Question.... (Processes of Logic)

Why don't you change what I'm saying? You claim you can do that, after all. Projection is a common denial technique. I'm not impressed. If you change your mind, it's not the same construct. If I "change" english to french in my mind, we're not speaking the same language. Haven't I answered this? "No". Not unless you consider "ceasing to exist" to be the same as "changing the number." You find American, Recieved British, and Australian to be different languages? Ludicrous. They're practically identical. Just as humans may be hardwired for mathematics and number, as well. That doesn't mean that number has physical reality. Oo, nice comeback. "Not everyone agrees with Chomsky". Fine, I guess. He's only the most influential linguist in the past 100 years. Seriously, that's your argument? "Not everyone agrees with Chomsky, so I must be right?" Except for people who agree that 1 + 1 = many, or Christians who believe that 1 + 1 + 1 = 1. Not any more so than counting your fingers is physical. We're not concerned with how something comes out of nothing. We're concerned about how something (numbers) can have been in nothing all along. That is not, at this point, cosmological in scope. Cosmology is a smokescreen at this point.Anyway, not everyone agrees with your cosmology. If numbers are just in my head, then they can't be there if my head isn't there. Ergo, nothing = no numbers. I don't really remember saying that. But I certainly don't believe that now. If there's no one to count, there's not five fingers - there's not any number of fingers. There may be fingers, but unless someone is there to count it's meaningless to talk about their number. And yet, all languages are predicated on it.Many people don't think math has independant reality. Since that's all it takes to convince you of a proposition, apparently, I guess the case is closed.[This message has been edited by crashfrog, 07-09-2003]

crashfrog responds to me:

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If the number of them ceases to exist when the fingers cease to exist, then the number must be part and parcel of the fingers. And if the fingers exist, then the number exists, too.

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But that's inconsistent with your other statements.

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Incorrect. It is the same statement I have been saying all along. The number exists and it exists in the collection of fingers. You have five fingers on the end of your hand. It is part and parcel of the fingers. You cannot have the fingers without the number of the fingers coming along for the ride. If the object exists, then the number of objects exists, too.

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If the number of a set ceases to exist when the elements of the set cease to exist, what happens when we get rid of all elements of all sets?

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We get the empty set.Were you expecting something else?

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The numbers should cease to exist.

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The empty set has no members. It's cardinality is 0.Were you expecting something else?

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But you claim they don't, that they persist "in the nothingness", whatever that means.

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It means that we have the empty set.The empty set is still a set.Were you expecting something else? You seem to be shocked that if I have five fingers and I take away five fingers, I am left with zero fingers.You seem to be shocked that the empty set is empty.

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You're caught in an inconsistency, here.

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No, you're caught in an incomprehension.------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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Incorrect. Mental constructs by definition exist only in your mind. Thus, they can be changed simply by changing your mind.

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You are missing something about the mental constructs in question-- they overlay a physical reality.

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But the constructs, themselves, are purely mental. There is nothing inherent in the particular combination of low-front-wide vowel, bilabial-unvoiced stop, lateral that is an apple or forces anything to happen. It is only because people have gotten together and all agreed that that particular combination of sounds is a representation of apples that it works. It's all mental. If we were to all decide to dump that connection, it would no longer work.

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The mental constructs can be changed at will-- think LSD-- but you are insisting that such changes alter the physical reality as well.

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No, NO, NO! I am not saying that at all. I am saying the exact opposite of that. Mental changes cannot affect physical reality precisely because they are mental. But number is a physical reality. That's why your mentation cannot affect it. No matter how hard you think about it, you cannot change the number of fingers on your hand. Why? Because number is a physical property and you're trying to change it with a mental process. It doesn't work that way. The only way to change a physical property is through a physical process.

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Consider the longitude/latitude coordinate system. This is a mental construct, no?

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The metric is, yes. And the orientation is arbitrary, though understandable. The physical location, however, and the relationship between that location and others is a physical property.

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This coordinate system overlays the surface of the planet. We can change the coordinate system at will. You could make up an unlimited number of ways to do it. But changing it does not change the geography of the planet.

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Precisely.But we can't change the number of fingers on your hand just by thinking about it. Thus, the number is a physical property, not a mental one.

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Yet, you insist that changing the mental construct of number, or grouping, MUST change the physical, or number is not a mental construct.

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No, NO, NO! I am saying the exact opposite. Changing the mental construct...calling it "six" instead of "five"...doesn't actually change the number of fingers you have on your hand. You can think and think and think some more, but you'll still only have five fingers on your hand.This is what I meant when I said you are confusing the map for the terrain. You are so hung up on the symbology that you are forgetting that the symbols are just a mental construct to help us understand what we're doing. The five fingers on your hand is not dependent upon us using the word "five" or the glyph "5." No matter what we call it, you still have only five fingers on your hand. No more, no less. The only way to change that is to physically do something to your hand.

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It doesn't make sense.

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I know. That's why I'm arguing with you. You're making no sense.

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I propose that changing the coordinate system MUST change the geography of the planet OR the coordinate system is not a mental construct after all.

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Thank you. You just made my point.So you agree now that the objects of mathematics are real.

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Thus, since changing the coordinate system does not change the planet, I conclude that said system is a real thing inherent in the planetary make-up.

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Thank you. You just made my point.So you agree now that the objects of mathematics are real.------------------
Rrhain
WWJD? JWRTFM!

I guess so. What is the empty set? (I know that it's the set that is empty.) Is it a number? Is it a thing? Is it nothing? If it's nothing, and the numbers are in it, how can it be empty?I'm just thinking aloud, but I don't see how the "existence" of the empty set in an empty universe has anything to do with the existence of numbers in an empty universe. Can you get numbers from the empty set?

crashfrog responds to me:

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Mental constructs, by definition, exist only in your mind. Therefore, all you need to do is change your mind.

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That doesn't follow.

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How could it not? A mental construct only exists because you're thinking about it. If you change the way you think, then the construct necessarily changes.

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A mental construct could be predicated on rules that prevent change.

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And how are you going to enforce that? The only way to do so is if everybody involved agrees that it can't be done...yet another mental action.I'm reminded of the old exercise in "lateral thinking" where you are given nine dots in a 3 x 3 square and are asked to connect all nine dots using only four straight lines such that you never lift your pencil from the paper.Many people have a problem with this because they have constructed a mental block: Don't go outside the boundary of the grid. Nobody told them of this rule, but they have created it. And thus, they can't make it work. To connect them with four straight lines without lifting your pencil, you have to go outside the boundaries:

*-*-*-
|\   /
* * *
|  X
* * *
|/   \

But I always managed to do it in three lines. I remember sitting in my sixth grade class when the "special counselor" gave us this problem and I told her that I could do it in three. She blinked and asked me to prove it and I did: Simply draw your lines at a slight angle such that you're drawing, essentially, a gigantic, italicized N. The upstroke hits the first dot on its left side, the middle dot in a diagonal through the center, and the top dot on the right side, then diagonally down the middle, and back up the same way.She protested: "You can't do that." Oh? Why? Who said that "connect the dots" meant "through the middle of each dot"? For a woman who's supposed to be helping us to "think outside the box," she seems to be stuck inside it.I then said I could even do it in one line, folded the paper in the appropriate way, and drew one line to connect them all saying, "Who said we couldn't move the dots?"The only way these "tricks" don't work is if we erect a mental block to them.

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If a community of speakers agrees that it won't change, it doesn't.

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And how long do you think that's going to last? All it takes is one person to think something different and the agreement that "it won't change" starts to crumble.

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The community of speakers that use math agree that math won't change. It's just a language with strict grammar.

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You mean if we all just agree among ourselves, one and one will really equal three? If we all just agree among ourselves, you'll actually have some number of fingers other than five?And please, let's not be disingenuous and confuse the word "five" for the number "five." As I have said multiple times, the symbology of mathematics is not mathematics. Forget the symbology. Screw the symbology.Now do you understand why I keep coming back to the same question?Are you saying that if you think hard enough, you can change the number of fingers on your hand?------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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If you don't like your own words, then change what you're saying.

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Why don't you change what I'm saying?

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Because I am not you. I do not have control over your mental or physical processes. I can only broadcast my own mental and physical processes and hope that you will pick them up.

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You claim you can do that, after all.

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No, not really. I claim that I can make changes and if you pick them up, then we have both agreed to the changes.

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Remember how you said that you didn't think I was the most honest of debators?
Did you ever stop to think that perhaps I have the same opinion of you?

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Projection is a common denial technique. I'm not impressed.

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If you're not impressed with yourself, why did you make the comment? Look, I'm sorry you don't like yourself and that you don't find yourself to be an honest debator, but don't project your personal insecurities onto me.

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Mental constructs by definition exist only in your mind. Thus, they can be changed simply by changing your mind.

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If you change your mind, it's not the same construct.

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But the construct is a product of your mind. It only exists as long as you're thinking about it. Change your mind and the construct changes. Fifty years ago, nobody would have thought that "spam" could have connection to a message. Now, lots of people do. We all changed our mind.

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If I "change" english to french in my mind, we're not speaking the same language.

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Indeed.But you're still speaking a language. You've just changed it. Language isn't real, remember? It's a mental construct.

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So you're saying the number of fingers on your hand does change when you stop thinking about them?

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Haven't I answered this?

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Yes, but you then contradicted yourself. That's why I jumped back to the question that generated the statement you just contradicted yourself on. If I ask you what one and one is and you say two and then you go on to say that if I bring in one apple and you bring in one apple, then the two of us will have enough apples to give one apple each to John, Jane, and Jill, you'll understand why I go back to the original question of what you seem to think one and one is. After all, you just contradicted yourself.If you agree that the number of fingers on your hand does not change when you stop thinking about them, then you agree that the number of fingers is a physical property of the fingers and is not a mental construction. Number is mathematical and if number exists, then mathematics exists.

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"No". Not unless you consider "ceasing to exist" to be the same as "changing the number."

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Of course I do. There's this thing called "subtraction," you know.

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That's why English in the US is different from English in the UK and both are different from English in Australia. They became isolated and changed. They evolved.

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You find American, Recieved British, and Australian to be different languages? Ludicrous. They're practically identical.

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Since I didn't say that, I'm wondering why you seem to think that I was implying anything close to "different languages."Let's try this again. See, I'm about to repeat myself since you just said something that doesn't follow...otherwise known as a "non sequitur."English in the US is different from English in the UK and both are different from English in Austrailia. They became isolated and changed. They evolved.What is the term used for a telephone that operates under radio frequencies controlled by broadcasters scattered throughout a geographic area?In the US, we call it a "cell" phone. In the UK, it's a "mobile" phone. In the US, a "mobile" phone is the one you use inside your own home, more commonly called a "cordless" phone.How did this happen? Simple: The community of speakers in the US are significantly isolated from the community of speakers in the UK. If it weren't for the fact that there is a significant flow of communication between the two countries and the fact that the community of English-speakers in the US is only a few hundred years old, the languages would be much more incongruent. We see similar differences between the French spoken in France and that spoken in Canada. Why? Because the groups are isolated. Again, there's a significant flow of communication and the geographic isolation is fairly recent, but we can see that the languages were splitting.

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And if humans are hard wired to have a huge preference for a single type of grammar, that just means we have an intense bias, not that there cannot be any other grammar.

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Just as humans may be hardwired for mathematics and number, as well. That doesn't mean that number has physical reality.

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You mean the number of fingers on your hand changes when you stop thinking about it?See, you just contradicted yourself. You said that the number of fingers on your hand doesn't change if you stop thinking about it and then followed it up with a comment saying that number isn't a physical property. Those two things can't both be true. If the number of fingers on your hand doesn't change when you stop thinking about it, then it is necessarily the case that number is a physical property, part and parcel of your fingers.

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By the way, Chomsky's concept of "deep grammar" isn't exactly universally accepted.

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Oo, nice comeback.

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I was being diplomatic. Would you rather I have said, "And Chomsky's full of shit"?

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"Not everyone agrees with Chomsky". Fine, I guess. He's only the most influential linguist in the past 100 years.

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And, of course, that means he cannot make a mistake, right?Logical error: Argument from authority.Einstein screwed up regarding the cosmological constant. Darwin was wrong about pangenesis. Watson and Crick made many mistakes regarding the structure of DNA at first. Newton was fundamentally wrong about the physics of motion.Just because somebody is brilliant doesn't mean he can't be wrong.

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Seriously, that's your argument? "Not everyone agrees with Chomsky, so I must be right?"

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Not quite. My argument is that your assertion that Chomsky is write is predicated solely upon the argument from authority: Chomsky said it, therefore it must be right.A counter to that is to show that there are significant, qualified people who disagree with him.But if you don't want me to be diplomatic about it, fine: Chomsky's full of shit.

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Everybody seems to understand that 1 + 1 = 2.

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Except for people who agree that 1 + 1 = many,

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You're confusing the symbology for the substance.Forget the symbology. I recall having asked you to do that in another post, long ago.

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or Christians who believe that 1 + 1 + 1 = 1.

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Logical error: Equivocation.

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Not quite right - technically, it's an "locutionary act".

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And that isn't physical?

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Not any more so than counting your fingers is physical.

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But counting is a physical act. You are having a physical reaction to the fingers.

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If numbers were all in your head, then they'd still be there even if there were nothing there.

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If numbers are just in my head, then they can't be there if my head isn't there. Ergo, nothing = no numbers.

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But since the numbers aren't in your head but exist outside of your head, the lack of your head is irrelevant.

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If there's no one to count, there's not five fingers - there's not any number of fingers.

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So if everybody were to drop dead right now with you standing in front of a full-sized piano, your hand would be capable of pressing every single key on that piano simultaneously?

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There may be fingers, but unless someone is there to count it's meaningless to talk about their number.

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Why? How does the physical structure of your hand change just because there is nobody there to look at it?Time for the zen question:If a tree falls in a forest and there's nobody there to hear it, does it make any sound?In my opinion, of course it does. Sound is not dependent upon the existence of a hearer. Sound is a vibration of a medium. Trees grow in air so if a tree falls through the air, it vibrates the air and thus, sound.

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Many people think there is no such thing as "deep grammar."

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And yet, all languages are predicated on it.

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And yet, Chomsky's full of shit.

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Many people don't think math has independant reality. Since that's all it takes to convince you of a proposition, apparently, I guess the case is closed.

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(*chuckle*) But Darwin said that gametes are formed via pangenesis.Since all it takes to convince you of a proposition is the prestige of the advocate, I guess the case is closed.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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No, you're caught in an incomprehension.

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I guess so. What is the empty set? (I know that it's the set that is empty.)

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So what are you asking me for if you know what it is?

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Is it a number?

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No, it's a set.

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Is it a thing?

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Yes. A set.

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Is it nothing?

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No, it's a set.

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If it's nothing, and the numbers are in it, how can it be empty?

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Because there are no "numbers" in it in the way you're talking. You have equivocated.[edited to rephrase the above since below I'm talking about 0.]

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I'm just thinking aloud,

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And I am responding directly. You see, that's what people with integrity do: Answer questions that are honestly asked.

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but I don't see how the "existence" of the empty set in an empty universe has anything to do with the existence of numbers in an empty universe. Can you get numbers from the empty set?

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You've got 0.------------------
Rrhain
WWJD? JWRTFM![This message has been edited by Rrhain, 07-10-2003]

Fine, then I can change the number of fingers on my hand without expecting you to see the change? That does seem to be what you're saying, but then, you're a tricky person to pin down on what, precisely, you're saying at any instant. I don't believe I'm the first, nor the only, person here to express frustration with your so-called "technique." To my knowledge, the only person to refer to me as a less-than-honest debater is you. Because that's what you said. Are you saying I shouldn't read and interpret your words?The exchange went like this, if you've forgotten:

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You will notice that human communities, when left to their own devices, will come up with completely separate languages.

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You're quite wrong about this.

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No, I'm quite right about this. That's why English in the US is different from English in the UK and both are different from English in Australia. They became isolated and changed. They evolved.

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You gave English in the UK, US, and Australia as examples in a discussion about "completely separate languages." Was I not, however, to assume that you meant that they were completely separate languages?See what I mean about being dishonest? You're either remarkably forgetful, or you're purposfully disingenuous. Given that you clearly have a very professional knowledge of mathematics I think I can rule out forgetfulness.Now, if you think occasioanl differences in neologism formation and ideomatic expression constitute "completely different languages", then fine. But no language has ever diverged from another to the point where they no longer share the same deep grammar. Ergo your position that communities develop "completely separate languages" is false. Do you honestly think that's better? As far as I can tell, you're discrediting Chomsky's position simply because it contradicts your own. I'll need some evidence that "he's full of shit.". I've seen the evidence for Chomsky's ideas and it's quite compelling. It's also not on topic, here. Sure, let's forget the symbology....Now what? What do we talk about? Since language can't communicate anything but symbols, any math we talk about is the "symbolic" math. For that matter, since we think in language too, any math we think about must also be the symbology.There's no mathematics we can perceive that isn't the symbology. This is what John was talking about, the basic shortcoming of Platonism. If we can't perceive any mathematics besides the symbolic, how do we know any math besides the symbolic exists? Universal agreement on which symbols to use isn't indicative of an underlying platonic form, as I think you yourself have made clear. It doesn't matter which symbols we use, I think you said. Hey, you're the one who made this an argument of authority. Did you forget? I brought up deep grammar and you rejected it simply because "everybody doesn't agree with Chomsky".If you want to argue deep grammar doesn't exist - as well you should, because it directly counters your proposition that all mental models are mutable - then you'll have to show some evidence that they don't exist. For instance, a language that isn't predicated on them.

Because I don't know what a set that is empty would represent. If a set is a relationship, how can you have a relationship about nothing? What do they do to dishonest questions, dishonestly repeated ad nauseum? How do you get the rest of the numbers from zero?

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How do you get the rest of the numbers from zero?

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They come from the nothing. Duh...!!!------------------
No webpage found at provided URL: www.hells-handmaiden.com

crashfrog responds to me:

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I claim that I can make changes and if you pick them up, then we have both agreed to the changes.

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Fine, then I can change the number of fingers on my hand without expecting you to see the change?

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No. Because you're trying to do a physical change and physical changes will be consistent across all people. Isn't that the point of science? To find the things that are simply because they are and aren't beholden to people's whims and mental opinions? No matter what a person may think, if he steps off the Empire State buiilding wearing nothing but a smile, he's going to plummet to the ground under the action of gravity.

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That does seem to be what you're saying,

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Not at all. Please show me where I ever said anything even remotely like this.

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Look, I'm sorry you don't like yourself and that you don't find yourself to be an honest debator, but don't project your personal insecurities onto me.

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I don't believe I'm the first, nor the only, person here to express frustration with your so-called "technique."

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Logical error: Argumentum ad populum. Surely you're not about to argue that things are true simply because many people say so, are you?Or perhaps I should point out Argumentum ad verecundiam. Surely you're not about to argue that things are true simply because somebody you respect says so, are you?

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To my knowledge, the only person to refer to me as a less-than-honest debater is you.

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There's a first time for everything.

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Since I didn't say that, I'm wondering why you seem to think that I was implying anything close to "different languages."

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Because that's what you said. Are you saying I shouldn't read and interpret your words?

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No, I'm saying that you should. And I didn't say that at all. Here is what I said, for the third time, since you seem to have missed it the first two times. Try to pay attention this time: Now, where in this does the concept of "different languages" come to play?Would you be happy if I used the word "dialect"?

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The exchange went like this, if you've forgotten:

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You gave English in the UK, US, and Australia as examples in a discussion about "completely separate languages." Was I not, however, to assume that you meant that they were completely separate languages?

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Yes. You are not completely ignorant of linguistics. And it is extremely disingenuous of you to claim that you seriously thought I meant that the various dialects of English are "different languages," especially since my statement is concerning how they have changed over time due to their isolation from each other. Yes, they are all still English, but there are statements that one speaker of English will make that will be incomprehensible to another not because of any error in usage or comprehension but because the language isn't used the same way.What did you think I meant when I said, "They became isolated and changed"?Yes, that statement followed one where I said "completely separate languages," but are you really that disingenuous? Did you really not understand the point of how languages change over time due to the isolation of communities of speakers from each other?

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See what I mean about being dishonest?

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Yes. Your dishonesty knows no bounds, apparently. You will feign ignorance at the drop of a hat if it suits you.

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You're either remarkably forgetful, or you're purposfully disingenuous. Given that you clearly have a very professional knowledge of mathematics I think I can rule out forgetfulness.

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This coming from one of the most duplicitous persons I've seen on here.

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I was being diplomatic. Would you rather I have said, "And Chomsky's full of shit"?

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Do you honestly think that's better?

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No, that's why I didn't say it at first. Simply put, Chomsky's wrong. Have you read Michael Halliday? What about the work of the generative semanticists? Have you heard of the colloquia that Postal, Ross, and Lakoff at MIT challenging Chomsky? F'rinstance, "Joan sliced the salami with a knife" is identical to "Joan used a knife to slice the salami."And most importantly, have you read Chomsky? He abandoned Deep Structure in favor of Logical Form and Phonetic Form. Even the theory of universal grammar didn't attempt to say that all languages have the same grammar. Just that there is a common set of rules for language acquisition which can explain phonemes, word order, etc.

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As far as I can tell, you're discrediting Chomsky's position simply because it contradicts your own.

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No, I'm discrediting it because even Chomsky doesn't believe it anymore.

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I'll need some evidence that "he's full of shit.". I've seen the evidence for Chomsky's ideas and it's quite compelling.

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So why did Chomsky abandon it?

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Forget the symbology. I recall having asked you to do that in another post, long ago.

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Sure, let's forget the symbology.

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Now what? What do we talk about?

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The mathematics.This means without the silly claims like if we call five "six," then it actually is six as if that were some sort of physical action rather than a semantic game. Whether we call the color of the sky "blue" or "azul" or something else, that doesn't change its actual color. Whether we call the number of fingers on your hand "five" or "cinco" or something else, that doesn't change the actual number.

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Since language can't communicate anything but symbols, any math we talk about is the "symbolic" math.

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Since we cannot communicate without the symbology of language, any reality we talk about is the "symbolic" reality.Do you also claim that apples only exist "symbolically" since the only way we can talk about apples is through the symbology of langauge?What I was talking about, crash, was your past behaviour of playing silly little games, saying that if we used the symbol "six" to refer to the number of fingers on the typical person's hand rather than the symbol "five," then that actually demonstrates a physical change in the fingers of your hand. The specific symbol used to represent the object is irrelevant since the symbol is not the object. An apple is not dependent upon us calling it an "apple."

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For that matter, since we think in language too, any math we think about must also be the symbology.

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Since we think about most everything in language (the Sapir-Whorf Hypothesis is false in any strong sense), this must mean that everything is merely "symbolic" and not real.

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There's no mathematics we can perceive that isn't the symbology.

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I perceive five on the end of my hand. There are five fingers there.Just as I perceive the cup sitting next to my keyboard.That I use the symbols "five" and "cup" is irrelevant. You're getting hung up on the symbols and ignoring the objects that the symbols are used to represent.

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This is what John was talking about, the basic shortcoming of Platonism.

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But John, too, is confusing the symbol for the object. He is confusing "Platonism" as used by Philosophy for "Platonism" as used by Mathematics.There's a wonderful example of how mathematicians use the term in the Nova episode, "A Mathematical Mystery Tour." John scoffed at the example I gave which was taken from that episode. A professor of mathematics is discussing this very issue with his class, specifically regarding the issue of the Continuum Hypothesis.Basically, the Platonist mathematicians would say that the Continuum Hypothesis is either true or false, we just don't know which.It isn't some sort of great embracing of the "essence." It's that there is an answer to the question of how big the set of Real Numbers is. However, we are unequipped to figure it out.

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If we can't perceive any mathematics besides the symbolic, how do we know any math besides the symbolic exists?

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The same way we can't perceive anything else besides the symbolic. Even when you look at an apple, you aren't perceiving the actual apple. You're only seeing the light that's being bounced off it.Are you saying that everything is symbolic?

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Universal agreement on which symbols to use isn't indicative of an underlying platonic form, as I think you yourself have made clear. It doesn't matter which symbols we use, I think you said.

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Precisely.So why did you decide to play semantic games that by simply calling the number of fingers on your hand "six," that actually changed the number?

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Since all it takes to convince you of a proposition is the prestige of the advocate, I guess the case is closed.

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Hey, you're the one who made this an argument of authority. Did you forget? I brought up deep grammar and you rejected it simply because "everybody doesn't agree with Chomsky".

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Incorrect. You're the one who made this an argument of authority. Did you forget? You brought up deep grammar simply because it was an argument of Noam Chomsky as if that made it irrefutable. Remember?

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If you want to argue deep grammar doesn't exist - as well you should, because it directly counters your proposition that all mental models are mutable - then you'll have to show some evidence that they don't exist. For instance, a language that isn't predicated on them.

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What...you mean Chomsky's own abandonment of the concept of deep grammar is insufficient?But let's take your challenge. There is a problem with it: It begs the question. I can only show you a language that differs from the "deep grammar" if we assume that the deep grammar exists in the first place."Joan sliced the salami with a knife."
"Joan used a knife to slice the salami."Different grammar, single language. How can one show a language that has a "different grammar" from the deep grammar of Chomsky when there is no deep grammar to begin with?------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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So what are you asking me for if you know what it is?

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Because I don't know what a set that is empty would represent.

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Lots of things. The simple answer is that it represents a set with no members. The consequences of this cover quite a bit. F'rinstance, the empty set is both open and closed.

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If a set is a relationship, how can you have a relationship about nothing?

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Um, I don't understand what is problematic about it. Do you have a problem with zero in general?

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You see, that's what people with integrity do: Answer questions that are honestly asked.

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What do they do to dishonest questions, dishonestly repeated ad nauseum?

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When I come across them, I still answer them honestly. I may then point out that the question doesn't make any sense, but I still answer the question. Or, if the question is pure nonsense, I point out that it can't be answered.

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You've got 0.

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How do you get the rest of the numbers from zero?

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In and of itself, you don't. We were talking about mathematics in nothing. If I have misunderstood, I apologize. The original question was: My reference was to the empty set. Would numbers exist if there was nothing to count? Yes. The empty set is a set after all. You get 0 out of it. You don't get other numbers out of it, but you still get numbers. And the number you get, 0, is part and parcel of the nothingness. That's the point behind 0.------------------
Rrhain
WWJD? JWRTFM!

If the question is the way a person is percieved, why isn't it appropriate to refer to the people doing the percieving? Then I can only ask, why would you bring this up when I asked you to provide evidence of "completely separate languages", if not to show an example of completely separate languages? Why are examples of slightly divergent dialects at all relevant to a discussion of potentially "completely separate languages", if there are such things? Sure, I understand that. That's obvious. It's also totally irelevant to a discussion of completely separate languages, so now I'm puzzled why you brought it up at all. Have you noticed a kind of "feature creep" in your posts? First you start with relatively tame assertions - "You might not be honest", "Not everybody agrees with Chomsky", etc. - and in a few posts, you're casting highly superlative dispersions - "Chomsky is full of shit", "You're the most duplicitous", etc. This is the kind of thing that makes it hard to lend credence to your assertions. That, and the question thing. Woo-hoo, so you finally looked it up. Took you a couple posts, but I guess your ignorance was beginning to show. Perhaps. We certainly can't be sure. And I'm certainly not the one claiming that, just because I can point to examples of "apples", that there's some kind of perfect Platonic Apple underlying reality.And that's basically it. Examples of "number" in the real world, no matter how much a community of speakers may agree on which number to use, have nothing at all to do with an independant physical reality of number. No, it just means that we can't use examples of symbol use to prove the existence of whatever the symbols refer to, as you keep doing. Oh, probably because you asked me about a hundred times and I decided to see what you would say. "No" apparently wasn't a good enough answer for you, but "Yes" didn't turn out to be, either. I can only speculate as to your reasons why that would be so. No, you brought it up when your only reason for it's dismissal was because of a lack of universal agreement among linguists.Why do I have to keep reminding you of your own arguments? As for that, I can only present your own words:

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Or perhaps I should point out Argumentum ad verecundiam. Surely you're not about to argue that things are true simply because somebody you respect says so, are you?

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As you've pointed out, I can only refer to the deep underlying similarities in the construction of language in defense of the Deep Grammar theory.I mean, you can point out the differences between dialects of english, but no matter how much the UK and the US diverge they're never become different in fundamental ways, in the way that English and Russian are different, for instance. Part of speech in English, no matter what coast, will always be determined positionally, not inflectionally.

Doesn't sound like you get numbers, plural - just a number, singular, zero. Forgive me but that seems like an important distinction.

As a humerous "proof" of my position, I offer this demonstration of the mutability of number:Hee hee!