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    Default Either This or That:The Laws of Non-Contradiction and The Excluded Middle

    Law of Noncontradiction

    In summary:It is false that both P and (not P) are true.

    Law of excluded middle - Wikipedia, the free encyclopedia

    In summary: P or (not P) is true.

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    It has come up in a few discussions that the Law of NonContradiction has been violated in many case.

    Some thing is both "a pile of stuff" and "not a pile of stuff" a pile of stuff depending on how you look at it.

    Shcrodinger's cat is both "alive" and "not alive" depending on how you measure it.

    Luke-Warm water is both "hot" and "not hot" in some ways.

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    But a little thought shows that all of these example truly fall short of violating the Law of Noncontradiction.

    The problem here is the selection of words used, not a matter of logic.

    The logically consistent picture will show that the word usage that we created is self-contradictory, and what we have created in reality is a violation of The Excluded Middle--an expected outcome of the use of clumsy concepts.

    ---
    What I mean by this is that the actual truth is:

    It is neither "a pile of stuff" nor "not a pile of stuff" (a violation of the excluded middle). Instead, the notion of "pile of stuff" is a logically inconsistant notion.

    The cat is neither "alive" nor is it "not alive" (again a violation of the Excluded Middle), but rather is a "superposition" of states of "alive" and "not alive."

    The water is neither "hot" nor is it "not hot," (another violation of the Exluded Middle), it is simply luke-warm.

    ---

    Any thoughts on my above statements?

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  2. #2
    Protocol Droid Athenian200's Avatar
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    Yes. It shows that logic is limited by language, which is in turn limited by the way the human mind tends to interpret reality. Unfortunately, one major flaw in how human beings tend to interpret things is that they tend to arbitrarily take two categories and make them polar opposites of each other, and lump everything into one of those two. The best examples would be good and bad, and is or is not, but there are plenty of others.

    I think that actual reality probably has a lot of qualities that we can't understand. For instance, a thing can embody things associated with one quality while also embodying things associated with the opposite quality, without changing the nature of those qualities (because the original concept connected a lot of things that were not necessarily connected in all cases). But the human mind tends to perform poorly with this idea, because it makes a lot of associations and connotations that make it difficult to entertain such precise awareness for very long, or to actually make a decision based on it.

    In other words, I think that something can both be and not be, and that this actually makes sense because our concept of "being" is an arbitrary one we use to organize our perceptions enough to work with reality in a meaningful way. The purpose of concepts is not to express raw reality perfectly, but to reduce reality to something our minds can work with. The very act of trying to understand something means to reduce it to concepts our minds understand (such as the division between totally being and totally not being one way), which results in complications when we reach beyond the perspective and context the concept was designed to work within.

    It's even possible that reality is both different and the same for people. Certain aspects of reality may well only be true for one person or a group of people, while others may be true for all. It's possible that there may not be a single reality, nor multiple individual realities, but rather several parallel realities that affect one another in some predictable, and some unpredictable ways, and sharing some but not other principles.

    Does that make sense?

  3. #3

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    That does make sense Athenian.

    The basic thrust of what I meant in the OP is that duality is an illusion, created by the descriptions we choose.

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

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    Yep, you're right.

    Probably the most important application of the Law of Noncontradiction is when looking at Existence vs. Nonexistence. Existence must always have existed because to say that it hasn't always existed would mean that at one point Existence was Nonexistent, which violates the law. This is why the Universe has no moment of causation, the Universe is the sum total of existence, and is therefore eternal.

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    desert pelican Owl's Avatar
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    Quote Originally Posted by ygolo View Post
    Any thoughts on my above statements?
    I don't think the law of excluded middle can be violated. For instance, if somehthing is luke warm, then it's not hot.

    Quote Originally Posted by ygolo View Post
    Some thing is both "a pile of stuff" and "not a pile of stuff" a pile of stuff depending on how you look at it.

    Shcrodinger's cat is both "alive" and "not alive" depending on how you measure it.
    The law of non-contradiction, and therefore the law of excluded middle, requires that something not be both A and non-A at the same time, in the same respect. Changing the way you look at a heap, or how you measure a cat, changes the respect, and therefore the concept involved is changed, so neither of those examples would be true violations of the law of excluded middle.

    I'd not say the concepts are clumsy. The language is clumsy--nay, the person using the language is clumsy--but a verbal problem is not necessarily a logical problem.

    Quote Originally Posted by Athenian200 View Post
    Does that make sense?
    No.

    Quote Originally Posted by Athenian200 View Post
    It shows that logic is limited by language, which is in turn limited by the way the human mind tends to interpret reality.
    How does the mind interpret reality if not logically? The laws of logic, (or, more properly, the laws of thought), must be obeyed if one's interpretation is to be coherent. If one abondons the laws of thought, then one also abandons coherence, and truth is the first victim of incoherence.

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    Protocol Droid Athenian200's Avatar
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    Quote Originally Posted by Owl View Post
    How does the mind interpret reality if not logically? The laws of logic, (or, more properly, the laws of thought), must be obeyed if one's interpretation is to be coherent. If one abondons the laws of thought, then one also abandons coherence, and truth is the first victim of incoherence.
    Okay, you got me there. We're stuck with the laws of thought because of how our minds work. But what I'm suggesting is that reality might not work according to the kind of logical rules we depend on to interpret reality.

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    desert pelican Owl's Avatar
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    Quote Originally Posted by Athenian200 View Post
    Okay, you got me there. We're stuck with the laws of thought because of how our minds work. But what I'm suggesting is that reality might not work according to the kind of logical rules we depend on to interpret reality.
    If that were the case, we would truly be SOL.

    But if it's clearly the case that we are thinking and communicating, then reality cannot violate the laws of thought. For if it did, then it might be the case that we aren't thinking and communicating. Furthermore, it might be the case that nothing exists, which is itself a precondition for thought, for the appearance of existence wouldn't gaurantee the reality of existence, (just as the appearance of thought wouldn't gaurantee the reality of thought); but if nothing existed, then there could be no thing that thinks.

    In the end, if one denies that reason is ontological, that it applies to being as well as to thought--that it governs being just as it governs thought--then one must also deny that it's clear that he's thinking, or that it's clear that any thing exists, but this is clearly self referentially abusrd.

    To put it another way: if it's not possible to doubt that you're thinking, then it's not possible that reason isn't ontological.

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    Protocol Droid Athenian200's Avatar
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    Quote Originally Posted by Owl View Post
    If that were the case, we would truly be SOL.

    But if it's clearly the case that we are thinking and communicating, then reality cannot violate the laws of thought. For if it did, then it might be the case that we aren't thinking and communicating. Furthermore, it might be the case that nothing exists, which is itself a precondition for thought, for the appearance of existence wouldn't gaurantee the reality of existence, (just as the appearance of thought wouldn't gaurantee the reality of thought); but if nothing existed, then there could be no thing that thinks.

    In the end, if one denies that reason is ontological, that it applies to being as well as to thought--that it governs being just as it governs thought--then one must also deny that it's clear that he's thinking, or that it's clear that any thing exists, but this is clearly self referentially abusrd.

    To put it another way: if it's not possible to doubt that you're thinking, then it's not possible that reason isn't ontological.
    You keep insisting on a perspective that's situated inside reason. From that perspective, of course you're right.

    Why do you insist that reality either does or doesn't violate the laws of thought? Couldn't it be that we can only perceive the aspects of reality that don't violate the laws of thought (because we use thought to describe our reality), and thus reality can never appear to violate those laws? The fact that we're thinking and communicating only indicates that we both perceive some of the same things in reality and process them in similar ways. Two colorblind people wouldn't have any reason to suspect the existence of color, for instance, although they would be able to discuss shape and size at length.

    Your definition of reality seems to be limited to what you accept as truth, which is a process that is wholly encompassed within the laws of thought. You don't seem to consider much beyond that. This is something about the nature of your mind. What I'm saying is, how much of what we consider reality is the result of projecting our own unconscious minds onto it?

  9. #9
    Filthy Apes! Kalach's Avatar
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    "Thoughts?"? Okay, let's start with "Jeepers!'

    Jeepers!

    Excluded Middle?!

    It's an astonishingly powerful principle--are you really so content with it?

    For example, to prove p all you need to do is prove not-p is not true. By Excluded Middle that makes p true. Not that you directly proved p or anything.

    And what's so upsetting about contradictions anyway? They only truly mess up logic if Excluded Middle applies.

    Why would we want logical systems that non-trivially tolerate contradictions?


    Dunno.

    But, hey, most languages in existence are a great deal more powerful than they truly need to be. Like, for example, English famously allows self-referential constructions like:

    This sentence is false.


    I wonder if even the human mind itself would exist if it had to obey excluded middle. Pragmatic, real time thinking systems have to deal non-trivially with contradictions, don't they?

    And what of subatomic physics?

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    desert pelican Owl's Avatar
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    Quote Originally Posted by Athenian200 View Post
    You keep insisting on a perspective that's situated inside reason. From that perspective, of course you're right.

    Why do you insist that reality either does or doesn't violate the laws of thought? Couldn't it be that we can only perceive the aspects of reality that don't violate the laws of thought (because we use thought to describe our reality), and thus reality can never appear to violate those laws? The fact that we're thinking and communicating only indicates that we both perceive some of the same things in reality and process them in similar ways. Two colorblind people wouldn't have any reason to suspect the existence of color, for instance, although they would be able to discuss shape and size at length.

    Your definition of reality seems to be limited to what you accept as truth, which is a process that is wholly encompassed within the laws of thought. You don't seem to consider much beyond that. This is something about the nature of your mind. What I'm saying is, how much of what we consider reality is the result of projecting our own unconscious minds onto it?
    If the laws of thought weren't ontological, then how would we know what parts of reality did or didn't conform to the laws of thought?

    Anything follows a contradiction. In the presence of a contradiciton, true and false lose their distinction, all becomes worse than false, and knowledge becomes impossible. But it is clearly true that something exists; therefore, it is necessary that there are no extant contradictions.

    Quote Originally Posted by Athenian200 View Post
    You keep insisting on a perspective that's situated inside reason. From that perspective, of course you're right.
    I'm committed to reason.

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