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Author | Topic: Question.... (Processes of Logic) | |||||||||||||||||||||||
Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
schrafinator responds to me:
quote:quote: In the sense that mathematics is discovered while baseball was invented, no. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Jackfrost asks of me:
quote: As others have mentioned, "Jesus Would Read The Frickin' Manual." As to your comment that seems to indicate that if everyone were blind, color wold not exist, I'd have to say that I respectfully disagree. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote: It may be.
quote: But you've done something to the apples: You've separated them. Can I get one apple to behave like two apples? If I have only one apple, I can throw it such that it'll hit the tree but I can't then hit the barn in the other direction since I no longer have any apples. But if I have two apples, I can. Obviously, there is something physically different about one and two.
quote: Because it's fun? It's interesting to see how other people think. My best friend and I have spent many a night until the wee hours of the morning arguing over whether or not infinity exists. I say yes. She, an astrophysicist by training, says no. We know we're never going to change the other person's mind, but it's fun to see why the other thinks that way.
quote: Things that are discovered exist despite a mind to perceive them. Things that are invented don't.
quote: I can show you five. Look at your hand. Right there in front of you is five.
quote:quote: But math is not the symbols. That's just convention. In calculus, we use Newton's methodology with Liebniz's notation. It isn't because Liebniz's notation actually changes anything...it's just easier to use.
quote:quote: With your indeterminate number of apples and without cutting any up or leaving your spot or having any returned to you, hit the barn, the tree in the other direction, and eat whatever's left. You can't do that with only one apple. A physical thing requires the existence of, if we're going to require you eating, three apples.
quote: And I'd say it does. You can see the apples, can't you?
quote:quote: But I'm saying the set exists. You can see the apples, can't you? If you're going to hit the barn, hit the tree, and eat apple, you're going to need more than one and more than two. It is because we have a set of apples numbering at least three that lets us do that physical thing.
quote:quote: And I don't see how you can't.
quote: So? The existence of two things necessarily results in a relationship between them that exists.
quote:quote: (*chuckle*) It may taste like a pomegranate, but we don't have those bazillion seeds and I'm not getting nauseous. Thus, it doesn't seem to actually be a pomegranate.
quote: Actually, I was about to say a similar thing to you. The only way you can refute my explanations is to completely ignore them and construct a strawman. Indeed...if I take one apple and add one orange, I don't get two apples but rather one apple and one orange. But, we weren't talking about adding an orange. That's a strawman. The question put to you was what you would get if you took one apple and added one apple.
quote: That's because there was no need. It is only because you decided to play games and introduce a strawman and I decided to play along that we got that far. So let's back up: "Surpise! It's an orange." Logical error: Strawman. We're not talking about adding an orange. We're talking about adding an apple. If you're going to deny the existence of the apples, then we really need to back up a lot. Does anything exist?
quote: Logical error: Strawman. We're not talking about ninja-supplied fake fruit. We're talking about apples. If I take one apple and add one apple, do I get something other than two apples?
quote:quote: You mean there are no apples? Does anything exist?
quote: You mean there are no real apples? Does anything exist? Do you exist? Are you about to embrace Cartesian Doubt?
quote: So answer the question: If I take one apple and add one apple, can I get something other than two apples?
quote:quote: Sounds like Cartesian Doubt to me. Does anything exist? Do you?
quote: So if I take one real apple and add one real apple, do I get something other than two real apples? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Jackfrost responds to crashfrog, who correctly gets it:
quote:quote: The manual that came with your software. "RTFM" is a common acronym among tech support types. Of the many questions that come in to your typical Help Desk, most of them could be answered by simply reading the manual that came with the software. By having to answer these questions, it makes it more difficult for the support person to answer the questions that aren't really dealt with in the manual [added by edit] because there is now less time to spend on the question, which is probably a more difficult question, too.[end edit] Other such acronyms are PEBCAK which is "Problem Exists Between Chair And Keyboard" (namely, the user) and "I-D-ten-T," though this is one that needs to be spoken since, when written down, it's "ID10T" which, you will notice, looks like the word "idiot."
quote: Because having a joke that doesn't actually degrade anybody isn't derogatory. Are you saying Jesus doesn't have a sense of humor? We have a national ad campaign of "What would you do-o-o for a Klondike Bar?" complete with music and a bunch of bumper stickers saying "WWJD?" and it's somehow offensive to playfully combine the two? If there's any degradation going on, it would seem to be directed at those who think that Jesus and his message can be reduced to bumper sticker mentality.
quote: No, it's a part of humor. Or is humor a sin? ------------------Rrhain WWJD? JWRTFM! [This message has been edited by Rrhain, 05-21-2003]
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
NosyNed responds to me:
quote: Um, Euclidean geometry is the geometry of the plane. Last time I checked, the surface of the earth is not a plane. Therefore, why should we expect Euclidean geometry to apply? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: To you, maybe, but you aren't the only person in the world to decide what is "useless" and what isn't. I can't see into the ultraviolet, but many insects are quite happy to do so...and the flowers actually reflect light in the ultraviolet.
quote: Presburger arithmetic. It models addition, but not multiplication. Presburger showed that there is an algorithm that can decide of any given statement is true or not. Fischer and Rabin then showed that all algorithms that can decide such statements have a runtime of 22cn for some c and n being the length of the statement.
quote:quote: Yes, but how many? It's the same question as asking what color they are. If they have color, they have number. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: Stop right there. It isn't modeling all of arithmetic...just addition.
quote: No, because it isn't modeling all of arithmetic.
quote: Look it up and find out. There is more to multiplication than "repeated addition."
quote: Read the proof and find out.
quote:quote: How is "counting them" fundamentally different from "looking at them"?
quote: I'm saying they are fundamentally equivalent, yes. Just as an object has size, shape, texture, color, it also has number.
quote: But just as many objects can be red, many sets can be five. Surely you wouldn't say that only a red apple can be red, would you? So why are you making a distinction that your fingers are somehow unique to being five?
quote: How many are there? You want to see red? Look at this apple (though you may need special equipment to see it). You want to feel smoothness? Touch this apple. You want to see one? Count this apple. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Chavalon responds to me:
quote: Would the number of fingers on your hand change if nobody was around to count them? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote: Because if it's still there when there's nobody around, it's a discovery. Math is still there, even when there's nobody around to think about it. Or do the number of fingers you have on your hands change when you're not looking? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
John responds to me:
quote:quote: Because you don't understand the rules of multiplication. What makes you think mathematical operators in the Complex number system are going to behave the same way they do in the Reals? i is not a Real.
quote:quote: Because false premises can lead to any conclusion you desire.
quote: Because they don't apply to the system in question.
quote:quote: Irrelevant. The question is not whether the system is "trivial. It is whether it can model arithmetic. The axioms of Presburger arithmetic, for example, are not that sophisticated. You can get addition, but you can't get multiplication. And as Presburger, himself, showed, they are both complete and consistent.
quote: I am not. I am accurately stating that the Incompleteness Theorems have very specific meanings and applications and attempts to use them outside of those specific areas is inappropriate. Just as those trying to use the Heisenberg Uncertainty Principle to explain human behaviour under observation, the Incompleteness Theorems cannot be applied to things other than axiomatic number theories sophisticiated enough to model arithmetic. Sounds to me like you are just being diversionary, and effectively just skipping around the issue-- which, if you've still missed it, is that logic and mathematics which you have made out to be absolute and infallible are the very things which get screwed by Godel's proof.
quote:quote: Neither do I...you cut out so much context that I'd have to trace the thread back by hand to find out.
quote:quote: Depends on what I'm trying to do. Again, sometimes it's easier to draw the negative space than the positive space. The definition of an infinite set is that it is not finite.
quote: Bingo. You just proved a negative.
quote: By negating a falsity.
quote:quote: No, now you're getting into Russell. "This statement is false," and all that.
quote: You're the one saying you can't prove a negative. But "This is false" is a negative and "It is true that this is false" is proof of that negative.
quote:quote: That's because you're reading what you wish I would have said and not what I actually did. Try again. But sometimes the only way to show something to be true is by showing something else to be false. You see that word "sometimes"? What do you think it means? Infinite sets are, by definition, not finite. In order to show a set to be infinite, you must show it not to be finite.
quote:quote: In reference to something else entirely. Why are you equivocating?
quote:quote: Yes. Do I really need to go through the proof of the non-existence of a largest prime?
quote: And that doesn't happen in mathematics because of what, precisely? Are you saying there might be a largest prime?
quote: You mean it is impossible to deduce anything?
quote:quote: What is an existential mathematical statement without the existential operator? That's the defining characteristic of an existential statement: It uses the existential operator. This is in contrast to a universal statement that uses the universal operator. They are negations of each other. The negative of the universal is the existential and vice versa.
quote:quote: See...this is what I mean by your complete destruction of context. What was I saying "Indeed" to? Any idea? Why did you remove all the context? What on earth are you talking about? If there is a largest prime, our system of mathematics would be contradictory, yes. Do you have proof of such?
quote: No, the incompleteness theorems again. Statements that can be decided will not be contradictory.
quote: No, axiomatic number systems complex to model arithmetic will be either incomplete or inconsistent. Not all of math is such a system.
quote:quote: No, the proof depends on the fact that you don't. The moment you leave the abstract, you have only proven the specific. We need to get this out of the specific and into the general. That's how inductive proofs work. Yes, you need to show a specific case, but the inductive step is that you generalize to all others.
quote:quote: Then there really is no need to continue. We have a fundamental difference. For myself and the vast majority of mathematicians, the objects of mathematics are real. I do not say that as if that is justification. I am simply pointing out that I am not an isolated instance.
quote: You mean the number of fingers on your hands changes if you're not paying attention? If you were to think really, really hard, you might actually have six on one and four on the other?
quote:quote: Incorrect. But since you cut out so much of the context, I can't really say more than that.
quote:quote: Of course not. He didn't even discover most of it. He was compiling the work of others. But, since you cut out all the context, you're missing the point. It is that a circle is not as you think it within the realm of plane geometry.
quote: That's because, once again, you are responding to what you wish I had said and not what I actually did. Go back and read it again. Notice the part where I mention Euclid compiling the work of others. What do you think that might imply? And considering that I am arguing from the position that the objects of mathematics are real, what do you think that means? Hint: Would it matter to me if Euclid existed at all? You even responded to it. Why didn't you pay attention? "...there was this guy named Euclid and he collected the works of other mathematicians." Hmmm...does that statement indicate that I think Euclid invented geometry? Think carefully, now. Answer based on what I actually said, not what you wish I would have said.
quote: No, the postulates are separate from the definitions. Haven't you read the books?
quote:quote: It's impossible to have only four points. If you have more than one, you have infinitely many.
quote:quote: And you'd be wrong.
quote:quote: Non sequitur. If you ask for examples and I give you examples, how is that not giving you the examples you asked for? Look, if you don't want to read them, that is not my fault, but for you to claim that I didn't give you the examples you requested is disingenuous at best.
quote:quote: Then is it not possible that these people know something you don't? That there is a point to asking the question? For example, one of the things in linear algebra is that a matrix is equivalent to a given matrix if each corresponding element is equivalent (Two m x n matrices A = aij and B = bij are equal if aij = bij for i = 1, 2, ..., m and j = 1, 2, ..., n.) Thus, you prove that A = A by showing that each element within it is equivalent.
quote:quote: But that doesn't mean the forward direction is invalid. All squares are rectangles. Not all rectangles are squares.
quote:quote: Like maybe the comment you made which prompted my response. With no antecedent, it's hard to say what "that" is that I seem to think is insufficient.
quote: And I think you're avoiding the fact that we discovered it.
quote:quote: Question: Are the axioms of geometry that of a number system sufficient to model arithmetic? Think carefully...consider the fact that not all numbers are constructible in geometry.... If so, then those Incompleteness Theorems apply. If not, well, then they don't.
quote:quote: Because there is no other way for them to behave.
quote:quote: But even randomness and chaos behave in a logical manner.
quote:quote: Incorrect. Or have you not heard of Chaos Theory? Gleick wrote a wonderful layman's book about the subject. Perhaps you've heard of it: Chaos. The chaotic behavior of the logistic map was what I wrote my Sophomore Thesis on.
quote:quote: Not if it can be shown that all of the things that are not the thing I'm looking for are of a piece and that piece cannot be true.
quote:quote: But 1 + 1 = 2 isn't an axiom. It's a conclusion. Russell worked very hard to show that. And mathematics wasn't created...it was discovered.
quote:quote: Nope...a simple request.
quote: If you have five of them, how can you have some other number of them? Do they change number when you're not paying attention? If everybody were to die and thus have nobody around to count them, would their number change? And how can you claim you don't perceive five if you count five? "Yes, I am sensing red, but I'm not seeing red." ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: S'aright. It's complicated. The axioms of Presburger arithmetic are simple, but they are based in symbolic logic and hard to transcribe.
quote:quote: That's only because you're faster at figuring out red than you are at figuring out five. If I give you a color that's very close to what you would consider to be the "border" between red and orange, you'd have to spend a bit more time thinking about what color it is, wouldn't you? Does that hesitation mean that color is something that is sometimes real and sometimes manufactured? Things exist only if we can so quickly process the information that we don't do it consciously? What about the people who can determine number as quickly as you can determine color? They do exist.
quote:quote: A set is an object.
quote:quote: Yes...and? Are you saying you don't have a set of five fingers on the end of your hand? That if you stop paying attention, you might return to a set of six?
quote: I would say you have the opposite problem. I am well aware of the difference between a set and its elements. Russell did quite a lot of work in that area and Russell's Paradox is specifically about that. But you seem to think that a set is not an object. If you stop paying attention to your hand, does the number of fingers on your hand change? If everyone were to die and thus there would be nobody around to count them, would the number of fingers on your hand change? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: You can play Monopoly without players? There's a good trick. Oh, the Monopoly set is there, all the pieces, the money, the board, the dice, etc., but with nobody to play it, it's nothing more than a bunch of brightly colored pieces of plastic and paper.
quote:quote: With nobody to play it, how is there a mortgage?
quote: I'm not saying that they are. But if everybody were to die, you'd still have five fingers on your hand. If everybody were to die, Monopoly would never get played. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: How is that not an object? How is the relationship between two objects not also something that exists?
quote:quote: Not even the fact that there are five of them?
quote: So? What does the fact that you need the group of them have to do with anything? Plurality is a property of multiple objects. Each finger by itself is only one.
quote:quote: Your body is going to decompose that quickly? You planning on diving into a vat of acid as your means of demise?
quote: So? You don't have five fingers on your hand?
quote: No, the null set is a set, too, but you're talking about the original set. That said, so? Are you saying you don't have five fingers on your hand?
quote: So you don't have five fingers on your hand? ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Chavalon responds to me:
quote:quote: Well, if nobody were around to see, there would be no concept of color, and therefore - it seems to you - imposssible to know whether there were such a thing as color. That's the question: If everybody were blind, would there still be color? Suppose everybody were to die right now, would your car no longer be the color that it is?
quote: Um, you do realize you just contradicted yourself. If it is an empty set, then it has no members and cannot have five of anything.
quote: 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. ------------------Rrhain WWJD? JWRTFM!
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
crashfrog responds to me:
quote:quote: There's two of them, aren't there?
quote:quote: Until you can remember that I understand that each individual finger is only one. But the five of them together are five. Are you saying you don't have five fingers on your hand?
quote:quote: So when you're not paying attention, there is some other number of fingers? If everyone were to die right now leaving nobody to count them, the number of fingers on your hand might change? If there were no people to see, would there be no such thing as color?
quote: So when you're not looking at something, it is meaningless to say what color it is? Things only have meaning when you're paying attention to them? You seem to be heading toward solipsism. Are you saying it's meaningless to talk about whether a tree falling in the forest with nobody around to hear it since the forest is meaningless with nobody around to recognize it let alone the tree and whether or not it makes a sound.
quote: But it isn't an assumption on my part. It's an observation. I look down at my hand and I see five. I am of the opinion that it doesn't matter if I'm looking at my hand or not...it contains the same number of fingers. The forest exists and if a tree falls with nobody around to notice it, it still makes a sound.
quote: How does one play Monopoly with no players? You cannot get the rules of Monopoly simply from the set. You have to impose the rules on the set. Your hand has five fingers no matter if somebody looks at them or not. They behave as five no matter what you do. Nobody makes them five, they simply are that way. Or do you not have five fingers on your hand? ------------------Rrhain WWJD? JWRTFM!
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