Question.... (Processes of Logic)

crashfrog responds to me:

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Then why do you keep denying that the group of fingers on your hand don't have the quality of "five"?

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Because there's a difference between counting something and arriving at the number five, and those objects themselves posessing any kind of self-sufficient "five-ness" that exists beyond socially agreed-upon models of mathematics.

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But what I'm saying is that I can't understand how you do that. "Five" is not something that you count. It's something that is. Indeed, you personally count so that you can declare "five," but that is just a slower version of what happens when you look at something and you declare "red." Your brain only has a few pigments but you are capable of seeing so many more colors because your brain thinks about it, counts up the strength of the signals being sent, and tells you "That's orange."So since your perception of orange and five are identical, one just a bit slower than the other, how is that indicative that there is something different about number? If I give you a color that is close between red and orange, you'll have to stop and pause to think about just what color it is. That doesn't mean that the color is somehow "invented" is it? It's just that your brain is too slow and not sensitive enough to make the distinction.So why pick on number? People are pretty good at quickly determining number for small things...it's only when they get large that they have to stop and think about it. But how is that a problem of the quality of the objects being observed rather than an issue of the one doing the observing?

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How can you look at something and see it and still claim it isn't there?

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Because I'm not "seeing" five, I'm assigning five, based upon rules that I agreed to when I decided to use numbers. The rules themselves are simply convention, not some inherent property of the universe.

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But you're calling it "five." If it weren't really five, why are you so certain that it is? Why do you treat it as if it is? Why do you never use "four" or "six"? Why do you continually say that you have five fingers if you don't, indeed, have five fingers?"I sense 'red,' but I don't see 'red.'"

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Because the universe exists.

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Granted, but that's something that must be assumed, not proven.

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So you do embrace Cartesian Doubt.I think we're hitting yet another impasse.

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As of yet, you have not demonstrated why it is fruitful or logical to assume that objects have an inherent property of "number". At least, you haven't done so with any rationale that couldn't also be applied to Monopoly.

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I would say I have, you just have stubbornly refused to accept it.Are things red even when there is nobody there to look at it?If so, then things are five, even when there is nobody there to count it. That's because just like color is an inherent property of the thing that exists, number is an inherent property of the thing that exists.

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But they also exist when I don't count them.

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See, that's your assumption again.

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No, that's the conclusion. The number remains the same when I'm not paying attention. I never return to my hand and find seven fingers. It's always five. No matter what, it's five.Just as my fingers have a color that is independent of any consciousness being aware of it, they have a number that is independent of any consciousness being aware of it.

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The universe exists. We both assume that.

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I conclude that, actually, since I discard Cartesian Doubt. A difference that makes no difference is no difference.

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But why assume the same is true for numbers but not for Monopoly?

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Because without players, Monopoly doesn't happen.But without consciousness, numbers still exist.

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By existence. Mathematics happens despite mathematicians, not because of them.

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I don't even begin to see how that answers my questions, much less makes any kind of sense.

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Does color exist despite the existence of people to see the color? If everybody were to die right now leaving nobody behind to look at it, would the color of your carpet change? Or, is the color of your carpet a property of its existence and it happens despite the looker, not because of it?Number is the same way: It is a function of existence. On a larger scale, the objects and functions of mathematics are a part of existence and happen despite the mathematicians, not because of them.

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You have to read the rules before you can actually play the game.

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You have to know math before you can do math.

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No, you don't.You don't think a falling ball knows physics, do you? And yet, it is behaving in accordance to physics. Physics is a property of existence.So why do you have to know mathematics in order to do math? An object being hit by five things resulting in five divots is not consciously doing math, but it is mathematical, nonetheless. Mathematics is a property of existence.

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You have to know the numbers before you can count with them.

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No, you don't.

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Or your society has to invent them. Not every society invents numbers.

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But they do math. Math predates writing.Numbers aren't invented...they're discovered.

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When you play Monopoly, you're using the Monopoly rules.

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But only because you've specifically done so. You don't have to play Monopoly on a Monopoly set. The existence of the Monopoly set does not force a specific behaviour.But if you have five fingers, then it behaves as only five can. Four is too small and six is too big. Now, while there are some things that you can do with five that you can also do with four, that's only because there is a mathematical property of being "as large as or larger" and thus five can do it...but three can't.

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It doesn't matter what physical objects you use to keep track of the game state.

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I know. But without anybody to play the game, it never happens. If you were to die right now, you'd never play Monopoly again.If you were to die right now, you'd still have five fingers on your hand.

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But the fact that the game state may be independant of the physical objects you use to keep track of it doesn't mean that the game Monopoly has some existence beyond the rules we agree on as a society.

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That's my point. The difference between five and Monopoly is that Monopoly doesn't have existence beyond ourselves. If we go away, then Monopoly will never happen.But if we go away, five will still happen.

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But the mere existence of objects brings along with them their mathematical properties.

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This is again your basic assumption.

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No, it's my conclusion.

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See, we keep coming back to this question because I literally cannot understand how you can separate the fiveness of five fingers from the five fingers.

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I'm not trying to do that. I'm trying to separate numberness from fingers (or any objects) in general.

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That's fine. I agree that the objects of mathematics are abstract.That doesn't mean they don't exist. You have five fingers on your hand because you have five fingers on your hand. Not six, not four, but five.

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There's just no reason to assume that numberness is an inherent property of objects.

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And I say the exact opposite. There's no reason to assume that numberness is not an inherent property of objects.

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It is a property of sets or groups of objects,

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Which is, itself, an object. A set is an object.

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but there's no real reason to grant that set or group independant existence either.

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The opposite: There's no real reason to grant that set or group non-existence.

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At the end of the day, objects are objects. They have inherent properties, but numberness isn't one of them. That's a property of relationships between objects, but relationships aren't really real.

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The opposite: At the end of the day, objects are objects. They have inherent properties and number is one of them. That is a property of relationships between objects which is an object, itself. Relationships are just as real as the objects they relate. As soon as you have an object, you have a relationship. There is no other way to be.------------------
Rrhain
WWJD? JWRTFM!

Because when I decide to use numbers, I agree to use the same numbers as everybody else. Just like, when you sit down to play Monopoly, you agree to play by the rules your group decides. It's just an arbitrary thing.If numbers are universal, why don't all cultures use numbers? How come the Arabs had to invent zero? If zero is a universal, why isn't it more... universal? I assume the universe exists simply because it's far more useful to do so. Not everybody feels that way - are Zen Buddists wrong? If so, how can you know? All you just demonstrated was that you have five fingers when you're paying attention. You assume, then, that means there's five even when you're not paying attention, but that's not something you just proved.Is the light on in the fridge when you close the door? By this logic, you must conclude that it is. Existence and occurance are different. Absent the players, Monopoly still exists. Absent mathematicians no math occurs. Your argument is a non-sequitor. It's these continued, nonsensical statements that make it hard to argue with you. How does five "happen"? Five is not an event, it's an abstraction. Yeah, it does. "Abstract" is the opposite of "Concrete". Concrete things exist, they have physical reality. Abstract things don't. That's what those words mean. Great, tautology. You're really reaching, aren't you? You've used numbers to prove that there's numbers. Great. I need something better. I need independant evidence that numbers exist beyond their use in describing relationships between objects. Yeah, there is a reason - there's no reason to assume there is. Therefore that's a reason to assume there isn't. A set is a concept. An object has physical existence. A concept does not. Concepts are not objects. That's confusing the model with reality. Only if an observer is there to observe the relationship. That's because relationships are concepts. Concepts don't exist outside of our heads because they're not objects.

crashfrog responds to me:

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If it weren't really five, why are you so certain that it is? Why do you treat it as if it is? Why do you never use "four" or "six"? Why do you continually say that you have five fingers if you don't, indeed, have five fingers?

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Because when I decide to use numbers, I agree to use the same numbers as everybody else.

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No, you don't. Show me how you could use your five fingers as if they were six simply by thinking hard enough.

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Just like, when you sit down to play Monopoly, you agree to play by the rules your group decides. It's just an arbitrary thing.

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But if I think hard enough, I can play another game than Monopoly with the Monopoly set.I can't make my five fingers behave like six simply by thinking about it.

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If numbers are universal, why don't all cultures use numbers?

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They do. They may not have words for them, but surely you're not confusing the name of an object with the object, itself, are you?

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How come the Arabs had to invent zero?

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They didn't. They discovered it. The concept of zero was around long before there was a consistent symbol for it. Don't confuse the name of an object with the object.

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If zero is a universal, why isn't it more... universal?

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Um, it is universal. Don't confuse the name of an object for the object. Just because you don't have a word for it doesn't mean you don't recognize it.Many languages don't have pure color terms for anything other than "black" and "white." That doesn't mean they can't talk about "red" things...they just use different terms for it. There is a difference between the name of an object and the actual object.

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So you do embrace Cartesian Doubt.

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I assume the universe exists simply because it's far more useful to do so. Not everybody feels that way - are Zen Buddists wrong? If so, how can you know?

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That's the point: You can't. Therefore, since a difference that makes no difference is no difference, we conclude that there is a universe that exists.

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The number remains the same when I'm not paying attention. I never return to my hand and find seven fingers.

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All you just demonstrated was that you have five fingers when you're paying attention.

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So things don't exist when you're not paying attention?Are you embracing solipsism, too?

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You assume, then, that means there's five even when you're not paying attention, but that's not something you just proved.

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A difference that makes no difference is no difference. If it is always five and is never anything other than five, how could it be something other than five?

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Is the light on in the fridge when you close the door? By this logic, you must conclude that it is.

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No, because I can see the switch and I can make the light turn off despite the door being open.Show me how you can make your fingers be six just by thinking about them differently.

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Existence and occurance are different. Absent the players, Monopoly still exists. Absent mathematicians no math occurs. Your argument is a non-sequitor.

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(Spelling flame! Oy! It's "non sequitur" with a "u" and without a hyphen.)No, absent the players, a Monopoly set exists, but the game doesn't. Absent mathematicians, mathematics occurs.Or are you saying the earth didn't orbit the sun until there were people to notice it?Are you embracing solipsism?One of the White Wolf games (those guys who brought us Vampire: The Masquerade) is Mage: The Ascension. The thrust behind the game is that magic is real and is a consequence of belief. Things are because people will them to be. Thus, way back when, the sun really did go around the earth because everybody believed it to be. Only when enough people shifted their way of thinking did the earth start to orbit the sun. Magicians have enough personal willpower to break the rules everybody else insists upon (but screw up and that collective disbelief will smack you down in a Paradox backlash.)I still have five fingers on my hand even when nobody's looking at it. It does not depend upon the collective will of anybody for it to be.

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But if we go away, five will still happen.

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It's these continued, nonsensical statements that make it hard to argue with you.

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Now you know how I feel and why I keep asking you the same question over and over. You make nonsensical statements that scream out for how to rectify them with that question. It's hard to argue with someone who says one thing and then immediately contradicts himself.

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How does five "happen"? Five is not an event, it's an abstraction.

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Five happens on the end of your hand.Or don't you have five fingers on your hand?See...we're back to that question. You say it doesn't happen, and yet right on the end of your hand I can see it. And you agree that there are five fingers there. So how can you say that it isn't really there?That's nonsense.

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I agree that the objects of mathematics are abstract.
That doesn't mean they don't exist.

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Yeah, it does.

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Then there is nothing more to discuss. We are at an impasse.------------------
Rrhain
WWJD? JWRTFM!

I guess so. (Thanks for the spelling tip, though. I'll try to watch out for that.)

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What makes you think i is positive or negative? I asked you this once before.

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I have not once said that i is either positive or negative. If you read my posts you'd know that. You've built a nice big straw man, tossed in some irrelevant terms, and danced right around the issue. Pathetic. Why is it so hard to address the thing head on? Want another chance?i is defined as the square root of negative one. How does one get a square root? Hint: You find a number which multiplied by itself gives the number in question. Now, riddle me this... What number multiplied by itself gives a NEGATIVE number? i is a number which multiplied by itself gives -1. There isn't one. How is that hard to grasp?So what to do? We made up a new number-- one that cannot exist in the Natural, Integer, Rational, or Real number systems. And we made up a new number system within which we could use this new number. But that is just the point. We have incompatible number systems, or unconnected number systems. There are gaps. Consider Relativity and Quantum Mechanics. The two are mutually incompatible, yet both are very well supported and function just fine within limits. Still, there is a gap and while there is a gap you can't claim that our understanding of physics is not contradictory. The same is true of mathematics.

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Only in axiomatic number systems sophisticated enough to model arithmetic.

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You simply repeat this over and over. Don't you realize you are missing the point?For one, this is diversionary. You have refused to answer one fundamental question: When you perform some calculation do you use some minimal system like Presburger arithmetic or do you use something a wee bit more complicated-- like third grade mathematics? You keep bringing this up, but it is silly to defend one axiomatic system by pointing out that another one is complete and consistent. That tactic can't possibly make sense to you.Now, let's see... Which number systems are sophisticated enough to model arithmetic? How about... ARITHMETIC?

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Not all mathematical systems fit that description.

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Fine. Do you argue that the whole is not inconsistent because some of the component parts, taken individually, are consistent? It appears that you do. Do you think a car is reliable when some of the parts work, some are missing, some cancel each other out, and some you just don't know about?

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The true statements that are generated in incomplete systems are still true.

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Because those statements are limited in scope. Yet you want to make global and universal claims? Such isn't reasonable.

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Because the question is nonsense. You are asking me to describe the color of a smell.

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Lets see what that question was, shall we? This was a reaction to your continual repetition of the mantra that the Incompleteness theorems do not apply to all systems. You are, however, avoiding the fact that the Incompleteness Theorems do apply to a large number of, frankly, unavoidable components of mathematics.

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Um, you do realize that you just tried to equate a field of study within mathematics with all of mathematics, yes?

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ummm.... no. It is a simple question. You have used mathematics numerous times in this thread. Are you not using about systems sophisticated enough that the incompleteness theorems apply? In other words, you bring up Presburger arithmetic over and over. Are you performing your calculations within such a system? Nope. So really, it is a red herring. You are making the error of which you accuse me, essentially, and are trying to buttress all of mathematics by reference to a tiny and barely functional axiomatic system which exists more outside of mathematics than inside it.

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Then there really is nothing else to discuss.

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Like arguing with a fundie...------------------
No webpage found at provided URL: www.hells-handmaiden.com

Hi again Rrhain. Having read your subsequent replies to John and Crashfrog, I think I understand your position now, although it appears you don’t understand mine. After all, the first thing I said to you after saying was , and yet you found yourself able to reply It seems that we must be using the word ‘five’ in different ways!
Plainly the point of difference is that you consider the fiveness inherent to the hand, wheras I regard it as a mental construct.
A couple of points in support of my position. You wrote - If nobody were around, there would be nobody to decide anything, so of course nothing would be decidable.
A blind society could - if they thought of it - make a spectrometer with audio or braille output. It could detect photons and allow them to infer the existence of light with different wavelengths.
An innumerate society could not build a number detecting machine. Number is qualitatively different to colour.And now, it’s show and tell time. There exists a clay pot (or existed, it was in a museum in Baghdad ) with cuneform writing on the lid, which said 16 ewes and 7 lambs, the property of(name)to be looked after by(name)and returned(date). Inside the pot were 23 little clay balls, 16 of one size, 7 smaller. Archaeologists think it was a reciept, recording a deal between a literate town dweller and an innumerate shepherd. The owner kept the lid, the shepherd the pot. It didn’t matter that he couldn’t count, all he had to do was to take the balls from the pot, drive the sheep through a narrow place, put a ball back in every time a sheep went past, and see if any balls or sheep were left over at the end.The point, of course, is that the concept of number is not innate, it is learned. By contrast, a person who had never interacted with other humans would know perfectly well what red is without being taught.
OK, so colour is not a useful analogy. Still, you can perfectly well say that the shepherd had a certain number of fingers, probably five, whether or not he knew it. I can reply that fingers are just fingers, sufficient unto themselves and needing no definition or conceptualisation, and that the fiveness could only be in someones head.So why bother with this (rather long) post? Because I’m interested in knowing why you are so sure that sets can inhere in objects - is there any possible publically verifiable proof that sets inhere in objects rather than being confined to people’s heads? You answered this before with but of course this is not to the point, as looking and recognising happen in my head, not my hand.

John responds to me:

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What makes you think i is positive or negative? I asked you this once before.

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I have not once said that i is either positive or negative.

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Yes, you did. You were the one hammering the "negative times negative is a positive" mantra and then claiming that this was somehow violated by i * i = -1.That necessarily impllies that there is something about i that is positive or negative.Thus, my response that the problem is not that there is a contradiction but that you have a fundamental misunderstanding. You're right...a negative times a negative is a positive but since i is not negative, there is no contradiction. And too, you're right...a positive times a positive is a positive, but since i is not positive, there is no contradiction.Or are you trying to claim you did not say the following in Message 98: Or are you trying to claim you did not say the following in Message 53: I don't know about you, but you seem to be saying something is wrong.

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If you read my posts you'd know that.

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Strange, I read your posts and I understood perfectly: You claimed that there might be some violation of "the basic rules of multiplication" (Message 80) in the way i works. I pointed out that there is no violation. You then hammered "negative times negative" and all that.Now, how is that not an indication that i is supposed to have some attachment of positive or negative to it? I know I didn't bring it up.I'm sorry you're having trouble remembering your own posts...now you can see why I ask you to provide as much context as you can.

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Why is it so hard to address the thing head on?

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You tell me...you're the one avoiding everything.

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i is defined as the square root of negative one.

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Yep. But this does not make it positive or negative.

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How does one get a square root? Hint: You find a number which multiplied by itself gives the number in question.

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Yep. Again, this does not make it positive or negative.

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Now, riddle me this... What number multiplied by itself gives a NEGATIVE number?

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That would be i. You see, i, being neither positive nor negative, doesn't contradict the rule you beat your head against. You're right...a negative times a negative is a positive but since i is not negative, there is no contradiction. And too, you're right...a positive times a positive is a positive, but since i is not positive, there is no contradiction.

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i is a number which multiplied by itself gives -1. There isn't one. How is that hard to grasp?

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And yet, there is. It's i. The complex numbers are quite important. Ask a system engineer...you need to keep all your roots in the left half-plane in order to maintain stability.

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So what to do? We made up a new number--

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No, we discovered that things were more complex than we thought.

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one that cannot exist in the Natural, Integer, Rational, or Real number systems.

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And that's fine. You will notice that there are numbers in the Integers that do not exist...cannot exist...in the Natural numbers. Similarly, there are numbers in the Rationals that cannot exist in the Integers. And the Reals have numbers that can't exist in the Rationals.So why is it so hard to comprehend that there are numbers that cannot exist in the Reals?You know why numbers like pi are called "transcendental"? Because they cannot be constructed with a straight-edge and compass. It isn't a question of irrationality since the square root of 2 is irrational and is not transcendental. Instead, it simply means that your method of number construction is not sufficient to snag all of them...there will be numbers that "transcend" your method.And similarly, there are numbers outside of the Reals.There are even numbers outside of the Complex. While you can't quite make a three-dimensional analogue of the Complex Plane, you can easily create a four-dimensional space which Hamilton described as "quaternions":a + bi + cj + dkwherei² = -1, j² = -1, k² = -1, ij = k, jk = i, ki = j, ji = -k, kj = -i, ik = -jYou will notice that these numbers don't follow commutativity.But wait, there's more. There are also the octonions where not only do we lose commutativity, we lose associativity, too.Both quaternions and octinions show up in physics.

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And we made up a new number system within which we could use this new number.

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No, we discovered it.

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But that is just the point. We have incompatible number systems, or unconnected number systems.

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No, we have a system which is more complex than you think. Certain numbers behave in certain ways. Other numbers behave in different ways.The quaternions behave as an integral domain except for the bit about commutativity. While the Integers are closed under subtraction, the Natural numbers are not. While the Rationals are closed under division, the Integers are not. While the Complex numbers are closed under exponentiation, the Reals are not.Have you considered the possibility that the problem is not with the numbers but with your understanding of the numbers?

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There are gaps. Consider Relativity and Quantum Mechanics. The two are mutually incompatible, yet both are very well supported and function just fine within limits. Still, there is a gap and while there is a gap you can't claim that our understanding of physics is not contradictory. The same is true of mathematics.

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But your example is not indicative. We understand how the numbers behave. You, or at least your argument, does not.There is no contradiction between i² = -1 and the rule that a negative times a negative equals a positive and a positive times a positive equals a positive.And that's because the rule is not "something multiplied by itself is a positive." Instead, the rule is that "a negative times a negative is a positive" and "a positive times a positive is a positive."Now, if i is neither positive nor negative, by what method do you expect to apply this rule? The rule only concerns itself with positives and negatives. Since i is neither, we have no expectation as to what we should get, at least as far as that one rule goes.The same thing exists with 0. Indeed, a positive times a positive is a positive and a negative times a negative is a negative, but 0 is neither positive nor negative. And thus, we don't have any expectation as to what we should get when multiplying 0 times itself.So here we have two numbers that are outside that rule...one number that when multiplied by itself gives a negative number and another number that when multiplied by itself gives a complete blank being neither positive nor negative.Have you considered the possibility that the problem is not with the mathematics but with your understanding of the mathematics?

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Only in axiomatic number systems sophisticated enough to model arithmetic.

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You simply repeat this over and over. Don't you realize you are missing the point?

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No, I realize that you are. You're the one insisting that the Incompleteness Theorems apply to everything.They don't.Not everything is an axiomatic number system. And of the axiomatic number systems, not all of them are powerful enough to model arithmetic.Therefore, just as the rule about multiplying positives and negatives don't apply to numbers like i and 0, the Incompleteness Theorems don't apply to things like Pressburger Arithmetic.

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You have refused to answer one fundamental question: When you perform some calculation do you use some minimal system like Presburger arithmetic or do you use something a wee bit more complicated-- like third grade mathematics?

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First, you never asked this question.Second, it's immaterial. When I perform simple calculations, I tend to do it by memory. After all, children aren't taught the ZF axioms of set theory and then run through Russell's Principia Mathematica in order to prove that 1 + 1 = 2.Instead, most people use a naturalistic mathematical comprehension: They see that 1 + 1 = 2 and thus embed that concept into their heads. When you ask me to calculate 5 * 4, I don't think about seeing a set of five objects and then duplicating it to four sets and then counting the sets. Instead, I just happen to have memorized that 5 * 4 = 20.

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You keep bringing this up, but it is silly to defend one axiomatic system by pointing out that another one is complete and consistent. That tactic can't possibly make sense to you.

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It is when the argument is "This trait applies to everything."If you are trying to make a universal statement, I merely need to provide an existential statement to disprove it.You keep saying that the Incompleteness Theorems apply to everything. Well, they don't. In fact, the very statement of the theorems explicitly describe what it is they do apply to and what they don't.Therefore, the next step is for you to demonstrate why the specific object you are attempting to apply the theorems to is of the type to which it applies. You've already made one mistake, trying to apply the rules of positive/negative multiplication to i which is neither positive nor negative.

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Now, let's see... Which number systems are sophisticated enough to model arithmetic? How about... ARITHMETIC?

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Um, you do understand that arithmetic is not a number system, yes?

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The true statements that are generated in incomplete systems are still true.

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Because those statements are limited in scope.

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And the problem with that is what, precisely?

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Yet you want to make global and universal claims? Such isn't reasonable.

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Except that some true statements are global.The Reals are closed under division. There is no largest prime.

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Then there really is nothing else to discuss.

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Like arguing with a fundie...

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I know...you are so certain that your preconceived notions are correct that even when presented with direct evidence showing you that you're wrong, you do everything you can to avoid it.Now that we have the ad hominem commentary out of the way, can we just let this drop?------------------
Rrhain
WWJD? JWRTFM!

Chavalon responds to me:

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Plainly the point of difference is that you consider the fiveness inherent to the hand, wheras I regard it as a mental construct.

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I know. I do understand what you are saying. I just don't understand how you can truly hold it. It is as if one were to say, "I see 'red,' but I'm not sensing 'red.'" How can one possibly see red and not actually be sensing it?

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If nobody were around, there would be nobody to decide anything, so of course nothing would be decidable.

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Why? Are you saying that things don't exist if there is nobody there to pay attention to them?

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A blind society could - if they thought of it - make a spectrometer with audio or braille output. It could detect photons and allow them to infer the existence of light with different wavelengths.

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So you're saying that things do exist even if there is nobody there to pay attention to them?

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An innumerate society could not build a number detecting machine. Number is qualitatively different to colour.

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I say no. An innumerate socity could easily build a number detecting machine. After all, mathematics predates writing.

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The point, of course, is that the concept of number is not innate, it is learned.

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And I say the opposite. The concept of number is innate, not learned. This is distinctly different from language. If you get to be a certain age, you will never learn language.

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By contrast, a person who had never interacted with other humans would know perfectly well what red is without being taught.

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Oh really? What is "red"?That same perception of color is the same perception of number. Red is not a name but a physical property. Five is not a name but a physical property. Red behaves differently than orange. Five behaves differently than four.

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OK, so colour is not a useful analogy.

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Actually, it's the perfect analogy. Number is the same thing as color. If you say that numbers don't exist, then you must also conclude that color doesn't exist but is nothing but a mental construct.

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Still, you can perfectly well say that the shepherd had a certain number of fingers, probably five, whether or not he knew it.

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But he did know it. I'm not saying he necessarily had a word for it. I'm saying he knew that the properties of his fingers (being five) were not the same as the properties of his eyes (being two).

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I can reply that fingers are just fingers, sufficient unto themselves and needing no definition or conceptualisation, and that the fiveness could only be in someones head.

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But it doesn't answer the question: Does this mean you don't have five of them on the end of your hand?

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So why bother with this (rather long) post? Because I’m interested in knowing why you are so sure that sets can inhere in objects

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Because when I look at the end of my hand, I find that there are five fingers there, there are always five fingers there, and no matter how much I try to think of them as some other amount, there are only five fingers there.If it weren't a property of their existence but a mental construct, then I could just think about it hard enough and the number of fingers would change.Are you embracing solipsism?

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is there any possible publically verifiable proof that sets inhere in objects rather than being confined to people’s heads?

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You mean if you think about it hard enough, you can wind up with six fingers on your hand? Here...think really hard and make my hand have six fingers. So far, I can only see five. Can you show me how to make it six?

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You answered this before with I think that it is amazing that you can look at the five fingers on your hand and not recognize that there are five of them.
but of course this is not to the point, as looking and recognising happen in my head, not my hand.

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Are you saying your hand doesn't exist if you don't pay attention to it?Are you embracing solipsism?------------------
Rrhain
WWJD? JWRTFM!

Interesting - how would such a machine operate? What physical properties of an object would it measure to determine how many of them there were? Except, obviously, in those cultures that don't develop mathematics. But if you don't develop language, you'll never develop math. That should be telling to you. That's not even true for things that actually are social, mental constructs. For instance, no matter how hard I think, the meaning of the words I'm using doesn't change - they have an agreed-upon social definition. That can change when we all decide it does.What we've tried to argue, and what you don't apparently understand, is that the numbers we use are social mental constructs - so, if you use numbers, you have to use the same numbers everyone else does.So, no, you can't make there be six fingers on your hand by thinking about it - but you can make there be an unnumbered amount of fingers on your hand by not thinking about it. I think what he's saying is that he can't answer questions about his hand without paying attention to it, so it's pointless to ask questions about his hand when he's not paying attention. Anything we think we know about his hand when he's not looking is just assumption on our part.You can think you know what happens to the light in the fridge when the door is closed - you can even test your theory by pushing the little doo-dad in the door frame - but even so, you still don't really know. You can only infer that the light goes off based on what it does when the door is open, but that's no proof of what happens when the foor is closed. Anything you think you know about your fridge when you can't observe it is simply assumption.

crashfrog responds to me:

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An innumerate socity could easily build a number detecting machine.

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Interesting - how would such a machine operate? What physical properties of an object would it measure to determine how many of them there were?

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Magnitude. A simple scale detects number without knowing what numbers are.If the scales don't balance, one has more than the other. We have no idea what the specific amounts are and for the process of determining "greater than," we don't need to.

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After all, mathematics predates writing.

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Except, obviously, in those cultures that don't develop mathematics.

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And yet, all cultures develop mathematics. Even animals develop mathematics. My best friend's cat, for example, knows the difference between odd and even. You can give him four treats or six treats and he's happy. Give him five, however, and he's wondering where the other one is.That's math.

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This is distinctly different from language. If you get to be a certain age, you will never learn language.

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But if you don't develop language, you'll never develop math. That should be telling to you.

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No, because it isn't true. Lots of things that don't have language have math. Math is part of existence.

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If it weren't a property of their existence but a mental construct, then I could just think about it hard enough and the number of fingers would change.

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That's not even true for things that actually are social, mental constructs.

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Sure it is. If I think about it, I can change the rules of Monopoly. If we were to play Monopoly, we might play by the "Chance/Community Chest money goes to Free Parking" rule...which isn't an official rule, either. All because we simply think about it and (*poof!*), there it is.

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For instance, no matter how hard I think, the meaning of the words I'm using doesn't change - they have an agreed-upon social definition. That can change when we all decide it does.

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Right, but you're making my point: No matter how much we all think, the number of fingers on my hand won't change. Even if we all decide to call it "six," there are still only five.

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What we've tried to argue, and what you don't apparently understand, is that the numbers we use are social mental constructs - so, if you use numbers, you have to use the same numbers everyone else does.

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I understand that you are trying to argue this. But you also haven't shown me any reason to believe you.If the number of fingers on my hand is a mental construct, then that number should be able to change just by us thinking about it.Are you saying that if we all thought really, really hard, there'd really be six fingers on my hand rather than five?

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So, no, you can't make there be six fingers on your hand by thinking about it - but you can make there be an unnumbered amount of fingers on your hand by not thinking about it.

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You mean my fingers don't exist if I'm not paying attention to them?Are you embracing solipsism?

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Are you saying your hand doesn't exist if you don't pay attention to it?

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I think what he's saying is that he can't answer questions about his hand without paying attention to it,

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But the question is what happens when he's not. Does the color of your car change when you're not paying attention?Then how can the number of fingers on your hand change when you're not paying attention?Or are we about to go down the route of solipsism?

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You can think you know what happens to the light in the fridge when the door is closed - you can even test your theory by pushing the little doo-dad in the door frame - but even so, you still don't really know. You can only infer that the light goes off based on what it does when the door is open, but that's no proof of what happens when the foor is closed. Anything you think you know about your fridge when you can't observe it is simply assumption.

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You mean I can't get into my refrigerator and look?------------------
Rrhain
WWJD? JWRTFM!

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.

Crashfrog,

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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.

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Pointless off topic nonsense coming up.........There is a "culture" that can only count to four. Integers beyond four are known by the phrase "hrair", which generally means many, or thousand. Hence their God is known as El-Ahrairah, or Prince with a thousand enemies.Bonus points to the first who can tell me where this culture exists.Mark------------------
Occam's razor is not for shaving with.

Mississippi?------------------
No webpage found at provided URL: www.hells-handmaiden.com

John,Nope, not even Alabamy.Mark

One cannot, of course see red without sensing it. The colour analogy does not hold. Only sentient beings can decide things, a lack of sentient beings must mean a lack of decisions. Do *you* believe that things only exist when sentient beings are around to make decisions about them? What number detecting machine? We can make things that detect the mass, temperature, pressure, length, charge, wavelength etc. of some specific bit of matter or energy, but the numbers we assign to these measurements are arbitrary social constructs such as SI units. How could a person in a society that counts "one, two, oneandtwo, twoandtwo, many" (and, yes, they did/do exist) deduce the existence of a specific large number from an unevenly loaded balance, in the same way that a blind person could deduce the existence of a specific wavelength/colour from a spectrometer?If number were like colour, it should be possible to build a machine that, when pointed at 3 apples, returns the answer '3', just as it could return the answer 'red'. Note that such a machine might be possible using a camera and a computer, but the fact that it would have to be programmed with algorithms in order to give it something equivalent to an understanding of set theory supports my idea that the set's in the eye of the beholder, not yours that it's in the apples.If such a machine were built, and could detect something intrinsic about 3 apples that caused it to return the answer 3, what would happen if you then - still thinking of the apples as a set of 3 - took one to Trincomalee, one to Vladivostok, and the other to Ouagadougou? How's the machine going to detect the threeness then?How about the threeness of this set: {A cute little kitten, Al Quaeda, The legacy of World War II}. How about {Alex Ferguson's determination to win the Champion's league again before he retires, Free market capitalism, A neutrino a billion light years from the sun}. Where's the threeness there? In what place? Is it detectable in any way except in people's heads?You are way out on a limb here. Of course I have. But my fingers just *are*. The fiveness is in my head.If a number detecting machine were pointed at my hand would it say 'one', the number of hands; 4, the number of short fingernails; 5, for the fingers; some number in the high dozens, the number of hairs; a very large number, for the creases; an even bigger one, the number of cells; a much, much larger one than that, the number of carbon atoms? Almost any number could be said to inhere in my hand. It depends on your point of view. A mental construct. Again, this is not to the point - at least not to yours. I can visualise my hand with 6 fingers, but it's in my head, and changes nothing about my actual hand, which, as we agree, does not change according to, or depend upon, my or any conceptualisation of it.