Truth is Relative

AnswersInGenitals writes:

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2 + 2 = 1 (modulo 3). There are just a finite number of rational numbers if you are considering a finite field. Two parallel lines: 1) never meet; 2) always meet; 3) don't exist depending on what geometry you are considering.

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And thus, we see why one who is not versed in a subject should not speak on it. This is the same error made by people who try to apply the Heisenberg Uncertainty Principle to sociology.Despite your claims, all those things are true since we understand the concept of axiomatic theory. The attempt to claim that somehow a true statement in one axiomatic system is in question because we've moved to another axiomatic system shows that one doesn't understand the concept of axioms.By the way: Modulo arithmetic doesn't deny the existence of numbers beyond the modulo. "Modulo" is a function, not a field.Too, the discovery of non-Euclidean geometry was spurred by the attempt to disprove Euclid's Fifth Postulate. For those who don't know, the Fifth Postulate is that if two straight lines are crossed by a transversal, the lines will meet on the side where the interior angles are less than two right angles. This can be restated equivalently that parallel lines never meet, but that was the reason why people were trying to disprove it. The phrasing of it seemed suspect and it was thought that it should somehow be derivable from the others.And yet, the only thing they could conclude is that it is, indeed, true all on its own, independent of everything else. But in the process, they discovered that they could simply replace the Fifth with other, similar postulates and come up with new geometries. Some of those geometries conform to objects we can easily conceptualize (spherical geometry) while others are a bit more difficult to handle.None of that detracts from Euclidean geometry. The truth of the Fifth Postulate is simply by fiat: It is true for it is a Postulate.Mathematics isn't going to help us in dealing with a question of sociology.

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So, even if there was total agreement that some statement were absolutely true, might that just be a temporary consensus awaiting discovery of a larger but more tenuous truth?

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No, because you misunderstand the mathematics involved. All of those statements are true. No, there is not some "more advanced (more general) mathematical structure" surrounding them. They simply are true.

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Some logicians attempt to bypass the problems of the self-referential statement but still create the innately contradictory situation through use of set theory

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See, here we go: The attempt to invoke the Incompleteness Theorems to solve a question not of mathematics but of sociology.Hint: There are consistent, complete axiomatic systems out there. The Incompleteness Theorems only apply to axiomatic systems of set theory that are powerful enough to model integer arithmetic.Do you really think that sociology is an axiomatic system of set theory that is powerful enough to model integer arithmetic? If not, then math isn't going to help you solve the problem.The findings of science only make sense in the context and field in which they were formulated. They do not function outside of those realms no matter how much the metaphor seems to apply.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn writes:

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If yes, then color does exist. Optically it may be viewed differently depending on the creature, but it does exist.

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Numbers, on the otherhand, do not exist in nature that I'm aware of.

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How is number not an intrinsic part of existence whereas color is?Are you saying that one object isn't really "one"?After all, the color of an object is relative depending upon how the two are moving with respect to each other. So why does number, which is relative to the relationships of objects to each other, get the short shrift?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn responds to me:

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I understand that a male gold finch sitting on the fence will look different depending on what eyes he is being viewed through

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That's not what I'm talking about. I'm not talking about the subjective experience of color. I'm talking about the actual wavelength of light that is being received. It is not constant but is relative to the observers motion relative to the object being viewed.There's a joke of a physicist who was contesting a ticket he had received for running a red light. He said that since color is relative based upon motion and since he was approaching the light, it's wavelength would have been compressed, shifting it toward the violet end of the spectrum and thus, he perceived it as green.The judge agreed and changed the violation to speeding since in order to shift the color sufficiently from red to green, he'd have to be moving near the speed of light.That's the point I'm making: Not even color is absolute since color is a function of wavelength and wavelength is relative.

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As far as I know, numbers do not exist in nature.

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I asked you a simple question. It would be nice if you answered it. Why is it that nobody ever answers my direct questions?Are you saying that one object is not "one"?

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How each species relates that there is a gold finch and cardinal sitting on the fence is relative to the species, but the birds are not a two.

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Why not? There's "two" of them. Do not confuse linguistics with mathematics.I know about the Piraha and they've been giving the Chomsky-ans fits since they don't have recursion which Chomsky says is inherent in all lanaguage. But I notice that you seem to have overlooked your own source:The Piraha don't have color terms, either. If you're going to say that there is no such thing as number because there is a language that doesn't use number, then you're going to have to say that there is no such thing as color, either, for the exact same reason.Color can be objectively defined. While the boundaries may be arbitrary, they are objective. Number is the same thing. Physically, a single object behaves one way. If you add a second object, they behave differently. Add a third, and things change yet again (and, in fact, become so difficult that we cannot solve the problem directly).What has changed? Number. It is because there is another, distinct and separate object involved and it is because the [I][B]TWO[/i][/b] of them are interacting.Edited by Rrhain, : Fixed a grammar and formatting error.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

Mr Jack writes:

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two piles of sand, add two more piles of sand and end up with one pile of sand.

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You do realize that you just contradicted yourself, right? If you're going to insiste upon "one pile of sand," then you didn't have "two piles of sand" to begin with.Of course, we're being disingenuous with the concepts here. "Pile of sand" is not well-defined. There's a joke about an engineer, a physicist, and a mathematician on a train. The engineer looks out the window and says, "Look! There's a goat in the field!" The physicist looks and says, "Yes, there is a white goat in the field!" The mathematician looks and says, "Yes, there is a goat in the field and the side that is facing us is white."The reason why you can have "two piles of sand" and end up with "one pile of sand" is because we are being lax over the definition of a "pile of sand."

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn responds to me:

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but when it comes to existing in nature I don't see that the statement concerning rational numbers is an example of absolute truth.

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Again, I ask you flat out:Are you saying that if we have one object, we don't have "one"?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn responds to me:

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Are you saying that if we have one object, we don't have "one"?

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Correct

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Then what do we have? Two?Tell that to the guy at the checkout stand when the bill comes to five dollars and you hand him only one.After all, by your logic, it isn't "one." It's something else.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

crashfrog responds to me:

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Then what do we have? Two?

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One object.

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So number is an inherent property that does exist. Thank you.That said, who cares about the object? I didn't ask about the object. I asked about its property. That is, if a red object doesn't have the property of being "red," then what is it? "Blue"? If one object doesn't have the property of being "one," then what is it? "Two?

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Sure. But by your logic, I can hand him five apples instead of five dollars, since both of them are "five".

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Huh? Where did that come from? An object can't have more than one property? If it has color, it can't have mass?

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But one object is not the same as "one".

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I never said it was. A red object is not the same as "red," either. A massive object is not the same as "mass." These are properties that are endemic to the nature of existence. They come along for the ride and help describe what they are. Are you about to apply the Heisenberg Uncertainty Principle outside of its defined parameters?And again I point out, both color and mass are relative.

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I think you're just going to have to accept that the kind of Platonism you espouse here may be endemic to mathematicians, but it hardly convinces anybody else.

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Isn't that the same argument creationists try to use? Hey, we know we're not biologists, not biochemists, haven't done any actual research into the subject, have only half-remembered what we've learned in school, and have certainly never done any advanced work in the field, but who the hell needs all of that? I'm just as smart as the people who spend their lives studying this subject and surely my opinion is just as valid as theirs!Great, so you aren't convinced about the reality of number. Neither are the creationists convinced by the overwhelming evidence regarding evolution, but we don't really pay them no nevermind, now do we? They aren't in a position to criticize due to their lack of experience in the subject.

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To anticipate a direction where this conversation might go, if mathematicians discover, rather than invent, mathematical truths (like numbers), then where do the falsehoods come from?

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Huh? Non sequitur. Please rephrase.

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The Library of Babel disproves Plato's Cave.

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Hint: Being a "Platonist" in the mathematical sense is not the same thing as being a "Platonist" as in Plato's Parable of the Cave.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn responds to me:

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What is your point in relation to the topic concerning my statement in Message 21: Numbers, on the otherhand, do not exist in nature that I'm aware of. and my subsequent explanations in Message 29 and Message 36?

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That such a statement is wrong: Numbers do exist in nature. They are part and parcel of existence. Existence cannot be without number.

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I would hand him one five-dollar bill.

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(*chuckle*) Yes, I get the joke, but what would that "five" dollar bill be worth? "Four"? By your logic, you could claim it is "six" and demand change.

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Although I have a set of magnetic numbers on my fridge, when I stand on my back porch I see no such numbers in nature.

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You are confusing symbology with substance. The specific characters in the specific sequence, "red," is not the actual color. It is just a symbol.

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Please clarify what you're getting at in relation to the topic.

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That your statement is wrong. Number does exist in nature. It is part and parcel of existence.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

crashfrog responds to me:

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That said, who cares about the object?

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You do.

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No, I don't. If I did, I would have said. Instead, I used an abstract term, "object." It is indicative of the fact that the specifics with regard to things other than number are immaterial with respect to the question of number. That is, number is not dependent upon color, mass, or socially constructed representations of fiduciary transactions. Those are other properties which number can come along with, but is not dependent upon.

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If one object doesn't have the property of being "one," then what is it?

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Asked and answered. It's one object.

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Then you agree that it is "one." Thank you for admitting that numbers do exist in nature.

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Are you just going to repeat questions I've already answered?

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What? I thought we just settled it: Number exists in nature. If it isn't "one," then is it "two"?Hint: It may just be that you haven't answered the question.

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Huh? Where did that come from?

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It came from your logic. Do you really need me to quote you again?

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Yes, you do. For it did not come from me. I was talking about number. You're the one who suddenly decided that apples and dollars were the same thing.If a "red" apple and "red" cherry are both examples of "red," then "five" apples and "five" cherries are both examples of "five." But an "apple" is not a "cherry." If we need an "apple," then it doesn't matter how many cherries you give for what we are looking for is an "apple," no matter how "candy-apple-red" it is.Thus, my question to you: Objects can't have more than one property?

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I really have no taste these days for your preferred method of arguing.

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Then do yourself a favor and don't respond. Nobody is forcing you to do anything you don't want to do, are they? You are in complete control of your posts.

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Hint: Being a "Platonist" in the mathematical sense is not the same thing as being a "Platonist" as in Plato's Parable of the Cave.

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Hint: it was just a slogan I used in summation.

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But you meant it. And unfortunately, the word doesn't mean what you think it means. You are falling for the same error of equivocation that creationists fall into when they try to claim that evolution is "just a theory."And as to your "analysis" of my debating style, well, I guess I'll fulfill one of your prophecies:Physician, heal thyself!Edited by Rrhain, : Fixed a grammar error and the use of the wrong adjective.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn responds to me:

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You are addressing quantity, I am not.

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What is quantity if not a physical manifestation of number?

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I'm talking about the symbology since the statement concerned rational numbers

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But numbers aren't symbols. They exist outside the symbology. Surely you're not going to say that the Arabic numeral 1 is somehow referring to something other than the Roman numeral I, are you?Just as it doesn't matter if you call it "red" or "rojo" or "rot," it doesn't matter if you call it "1" or "I" or "." They all refer to the same thing. The symbol is nothing but a convention to help us beings who use langauge discuss it.

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I agree that quantity exists in nature; but since the symbology depicts negatives, do negative quantities exist in nature?

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Of course. Have you never seen a hole? You even get imaginary numbers, or have you not done any systems engineering where you try to get the solutions to your equation to be in the left half-plane in order to ensure stability?This is the point of applied mathematics: Practical, real-world uses of the things pure mathematics finds. It's why, as my physics professor said on day one: Chemical engineering is really just applied chemistry. Chemistry is really just applied physics. And physics is really just applied math.The universe is inherently mathematical in nature.

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Is it a true statement that there are infinitely many quantities in nature?

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Quantities of what? I don't understand the question.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

JavaMan responds to me:

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Numbers are mental abstractions.

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So if you have "one" object, it isn't an example of "one"? What is it if not "one"? "Two"? What the object is is irrelevant. Number is abstract, yes, but that doesn't mean it isn't real.

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Perception of 'red' is perception of some property in a thing

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Indeed. And how does that not apply to number? If you have "one" object and then introduce another object, they start to behave differently. For example, they exert a gravitational force upon each other...a force that would not exist were there not a second object. And if you add a third, the model becomes so complex that we have yet to figure out how to do it directly. That's why it's called the "Three Body Problem."

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For example, if I have two golden finches, can you point to any property in either finch that contains its 'twoness'?

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Yes. The fact that they behave differently because there are "two" of them and not just "one" or "three." It's what defines them as a pair, a couple, a dyad, a duo. Show me how you can take "two" finches and somehow have them behave precisely and in all ways as "three."

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And it is because numbers are purely mental phenomena that we can have absolute certainty about the statements we make about them.

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And we can say the same thing about color since it, too, is a mental abstraction.

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If they were real properties of things, we would have the same difficulty we have with other properties of things - i.e. any statement we made about them could only have high probability associated with it, never absolute certainty. (This, at bottom, is the difference between science and mathematics).

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No, not quite. The problem with science is that as an observational process, we are never certain we have managed to observe everything. We might have, our model might be absolutely perfect, but we can never be sure. The process of mathematics is one where we can assert that we have. In the modeling of weather, we find that things can be extremely sensitive to initial conditions. It isn't that the model is wrong...it's that starting with 0.6254 isn't enough to completely define things.There's an old joke:Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think they're physical chemists.
Physical chemists think they're physicists.
Physicists think they're god.
And god thinks he's a mathematician.The very nature of the universe is inherently mathematical.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

purpledawn writes:

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My thoughts are concerning what occurs in nature without manipulation by man. Grinding up the wood and adding an alkaline or acidic solution is something that man has done.

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Oh, not this tired argument...that somehow because a human being was involved in getting the substance into an alkali solution as opposed to an acidic one, that changes how the substance would have reacted and makes the entire thing artificial. That somehow, the mere presence of a human being forced the substance to change color in a way it never would have done had the exact same thing happened but the human being were not present.

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Color seems to have a purpose in nature

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Yes, but it is the perception of the specific ranges of wavelengths that are involved that causes the purpose.Personally, I do think that color exists. "Color" is simply a way to describe various wavelengths of light. We have imposed arbitrary and artificial divisions upon what separates "red" from "orange," but that's just a convenience for us to be able to communicate about the actual wavelength.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.