Monday, September 9, 2013

The Laws of Thought

The Laws of Thought (or Laws of Logic) are fundamental to good argument, and are often violated or misunderstood, and a fascinating question is: what is their epistemological status?

The Laws of Thought can be set out as follows:
(1) the Law of Identity
This can be stated simply as the idea that any entity x is identical with itself (or x = x). With respect to propositions, it means that, if a proposition p is true, then it is true (or p → p).

A violation of the Law of Identity is the informal logical fallacy of equivocation: changing the meaning of terms in an argument or using the same term in different senses.

(2) Law of Noncontradiction
This can be stated as the idea that one cannot assert as true a proposition p and its negation at the same time (or p ∧ ¬p is false). Such a statement is self-contradictory. That is to say, the proposition p and its negation (¬p) asserted as true at the same time are mutually exclusive.

The source of the Law of Noncontradiction is Aristotle’s Metaphysics, although he gives three versions of the law, in (1) an ontological, (2) psychological and (3) logical sense.

(3) the Law of Excluded Middle
This states that every meaningful proposition is either true or false. There is no third option. Put another way, either the proposition p is true or its negation (¬p) is true. Symbolically, this means that p ∨ ¬p must be true.
It is also generally believed that laws (1) and (3) are tautologies.

There are of course many other tautologies important for deductive logic, such as De Morgan’s theorems, but the laws of thought remain fundamental.

But, as noted above, what is their epistemological status? Are they simply analytic a priori? And even if we can interpret them in that sense when considered only as pure tautologies, could they also be given an empirical synthetic a posteriori status when asserted as true of the real world? (just as pure geometry and applied geometry each have a different epistemological status.)

For it seems that the law of identity also expresses, or is bound up with, a deep metaphysical truth about existence: existence and identity are closely related concepts, as was stressed by Gottlob Frege and Quine (Scruton 1994: 143).

Indeed, Bertrand Russell gave the laws of logic an ontological interpretation:
(1) law of identity: ‘whatever is, is.’

(2) the law of contradiction: ‘nothing can both be and not be.’

(3) the law of excluded middle: ‘everything must either be or not be.’
Russell thought that these were “self evident logical principles,” but the possibility that the law of excluded middle may not apply to certain quantum mechanical phenomena (Quine 1986: 86–87) should alert us to the idea that the laws of thought are ultimately empirical statements derived from human experience of the macroscopic world. (And this does not falsify the law of excluded middle with respect to the macroscopic world at all, but confines or limits it as a truth to that domain.)

That is to say, surely it is not unreasonable to assert that “every thing that exists is identical with itself” is, in the end, an empirical observation of the fundamental nature of the world of human experience. Of course, we cannot even conceive of how it could be false, but then human beings most probably could not conceive of the counter-intuitive truths of quantum mechanics until the 20th century.

Even in the realm of the laws of thought, when these laws are asserted as truths of the real world, they arguably must be considered empirical.

Links
“Law of Thought,” Wikipedia
http://en.wikipedia.org/wiki/Three_classical_laws_of_thought#Aristotle

“Law of Noncontradiction,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_noncontradiction

“Law of Identity,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_identity

“Law of Excluded Middle,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_Excluded_Middle

BIBLIOGRAPHY
Scruton, R. 1994. Modern Philosophy: An Introduction and Survey. Penguin Books, London.

Quine, W. V. 1986. Philosophy of Logic (2nd edn.). Harvard University Press, Cambridge, Mass.

21 comments:

  1. I was fascinated to read recently a new theory of reasoning which suggests that the fallacy of confirmation bias is actually a feature of reason not a bug.

    Mercier, Hugo & Sperber, Dan. 'Why Do Humans Reason. Arguments for an Argumentative Theory.' Behavioral and Brain Sciences. (2011) 34: 57 – 111. doi:10.1017/S0140525X10000968. Available from Dan Sperber's website.

    My precis is here: http://jayarava.blogspot.co.uk/2013/05/an-argumentative-theory-of-reason.html

    I see real problems with "(2) the law of contradiction: ‘nothing can both be and not be.’" Famously Schr√∂dinger proposed his thought experience to show that this must apply to unobserved sub-atomic particles but it was shown to be wrong. Thus there is at least one domain of knowledge where this "law" simply does not apply.

    As far as being or not being, as a scholar of Buddhism it is for me axiomatic that these statements are two extremes of ontological thought; and that experience is neither absolute being nor absolute non-being, but is always either coming into being or going out of being.

    Similarly, if we cannot pin experience as either being or not being, but have to admit that experience has a rather indeterminate ontological status then law 1 is also a rather dubious statement. How could we possibly know what is when we only have experience to judge it. We might and do infer things about what is, but these inferences can only be tested in experience.

    So, far from being laws of thought, these ideals are pretty much useless in the domain of human experience.

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    1. Interesting, but even if quantum mechanics requires rejection of some laws of thought, I think they still apply to the macroscopic world of human experience (as I said above).

      For example, do you think there is such a thing as a "square circle"? If not, why not?

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  2. You write: " ... just as pure geometry and applied geometry each have a different epistemological status."

    I suggest you insert a link to your post "Bob Murphy All At Sea ...," where you very nicely explain the difference of epistemological status.

    Thanks for another most inspiring post on fundamental methodological issues.

    Georg Thomas

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    1. Thanks, that is a useful suggestion, and I have added the link.

      regards

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  3. Jayarava Atwood.

    If you think about it non-contradiction still holds even with your example. What the second law, actually is saying is that a thing cannot be and not be, IN THE SAME TIME, PLACE, and UNIVERSE. In one unobserved universe, Schrodinger's cat is alive, in another it is dead. . There is no contradiction here.


    Oh, and LK, there is a problem with "modal" logic and newfangled logic that claims to get around the law of the excluded middle, or bivalence.

    Lets assume a proposition with THREE values, true false, and unknown. If you think about it, "unknown" really falls under the "truth" category, when I state "it is true that john doesn't know if there is extraterrestrial life.

    Bottom line, the three laws are absolutes. And we shouldn't try to imagine a world without them, else we'll go insane.

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    1. Edward, you write: " ... the three laws are absolutes. And we shouldn't try to imagine a world without them ..."

      What do you make of this story?

      LK and Georg are standing next to LK's car. A pretty woman appears on the other side of the car. The woman is waving in the direction of the two men.

      Georg walks around LK's car to approach the woman.

      LK simply walks straight through his car to say hello to the woman.

      When Georg tries to do the same thing (walk through the car), it doesn't work.

      Now let's say, "to be", "to exist" is defined as being visible and capable of acting as a physical obstacle.

      When LK walks though the car, it becomes invisible to him and loses its quality as a physical obstacle.

      If Georg makes the same effort, at the same time as LK, the car remains visible and an impenetrable obstacle.

      Could we not argue - without going insane -, indeed have we not successfully managed to imagine that

      the car IS and IS NOT at the same time?

      Kind regards

      Georg Thomas

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    2. (1) But LK and Georg don't attempt to walk through the car at the same time. In your imaginary example, one can simply reply that perhaps the car was -- by some unknown advanced science and technology -- transported somewhere else when LK (me) walked through, but was brought back when Georg tried the same thing.

      This no violation of the law of contradiction.

      (2) If LK and Georg tried to walk through at the same time with different results, OK, then perhaps such a thing *might* be empirical evidence that the law of contradiction is violated.

      So point is only that we can, hypothetically speaking, imagine a possible world where the law of contradiction is violated.

      But once we throw logic to the wind all sorts of things might be possible.

      E.g., can we have a square triangle? Is such a thing even possible, and not a hopeless contradiction in terms?

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    3. Having thought about my off-the-top example more carefully, I don't think it does actually represent a violation of the law of non-contradiction.

      There is no subject involved that is actually faced with such a violation. For LK, the car simply does not exist; he is not struggling with a situation where both happens to him: car-existence and car-nonexistence.

      Similarly, for Georg, the car simply exists; there is no conflict for him between car-existence and car-non-existence.

      It is a matter of physics (or imaginary physics) to make the situation plausible; but there is no violation of the second law of thought. No more than when LK is able to buy a Rolls Royce, while Georg is unable to buy any car at all. Money exists (in the pocket of LK) and does not exist (in the pocket of Georg), at the same time.

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  4. Have you read An Investigation of the Laws of Thought by George Boole, LK?

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    1. I have not read George Boole's book, though I know it is ranked as important in the history of logic.

      I suspect Frege's work is generally judged more important than Boole's.

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    2. I don't know enough to make that claim, but I believe that George Boole would be worth reading nonetheless.

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  5. I'm afraid I disagree rather strongly: the bivalent logic you are discussing is just as much based on an assumption of two values as plane geometry is based on an assumption of non-intersecting parallel lines.

    And just as plane geometry is only one of many geometries (such as spherical and hyperbolic geometry), so binary logic is only one of many logics (such as the three-valued logics.)

    In addition, applied to the real world the law of identity does not work when time is considered. It's not the same river one day as the next: the water has changed by movement, precipitation, etc. This is one of the obvious reasons why claims of Ayn Rand that her logic starts with A is A shows Rand is a bullshitter. If she says A is A about the real world, which includes time, it doesn't hold.

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    1. "In addition, applied to the real world the law of identity does not work when time is considered. It's not the same river one day as the next:"

      Indeed, but traditionally the assumption is that the law of identity is a statement about entities at a particular time and at that time only.

      This point is stressed by Copi and Cohen, Introduction to Logic, 14th edn., in their discussion of the law.

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    2. Agreed: that's why I pointed out that Ayn Rand, who doesn't specify her logic as applying to only one instant, is full of shit.

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    3. Even if we accept the law of identity, then Rand's whole theory is still a non sequitur.

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  6. Georg,
    "Now let's say, "to be", "to exist" is defined as being visible and capable of acting as a physical obstacle.

    When LK walks though the car, it becomes invisible to him and loses its quality as a physical obstacle.

    If Georg makes the same effort, at the same time as LK, the car remains visible and an impenetrable obstacle.

    Could we not argue - without going insane -, indeed have we not successfully managed to imagine that

    the car IS and IS NOT at the same time?




    Sure, if you make up your own definitions, than you can say anything you wish. However what usually happens when we observe a seeming contradiction is that we don't understand something, there a "fudge" factor, a new variable that explains everything. In your example, I would say that LK has comic-book special mutant powers

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  7. Mike Huben

    "In addition, applied to the real world the law of identity does not work when time is considered.

    But time SHOULD be considered! (LK is right here) But if you say then that the three laws are trivial and of limited value in the real world, well I agree in a sense, (Im not a Randian) What they are useful for are starting points in the mathematical and conceptual world.

    we also need the three laws to avoid faith based thinking and magical thinking. Thats why they're important and all the newfangled rubbish about "Boolean logic" or "modal" logic falls apart.

    Give me any example, Huben, and I can ground it in one of the three laws

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    1. I am not sure the modal logic of possible worlds falls apart.

      Since a "possible world" is a counterfactual world and either (1) not posited as real or (2) (in actualism) posited as real but causally isolated and different from ours, there does not seem to be violation of laws of logic in our world.

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    2. Edward, allow me to point you to the wikipedia pages on three-valued logic, four-valued logic and quantum logical qubit. These have equivalent but different laws, just as spherical and hyperbolic geometry have different ideas of parallel.

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  8. LK
    "

    But even a possible world has its own basic laws

    Just to give a fanciful example, imagine a universe where the Harry Potter characters, magic and all, are real. Would magic in that world be a violation of the laws of thought?

    Not at all. Various places in her books, Rowling states that magic rendered electronic devices inoperable at Hogwarts. This suggests "magic" in that world to be an sub molecular "force" like electromagnetism, with its own laws and restrictions.

    Nothing supernatural about it. So even if the multiple universes theory of quantum mechanics is correct, and those alternate universes have different laws than our own, those laws still wouldn't violate the Big Three

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  9. Lord Keynes, thank you for fighting the trolls. It must be exhausting but even if it doesn't convince the troll it does convince the other 99% of viewers that do see it.

    Trolls today are terrible, not because trolls are terrible as they have a vital purpose, but because they are sloppy crazy and usually are just engaging a "protesting too much" projection.

    cheers

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