The laws of thought as axioms?

[VarunSoon]

Are the three laws of thought (identity, non-contradiction, and excluded middle) really the foundational axioms of deductive logic?

Does they not depend on the definition of truth values and the definition and properties of logical connectives?

The three laws can be determined to be true in all circumstances by just looking at their truth table (so we do NOT need to presume them to be true).

[Namelesss]

Are the three laws of thought (identity, non-contradiction, and excluded middle) really the foundational axioms of deductive logic?

Does they not depend on the definition of truth values and the definition and properties of logical connectives?

The three laws can be determined to be true in all circumstances by just looking at their truth table (so we do NOT need to presume them to be true).

QM has refuted/eviscerated all of Aristotle's so-called 'laws of logic'!
Pragmatic is about it, far from Universal Truth!

"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." -Robert Anton Wilson

"For every Perspective, there is an equal and opposite Perspective!" - The First Law of Soul Dynamics

[Eduk]

For QM to have refuted logic it would first have to be understood. What causes it would have to be understood. Its mechanism would have to be understood. Thus far QM is not understood, some physicists would argue against even trying to understand it (others would argue the opposite). When a layman says QM proves X then you must view this claim with high suspicion as what they are saying is that 'this thing I don't understand' proves X.

Are the three laws of thought (identity, non-contradiction, and excluded middle) really the foundational axioms of deductive logic?

A=A is an axiom. It's a decent axiom. If you can come up with better then please publish your work and I'll look forward to reading it (I hope you get rich and famous). I've read Aristotle's work and personally I was impressed. I think if you come up with a theory that contradicts formal logic then you will need some exceptional justification.

Having said that it is possible that the laws of logic do break down under certain circumstances. It's just that those circumstances are unknown and what the laws break down to is unknown. Formal logic is a tool, a useful tool, a tool no one has bettered, treat it as such. I don't throw away my hammer if it can't saw a branch.

[Steve3007]

There is nothing in the discoveries of quantum mechanics which violates those three laws of propositional logic: identity, non-contradiction, and excluded middle. They are laws about the validity or otherwise of propositions, not empirical laws about physical observations.

-- Updated Thu Nov 23, 2017 10:57 am to add the following --

Eduk:

Thus far QM is not understood, some physicists would argue against even trying to understand it (others would argue the opposite).

It depends what exactly you mean by "understood". QM is a highly accurate and successful theory in describing and predicting a large subset of all possible empirical observations. (Note: still a sub-set, not the whole set). It could be argued that they ability to describe and predict observations is actually the only way to define the concept of "understanding".

-- Updated Thu Nov 23, 2017 11:22 am to add the following --

Nameless:

"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." -Robert Anton Wilson

A statement which is all of the above will generally turn out, on closer inspection, to be many different statements, and possibly value judgements, rolled into one. A statement which is true in some circumstances but not in other circumstances is not a single statement.

For example, you may say that the statement "it is raining" could be true in one place and false in another, or true in one sense and false in another, depending on your definition of the word "rain".

A classic example (from Bertrand Russell) of a statement which appears to be one statement but which is implicitly more than one is:

"The present king of France is bald."

which appears to be a single proposition but which is actually two:

"There currently exists a king of France."
"That person is bald."

[Eduk]

It depends what exactly you mean by "understood".

Yes I apologise I'm not a physicist and I'm surely not using the clearest terminology. It is as you say very successful in its predictions and I am in no way criticising QM. But conceptualising quantum matter and really understanding why matter acts as it does is not understood. So if you make a claim that QM proves X where X is anything other than the quantum properties of matter then you are on dodgy ground.

[Steve3007]

I wasn't intending to defend QM against criticism. There's nothing wrong with criticism. I was just sharing my thoughts - my own understanding.

Again, when we say "But conceptualising quantum matter and really understanding why matter acts as it does is not understood." we have to try to work out exactly what it is that we're hoping to achieve. What exactly would be an answer to the question "why"? In the context of science, answers to the question "why" seem to me always to be references to underlying mechanisms - descriptions of larger sets of possible observations. It's always possible to simply keep asking for ever deeper mechanisms - descriptions of ever larger sets of possible observations.

But I think we sometimes mistakenly think that "why" must mean more than that. We just don't know what.

[Eduk]

Let me put it another way.

We all know of the force of gravity. We can make predictions based on this knowledge. But we don't know why gravity has this effect or really what gravity actually is.

Now if I am making a catapult and working out the angle I need to throw a rock X distance then I don't need to know what gravity 'really' is, I just need to know the equations and the predictions. But if I am trying to resolve quantum mechanics with gravity then maybe I do need to know what gravity really is. Who knows what the application of such knowledge could bring.

There are problems to which 'why' is irrelevant and there are problems to which it is relevant.

'Why' is a question all children ask and in many ways chipping away at 'why' is one of the great endeavours of mankind. Whether we will ever get an answer is unknown but a lot of utility has come from asking and then trying to answer.

[Steve3007]

Eduk:

Let me put it another way.

OK. And I will give my own wording/interpretation of the examples you use.

We all know of the force of gravity. We can make predictions based on this knowledge. But we don't know why gravity has this effect or really what gravity actually is.

We all know that there are certain patterns in the way that massive objects (objects with mass) are observed to move. We've found (with the help of Newton and others) that it is possible to use those patterns to quite accurately describe all of those observations in a single relatively simple mathematical statement. We call that description "the law of universal gravitation". We've then found that we can actually describe an even wider set of observations of these objects with an even greater level of accuracy with a new law of gravitation (General Relativity) - a new mathematical description - which simplifies back to the original description when we don't need that greater accuracy/applicability.

So all of this is descriptions of observations being enveloped/superseded by new descriptions of larger sets of observations. We think it likely that this process of enveloping small old descriptions with big new ones will continue.

Note: I use the word "envelope" to emphasise that the old small description remains intact, as a special case of the new one. Inside it, as it were.

Now if I am making a catapult and working out the angle I need to throw a rock X distance then I don't need to know what gravity 'really' is, I just need to know the equations and the predictions. But if I am trying to resolve quantum mechanics with gravity then maybe I do need to know what gravity really is. Who knows what the application of such knowledge could bring.

Given what I have said above, I would argue that there is not the fundamental difference between the two processes (the catapult and the Gravity/QM unification) that you have implied here. It is not (in my view) a case of understanding "why" in the latter case but not in the former. In both cases, it means trying to create descriptive laws which describe observations. In the latter case, those observations that we are attempting to describe with a single law are the ones that are successfully described, separately, to a particular level of accuracy, by QM and General Relativity.

If we do come up with such a law, which describes all the observations that were described separately by QM and GR, then, just as before, it will collapse back into one of those two for particular subsets of observations.

The key point: We won't be answering the question "why?" any more than we were with Newton's law of gravity. We'll simply be broadening our descriptive power.

-- Updated Thu Nov 23, 2017 12:33 pm to add the following --

(I that last paragraph, I think I should have said "We won't be answering the question "why?" any more or less than we were with Newton's law of gravity. If we define answering the question "why?" as doing what I've attempted to describe here, then that's fine. It's just a word.)

[Eduk]

The key point: We won't be answering the question "why?" any more than we were with Newton's law of gravity. We'll simply be broadening our descriptive power.

Ok I think I get your point, correct me if I am wrong.

You are saying that Newton's laws don't answer why something falls. Or that Einstein's laws don't answer why something falls. They just answer how it falls with greater and greater descriptive power?

But I have two points I would make.

Firstly I wasn't really meaning to use why in the strictest possible sense, just the normative sense. In this manner say why a rock falls or saying how it falls can amount to the same thing. As in this is just a question of semantics rather than meaning.

Secondly the question of why still remains. Perhaps it is unanswerable. Perhaps not.

[Steve3007]

Yes, that is what I meant, and I agree with your points. We often do use the words "why" and "explain" rather than "how" and "describe" for these processes. I'm not too bothered about that. They're just words.

The interesting thing relates to your second point: We often seem to have an instinctive feeling that the process I've described is superficial and unsatisfactory, and there must be something more. Perhaps the question "why?" when we see it as distinct from the question "how?" is unanswerable. But I think it's interesting, as a matter of human psychology, that we seem to keep trying to answer it anyway.

[Eduk]

We often seem to have an instinctive feeling that the process I've described is superficial and unsatisfactory

OK but I think, again correct me if I am wrong, that you are talking about a very special case of dissatisfaction?

Let's take the big bang theory.
Q. Why did the big bang take place.
A. Unknown.

Person A: concludes that the big bang theory is therefore incomplete, doesn't answer the question they want answering and is therefore reasonable to ignore, denigrate etc.
Person B: concludes that the big bang theory is an incredible theory worthy of spending life times in the application of, while at the same time hoping that their question could be answered.

Both person A and person B are dissatisfied but with contrasting conclusions and to contrasting extents.

I assume you are ok with Person B, but not so ok with person A?

[Namelesss]

For QM to have refuted logic it would first have to be understood.

No.
The bit of evidence that refutes Aristotle's exclusionary errors needs to be witnessed.
It was/is.

What causes it would have to be understood. Its mechanism would have to be understood. Thus far QM is not understood, some physicists would argue against even trying to understand it (others would argue the opposite). When a layman says QM proves X then you must view this claim with high suspicion as what they are saying is that 'this thing I don't understand' proves X.

You are engaging in logical fallacies here.
I never said 'proves' anything, nor did Wilson.
Moving the goalposts?
(Truth is "inclusive"!)
You are making all sorts of demands, that need to be fulfilled (impossible demands at that) before anything can be examined? Like the evidence?
You are attempting to hatchet job me as a means of.. what, avoiding a discussion of what understanding and evidence we do see that supports what I said? Left handed ad-hom?

A=A is an axiom. It's a decent axiom. If you can come up with better then please publish your work and I'll look forward to reading it (I hope you get rich and famous).

And now the sarcasm? (sheesh!)
If you had read carefully, the claim was INCLUSIVE! Yes, A=A, but also... etc...
All are Truth!
That was Aristotle's error, his either/or but not both was his fatal flaw.

I've read Aristotle's work and personally I was impressed. I think if you come up with a theory that contradicts formal logic then you will need some exceptional justification.

I don't need a theory, QM has one, and it has been correct in it's predictions... 100% of the time!
And this isn't even theory, IT'S perceived EVIDENCE that contradicts (as science has been doing for decades) the exclusivity of any single Perspective as 'The Truth' (tm)!
This, in itself makes all the logic in the world that we have been muddling through our existence nothing more than a sharpened piece of flint pragmatism because we don't perceive the higher, deeper Reality that QM describes, yet (other than in 'bits and pieces', and this is one of them)!

Formal logic is a tool, a useful tool, a tool no one has bettered, treat it as such.

It is my experience that 'formal logic' is how liars prove that black is green, having bupkis to do with Reality/Universality!
Yes, it is a very specialized tool, a very local specialized tool, like a Rubic's Cube, or a bone arrowhead! *__-
Mental masturbation.
But it feels good, and works in our little corners.
For the moment.
It will be soon obsolete.

I don't throw away my hammer if it can't saw a branch.

Your hammer has been driving those screws for a long time.
You are used to it, it works rather well when you soap 'em up.
You are comfortable with the whole idea.
As we learn the nature of a good screw, we might just replace the hammer with a screwdriver (or kill the messenger).
And the world became a different place! *__-

[Eduk]

Your hammer has been driving those screws for a long time.

Yes of course I am being sarcastic. But at the same time if you could obsolete formal logic then that would be an amazing achievement. You would indeed become quite famous. And I would genuinely enjoy reading your book. Of course the sarcasm comes in that my expectation of you achieving such a goal is zero.

It is trivial really. If you say formal logic will soon be obsolete then demonstrate it. Make it obsolete. The rewards for doing so will make writing on this forum seem, by contrast, a complete waste of time.

[Namelesss]

"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." -Robert Anton Wilson

A statement which is all of the above will generally turn out, on closer inspection, to be many different statements, and possibly value judgements, rolled into one. A statement which is true in some circumstances but not in other circumstances is not a single statement.

Yes, Wilson's quote is comprised of numerous statements, all true. So?
'True' and 'false' are no more than two mutually arising opposite Perspectives of the same event, as are all apparent dualistic opposites!
It's true, she's pretty/it's false, she's homely!
Same woman, different truth, different Perspective, SAME MOMENT. Holistic.
Reality/Truth is 'inclusive'! ALL inclusive!

For example, you may say that the statement "it is raining" could be true in one place and false in another, or true in one sense and false in another, depending on your definition of the word "rain".

Yep! And all true!

[Eduk]

I don't need a theory, QM has one, and it has been correct in it's predictions... 100% of the time!

Sorry I have never read anything about QM making any claims on formal logic. QM deals with matter at the quantum level, not formal logic. Or at least to be precise I've never read anything written by a physicist which was the scientific consensus and directly arrived from QM. I have read lots of nonsense from people who know nothing about QM.