be profound?
Computer Science is an applied mathematics, go figure it's very much related to mathematics.

quote: I never said that the symbolism wasn't conventional (in fact I said that it was) but the fact it expresses is not conventional - especially not if it is based on observation.

Ah, this is frustrating...
Mathematics *IS* the conventions that are used in describing the naturally occuring phenomenon. Of COURSE the events that occur like having 4 objects when you have 2 and add 2 more are not man made, I wasn't sure anyone would be stupid enough to argue that.

Mathematics is the set of rules, theorems, and conventions around to describe said phenomenon. As such, it is a man-made construct. I've said this about 100 times now.

quote: If I am a moral relativist like you, I could say that "murder is wrong" expresses a convention rather than a fact since there are no objective moral values.

Duh. There is no absolute right/wrong for anything moral-related, so of course it is a convention.

quote: "Murder is wrong" is not true because it doesn't correspond to a fact - like "Water always boils at 100 degrees at sea level" does. Are you saying that 2+2=4 is like "murder is wrong"? I wouldn't - I think 2+2=4 is true.

Where do you get this stuff, really?

2+2=4 is a man-made construct (indeed, it's arithmetic, which is a subset of mathematics).

I have absolutely no idea why you're trying to compare this to a statement like "murder is wrong", because my trousers are blue.

quote: I comprehend that that is a reasonable position one might take after thinking about it. But that doesn't prove your position since you claimed that 2+2=4 is based on observation (while not saying what you mean by "based") and since 2+2=4 is a mathematical truth your case that mathematics is conventional collapses. It might be partly or mostly convetional, but that's not what you said.

ROFTLMAO. You've got to be kidding me, right? Please tell me this is some kind of joke... Or at least please tell me you were lying when you said you were a professor of philosophy...

2+2=4 is a mathematical truth because mathematics is a set of rules and theorems formulated upon observational fact. The reason it's true is because it satisfies the mathematical rules, and those rules are true because they satisfy observational fact.

	17-03-2003 08:21									#59
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The simple problem here is you don't understand what mathematics is.

I've said this 100 times now, but it's worth saying again since apparently you don't read it:

Mathematics are not the actual events that happen, i.e., the actual event that when you have two objects and add two more you have four.

Mathematics are the rules, theorems, and conventions we, as humans, have adopted to help to describe, analyze, and calculate those events.

As such, mathematics is a man-made construct to help us understand natural events.

	17-03-2003 08:21									#60
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quote: Originally posted by Asher Because they were ridiculous, like attributing any philosopher who ever thought of an idea 1500 years ago that a modern scientist actually was able to prove. You BAMed about that -- insisting that the philosopher was essential there.

That's an oversimplification. I said that if the underdetermination thesis is true then Democritus deserves some credit, because if the underdetermination thesis is true, imaginative conceptual innovation becomes much more important. That's my argument - not what you said. And you accuse me of attacking straw men.

quote: It's silly. And that's why I dismissed them, there's so many philosophers spewing so much bullshit that one of them is bound to be right occasionally.

As if this could be true about innovations in political theory.

quote: And even so, no one came even close to proving that you need to study philosophy to be a philosopher. Why can't a mathematician be a philosopher, why does he need to take university level philosophy courses? You and whoever else gleefully defended philosophy avoided those issues constantly, probably because you know philosophy is a ridiculous discipline and anyone in any faculty can be a philosopher...

Well you need to know what philosophy is to be a philosopher: so it would help to read some philosophy books.

I never avoided this issue at all. My own position is that departmental divisions exist largely for pragmatic reasons. So there are some philosophically minded mathematicians and mathematically minded philosophers in universities. It's best to keep the more philosophically minded people together since they have common interests. For example, anthropologists are interested in the Sapir-Whorf thesis because it impacts their research. They don't have the time to spend thinking about whether it is a coherent thesis or not. So philosophers do and anthropologists quote them in their books. Similarly if some new evidence arises that seems to speak for the Sapir-Whorf thesis (like the Hopi Indians) philosophers attempt to see if a modified counter thesis will still work. Contemporary philosophy is not a wholly unempirical discipline - it exists at the extreme end of a continuum between the abstract and the empirical (at least that's my view).

Perhaps philosophy will cease to exist. I'm perfectly prepared to accept that it might (although history of philosophy is here to stay - so I'm alright for a job). But right now we have a contribution to make.

quote: That is some screwed up logic.

Hardly a rapier like response.

quote: If an entire region votes that they'd be better off leaving a country, it's not undemocratic for them to leave. It WOULD be undemocratic to FORCE them to stay so you could milk them for their oil money, for instance.

Same bad answer. Why a region? Why not a group or a race or an individual? What's so special about a region? As someone else objected - this would mean that parts of Alberta are justified in breaking off if they want to - all the way down to individuals.

Unless you provide some compelling reason as to why a region is so special then you must think that it's OK for anyone to "secede" and that would wreck democracy because the people that didn't like the way the vote turned out would "secede".

Plain and simple.