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

[ygolo]

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.

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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.

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Any thoughts on my above statements?

 

[Athenian200]

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?

 

[ygolo]

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.

 

[Didums]

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.

 

[Owl]

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.

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.

Does that make sense?

No.

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.

 

[Athenian200]

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.

 

[Owl]

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.

 

[Athenian200]

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?

 

[Kalach]

"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?

 

[Owl]

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.

You keep insisting on a perspective that's situated inside reason. From that perspective, of course you're right.

I'm committed to reason.

 

[Anja]

Thanks for this! As INFP it's a conundrum I've danced with for a long time. And you are all doing better than I could to put it into language.

It's surprising to me how many seek definitive answers to things which seem too complicated to me to answer simply "yes" or "no".

 

[Athenian200]

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?

What if we don't know that because we *can't* know that, because it's contrary to our way of knowing?

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.

You're just citing the standards of reasoning as justification for your position. Can't you even see what you're doing? You've built up these ideas and and you're just insisting on interpreting everything according to them as long as there is a perspective from which you can do so. Which, ironically, is exactly what I was suggesting that people did when they applied reason to reality.

 

[Kalach]

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.

To be frank, I forget why that is naught but a statement of Excluded Middle, but it is. Or at least, the Law of Non-Contradiction and that of Excluded Middle tend to go hand in hand.

Moving right along, consider this:

1. for any p, either p or not-p.
2. so for any q, if q is true then either p or not-p

Step 2 is interesting. The "if..then" statement is counter-intuitive, but automatic given Excluded Middle. Intuitively, for a conditional statement to be true, there should be some connection between the antecedent and the consequent, but Excluded Middle guarantees us (p or not-p) for any p, so that implication isn't ever going to crap out.

So how about we strengthen implication to rule out counter-intuitive cases? That's to say, how about we monkey around with the semantics of "if...then" to reflect what we actually do when we use reasoning. You can guess what's going to happen, right?

It so happens that if you start to monkey around with the semantic definition of "if...then" to reflect our need for there to be some connection between the "if" part and the "then" part... wait for it... one often ends up denying Excluded Middle.

Because Excluded Middle always does weaken the truth conditions for any conditional statement!

Anyhoo... what I mean to say is, there's lots of differing semantics available for implication, and they reflect differing requirements on the logics in question.

One aspect of the whole kit and kaboodle is the gnarly question, what are the real semantics we really use when we say "if this is true, then that is true too"?

And that's when we might want to start taking a close look at paradoxes.

 

[Nonsensical]

I do not have the intellect, at my age, to debate anything here, and in general, to put it simply, I think that us humans assume things, we think we know stuff, and we don't have any proof of anything. Think about it, how do we know that any of our presumptions are correct? Nothing, in theory, is testable. People will argue with this, because it is my uneducated/unintellectual veiw.

 

[antireconciler]

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?

In short, if reality violated the laws of thought, of reason, then either (1) so to do your thoughts about that reality, or (2) your thoughts cannot be veridical.

If (1), then your thinking is irrational. This is another way of saying it is incorrect, and that you need to revise the premise.

If (2), then your thought which was supposed to be about an irrational world is not in fact about it at all. Your own thought has slipped off the subject it was conceived of exactly to grasp, exactly because it cannot be grasped. The consequence is that your thought has no meaning because it can't have meaning except for what YOU have given it. But the meaning you have given it does not match the state of the world because it cannot match the state of the world. This is another way of saying you are incorrect, and that you need to revise the premise.

But if you don't care for the short version, I have another you might enjoy ...

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.

I'm committed to reason.

High five!

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.

I wonder if we can suggest that violations of the excluded middle are always the result of a category mistake, and not actual violations of the principle itself. I suppose that would require us to be able to communicate effectively while making such mistakes though. For example, even if there is no specific property "hot" which water must either be or not be (which we would conclude then cannot apply to water), we can at least communicate with it meaningfully.

Then again, perhaps all properties are like this. I wonder. What do you think? Even the seemingly exact locations of things have implicit probabilities. Maybe things can't just simply HAVE or NOT HAVE properties ... then every (finite) thing would violate the excluded middle. ??