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This article states that there are more than just one form of logic: http://aeon.co/magazine/world-views/logic-of-buddhist-philosophy/ http://aeon.co/magazine/

by zera11 12y ago

This article states that there are more than just one form of logic: http://aeon.co/magazine/world-views/logic-of-buddhist-philosophy/ http://aeon.co/magazine/world-views/logic-of-buddhist-philos...

javert 12y ago
And that is a blatant lie. By a famous philosophy professor, no less, which just means it a worse lie. All statements are true, false, arbitrary, or nonsensical. Contrary to Priest, a statement can't be true and false. (It can be neither true nor false, by virtue of being arbitrary or nonsensical.) A self-referential sentence, like "This sentence is false," is simply nonsensical. Famous philosophers have written whole books on the premise that this is an important problem, but it isn't. Graham Priest would probably gesticulate that I just don't "get it," but no, I do get it. I've read the article, and it's bullshit.
- pron 12y ago
  You can define any consistent logic system you want. It would help if you think of "T" and "F" merely as two symbols rather than having semantics that seem familiar to you in the real world. But once you assign the meanings "true" and "false" to those symbols, you venture beyond mathematics into the realm of philosophy (in particular, epistemology). The problem is that while you can define "true" and "false" in a common logic system, taking the same definitions into the real world isn't so smooth. The main problem is that in the real world you don't have axioms -- you have assumptions which might be "true" or "false" (whatever that means once we go beyond our measurement range). This alone pretty much precludes almost everything in the real world from being "true" in the mathematical sense. These assumptions are so pervasive that even the most basic quality, or concept, underlying all of science -- namely, causality -- is a mere assumption. Therefore, your statement "All statements are true, false, arbitrary, or nonsensical" can only be defined to hold in a system of logic, but doesn't necessarily translate into the real world. Mathematically speaking, nothing we know of the physical universe is known to be either true or false. In fact, you can't even conclusively (again, in the mathematical sense) say that two statements about the physical universe contradict, because we don't "know" anything about the physical universe in the same sense as we know something in a mathematical logic system. In short, your opinion is neither true about mathematics (where you can define any system you want) nor about the physical universe, where you can't directly apply any mathematical logic system, and in particular the one you think is "the one true logic".
  - atlantic 12y ago
    Excellent comment. Thanks.
  - javert 12y ago
    This is pure skepticism. Your position is: "We don't know anything about the real world." That is absolute hokum. The Earth orbits the Sun, living things need fuel to survive, two units combined with two units sums to four units. I could go on and on. You need good epistemology to explain why this is, since while it's common sense, I agree that common sense is not sufficient when we're talking about philosophy. Clearly you have not discovered good epistemology.
    - gshubert17 12y ago
      Isn't his position that mathematical (2+2=4) and logical (!T=F) knowledge is a different kind of knowledge than empirical (temp=20C) or scientific (F=ma)? I took this to be similar to what Einstein [1] said: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." [1] http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_g...
      - pron 12y ago
        Thanks for the Einstein reference. I wasn't familiar with it. However, my comment expressed little more than well established principles in epistemology and the philosophy of science. Einstein in his essay discusses the same general issue. My favorite demonstration of the difficulty of defining (non-mathematical) knowledge is the Gettier problem. The coolest thing about it is that if we try to come up with a definition of knowledge that is always agreed upon by everybody -- one that fully reconciles what we can intuitively and "logically" consider to be knowledge with all forms of the Gettier problem[1] -- we find ourselves with such a narrow definition that hardly covers anything we consider to be "known". This means that in science, as with everything else, we must adopt more lenient -- or pragmatic -- definitions of knowledge, but those definitions are not rigorous in any mathematical sense, and are always lacking. [1]: http://en.wikipedia.org/wiki/Gettier_problem http://en.wikipedia.org/wiki/Gettier_problem Also, see: http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Epistemology http://en.wikipedia.org/wiki/Epistemology
- xmonkee 12y ago
  >There is also “awareness”, but awareness is not a thing or localized in a particular place, so to even say “there is also awareness” is already a tremendous problem, as it implies separateness and existence where none can be found. To be really philosophically correct about it, borrowing heavily from Nagarjuna, awareness cannot be said to fit any of the following descriptions: that it exists, that it does not exist, that it both exists and does not exist, that it neither exists nor doesn’t exist. Just so, in truth, it cannot be said that: we are awareness, that we are not awareness, that we are both awareness and not awareness, or even that we are neither awareness nor not awareness. We could go through the same pattern with whether or not phenomena are intrinsically luminous. -Daniel Ingram You're too quick to reject it. The classic dichotomy works well in the objective sphere, but not so well on the boundary of objective and subjective.
  - javert 12y ago
    This quote is just a load of crap. There is awareness---I am conscious, so are you. It's a fact. It's true. There is simply no problem, here. It is not a great mystery. We don't know precisely how consciousness works, of course. There is no boundary of the objective and subjective, because there is no such thing as subjective truth, which is an oxymoron. For example, if vanilla is my favorite ice cream, that is an objective truth about my personal preferences.
    - xmonkee 12y ago
      How is it a fact? It's your fact, subjective fact. That we both have an agreement doesn't make it objective. You can't prove that there exists no man that will say he doesn't possess awareness. Even if everyone agreed that vanilla is their favourite flavor, it won't make vanilla objectively the best flavor of all.
- thisrod 12y ago
  > All statements are true, false, arbitrary, or nonsensical. In which category do you place the arithmetical statement that Godel showed how to construct?
  - lmm 12y ago
    It was a true statement. (It's not provable, but we should not expect to be able to prove all true statements)
    - eli_gottlieb 12y ago
      I've been meaning to ask, what does it mean to say that a mathematical theorem is true but not provable? I thought Goedel Sentences are true in the sense of being provable within a "larger" system of axioms.
      - lmm 12y ago
        For e.g. the continuum hypothesis, there are models which obey the ZFC axioms in which it is true and models which obey the axioms in which it is false. The Gödel sentences are less interesting; any model in which those sentences were false would be a model in which PA was inconsistent. Which sure, can exist (e.g. the "self-hating theory", PA plus the axiom that PA is inconsistent, is a somewhat legitimate set theory with some interesting properties). So saying the Gödel sentences are true was not entirely accurate; rather, it depends which model we're working with. But a model which declares PA is inconsistent doesn't seem like the sort of model that we'd want to do physics with. You're right that there are "larger" theories that can prove the consistency of PA, e.g. PA + existence of a large cardinal proves the consistency of PA. But, per Gödel, no consistent axiom system large enough to contain PA can prove its own consistency. This is probably a lot less bad than it sounds though; after all, if we have some unknown axiom system T, and we have a proof in T that T is consistent, does that really tell us anything? Because if T isn't consistent, then it can prove anything, including that T is consistent.
        eli_gottlieb 12y ago
- pharrington 12y ago
  All statements are true, false, arbitrary, or nonsensical. I'm missing something here. Is the statement "the three angles in a triangle add up to 180 degrees" true, false, arbitrary, or nonsensical? What do you call a statement that lacks (or reveals the lack of) crucial context?
  - arethuza 12y ago
    In that particular case, any proof that the angles of a triangle add up to 180 degrees has to start from the relevant axioms - and if you include the Euclidean parallel postulate then yes, that can be proved. What would the "crucial context" outside of the axioms you start with and inference steps to get from the axioms to your statement be?
  - tomp 12y ago
    The statement is true.
    - ajtulloch 12y ago
      The statement given is equivalent to the parallel postulate, and thus is true in a Euclidean geometry. The statement is tautologically false in a non-Euclidean geometry. http://en.wikipedia.org/wiki/Parallel_postulate http://en.wikipedia.org/wiki/Parallel_postulate http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History
- TheOtherHobbes 12y ago
  >All statements are true, false, arbitrary, or nonsensical. And which was that? AI depends heavily on statements that are somewhat true and somewhat false at the same time. How distorted does a letter shape have to be before it stops being readable? How much does readability depend on context? How much does meaning depend on context? What if input is inherently ambiguous and noisy but there's a signal under there somewhere? As for smarts, there are different kinds: Abstract symbolic reasoning (e.g. pure maths) Using abstract symbolic reasoning to predict possible futures (physics, engineering, finance, AI) A talent for optimising choices towards an explicit goal through abstract reasoning about possible futures (all of the above, with brain-powered decision making) The same, but using unconscious processes ('intuition') that are not explicitly abstract or logical (all brain, no AI so far, but still effective) The author seems to be suggesting that the first two kinds of smarts don't necessarily translate into the second two kinds, for various reasons. And not all smart people realise this.

by zera11 12y ago

This article states that there are more than just one form of logic: http://aeon.co/magazine/world-views/logic-of-buddhist-philosophy/ http://aeon.co/magazine/world-views/logic-of-buddhist-philos...

javert 12y ago

And that is a blatant lie. By a famous philosophy professor, no less, which just means it a worse lie. All statements are true, false, arbitrary, or nonsensical. Contrary to Priest, a statement can't be true and false. (It can be neither true nor false, by virtue of being arbitrary or nonsensical.) A self-referential sentence, like "This sentence is false," is simply nonsensical. Famous philosophers have written whole books on the premise that this is an important problem, but it isn't. Graham Priest would probably gesticulate that I just don't "get it," but no, I do get it. I've read the article, and it's bullshit.

pron 12y ago
You can define any consistent logic system you want. It would help if you think of "T" and "F" merely as two symbols rather than having semantics that seem familiar to you in the real world. But once you assign the meanings "true" and "false" to those symbols, you venture beyond mathematics into the realm of philosophy (in particular, epistemology). The problem is that while you can define "true" and "false" in a common logic system, taking the same definitions into the real world isn't so smooth. The main problem is that in the real world you don't have axioms -- you have assumptions which might be "true" or "false" (whatever that means once we go beyond our measurement range). This alone pretty much precludes almost everything in the real world from being "true" in the mathematical sense. These assumptions are so pervasive that even the most basic quality, or concept, underlying all of science -- namely, causality -- is a mere assumption. Therefore, your statement "All statements are true, false, arbitrary, or nonsensical" can only be defined to hold in a system of logic, but doesn't necessarily translate into the real world. Mathematically speaking, nothing we know of the physical universe is known to be either true or false. In fact, you can't even conclusively (again, in the mathematical sense) say that two statements about the physical universe contradict, because we don't "know" anything about the physical universe in the same sense as we know something in a mathematical logic system. In short, your opinion is neither true about mathematics (where you can define any system you want) nor about the physical universe, where you can't directly apply any mathematical logic system, and in particular the one you think is "the one true logic".
- atlantic 12y ago
  Excellent comment. Thanks.
- javert 12y ago
  This is pure skepticism. Your position is: "We don't know anything about the real world." That is absolute hokum. The Earth orbits the Sun, living things need fuel to survive, two units combined with two units sums to four units. I could go on and on. You need good epistemology to explain why this is, since while it's common sense, I agree that common sense is not sufficient when we're talking about philosophy. Clearly you have not discovered good epistemology.
  - gshubert17 12y ago
    Isn't his position that mathematical (2+2=4) and logical (!T=F) knowledge is a different kind of knowledge than empirical (temp=20C) or scientific (F=ma)? I took this to be similar to what Einstein [1] said: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." [1] http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_g...
    - pron 12y ago
      Thanks for the Einstein reference. I wasn't familiar with it. However, my comment expressed little more than well established principles in epistemology and the philosophy of science. Einstein in his essay discusses the same general issue. My favorite demonstration of the difficulty of defining (non-mathematical) knowledge is the Gettier problem. The coolest thing about it is that if we try to come up with a definition of knowledge that is always agreed upon by everybody -- one that fully reconciles what we can intuitively and "logically" consider to be knowledge with all forms of the Gettier problem[1] -- we find ourselves with such a narrow definition that hardly covers anything we consider to be "known". This means that in science, as with everything else, we must adopt more lenient -- or pragmatic -- definitions of knowledge, but those definitions are not rigorous in any mathematical sense, and are always lacking. [1]: http://en.wikipedia.org/wiki/Gettier_problem http://en.wikipedia.org/wiki/Gettier_problem Also, see: http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Epistemology http://en.wikipedia.org/wiki/Epistemology
xmonkee 12y ago
>There is also “awareness”, but awareness is not a thing or localized in a particular place, so to even say “there is also awareness” is already a tremendous problem, as it implies separateness and existence where none can be found. To be really philosophically correct about it, borrowing heavily from Nagarjuna, awareness cannot be said to fit any of the following descriptions: that it exists, that it does not exist, that it both exists and does not exist, that it neither exists nor doesn’t exist. Just so, in truth, it cannot be said that: we are awareness, that we are not awareness, that we are both awareness and not awareness, or even that we are neither awareness nor not awareness. We could go through the same pattern with whether or not phenomena are intrinsically luminous. -Daniel Ingram You're too quick to reject it. The classic dichotomy works well in the objective sphere, but not so well on the boundary of objective and subjective.
- javert 12y ago
  This quote is just a load of crap. There is awareness---I am conscious, so are you. It's a fact. It's true. There is simply no problem, here. It is not a great mystery. We don't know precisely how consciousness works, of course. There is no boundary of the objective and subjective, because there is no such thing as subjective truth, which is an oxymoron. For example, if vanilla is my favorite ice cream, that is an objective truth about my personal preferences.
  - xmonkee 12y ago
    How is it a fact? It's your fact, subjective fact. That we both have an agreement doesn't make it objective. You can't prove that there exists no man that will say he doesn't possess awareness. Even if everyone agreed that vanilla is their favourite flavor, it won't make vanilla objectively the best flavor of all.
thisrod 12y ago
> All statements are true, false, arbitrary, or nonsensical. In which category do you place the arithmetical statement that Godel showed how to construct?
- lmm 12y ago
  It was a true statement. (It's not provable, but we should not expect to be able to prove all true statements)
  - eli_gottlieb 12y ago
    I've been meaning to ask, what does it mean to say that a mathematical theorem is true but not provable? I thought Goedel Sentences are true in the sense of being provable within a "larger" system of axioms.
    - lmm 12y ago
      For e.g. the continuum hypothesis, there are models which obey the ZFC axioms in which it is true and models which obey the axioms in which it is false. The Gödel sentences are less interesting; any model in which those sentences were false would be a model in which PA was inconsistent. Which sure, can exist (e.g. the "self-hating theory", PA plus the axiom that PA is inconsistent, is a somewhat legitimate set theory with some interesting properties). So saying the Gödel sentences are true was not entirely accurate; rather, it depends which model we're working with. But a model which declares PA is inconsistent doesn't seem like the sort of model that we'd want to do physics with. You're right that there are "larger" theories that can prove the consistency of PA, e.g. PA + existence of a large cardinal proves the consistency of PA. But, per Gödel, no consistent axiom system large enough to contain PA can prove its own consistency. This is probably a lot less bad than it sounds though; after all, if we have some unknown axiom system T, and we have a proof in T that T is consistent, does that really tell us anything? Because if T isn't consistent, then it can prove anything, including that T is consistent.
      - eli_gottlieb 12y ago
pharrington 12y ago
All statements are true, false, arbitrary, or nonsensical. I'm missing something here. Is the statement "the three angles in a triangle add up to 180 degrees" true, false, arbitrary, or nonsensical? What do you call a statement that lacks (or reveals the lack of) crucial context?
- arethuza 12y ago
  In that particular case, any proof that the angles of a triangle add up to 180 degrees has to start from the relevant axioms - and if you include the Euclidean parallel postulate then yes, that can be proved. What would the "crucial context" outside of the axioms you start with and inference steps to get from the axioms to your statement be?
- tomp 12y ago
  The statement is true.
  - ajtulloch 12y ago
    The statement given is equivalent to the parallel postulate, and thus is true in a Euclidean geometry. The statement is tautologically false in a non-Euclidean geometry. http://en.wikipedia.org/wiki/Parallel_postulate http://en.wikipedia.org/wiki/Parallel_postulate http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History
TheOtherHobbes 12y ago
>All statements are true, false, arbitrary, or nonsensical. And which was that? AI depends heavily on statements that are somewhat true and somewhat false at the same time. How distorted does a letter shape have to be before it stops being readable? How much does readability depend on context? How much does meaning depend on context? What if input is inherently ambiguous and noisy but there's a signal under there somewhere? As for smarts, there are different kinds: Abstract symbolic reasoning (e.g. pure maths) Using abstract symbolic reasoning to predict possible futures (physics, engineering, finance, AI) A talent for optimising choices towards an explicit goal through abstract reasoning about possible futures (all of the above, with brain-powered decision making) The same, but using unconscious processes ('intuition') that are not explicitly abstract or logical (all brain, no AI so far, but still effective) The author seems to be suggesting that the first two kinds of smarts don't necessarily translate into the second two kinds, for various reasons. And not all smart people realise this.