PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
|
From: Curt Welch on 15 Jul 2010 01:49 "K_h" <KHolmes(a)SX729.com> wrote: > "Curt Welch" <curt(a)kcwc.com> wrote in message > news:20100713005651.989$X2(a)newsreader.com... > > "K_h" <KHolmes(a)SX729.com> wrote: > >> "Curt Welch" <curt(a)kcwc.com> wrote in message > >> news:20100712153958.337$gS(a)newsreader.com... > > > >> >> What is your definition of physical? > >> > > >> > The same as everyone I believe. All things which are part of the > >> > universe are physical - all properties and effects that exist are > >> > physical. > >> > >> Because you say so? Yeah, that's intelligent and thoughtful. > > > > Dude, don't be stupid. You asked for my definition of a word and I > > gave it to you. Are you so stupid to not understand that when I give > > you my definition, that is must be "because I say so"????? > > You have not provided a definition. Writing "the same as everyone I > believe" is not providing a definition and therefore is not answering the > question. I was trying to guess what you were looking for, and I guess I got it wrong. Now I'm again trying to guess what you are looking for and I'm still confused. I assumed you were asking for a definition so you could be sure you understand what I meant when I used the word to make sure I view of physical agrees with yours. I've written enough so that my view should at this point be more than obvious to you. But yet you still ask for a definition of something that should be obvious to you. So I'm left wondering what your point is. is your question a test to see if I can define it? Well, again, from above, here's the deification I gave you when you first asked so saying I didn't give you a definition is kinds lame.: All things which are part of the universe are physical - all properties and effects that exist are physical. Or, if the way I wrote that didn't strike you as a definition, let me reword it to help you out: physical - 1. a. All things which exist in the universe. b. All properties and effects which exist in the universe. Maybe this one would be better for you: Everything which can be sensed or measured. Here's a third: Everything that a human can be aware of. Here's a forth: Everything that exists. In order to create a definition that is useful for you and I to communicate, we need to first agree on a set of axioms to define with. The "physical universe" is itself commonly such an axiom and as such, can't be defined in simpler terms because there are no simpler axiomatic terms to define it with. So what we are normally left with in creating definitions for such works is simply showing their relationship to other words. And of course, the axioms are defined by pointing to the thing we are talking about, so look at what your finger is pointing at, that's something which is physical. And if you want to know more, all you should need to know is that I'm a believer in physicalism (which I've said already), and that I use the term physical as you would expect someone who is a physicality to use it. http://en.wikipedia.org/wiki/Physicalism Still want me to define it? All that is not enough? Then PLEASE, stop saying, "you haven't defined it" and tell me what you are looking for. > No, I want you to provide a clear and comprehensive definition of > physical. Ok, so here it is again, the answer I gave you the first time you asked: All things which are part of the universe are physical - all properties and effects that exist are physical. Please explain to me what is not clear about that for you and what is not comprehensive about that for you. > The "because I say so" did not, and does not, apply to > whatever definition of "physical" that you provide. It only applied, and > applies, to your claim that the said physical universe is all that > exists. That claim requires justification and you never provided one. So make up your mind. Do you want a definition, or a justification for my definition? You understand that those two things are totally different right? The justification can be found in the literature of everyone that has tried to justify the physicality stance. For some insight in that, check out the "Arguments for physicalism" in the reference above. If you want more of my words, on the justification, I can write them for you. However, it would be far more useful if YOU were to explain your position, and what you think is missing from mine, so I can address the issues that are important between our views instead of talking to a wall which is all I can do when you keep saying "you haven't defined it". > Then you should have written something like "in my opinion there are no > non-physical attributes". In my option, I would be wasting my time, if I had to write, "in my option" in front of everything I wrote. Just assume, from this point forward, that everything I write is my opinion and not your opinion, OK? > But you did not dso that. You made a factual > claim when you wrote: "Because there are no non-physical attributes". > It's great that you state your beliefs so long as you don't state them as > facts. To me, it is a fact. It's a very obvious fact. Just because 98% of the people in the world might happen to think differently, doesn't change my opinion that this is a fact that I have right, and they have wrong. I do not write "in my opinion" on facts that are obvious right just because I'm living in a time where some large percentage of the population is ignorant on the issue. I'm I right? No one knows. But it's what I believe to be a fact (as strong or stronger than most facts) (remember I don't believe in absolute truth so there are no absolute facts either - just relative measures of probabilistic strength). > > Existence to me means "objective data". > > My definition of existence includes "objective data" as well. Every > digit in the decimal expansion of the square root of 2 is objectively > defined. So all of those decimals, in their order in root 2, are > objective data. Therefore, root 2 exists according to our common > definitions. The objective data in root 2 is uniquely, unarguably, and > unambiguously fixed and is therefore absolute. Well, close but no. A definition does not make a thing exist. That's as stupid as saying if I define the word gafart to mean "pink flying elephants" then you and I will agree that pink flying elephants exist. No, the only thing that objectively exists here are the words I typed in the message, and the physical effect they had on our brains when we read them. Likewise, if you say you have defined "EVERY DIGIT" of the square root of two, you have done nothing more than I did with gfart. You specified a procedure for creating the digits, but you did not, actually create them, just like I did not actually create a gfart. Defining the digits, is not the same as creating them. You did not create them, so they do not exist. We could create a large number of them, but never could we create all of them, so at no point in the figure, is it reasonable to assume all the digits could ever exist. If we build a computer to compute the digits, we have created a computer, and we can use it to create many digits, but again, never could we use it to create them all. Objectively defined is not the same as objective data of it's existence. But without that large error in what you write, there's a more subtle problem with _what_ we create when we do that (numbers vs signs - aka ink marks on paper). But I'll not waste time writing about that yet. > > Times up. My guess is that you still have no clue what I meant because > > your narrow mind can't grasp a simple concept which is at odds to your > > fundamental beliefs. > > Stop the insults. Stop claiming others have narrow minds. If that's what you need. > > I'll repeat what I've already written many times in this thread. There > > are no absolute truths. There are only truths so close to being > > absolute, that there is no point us us ACTING as if it were not an > > absolute truth. That is, truths are probabilistic. They have some > > probability of being true based on how much experience and evidence is > > available to support the truth. No amount of experience, or evidence, > > can ever create an absolute truth. It can only create truths beyond a > > reasonable doubt. At some level of probability, we are willing to > > start acting AS IF the truth were 100% correct (absolute) but never > > does the evidence allow us to know the truth is 100% correct. Nature > > is not absolute - it's probabilist at the lowest levels. The brain > > does not create behavior absolutely, it's selection of behavior is > > probabilistic at all levels. > > What you write is true for some things but not others. To me, it is > self-evident that the truth underlying the statement "1+1=2" is > absolutely certain and therefore qualifies as an absolute truth. But you > are claiming it is not 100% certain so I respectfully ask you to assign a > probability to "1+1=2" in reply to this post. Well, the problem here is that there is no "truth underlying" the message. That is, what is most likely self evident to you, is that the language "1+1=2" has the exact same "underlying truth" as the language "true". It's "absolutely true" by definition. But this returns us to the gfart error from above. Using words to define something is not the same as making it exist. Just because you say it's an absolute truth, doesn't mean absolute truth exists. So maybe we need to step back and look at how truth (absolute or otherwise) exists at all. It exists as a language description of the physical world. If I say, "I have ten fingers" either that is a truth, or not. We test the truth by comparing the condition of the universe, with the language, to see if they match. If the language is an accurate description of some (past or present) condition of the universe, it's a truth. Otherwise, it's not a truth. Absolute truth requires that we we can verify, with 100% certainty, that some language description, matches some aspect of the universe. The physical nature of language, and information flow in this universe however, guarantees that such a verification can't be done with 100% certainty. This is why there are no absolute truths. So back to your specific question. You say the underlying truth of the message "1+1=2" is absolutely certain. In this case, it's true by definition. So the first problem here is that we can define absolute truth, using language, even if it doesn't exist, and create the gfart problem. I can define absolute truth as: absolute truth - Any language description of some aspect of the universe which has been verified to 100% certainty to be a correct description. So now I've defined the words "absolute truth" in a clear and concise manner, but just because I defined it doesn't mean it can exist - which for the best understanding of the nature of our universe, it can't exist. Now I create another definition: The language "1+1=2" is an absolute truth. So now I have defined absolute truth even though it's a gfart, and I defined that the language you ask about, is an absolute truth, even though, absolute truth can't exist. So now you say the "underlying truth" is absolute. Well, if you are making a reference to the way the language is defined "by saying underlying truth", you are generally right. But now, to verify that it is an absolute truth per the language, we have to compare the language "1+1=2" with the definition, and see if it's a match. So again, we are required to compare language, with some aspect of the universe, to see if there is a match. And it's only an absolute truth again, if we can be 100% certain that we have correctly done that compare. Which we can't. Not to 100% certainty. This second problem, is that you, and I, and everyone reading these messages, can't be absolutely sure that we correctly matched the 1+1=2 language to the definition, because like all language and information flow, we are faced with some probability of error and information loss. So for the same reason I say there are no absolute truths, we are also faced with the problem of absolute verification that the language is a correct reference to an absolute truth definition! In other words, dose the string "1=1=2" match the definition I wrote above? If we got 100 million people to check for a match, as you and I have done, would they all conclude it was a match, or might one out of 100 million, conclude it wasn't a match? I don't know what the probability of someone making an error on this match, but I now it's not zero. If enough people check it, or if one person attempts to check 100s of millions of language samples to verify which ones represent a truth in the language, they will at some point, make a mistake, and not know they made the mistake. And whatever that error rate is, is the uncertainty in the "underlying truth" of 1+1=2. Now, what I suspect you are doing however is assuming absolute truth does exist, and once you assume that, you are assuming that "the underlying truth" is what the language is making a reference to - aka the absolute truth that exists. By using the words "underlying truth" you are attempting to eliminate any potential confusion, or error, in the processing of the language, and instead, are saying, "assuming we understand with 100% certainty what truth we are talking about with this language", that underlying truth, exists! That almost works, except it's only valid if you make the logical error of assuming what you are trying to prove. It's the fallacy of begging the question. It's only true if you start with the assumption that absolute truth exists before you evaluate the logic of the argument. > >> > It's no different than an engineer making drawings of a machine they > >> > are thinking of building and then doing various calculations using > >> > the drawing as a simplified model of the thing that does not exist. > >> > The drawings, are not the thing. I can draw a 1" cube and write on > >> > the drawing that it's weight is a million pounds. This is a > >> > fabrication. It's a lie. It's just something I made up perhaps to > >> > explore the idea of what would happen if such a cube exited and I > >> > had access to it. > >> > > >> > All of mathematics is a fabrication. It's a story we tell about a > >> > place that doesn't need to exist. > >> > >> No, the truth underlying math is not a fabrication and it does exist. > > > > Yes, it exists, but only in the form of brain activity. > > Again, you are claiming this as a factual certainty. If you had written > "in my opinion it exists only in the form of brain activity" I would > still disagree but not query you about it further. Look, the truth > underlying "1+1=2" exists objectively as "objective data", to use your > earlier words. So it exists outside the brain as objective data and so > it is an objective fact. Yes, we can turn all that language into objective data. But we can never, with 100% certainty, verity the sample, matches the definition. We can verify it with extremely high degrees of accuracy by careful double checking and other techniques, but that high degree of accuracy can never reach 100%. A careful testing with machine assistance could probably yield an error rate of one error every 10 billion years (dong 1000 checks per second), but 1 error every 10 billion years is still not ABSOLUTE CERTAINTY. It's way past the point of being practical certainty, but not absolute certainty. > > It exists in our mind in the world of mathematics which was created by > > a clever arrangement of words - by language. Those words are > > descriptive, but their descriptive power was created by the physical > > world, not by our mind. They describe real features of the universe. > > But when combined in new ways, they describe a feature never before > > seen in the universe - a made up story. The mathematical truth you > > talk about is just such a story. It doesn't "exist" in any sense until > > the story is created, and understood by some human or other human-like > > thinking machine. And then, it only "exists" as long as that human, or > > some other human, that also knows the story, exists. > > This is wrong. Consider PI = 3.1415... and note that its first digit is > a 3, its second digit is a 1, its third digit is a 4, and so on. There > are various formulas that allow one to calculate ANY of its ALEPH_0 > digits. But those formulas take time to compute and so many, in fact > infinitely many, of its digits can't be calculated by humans -- unless > some breakthrough happens in pure theory that allows one to calculate the > nth digit of PI by some simple but clever formula f(n). As we have learned, there are neat formula for doing that! But that doesn't change anything big here. Your point is still the same either way. > Just because we > cannot calculate those digits doesn't mean their true values are not > already fixed as objective data. Fixed yes. Per how we talk about such things. But for starters, the gfart error returns in your argument because defining is not the same as creation. In math, we talk AS IF, defining was the same as creating, but it's not. And this is another one of the areas where math simply diverges from reality because math is an activity of paying with words, it's not playing with reality. It starts by playing with words that almost represent things we can create, like the numbers 1, 2, and 3, then diverges into stuff we can't do, with the magic of words, like create all the whole numbers. That's fine in math, because math isn't about doing. It's about exploring what can be said with words. So I understand why anyone well entrenched with math would confuse creation, for defining, but in reality, these two things are very different. Defining something with words does not make it exist. All that exists in that case, is the definition. A definition of something that doesn't exist, is not "objective data" (for the existence of the thing). Objective data that supports the existence of the thing is the type of objective data needed. WE need a picture of the one millionth digit of PI before the one million digit of PI actually exists I can write the number 345 and talk about the objective data of the last digit being 5. But if I write, "divide 690 by two and take the last digit" I have not created the number 5. I've just "written code" to explain how to create the digit. I can write a recipe for how to bake a cake, but in doing so, it would be wrong (would it not) to claim, as you are doing, that I have created a cake by writing the recipe? > What is the 10^billion-th digit of PI? > By your belief system it actually has no value unless it is calculated. That's right. By the exact same belief system that tells me the cake doesn't exist unless it's actually baked. There is no difference here. > That contradicts the fact that all digits in PI are totally fixed and > "objective data" -- to use your earlier phrase. To justify your > non-realist philosophy of mathematics you would have to SHOW that the > decimal expanse of PI is ACTUALLY not already fixed and fully specified. No, I don't. For the same reason that the "cake" becomes fixed the minute I write the recipe, but just because it's "fixed' doesn't mean it yet exists. The problem is that when we do math, we intentionally start to confuse ourselves about these issues. We learn to think of PI as being such a fundamental aspect of the universe of math, we feel it must "exist" in some realm. But it doesn't. The only thing that actually exists, is the language that defines it, and stuff like computers that can (given enough time) calculate lots of the digits (but never all of them). > Stop the insulting claim that I don't understand what you are claiming. ok. > What you are claiming is partly true: there are many things that are not > absolute truths. For instance social customs. In Japan it is customary > to give a quick bow to others as a sign of respect. No such custom > exists in other countries. So Japanese courtesy bows are not absolute > truths of human behavior. Some truths are only tentative. For example > many of Freud's theories about the subconscious. Some are probably wrong > but a few of them may turn about to be correct. In those cases absolute > truths may exist but their correctness has yet to be determined. > > > First off, I am not denying mathematics. I'm just saying the world of > > mathematics which is full of the use of the concept of absolute truths > > is just a story we made up. The _concept_ of absolute truth very much > > does exist in these stories we make up. Nothing I have said "denies > > mathematics" as you claim I say. I only deny that the STORY we tell in > > doing math is a valid description of any aspect of the universe we > > exist in. That was my only point. Your belief that I am somehow > > denying math is just unfounded and shows how confused my words are > > making you. > > By claiming that the "story of mathematics" is solely a human invention > you are denying mathematics itself. Mathematics is not like the story of > the Wizard of Oz. Sure it is. It's exactly the same thing. It's a fabrication created by humans by the power of language - by putting words together in interesting ways to see what results. The difference with math is that it creates for us a unique type of tool that is not crated for us when we write something like the wizard of oz. It is none the less, nothing more than a story made up by humans. Another difference is that the odds that other people (or alien life forms) would make up the same story, is very high for basic math concepts, but very low, for the wizard of OZ. But that's just because math embraces highly simplistic concepts at it's core and then explores what implications those highly simplistic concepts logically lead to. > Your claim that mathematical truths are not a valid > description of "any aspect of the universe" is empirically false. The > Earth-moon system is a system of 2 worlds so even simple counting numbers > apply to the cosmos. Physical laws obey mathematical laws -- with the > possible exception of state reduction. State reduction is exactly the fundamental problem of it all here. We can never be 100% sure there are "exactly two" (and only two) bodies in the earth moon system. In order to determine there are two bodies, and only two bodies in the system, have have to reduce the highly complex state of all the atoms, and all the subatomic states of all the matter in the system, into some classification of "bodies" so that we come up with 2. And no matter what hardware we use to attempt to count the number of bodies we can never be 100% certain that the output count from the hardware is 100% accurate description of the system, so the output count of "2" can never be an absolute truth. When we use well known "facts" about the universe as examples, and we use facts that we believe are very long lasting, it is natural for us to feel AS IF we are talking about an absolute truth. But when you read the fine print (so to say) of how the universe works, we find this all falls apart and nothing is ever absolute, even though much is so close to absolute, there is no reason not to act AS IF it were absolute. But just because we have been trained to think, and act, as if all this stuff were absoluteness, doesn't doesn't mean any of it actually is. And that's exactly why I like to bring it up in threads like this because it's a very interesting "fact" about the universe that's counter intuitive to most people's understanding. > >> For example you are claiming that the physical world > >> doesn't exist since its existence would be an absolute truth. > > > > Well again, projection. You don't understand what I'm claiming because > > again, the only way you can think is in your narrow minded world of > > absolute truths. The only way you can understand existence is as a > > collection of absolute truths, so if absolute truths "don't exist" then > > nothing exists for you! > > > > But in a world where absolute truths don't exist, things must work > > differently. Existence is always probabilistic. Our knowledge of what > > exists is likewise probabilistic. The things that we talk about, or > > believe are absolute truths, are instead, just extremely likely to be > > so. So extremely likely, that we can safely choose to act as if they > > always were, and always will be, true. > > > > Our perception system works so well that most of what be believe we are > > seeing, does in fact exist. The odds of our perception system > > correctly recognizing what "exists" is very high. But it's not > > perfect. It makes errors all the time - perception is not absolutely > > correct - which means what be believe exists, is not always correct - > > in any sense. > > Again more insults. You claim that (1) I don't understand you, (2) I am > narrow minded and (3) everything is probability. 3 is the interesting one. The others were just to get your attention and make you write some stuff. > All three are false as > I explained above. True, some things are probability and some "truths" > are not absolute. I am just not making the same absolute sweeping > generalizations that you are. Well, to be honest, I'm not sure how close to "absolute" the idea that there are no absolute truths actually is. But as far as I can tell, there really are none. And without a doubt, much of what people assume are absoluteness, are not even close to such because the error rate of human behavior is very high and most claims of absolute truths (like your examples) use humans in the evaluation test. Which means what you are thinking, is more like, "it would be an absolute truth if we choose to ignore the times the humans would make errors". But we don't have the option to ignore the errors! And those errors is why there are no absolute truths. > > Here's a little page on Absolute truth. It makes the same errors you > > do and clearly written by someone that can't understand anything but > > absolutes. > > > > http://www.absolute--truth.com/ > > > > For example, they write: > > > > "There are no absolutes." First of all, the relativist is declaring > > there are absolutely no absolutes. That is an absolute statement. The > > statement is logically contradictory. > > > > It's only logically contradictory if you believe such statements are > > attempting to communicate an absolute truth. But since the point of > > the statement is to declare there are no absolute truths, that clearly > > can't be point the statement is trying to communicate. What it's > > trying to communicate, is that the probability is so great that there > > are no absolute truths, that we are free to ACT AS IF the statement was > > an absolute truth. As I explained above. > > What is the probability that there are no absolute truths? I say zero > because things like PI and "1+1=2" are absolute. But the first thing to > note is that probabilities require mathematics and a sample space. What > is the sample space in your philosophy? How is it defined? It's defined the same as an everyone else, _except_ nothing is absolute, they exist only as very highly likely events. Such as what is the probability that we can can tell if the digit 1 is different from the digit 2 without error? We can determine that correctly to a very high level of accuracy, but not to the level of 100% accuracy. The foundation of math assumes there are ways to tell if two digits are the same, or different, to 100% perfect accuracy. But again, this is a fundamental issue of where what is defined in the language of math, doesn't exist in our universe. > > The universe we live in is probabilistic at all levels. No where in > > the universe does there exist anything that is 100% probable. > > Not really. Even in quantum theory there is a 100% probability that the > quanta you measure will be somewhere. In fact, this is called the > normalization condition. Here it is: let psi and cpsi be the wave > function and its complex conjugate respectively. Then the normalization > condition is: > > Integral_(cpsi*psi)_dtau = 1 Again, you have used language to try and define an absolute truth. But what is our level of certainty that this truth (or any other truth), is a fundamental truth of the entire universe? This gets to another side of this whole issue which is the question of what might exist, vs what knowledge of that existence we might have. To test a fundamental truth, we must compare language to some aspect of the universe. This means we must have a machine that computers a true false answer. What is the odds that the machine will always work "correctly"? The odds are less then a100% no matter what the machine is. This means that "knowledge" is limited by the trust we have in the operation of such machines whether that machine is a human, or a computer, or some other instrument they built. Our knowledge about absolute truth can't be 100% certain, even if there exists some absolute truth of the universe. If our knowledge can never be certain, then the truth can never exist FOR US. That is, it becomes impossible for us to prove if any suspected absolute truth, is actually an absolute truth or not. If there is something we don't know, we can just say we don't know. But if we know something is impossible to know, that means there can never exist objective data to show that it it does exist - which gets back to the definition of physical, and "exist" I have used. If the objective data can never exist, the "thing" can be said to not exist, instead of us just saying we don't know. But how valid it is to say the "thing" (some absolute truth about the universe) doesn't exist, is tied directly to the probability of our trust in the impossibility of the availability of the objective data. And though my trust that this data is not possible to get is high, it's not as high as many other "sure bets" I'm willing to talk about. But it's very high none the less, and high enough that I feel comfortable using the language "there are no objective truths". If it can't be sensed, we say it doesn't exist. And even if absolute truths of the universe exists (maybe for some God like creature that crated it), if we can't sense it, and we can't communicate with the "god-like creature", then it doesn't exist for us and the correct language for us is to just say it doesn't exist. -- Curt Welch http://CurtWelch.Com/ curt(a)kcwc.com http://NewsReader.Com/
From: Vesa Monisto on 15 Jul 2010 14:30 "Curt Welch" <curt(a)kcwc.com> wrote: > "K_h" <KHolmes(a)SX729.com> wrote: > >> By claiming that the "story of mathematics" is solely a human >> invention you are denying mathematics itself. >> Mathematics is not like the story of the Wizard of Oz. > > Sure it is. It's exactly the same thing. It's a fabrication created > by humans by the power of language - by putting words together > in interesting ways to see what results. What bold movements! ... > The difference with math is that it creates for us a unique type of tool > that is not created for us when we write something like the wizard of oz. > It is none the less, nothing more than a story made up by humans. .... head on, and then over-correcting nearly into the own-side ditch ... ;) On the road, still. -- I'm not fluent enough in English (learnt as my 4th 'lingua') to take part in *serious* 'debattles' (language games), but I'll tried to translate some quotations from some creative mathematicians. Frege (1884): 'The number which belongs to the concept F is the extension of the concept "equal to the concept F".' ("Die Anzahl, welche dem Begriffe F zukommt, ist der Umfang des Begriffes "gleichzahlig dem Begriffe F".") Frege's boldness went to the ditch called Russell's paradox. -- Long story, not relevan here. Kronecker (1886): 'God made the integers, all the rest is man's work.' ("Die ganzen Zahlen hat Gott gemacht, alles andere ist Menschenwerk.") Platonism is seen as direct (na�ve/surreal) realism; as a kind of ditch. Dedekind (?): 'The numbers are free creations of man's mind, they serve as a means of apprehending the difference of things more easily and more sharply.' ("Die Zahlen sind freie Schoepfungen des menschlichen Geistes; sie dienen als ein Mittel, um die Verschiedenheit der Dinge leichter und schaerfer aufzufassen." ) Yes, pro-grammatical 'fundamentals' for jigging and tooling, artificial facilities *without ontic commitments*. -- So, I'm on Dedekind's side, but I'll try to understand even Kroneckerian projections, especially after reading E.P. Wigner's story "The unreasonable effectiveness of mathematics in the natural sciences" (1960). -- Conservation principles, symmetries, invariants, copies everywhere! even those had merely idealized doings with 'absolute certainty'. There are always deformations (curvatures) in actual topological spaces but at least locally space is homogeneous and isotropic. That's math and math is 'flat' (= the same everywhere) for to be used as a neutral fundament, "as a means of apprehending the difference of things more easily and more sharply". Not stories but a kind of 'tabula rasa' for stories, programming language for pro-grams grammed later (late binding in actual situations). -- But how to make some MST? For to be used in MSTs even the thema of 'truth' has variations: a) The *pure* mathematics MUST be *coherent*. -- 5+7=12 is *coherently* true, because there must be equal amounts of value-stuff (data) on both sides of "=" when used as equality. -- This truth-principle makes possible many kinds of manipulations: 5 = 12-7, 7 = 12-5, 5+7-12 = 0, ... 5+7-1 = 12-1, ... ad inf. -- Pure math as a mental jig and toolbox MUST be reliable and 'certain' (without exeptions), i.e. coherent, without formal errors. b) The *applied* mathematics MUST be *correspondent*. -- 5 boys and 7 girls = 12 children; only occasionally true when *corresponding* an actual fact. Potentiality b+g = c in all families. -- Countings, measurements, mappings (without errors) . c) There are many other "truth theories" for different aspects of The Truth (as a pointer to the possibilities of being satisfied): pragmatic, deflationary, redundancy, minimalist, disquotation etc. -- They are not relevant here, because it's enough to put coherence and correspondence to work together, *without confusing them*. MST: How to integrate these two KINDs of truths into a working complex simple enough to be handled automatically, without thinking. (MST must save energy, not consume it to control hierarchy policies (SU) or let consumers pay the minus-times-minus-is-plus-Mads (US).) b + g == c // formal equality as coherence ('isis' "==" as the mark) = op = = // applied correspondence ('is a' "=" as the assign.mark) 5 + 7 == ? // b(oys) happens to be 5, g(irls) happens to be 7. (Seen visually, as a graph: horizontally as coherence "==", vertically as correspondence "=" (a priori = top-down, a posteriori = bottom-up). In C-languages the "overloaded" math mark "=" is differentiated to two marks a) equality "==", inequality "!=" and b) assignment "=", the first used with coherent truths, the second for truths corresponding to actual cases/events (e.g., b = 5). This differentiation is done because compilers would otherwise be 'stupid' and do either one of two errors: to think that there is in the nature something corresponding coherence, or to think that numbers are given from nature giving coherence, too. C.G. Jung told that he became a deep-psychologist because he couldn't understand math. He understood very well why 1+1=2 but not at all how A could be 5, A = 5, e.g. -- He obviously had stagnated into a coherentist paradigm. Nowadays the pro-grammatical hybrid (MetaS) A = A+1 gives problems to yangsters (-- only if teached by the olders). That seems to be mathematically incoherent but is programmatically metacoherent, because compiler can interpret it as "put to the by "A" addressed memory place A the value 1 added to A's former content." "Metasmart!", could Bil Gates say remembering his first 4k Basic interpreter. Mere syntax could be used to resolve semantical meaning- differences. Directions ( __, | ) added to scalars give vectors or any at least two dimensional (like category-theoretic) structs, in this case: b + g __ c // any addressed memory places as containers | | 5 + 7 __ ? // any memory place contents (data) Words can be mapped to words (semiotic marks to other semiotic marks) IOR to some natural (physical) things emptied by the proverb 'to exist' from all natural contents for to be assigned with the human sensual and actual data. The private thing is whatever it happens to be ("Ding an sich") but we have it ("Ding fuer uns") publiced with our own manmade attributes. No wonder that right calculations can give utterly wrong results. (For example economy is not mere calculations of 'eternal objects', even 1+1= 2 and (3-4)^2 = PLUS 1.) (Sorry about typos! - I hope some of those ideas were at least readable. ;) V.M. ("What it were like to be a Bat?" -- Easy! Bats see Bugs everywhere!)
From: Wolf K on 15 Jul 2010 18:58 On 15/07/2010 14:30, Vesa Monisto wrote: [...] > Dedekind (?): 'The numbers are free creations of man's mind, > they serve as a means of apprehending the difference of things > more easily and more sharply.' > ("Die Zahlen sind freie Schoepfungen des menschlichen Geistes; > sie dienen als ein Mittel, um die Verschiedenheit der Dinge leichter > und schaerfer aufzufassen." ) [Snip interesting anthology] Actually, it's in our genes. Language merely allows us to extend the limited number sense we're born with (and which we share with other animals) to, well, to infinity. wolf k.
From: Vesa Monisto on 15 Jul 2010 21:54 Wolf k wrote: > Vesa Monisto wrote: >> [...] >> Dedekind (?): 'The numbers are free creations of man's mind, >> they serve as a means of apprehending the difference of things >> more easily and more sharply.' >> ("Die Zahlen sind freie Schoepfungen des menschlichen Geistes; >> sie dienen als ein Mittel, um die Verschiedenheit der Dinge leichter >> und schaerfer aufzufassen." ) > >[Snip interesting anthology] > > Actually, it's in our genes. Language merely allows us to extend the > limited number sense we're born with (and which we share with other > animals) to, well, to infinity. But (there are always buts for the existence of But) it might be a product of mental/behavioral *economy*, too. Genetic IOR 'fenetic'. From numbers to variables to pointers, and then we have the modern metastructure P(A(D)) = Pointers(Addresses(Data)), which could be expressed by 1 to many "<)" relations "P<)A<)D", 1-1-1 at time. -- MST is for economy, for saving energy/resources, e.g., by P(A(D)). BTW, I translated "Geist" by "mind" but could have used a word "spirit" or "genius" (all mere alias-pointers to excellent inner behavior). V.M. (What were it like to be a But? -- I don't know, just corrected my grammar ;)
From: R. Srinivasan on 19 Jul 2010 07:20
On Jul 17, 8:09 am, c...(a)kcwc.com (Curt Welch) wrote: > "K_h" <KHol...(a)SX729.com> wrote: > > "Curt Welch" <c...(a)kcwc.com> wrote in message > >news:20100715013832.531$Gi(a)newsreader.com... > [...] > > > Well, this is simply wrong. The truth underlying "1+1=2" is an absolute > > truth. [...] > [...] > > Gee, how many times do I have to tell you that absolute truth doesn't exist [...] > > I wouldn't go so far as to say that absolute truth does not exist. However, I would definitely claim that absolute truth is not something that human beings can discuss intelligently. And, to quote Wittgenstein in a different context: "That which we cannot talk about, we must pass by in silence". I claim that human beings can only discuss *formal* truth intelligently when it is characterized as provability. Further, provability is always with respect to (axiomatic) theories, and therefore truth (for formal propositions) must be with respect to such theories. When human beings formulate a theory, they are basically asserting a number of truths *axiomatically*, via provability of various propositions in such theories. When this line of thinking is taken to its logical conclusion, one gets the logic NAFL and one can show that infinite sets are not permitted in such a logic. Again, it is not the claim of NAFL that "absolute truths" do not exist; it is just that formal logic is not about such absolute truths, even if they exist. Let us look at the claim made by K_h that '"the truth underlying '1+1=2' is an absolute truth". From other posts of K_h, it is clear he claims that such a truth is existent in *our* universe, rather than in some ideal Platonic world. Let us see if we can falsify this claim. There is a theory of cosmology to the effect that our universe has zero total energy and in fact originated from absolutely nothing: http://161.58.115.79/pubs/mercury/31_02/nothing.html So as per this theory (which I do not necessarily agree with) there was a time when there was absolutely "nothing" in our universe. To quote selectively from the above reference: "....the universe is the ultimate free lunch! It came from nothing, and its total energy is zero. ...The meaning of "nothing" is somewhat ambiguous here. It might be the vacuum in some pre-existing space and time, or it could be nothing at all that is, all concepts of space and time were created with the universe itself." In fact I agree with the latter part of the above quote. If there is nothing in the universe, then we do not have a length scale, and we have nothing to characterize time or mass either. So the concepts of space, time and matter become meaningless. Let us go back to the time when there was (supposedly) absolutely nothing in the universe. In fact, there is no proof that the universe will not relapse to such a state in the future (presumably via the "Big Crunch" predicted by general relativity, when all matter in the universe collapses). I claim that in such a universe, there is no evidence whatsoever for "1+1=2" (leave alone evidence for infinite sets). In fact, one can reasonably conclude only the existence of the number zero, or the empty set, which would characterize the universe itself. I am sure K_h is now going to invoke stuff like "quantum fluctuations" and "virtual particles", and so on, which must characterize the vacuum as per quantum field theory. However, the existence of virtual particles is pure theory and not observable. See the following website: http://www2.slac.stanford.edu/vvc/theory/virtual.html Quote: "It is meaningless to argue whether they[virtual particles] are or are not there, as they cannot be observed. Any attempt to observe them changes the outcome of the process". Clearly if one wishes to demonstrate "1+1=2" with physical objects, then these must be concrete physical objects. E.g. "If we put one apple into an empty basket, and then put one more, we will find two apples in the basket". You can't do that with virtual particles. Even if you could put one into the (hypothetical) basket, it will disappear in next to no time. In conclusion, the truths that K_h is talking about can be characterized as "absolute truths" only when one postulates an ideal Platonic world, independent of our universe. In such a Platonic world, K_h can posit the existence of numbers, infinite sets and the like as concrete physical objects. I assert that classical infinitary reasoning is sustainable if and only if one subscribes to Platonism in this form. The logic NAFL which I have proposed rejects Platonism, and hence rejects classical infinitary reasoning. RS |