A Tale of Two Defintions: The definition of "Logic"


BaalChatzaf

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[i mentioned 4 items. You only dealt with the first? We disagree about existence and consciousness being a "trivial truth" derived from mathematics, even if you want to call it a tautology. From what I observe, the conclusion is based on experience, not merely a word game.

I never said that existence and consciousness are derived from mathematics, nor that these are a "trivial truth".

Here is another item pure math tells us about reality. It tells us that reality is constructed so as to contain correspondence to its formulations (if they are correct).

That is simply wrong. You are still confusing a theory with its applications. Some mathematical systems may be used in physical theories, but mathematics doesn't tell us which ones. Take for example geometry: there are different kinds of geometrical theories that are all equally consistent. But if one of them fits in a physical model, the other ones don't. Mathematics itself cannot tell us, only empirical evidence can do that, and that is what it means that mathematics doesn't tell us anything about reality. A mathematical model can be perfectly consistent and yet not be applicable for a physical theory. The truth or correctness of model therefore doesn't tell us anything about reality. That is the essence of the term pure math.

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Where in the cosmos will you find a Klein Bottle?

Bob,

Huh?

In a Klein Bottle. They are built all the time.

Michael

A true Klein Bottle can exist only in four spatial dimensions. The three-d versions merely suggest what a Klein Bottle looks like. A true Klein Bottle does not intersect itself, for starters.

Ba'al Chatzaf

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As to point 1, substitute my "mathematics" with your "any thought." That is how I got to your "trivial truth."

You mean: cogito ergo sum. But that refers to the thinking process itself, not to the content of your thinking, and that is what we are talking about. If the content is for example "A is not A", what does that tell us about reality?

On point 2, I said you would not agree. But there is a reason why it all works and it is more than coincidence.

It does not always work for physical models. We don't know why some models work and others not, that is just the way reality is. Perhaps there are other universes where some of the models that work in the universe we know don't work and other models that don't work in our universe do work, we just don't know.

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You mean: cogito ergo sum. But that refers to the thinking process itself, not to the content of your thinking, and that is what we are talking about. If the content is for example "A is not A", what does that tell us about reality?

Dragonfly,

No, I don't really mean cogito ergo sum. I meant what I said, which has an entirely different meaning. On your other point, if the mental content is "A is not A" and that is taken as knowledge (i.e., a law of nature) by the agent, he invalidates his own consciousness by denying it identity. In other words, cognitively he is a lunatic.

If he does not take that as knowledge, this is merely an untrue proposition he is mulling over.

We don't know why some models work and others not, that is just the way reality is.

I guess this is merely perspective, but I put a big honking YET on that statement. I do not believe that just because we do not know NOW why some models work and others do not, we will NEVER discover the correspondence.

Michael

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No, I don't really mean cogito ergo sum. I meant what I said, which has an entirely different meaning. On your other point, if the mental content is "A is not A" and that is taken as knowledge (i.e., a law of nature) by the agent, he invalidates his own consciousness by denying it identity. In other words, cognitively he is a lunatic.

He may be a lunatic, but it shows that from the fact that his thinking implies existence and consciousness does not imply that the content of his thinking tells us anything about reality, these are two quite different things.

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I guess this is merely perspective, but I put a big honking YET on that statement. I do not believe that just because we do not know NOW why some models work and others do not, we will NEVER discover the correspondence.

Michael

Humans have three pound brains and a potential lifetime of a century or two. There is a limit to how smart we can get and how long we can live. Even with crutches and force multipliers like computers there is a limit. A computer, in a sense, cannot be much smarter than the program that runs it and the program has its limitations (time and memory). Memory and running speed are ultimately bounded by the Heisenberg Uncertainty Principle. We still have quite a ways to go in that direction, but there are limits. The space we have at our disposal is ultimately bounded by the speed of light and relativistic mass with its associated energy. The human race need not worry about these Ultimate Limits for some thousands of years to come, assuming that technology progresses as it has, but a day will come when we can go no further in terms of raw capability. I rejoice that I will not live to see That Day.

Someone said that Nature in order to be commanded, must be obeyed. One aspect of obedience is to recognize natural limits. Right now Mankind is in its childhood and we are playing in the Sand Box. Like children we can pretend there are no limits, but when we Grow Up we will have to recognize what they are and learn to live within their bounds.

Ba'al Chatzaf

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I guess this is merely perspective, but I put a big honking YET on that statement. I do not believe that just because we do not know NOW why some models work and others do not, we will NEVER discover the correspondence.

Michael

Humans have three pound brains and a potential lifetime of a century or two. There is a limit to how smart we can get and how long we can live. Even with crutches and force multipliers like computers there is a limit. A computer, in a sense, cannot be much smarter than the program that runs it and the program has its limitations (time and memory). Memory and running speed are ultimately bounded by the Heisenberg Uncertainty Principle. We still have quite a ways to go in that direction, but there are limits. The space we have at our disposal is ultimately bounded by the speed of light and relativistic mass with its associated energy. The human race need not worry about these Ultimate Limits for some thousands of years to come, assuming that technology progresses as it has, but a day will come when we can go no further in terms of raw capability. I rejoice that I will not live to see That Day.

Someone said that Nature in order to be commanded, must be obeyed. One aspect of obedience is to recognize natural limits. Right now Mankind is in its childhood and we are playing in the Sand Box. Like children we can pretend there are no limits, but when we Grow Up we will have to recognize what they are and learn to live within their bounds.

Ba'al Chatzaf

"Someone said that Nature in order to be commanded, must be obeyed. One aspect of obedience is to recognize natural limits. Right now Mankind is in its childhood and we are playing in the Sand Box. Like children we can pretend there are no limits, but when we Grow Up we will have to recognize what they are and learn to live within their bounds."

And you actually as an allegedly rational sentient entity believe that statement?

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Mathematics is not only similar in structure to the world we live in, it is also similar in structure to our nervous systems.

Once a statement is cast into mathematical form it may be manipulated in

accordance with these rules and every configuration of the symbols will represent

facts in harmony with and dependent on those contained in the original statement.

Now this comes very close to what we conceive the action of the brain structures to

be in performing intellectual acts with the symbols of ordinary language. In a sense,

therefore, the mathematician has been able to perfect a device through which a part

of the labor of logical thought is carried on outside the central nervous system with

only that supervision which is requisite to manipulate the symbols in accordance

with the rules. (583) HORATIO B. WILLIAMS

You see, the "thinking" is encoded into the language and may be shared with others so they don't have to discover the process themselves.

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Selene,

Bob is great for telling people what is impossible.

I would loved to have known him with us both living in, say 1870 or so, and me telling him that in less than a 100 years, a person could be in the USA and watch and hear another person in China doing things and talking at the time he was doing them and talking, and this would happen because invisible waves were sent from China, bounced off of a piece of metal circling the earth, and the ricochet would be received by a box where he could view and hear it all.

I think Bob would have laughed his butt off.

Michael

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Selene,

Bob is great for telling people what is impossible.

I would loved to have known him with us both living in, say 1870 or so, and me telling him that in less than a 100 years, a person could be in the USA and watch and hear another person in China doing things and talking at the time he was doing them and talking, and this would happen because invisible waves were sent from China, bounced off of a piece of metal circling the earth, and the ricochet would be received by a box where he could view and hear it all.

I think Bob would have laughed his butt off.

Michael

Selene and Michael, what universe are you living in? I'm serious. Bob says "Nature, to be commanded, must be obeyed" -- which is Rand channeling (I believe) Francis Bacon -- and it expresses the inescapable metaphysical insight that everything has a nature, everything has a specific identity, including limits on what it can or cannot do, and that this includes human beings. Bob has said that we are still capable of an incredible amount of progress, but that there are limits even to that.

Exactly how is Bob "telling people what is impossible"? (I saw no smiley face when you said that.) He is simply saying that you can't do what you can't do -- you can't do what your nature and its limits do not allow. How is that repressive or stultifying? It's just recognizing reality! Isn't that what Rand's philosophy is all about? Go as far as you can go, and celebrate it -- but recognize your limits, and don't bemoan what you can't do.

REB

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Roger,

I agree with the Nature to be commanded needs to be obeyed part. But Bob gets specific, not general, and pontificates about what he cannot know. There is no way he could possibly know whether we will be able to break the light barrier one day or not, but he claims we will never be able to do so. This is freezing future discoveries to the present level of knowledge.

Kinda like our guy in the 1870's. At the level of knowledge they had then, we would have never been able to broadcast anything. Fortunately, the bank of human knowledge grows.

Michael

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Speaking about going faster than the speed of light makes no sense within the context of special relativity. Who is to say someday there won't be a more general theory explaining how we could go through a worm hole and end up on the other side of the universe, but it won't be called 'velocity' the way we speak about it today. These are simply semantic issues.

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I would loved to have known [bob] with us both living in, say 1870 or so, and me telling him that in less than a 100 years, a person could be in the USA and watch and hear another person in China doing things and talking at the time he was doing them and talking, and this would happen because invisible waves were sent from China, bounced off of a piece of metal circling the earth, and the ricochet would be received by a box where he could view and hear it all.

I think Bob would have laughed his butt off.

Maybe, maybe not. If you had actually mastered time travel, or could truly peer into the future, he might have considered you a magician or a true precognitive -- and been frightened. If you were able to give a bit more detail ('waves of what?' -- 'is this like the telegraph?') of the transmission, he might have said, "hmm, are you sure your name is not Jules Verne, are you not cribbing from his writings about tele vision?"

He might have said, "I want you to talk to my friend Maxwell. This sounds like some of his work in electromagnets, by golly!"

Or, he might have asked, "And did you know, Mr Kelly, that in less than two hundred years, the earth will warm, the seas will rise, and humankind will escape to Mars? And that orbiting satellites will first send tele vision in 1962?"

The problem with analogy, as with hindsight, is that it is either almost exactly wrong, or nearly exactly right. It very much depends on the use to which it is put.

Edited by william.scherk
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Roger,

I agree with the Nature to be commanded needs to be obeyed part. But Bob gets specific, not general, and pontificates about what he cannot know. There is no way he could possibly know whether we will be able to break the light barrier one day or not, but he claims we will never be able to do so. This is freezing future discoveries to the present level of knowledge.

Kinda like our guy in the 1870's. At the level of knowledge they had then, we would have never been able to broadcast anything. Fortunately, the bank of human knowledge grows.

Michael

I'm reminded of some of the stories about the days of air travel just before the first pilot managed to break the ~sound~ barrier. Back then, people said you couldn't break the sound barrier, but not because nothing could travel faster than sound (indeed, light and other forms of EM do just that). Instead, the reason given was that the turbulence around Mach 1.0 would supposedly cause the planes to break apart.

So far as I know, there is no parallel ~mechanical~ impediment to FTL travel. It is, as GS points out, a consequence of Special Relativity, which is our current comprehensive theory about motion in the universe. Quoting the entry from Wikipedia:

Special relativity reveals that c is not just the velocity of a certain phenomenon - light - but rather a fundamental feature of the way space and time are tied together. In particular, special relativity states that it is impossible for any material object to accelerate to light speed.

As GS also points out, there may (may) be a way to skin the FTL cat, but that would entail finding a "shorter distance" between the two points than we currently know to be the shortest route through "regular space." GS calls this a "semantic" issue. I'd call it a ~conceptual~ issue. But the point is that, without something ~like~ a wormhole, Special Relativity -- which, btw, is well in keeping with Aristotle's and Rand's view of motion as being relative, not absolute -- dictates that the speed of light is the upper limit of velocity of anything, matter or energy, travelling through space.

Also, btw, has anyone else noticed that Einstein's formula, E = mc^2, can be restated so that the square root of the ratio of E to m (energy to mass) is always a constant, viz., the speed of light? I once wrote an essay about this (it may be posted elsewhere on OL) about Martians who were able to directly perceive and measure the amount of mass and energy in every substance and found that they were always in the same relation. It was a fun little piece of fiction/thought experiment, but to me, it was just a way of concretizing the fact that the speed of light is a fundamental feature of the way matter and energy are tied together.

I guess that, to suspend or inactivate (?) the speed of light as a limit, you would have to find a way to create a zone where matter and energy did NOT relate to each other in the same constant way. Whether something like wormholes is a feasible way of doing so, or something else we haven't yet imagined would be needed, I don't know. But I eagerly await what the next few generations of geniuses will come up with.

REB

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I'm reminded of some of the stories about the days of air travel just before the first pilot managed to break the ~sound~ barrier. Back then, people said you couldn't break the sound barrier, but not because nothing could travel faster than sound (indeed, light and other forms of EM do just that). Instead, the reason given was that the turbulence around Mach 1.0 would supposedly cause the planes to break apart.

So far as I know, there is no parallel ~mechanical~ impediment to FTL travel. It is, as GS points out, a consequence of Special Relativity, which is our current comprehensive theory about motion in the universe. Quoting the entry from Wikipedia:

Yes there is. TO travel FTL one would need an infinite amount of energy. The relativistic mass becomes infinite at the speed of light.

Special relativity reveals that c is not just the velocity of a certain phenomenon - light - but rather a fundamental feature of the way space and time are tied together. In particular, special relativity states that it is impossible for any material object to accelerate to light speed.

And forget worm holes. There is not an iota of evidence supporting the existence of worm holes. Until such evidence materialized it is just science fiction.

As far as we know light takes the shortest path from one event in spacetime to another event. There is no evidence -whatsoever- for shortcuts. Not a crumb. And until someone comes up with the evidence it can only be regarded as baseless speculation. Fine for science fiction, not fine for physics.

Ba'al Chatzaf

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And forget worm holes. There is not an iota of evidence supporting the existence of worm holes. Until such evidence materialized it is just science fiction.

As far as we know light takes the shortest path from one event in spacetime to another event. There is no evidence -whatsoever- for shortcuts. Not a crumb. And until someone comes up with the evidence it can only be regarded as baseless speculation. Fine for science fiction, not fine for physics.

I hope I didn't give the impression that I believed in "worm holes", I only used that as an hypothetical example.

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Selene,

Bob is great for telling people what is impossible.

I would loved to have known him with us both living in, say 1870 or so, and me telling him that in less than a 100 years, a person could be in the USA and watch and hear another person in China doing things and talking at the time he was doing them and talking, and this would happen because invisible waves were sent from China, bounced off of a piece of metal circling the earth, and the ricochet would be received by a box where he could view and hear it all.

I think Bob would have laughed his butt off.

Michael

Newton showed how to orbit a canon ball in 1688. So the idea of a man-made satellite did not violate any physical laws. Newton also showed the existence of -invisible- light with his prism experiments, infrared and ultra violet. So there was no problem with fundamental laws. It was then as it is now a matter of technology.

The only thing impossible are outright logical contradictions. Pointing out the certain things violate basic physical laws is another matter entirely. Maybe the laws are not entirely correct. Violation of physical law is not logical impossibility since our physical laws are based on experience. Newly discovered facts could alter the situation.

I am telling you that there are physical difficulties. The basic difficulty is that we DO NOT KNOW REALITY to rock bottom. We are fifteen orders of magnitude from Planck Length. We simply do not have evidence that our wet dreams are feasible. Until we do, our dreams must remain dreams or Science Fiction. There is not an iota of evidence that indicates we have or can have soon any technology for moving massive objects even at one tenth the speed of light. We simply do not have the technology and until we do we cannot reasonably contemplate travel to other star systems. Even at c/10 it would take forty years to get to the nearest star, Alpha Centuri. It would take eighty years to get to the star Sirius. And we do not know if there are any habitable planets near these stars. So we have no basis for anticipating a trip any time soon. These tasks are not logically impossible, but they are completely beyond current technology and any likely technology to emerge in the near term. At this moment the fastest our space craft will travel is of the order of 100,000 mph and that using gravity boosts from the large planets. Using the current burn and coast modality the shortest trip to Mars would take six months (calculating when Mars is the closest to Earth). The crew would have to wait two years to get another short trip back home.

Forget traveling -at- the speed of light. That would require infinite energy. Where would we get it? Light takes the shortest distance from one point to another, so forget worm holes. There are no shortcuts.

Ba'al Chatzaf

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I would loved to have known [bob] with us both living in, say 1870 or so, and me telling him that in less than a 100 years, a person could be in the USA and watch and hear another person in China doing things and talking at the time he was doing them and talking, and this would happen because invisible waves were sent from China, bounced off of a piece of metal circling the earth, and the ricochet would be received by a box where he could view and hear it all.

I think Bob would have laughed his butt off.

Maybe, maybe not. If you had actually mastered time travel, or could truly peer into the future, he might have considered you a magician or a true precognitive -- and been frightened. If you were able to give a bit more detail ('waves of what?' -- 'is this like the telegraph?') of the transmission, he might have said, "hmm, are you sure your name is not Jules Verne, are you not cribbing from his writings about tele vision?"

He might have said, "I want you to talk to my friend Maxwell. This sounds like some of his work in electromagnets, by golly!"

Or, he might have asked, "And did you know, Mr Kelly, that in less than 200 hundred years, the earth will warm, the seas will rise, and humankind will escape to Mars? And that orbiting satellites will first send tele vision in 1962?"

The problem with analogy, as with hindsight, is that it is either almost exactly wrong, or nearly exactly right. It very much depends on the use to which it is put.

Excellent points. When I was teaching rhetoric I used my own model of arguments to teach my students "reasoning" and critical thinking. I hope the triangle of argument comes through in the perspective it was sent in.

G

I D

P A P

The PIG being induction and the GDP being deduction and the PAP being analogy. P=particular; G=generalization; I=induction; D=deduction; and A=analogy[which I maintain is a reasoning process that we do not fully understand, but exists.

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The problem with analogy, as with hindsight, is that it is either almost exactly wrong, or nearly exactly right. It very much depends on the use to which it is put.

William,

Great to see ya'. Glad to see I struck a nerve.

Don't mind me and Bob, though. We do this crap all day long. It's like playing Chinese checkers.

:)

Michael

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[ . . . ]

A=analogy[which I maintain is a reasoning process that we do not fully understand, but exists.

-- that's an intriguing statement. Have you read Steven Pinker's new book, "The Stuff of Thought"? It has some equally intriguing ideas, and comes close to supporting your intuition about analogy.

At several points, but especially in the chapter 'The Metaphor Metaphor,' Pinker suggests that the power of analogy for science and reasoning in general is not from 'mere similarity of parts' in the two instances being compared. Rather, it is relations between the parts -- a disciplined tracing of the concept implicated in one domain can open a window to understanding in the other. Some concepts are so fresh or unfamiliar that the insight of a frame-shift/Gestalt is very useful. Because of the power of analogy to help our conceptual understanding 'snap to,' fallacious examples can be just as mentally satisfying as more appropriate ones.

I twit Michael now and again for inapt analogies. As he suggests, it is my touchy elbow. The 'eureka' snap of concepts falling into place is great fun, but always needs checking. One of my favourite dumb analogies (this spouted out in the context of visionaries/crackpots/pseudoscientists like Velikovsky): "You may laugh at his theories -- they laughed at Galileo!"

-- to which many wits have retailed the only proper answer: "They also laughed at Bozo the Clown."

Edited by william.scherk
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[ . . . ]

A=analogy[which I maintain is a reasoning process that we do not fully understand, but exists.

-- that's an intriguing statement. Have you read Steven Pinker's new book, "The Stuff of Thought"? It has some equally intriguing ideas, and comes close to supporting your intuition about analogy.

At several points, but especially in the chapter 'The Metaphor Metaphor,' Pinker suggests that the power of analogy for science and reasoning in general is not from 'mere similarity of parts' in the two instances being compared. Rather, it is relations between the parts -- a disciplined tracing of the concept implicated in one domain can open a window to understanding in the other. Some concepts are so fresh or unfamiliar that the insight of a frame-shift/Gestalt is very useful. Because of the power of analogy to help our conceptual understanding 'snap to,' fallacious examples can be just as mentally satisfying as more appropriate ones.

I twit Michael now and again for inapt analogies. As he suggests, it is my touchy elbow. The 'eureka' snap of concepts falling into place is great fun, but always needs checking. One of my favourite dumb analogies (this spouted out in the context of visionaries/crackpots/pseudoscientists like Velikovsky): "You may laugh at his theories -- they laughed at Galileo!"

-- to which many wits have retailed the only proper answer: "They also laughed at Bozo the Clown."

Well put.

"Some concepts are so fresh or unfamiliar that the insight of a frame-shift/Gestalt is very useful. Because of the power of analogy to help our conceptual understanding 'snap to,' fallacious examples can be just as mentally satisfying as more appropriate ones."

Your description aproximates my "western" mind frame attending my first Tai Chi class. The instructor was exceptional and made statements that made my thoughts "snap to" and consider many new "windows" or perceptual facets.

Niels Bohr is an interesting phycisist and is know for his response to Einstein's comments about not believing that God would play dice with the Universe by saying that Einstein ought stop telling God what to do.

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~ 'Dice', 'God', or, as Hawking adds: "in a dark corner we can't even see."

~ Sounds like listening to Apollo and Dionysus arguing about Zeus' intentions.

~ Einstein established 1/2 of what God's pattern for the cosmos is...so far as we can see now; Hawking's working on the other 1/2.

~ Hopefully, within our lifetime, Janus will turn into the Gemini Twins.

LLAP

J:D

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