Question.... (Processes of Logic)

Um, a scale detects mass, not number. That's why if I put one gold coin and one feather, the scale tips towards the coin, despite there being only one of those objects. How is that detecting number if a scale can't detect number? Do they? Plenty of cultures create artifacts that have "mathematical" properties (weaving patterns, etc) but that's simply indicative that we apply mathematics as a description to patterns. The culture itself certainly has no knowledge of the processes of math. Firstly, you have no idea what the cat is reacting to. You have no idea what kind of mental model the cat is operating from. And likely, the cat was probably trained to do so - no animals do math unless trained to do so by humans. Further confirming that math is a human invention. Once again, your basic assumption with no evidence whatsoever. Your repeated assertions of math's independant existence fail to convince me. Is this how you argue? Repeat your assumptions over and over again? Like Salty? You can't. Your group has to agree. The rules change only when your entire group agrees that they should. Math is just a game that most, if not all, humans agree to play. If every human agreed that math worked differently, it would. No, in that case there'd be six - but six would have all the same properties that five used to. Unless we changed more of the system. Why would you have to think any harder than normal? All that would have to happen is we'd have to agree that there were six. "We" as in all human beings. Are you asking me this again? No, I'm not saying that. Read my posts agin to find out what I am saying. I'm tired of spelling it out for you. I don't know. I can't answer questions about my car when I'm not paying attention to it. I assume the color doesn't change, but that's just an assumption. Go ahead - stay in there, while you're at it.Even then, you've only proved that the light goes off when the door is closed and you are in there. It's merely assumption that that applies to the general case of fridges with closed doors. So what?No amount of observation can prove the nature of things when you aren't observing them. It's merely assumption that your observations represent any kind of general trend applicable to unobserved events. At the quantum level, that's not even true - things are different when you're not looking.

But that's not what you claimed it would do. You claimed to have a machine that would detect the number of objects, since that's what we were talking about. All you have is something that determines between "heavier" and "lighter". As narrow as your idea of math is broad enough to encompass all human endeavor, it seems. Not unusual for a mathemetician. Honestly I have been finding it a little suspicious that you have so many positive counterexamples from your own experience. Apparently you live in a community of people whose animals count, use the word "niggardly" regularly, have little to no difficulty thinking of people as ungendered persons, use pronouns in ways that exist only in dictionaries, and a host of other conviniently unusual traits that counter all the negative universal statements a bunch of us have made.Wouldn't you find that just a little suspicious? If you want me to accept your cat counterexample you'll have to do a bit more than complain about being called on the carpet. That's simply too unbelieveable for me to take your word for it.

But "more" is not itself a number, which is what you said your machine could detect. You're just shifting the goalposts. I don't find it in the least bit insulting to ask someone making repeated, unusual claims to cite evidence. if you do perhaps you should retreat from scientific or logical discussions. This is simply feigned protestation to conceal a lack of evidence for your more outlandish and unsupported claims. Your personal credulity is hardly a major point in favor of your arguments. And in this case, it's pretty obvious that there are more things in your philosophy, Hamlet, than are found in heaven and earth. No, I simply questioned your conclusion, expressed that I found it highly difficult to believe, and asked for corraborating evidence. If you find that insulting, I find you rather thin-skinned. That's hardly my problem. You brought up the cat; it's your responsibility to demonstrate evidence of this incredible claim. Certainly. Show me evidence that my pre-conciveved notions are wrong and I'll consider it. If I find my notions incompatible with the data I'll change them. So far, though, you haven't offered data - just a story that very well could be made up. I don't find that very compelling.

Fine, I have six fingers. Wasn't that hard, actually.

I mean "six", as in 5 + 1 - as in, "one two three four five six." Tell ya what - prove to me your friends have a cat that detects parity, and I'll prove to you I have six fingers. Or don't you trust me? Only seems to work for my hand, sorry. I don't know why.

No hesitation. Come on down. But bring the cat. Those are fascinating examples, but what do they prove? That animals have precursors to human intelligence and can be trained in, or learn, some of the same mental models humans have? I'm not impressed because human intelligence is a social phenomenon anyway, so it's not surprising that something like it can bve found in social creatures. 3) Animals can be trained to use the same mental models humans do, like numbers, or language.Just as a map is a representation, a mental model, of the spacial relationship of objects, numbers are simply a mental representation of another kind of relationship. Or, do you think maps have an existence beyond our use of them? That maps are discovered, not invented?

Actually (and my statements may not have accurately reflected this) but I didn't mean to decribe math as a unqiuely human endeavor, but rather an endeavor unique to symbolic, social intelligence. While humans consitute the most advanced example of that I don't believe we're the only ones.If space aliens visit us, I assume they'll have some kind of math. If they're able to communicate with us at all it's likely we'll find they have the same numbers. But only because their minds are similar to ours, not because numbers have some kind of independant phsyical reality. I read the exact opposite. Your citations demonstrated animals trained by humans to absorb human-like mental models. I don't know how you think it could be otherwise - what techniques could humans use that would not result in human-like mental models? That animals can absorb human-like mental models because intelligence is a social phenomenon. I said that already. All creatures are social to some degree. Including hummingbirds. I can understand how you would have inferred that - that's not really my position. My position is that math is simply a mental construct because number is not a physical property of matter but rather a property of imaginary sets of objects, which exist only in our heads and which we communicate to each other via mathematics, language, and other ways of describing relationship. Most animals have some capability to communicate mental models, so it's not surprising to me that animals can be taught - or even learn themselves - other kinds of mental models, such as "number". Especially when humans are communicating to them.That still doesn't prove that numbers have a unique, self-sufficient physical reality. Actually, my incredulity stemmed from the fact that your example was all too convenient. But even if it's true it doesn't speak against my position - the cat detects parity because it absorbed a mental model of parity through communication, not because parity is some inherent property of an object. You don't seem to understand what we're arguing. And honestly, if you refuse to understand, why should I argue with you? I'm actually getting a little tired of this because you just repeat your assumptions over and over again and ignore any challenge to them. You're not a very good debater. I don't really see any reason to continue.

No, it's just a description of relationships that exist only in our heads. The objects themselves are physical, yes. But the set of objects your counting - the set itself - is something you make up. Sure, but then Monopoly IS, too.

Uh-oh, potentially irrelevant mention of Godel's theorem... Rrhain's gonna jump right down your throat. Doubtless he'll bring up Pressberger arithmetic without ever explaining its usefulness.

Right, but if you assume that the map is the same as the physical reality, then you confuse the model with the reality. You reify, in other words.If this wasn't true, how could maps be wrong? We know that some maps are wrong, however, suggesting that maps are simply another kind of mental model. Based on reality, sure, but no more real than any other mental models. I've never heard an argument for the ontological existence of mathematics that couldn't be applied to Monopoly, as well.[This message has been edited by crashfrog, 06-17-2003]

You've asked this about a hundred times, and it's been a straw man every time - changing five to six is not a necessary result of math being simply another kind of language or conceptual framework instead of a really real thing. It's as dumb as saying you can change who's in the Oval Office now by voting really hard. It's meaningless. I can't change the meaning of words just by thinking hard, even though language is just a mental concept. Why should numbers change under the same circumstances? It's only "really" six (in my defense) because "six" isn't real. A fruitful (pardon the pun) question might be - would numbers exist if there was nothing to count? If so, where would they be?

Since when? That's never been a requisite for mental concepts, as far as I know. Ah, now I begin to understand your misapprehension.People - emphasis on the plural - can change language, because languages are defined by communities of thinkers, not an individual. Just as the President is elected by a community, not by an individual. And just as one person can't change the election by voting "harder", no one person can change language by thinking any harder than they usually do.I mean, if what you say is true - that one or even several thinkers could alter the meaning of a word for everybody else - then why would Hormel (and I'm oh-so-glad you brought up the example of spam) have to sue to prevent the use of the word "spam" in reference to junk email? If what you say is true they could change the meaning by thinking hard. They wouldn't have to bother with the lawsuit.It's obvious (to everyone but you, perhaps) that languages aren't thought into being by an individual, but rather agreed upon by a community. Sometimes the community agrees that the language won't change, as is the case with "dead" languages. Esperanto has not changed significantly since it's inception, nor LogLang or any other contrived language. That they are more constant than English is not indicative that they represent some kind of independant reality. If this is true, then do it. Change the meaning of a word in a way that would be congruent to how you're asking me to change the number of fingers on my hand just by thinking about it. Why don't you make more of my fingers "thumbs"?While you're at it, change who the President is by voting really hard. Ooh, spooky. Now how about an answer that's not mystical claptrap?It's becoming obvious that Platonism is an occupational hazard for mathematicians. I can only surmise that it's because the idea that everything they've studied and worked on for so many years could be nothing more than ideas in their heads is a hard cheese to swallow. But then, linguists have exactly the same problem - they're studing something that exists only as something in the heads of a community of thinkers - without any such delusions of independant reality. And make no mistake, there are deep grammars that are every bit as universal and "real" as any truth in mathematics. But that's no more evidence for the independant reality of language than universality of number is evidence for the independant reality of math.Languages share deep, universal structures to as large an extent as cultures share numbers. But we don't hear you arguing for the independant existence of language. I can only assume this inconsistency is the result of a mental timidness that won't allow you to view mathematics as what it truly is - just another human langauge with very, very strict grammar.[This message has been edited by crashfrog, 07-08-2003]

Another mental construct that's immune to "change by thinking hard" is ownership. Rrhain owns his computer, but that's not a physical property of the computer. There's no way to determine ownership unless Rrhain's left his name and address in it. But I can't make his computer mine just by "thinking really hard".Clearly the "thinking really hard" argument is a straw man.

When I read your responses, it's like you're responding to a totally different post and then putting my quotes in to make it look like a reply. This doesn't even begin to address my point. Try actually reading my posts. Mental malleability is not inherent in every mental construct. Math could simply be (and my position is, it is) a language with a very strict grammar. You're quite wrong about this. All languages obey basic deep grammars (which first began to be outlined by Chomsky). No human has ever invented a language that runs counter to those deep grammars. They're so universal that it has been proposed that they're actually hardwired into our brains. But their universality doesn't mean they have independant existence outside of our minds. Why? Deep grammars are just a mental concept, and we don't find all sorts of mutually exclusive grammars. Instead we find just one deep grammar. Ah, but you made the claim that they would be able to - by "thinking hard" as you put it. You said that by "thinking hard" they could change the meaning of words. So, can they change the meaning, or can't they? You don't seem too sure about this. Sorry, I was talking about you, not us. Change my fingers into thumbs. Not quite right - technically, it's an "locutionary act". We weren't talking about cosmology. You certainly made no cosmological statements. I just asked you where the numbers are if there's nothing to count. I mean, there's zero, obviously, but where are the rest of them?They can't be "in the nothingness", because if they were, there wouldn't be nothing, would there? Or do you think numbers are nothing? That would be equivalent to my position, I guess. This is what I mean about asking the same questions over and over again. Remember when I answered this with a "no"? Guess not. Just because we all agree that I have five fingers on my hand doesn't mean that five has an independant existence. Everyone who develops language agrees on certain deep grammars - universally. That doesn't mean that they have an existence outside of our heads. Go ahead and do so. Change the deep grammars. You won't be able to change them anymore than I can think an extra finger onto my hand. That still has nothing to do with the independant physical reality of number or language.

Another question that you keep asking, and the answer is "no". If the fingers cease to exist then the number of them ceases to exist as well. What's hard to understand about that?