Question.... (Processes of Logic)

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The mathematics that exists in reality.

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The question, Rhhain, is which part is the REAL part?You cannot answer the question, "Which is the real part?" with "The part that is real." Come on. You can do better than that.

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An apple exists regardless of the representation we use to describe it.

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Yes, AN apple does exist regardless of what we choose to call it. But Apple with a capital 'A' is another story altogether. There is no such animal, no matter what we choose to call it. It is an abstraction. Math is in the later category, not the former.

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You confuse the map for the terrain.

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If this is the case I am sure you can point to a mathematical entity-- a five, for example. Not five things, which is an abstraction. Not a character or a word which are mere representations of an idea, but to the real thing-- Five in its unadulterated glory, in the same sense as you can point to an apple.------------------
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Oh, you're not about to equivocate on the world "real" are you?

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No. I am not nearly as equivocative as yourself. Nor do I avoid the question by suggesting, without cause, that someone is about to make a logical fallacy.

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But what else is there?

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Lol..."What observable events are God's doing?" "Why, the part that God did.""Which elf shot Santa?" "Why, the elf that shot Santa, of course.""Which number is the largest of them all?" "Why, the largest one, obviously."Can't you see how stupid that answer is?

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I've given you plenty of examples. For example, the five fingers on your hand.

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So, you've proven that I can group objects. Where is the proof that number exists outside the brain that is doing the grouping?

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Or are you saying that if you think about it really hard, you can change it to six?

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This isn't mathematics, Rh. It is physics. We know that one cannot make an extra finger grow by thinking really hard, but this has nothing to do with math. It is a red herring.

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As in ONE apple.

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Congratulations! You've labeled an object! It isn't possible, in English, to refer to an object without refering to a number-- one or many. Let's not trip over language, eh?

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Or are you saying that if you think really, really hard, you can turn AN apple into SOME apples?

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Where did you get this? No one has made any such claim.

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Huh? Didn't we just agree that it didn't matter what you called it? An apple is an apple?

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You seem to have no idea of the meaning of Platonist, which is what you have labeled yourself. Strange...apple == an object on the kitchen table
Apple == the essence of apple, its perfect formSee, Platonism works like this. Everything we observe, every object is a reflection of its perfect Form. ( Capitalizing the Form's name has been traditional in Philosophy for quite some time. Can't imagine how a Platonist like yourself could have missed that. ) The Forms are real, the objects we see are merely reflections. Pointing to the 'reflections' DOES NOT prove the existence of the Forms, but only the existence of those reflections. The problem Platonism has is that there is no logical way to get from the 'reflections' to the existence of the Forms. You just have to assume the whole weltanschauung. That leaves us with just the reflections, and reflections without Forms makes no sense. Thus we ditch the Forms and accept what we can actually observe.

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Um...last time I checked, my friends all used Apples. They don't like Windows.

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Cute. And OS X does kick much butt. However, you used to joke to avoid the issue. You are arguing for the existence of abstractions. And are defending the claim by pointing to physical opjects. It doesn't work.

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No, five things is a concrete example of five.

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Nope. Five things is a concrete example of five things. The 'five' is a label, an abstraction-- so is 'one', 'red', 'hard', etc. though they can all be related to something physical. With no one to do the labelling the things would remain-- we assume -- but the label would not, any more than the label 'apple' would exist if there were no English speakers. The things are real, math is a way to group them-- like kinship is a way to group people. It might be based on certain physical relationships but the kinship system is nonetheless an abstraction and does not exist except in the minds of those who know about it. Even such concepts as 'mother' and 'father' are fluid across cultures ( but becoming less so as all the nifty cultures are getting drowned out by the industrial age ).

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Let me see if I can understand your logic. You want me to show you a real version of an "apple," but you will not accept a piece of fruit because that's an "abstraction"?

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But this isn't what is being asked of you. I'll accept an apple as an apple. I won't accept an apple as ONE, which is what you want to do with it. Nor would I accept an apple as Red, Sweet, or as proof of any other abstraction.

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I have never been referring to the symbology.

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Sure you have been. Your arguments are nothing but references to the symbology.The funny thing is that even if we assume the truth of Platonism, your arguments through most of this thread don't work. The only mathematics we can use are our representations of mathematics and this is different from mathematics. See, your post # 156. Unless our representation of math is identical to math then we cannot have the certainty about it that you have insisted we have.------------------
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If that were the case, then you could think really hard and change the number of something since number is a mathematical property.

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Do you really not understand the difference between an objects and a count of the objects?

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But if you can't change the number of something simply by thinking about it, then number must necessarily be something that exists outside of a person's mind.

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No, Rh, the THING exists outside the person's mind, not the count of it. Number is not a THING. Number is grouping. That's just the problem. You are thinking of number as if it were something like color or texture. Here is an experiment.There are X identical objects on my desk. I'll ship these objects, one each, to several independant labs. Now here is the question I'll ask each lab, "How many objects were in the original group of objects on my desk?" If number were a real thing, a genuine property of reality, there should be a test these labs could perform to answer this question. What test would that be? They could test for color, texture, density, and a hundred other things; but what would be the test for number? How do we measure the number-osity of the objects? None of the other properties of the objects change just because the objects have been moved and no longer sit side by side. Color, mass, texture... all stay the same. The only things that change are relationships. Relationships are abstractions, not things.Consider this relationship. "Harrap's New College French and English Dictionary is a foot from my left arm." This relationship is the same as the numerical relationships between objects, yet is this also a 'real' thing? I can't change this relationship by thinking reeeeaaaaalllllly hard. Is it an entity? Nope ( though by your formula for determining a things reality, it must be. ) If you answer otherwise, any such arbitrary relationships become 'real' things. This is a major problem with Platonism, and, well, it was realized as early as Aristotle. So you are a bit behind the curve.------------------
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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. The mental constructs can be changed at will-- think LSD-- but you are insisting that such changes alter the physical reality as well. Consider the longitude/latitude coordinate system. This is a mental construct, no? 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. Yet, you insist that changing the mental construct of number, or grouping, MUST change the physical, or number is not a mental construct. It doesn't make sense. 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. 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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How do you get the rest of the numbers from zero?

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They come from the nothing. Duh...!!!------------------
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No, NO, NO! I am not saying that at all. I am saying the exact opposite of that.

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Yeah, you are. Read your own arguments.

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Mental changes cannot affect physical reality precisely because they are mental.

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Thanks, Rh, for pointing out an issue not in question.

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But number is a physical reality. That's why your mentation cannot affect it.

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Wrong. It doesn't follow. Actually, I can do anything I damn well please with number. It is only when trying to make number/mathematics match up with an physical world that there are limitations. That is the point. There is the physical, and there is our analysis of it. You are taking the analysis for a real live physical thing. It just ain't so.

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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.

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No. Wrong answer. I can't change the number of fingers on my hand because I don't have psychic powers. Rhhain's numbers-are-real argument: Humans don't have psychic powers, therefore number are real things. What you ask isn't that I change the 'number' of fingers, but that I grow a new finger or magically make one appear. It has nothing to do with number. It has nothing to do with 'five' magically inhering in my fingers. It has to do with mass/energy equivalencies, atomic structure, chemical bonds, etc. Mathematics is a mental construct layed over those processes. We can change math. That such change doesn't change the physical system it overlays irrelevant.Let's parse this argument you've been making.1) If a thing(s)-- in this case, number-- exists in reality, then one cannot change it by thinking really really hard.
2) One cannot change the number of objects by thinking really really hard.
3) Therefore, number is real.I looked in my handy Symbolic Logic by Irving Copi and, surprise surprise, this ain't a valid formula. It is a fallacy called affirming the consequent. So drop it.Now, I know what you are thinking, "That isn't the right formulation." Okey dokey. Let's flip it.1) If one cannot change it by thinking really really hard, then a thing(s)-- in this case, number-- exists in reality.
2) One cannot change the number of objects by thinking really really hard.
3) Therefore, number is real.hmmm.... looks better that way, at least it isn't fallacious, but lets look deeper.That a real thing cannot be changed simply by changing one's mind seems to be reasonable claim. However, the valid formulation of that claim is that of the first argument presented above, and that argument suffers from a logical flaw. There is no way to derive the second formulation from the first and I can't see it standing on its own. That something does not change when we try to think it into changing is just not sufficient reason to call it real.So what is your argument again?

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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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Nope. Can't use that one. See above.

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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.

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YES, YES, YES!!! You are saying exactly what I propose. Read it again. What I wrote is nearly identical to your 'refutation.'Rh: Changing the mental construct...calling it "six" instead of "five"...
John: ... changing the mental construct of number...Rh: ...doesn't actually change the number of fingers you have on your hand.
John: ... MUST change the physical OR...Rh: You can think and think and think some more, but you'll still only have five fingers on your hand.
John: ... number is not a mental construct.The only real difference is how you phrased the conclusion. It is the same damned argument. Did you confuse yourself?

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This is what I meant when I said you are confusing the map for the terrain.

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Sorry, bud, you've got that backwards. Math is the map. It is not I who continually claims it to be somehow a real thing. You walk into a room and step off twenty paces from the door to the far wall-- ie. you draw a map with numbers. You overlay the reality with math. 'Twenty paces' does not reside in the room. You impose it. It is shorthand.

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

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childish...

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Thank you. You just made my point.

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Are you serious? You are now making the claim that the longitude/latitude coordinate system we use to navigate is a REAL THING?!!!????? WE MADE THAT UP!!! You can't be serious.Let's back up. You state...

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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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You agree that the metric is a mental construct. You state that the orientation is arbitrary. So far two elements are human inventions. Now for the last sentence. Yes, the relationships are physical properties, but the relationships aren't math. The relationships could sit forever and math would not jump out of them. Math is how WE DESCRIBE those relationships. It is not the relationships themselves.

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Thank you. You just made my point.

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So, you official position is that the logitude/latitude coordinate system is a real thing? It inhers in the planet? Come on? How about the Mayan calenders? Do those inher too? Swatch time? Time zones? The patterns of the Constellations-- surely those too are real? They are patterns after all.------------------
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