Are the rules of logic immutable?

[OccamsRazor]

In the past my philosophical stance was always based on a single overarching truth. This was that the laws of logic and mathematics were immutable and could not be changed for any description of reality that one may provide.

More recently I have been grappling with the question, what if the rules of logic and mathematics are not immutable but subjective or specific to our incarnation of reality?

In Michael Frayn's book The Human Touch he makes the statement:

Logic is just a system we have made up, not an inherent condition of the natural world.

Is this true? Is logic changeable?

In another thread I saw the following statement:

I don't quite know how knowing something about events inside a system from outside of the system is on the same level of impossibility as a logical impossibility. There cannot be a square circle, a rational root of a prime number or the simultaneous existence of an irresistible force and an immovable object. These are logical impossibilities..

Is this true? Could a being outside our own manisfestation of material reality not create such logical impossibilities?

I can see that here many readers of this post would begin to state that logic and mathematics were immutable. That there indeed could not exist a rational root of a prime number and these are objective truths.
This leads on to the question, how may one prove it? Bearing in mind that any proof of the immutability of logic must have its basis in logic. The question is, how can immutable logic prove istelf to objectively exist?

If we then decide that, possibly, logic is not immutable then where does this leave us? Can we ever make a metaphysical argument without firstly assuming that mathematics and logic are immutable?

[Bugmaster]

If you want to call some things thinking like intentional behavior. Then Ok.
But at the core of thinking there is what I can only see as a universal subset of rules that will be common to every thinker, not because it is found to be common, but they need to be following these rules to be able to think clearly.

Right, so what you're saying is, "our way of thinking is the only possible way of thinking". You might be right, I don't know, but your statement is strong enough to merit additional justification.

With these propositional forms we can say things like
"All swans are white"
"All swans are not tigers"
"Some men are fathers"
Some men are not fathers"
These are basic logical relationships.

Yes, but even on our own planet, we have logic that doesn't follow these rules. For example, we have "fuzzy logic" that uses probabilities, not boolean true/false statements. We have neural networks that come to a conclusion in parallel, without going through a logical chain of arguments; some of these networks act as intuition in our own brains, and some we have constructed to grow radio antennae for us and whatnot. And that's just the things off the top of my head; I'm sure there are more. And that's just on Earth !

Nonetheless, I would agree with you that it is unlikely that radically different ways of thinking may not exist, and in fact probably do not exist. But, you are saying that they cannot exist, and I just can't justify that.

The gun turrest seems a threat, but that could just be threatening bevahiour without any thinking actually going on. It is probably safer to presume there is thinking going on behind that behaviour otherwise how are we to negotiate our surrender?

No, it's always safer to find out what's true, as opposed to what's convenient. I agree with you that your first action on seeing that alien gunship should be to try and communicate with it, assuming that it's crewed by people who think like we do -- but only because this situation is more likely, not because it'd be more convenient.

[Furrowed Brow]

Hi Bugamster

If you want to call some things thinking like intentional behavior. Then Ok.
But at the core of thinking there is what I can only see as a universal subset of rules that will be common to every thinker, not because it is found to be common, but they need to be following these rules to be able to think clearly.

Right, so what you're saying is, "our way of thinking is the only possible way of thinking". You might be right, I don't know, but your statement is strong enough to merit additional justification.

Buggy, I'm not an imperialist that expects every other culture to adopt our queen, judicial system, civil service and logic. The first three are contingencies, whilst the fourth is not. I really don't think rules like "that thing is not like that other thing" are our way of thinking, therefore they must be universal. I think they are universal so that is the way we have to think.

Yes, but even on our own planet, we have logic that doesn't follow these rules. For example, we have "fuzzy logic" that uses probabilities, not boolean true/false statements. We have neural networks that come to a conclusion in parallel, without going through a logical chain of arguments; some of these networks act as intuition in our own brains, and some we have constructed to grow radio antennae for us and whatnot. And that's just the things off the top of my head; I'm sure there are more. And that's just on Earth !

Ok. I'm going to agree that some large part of human behavior derives from fuzzy logic. And that neural nets are very effective at pattern recognition. And that these and perhaps other methodologies help the human brain and nervous system negotiate their environment.

But are you saying neural cannot comprehend a position like "that thing there is not like that thing there" or fuzzy logic cannot comprehend that thing there is 100% not like that thing there".

The methodologies might be different, their ability to express alternatives may be more comprehensive, and subtle than true/false logic. But that is perhaps my point. Propositional logic, and predicate logic can only be universals if there basic logical connectives are subsumed by all alternative logics.

[LightGrenade04]

In the past my philosophical stance was always based on a single overarching truth. This was that the laws of logic and mathematics were immutable and could not be changed for any description of reality that one may provide.

More recently I have been grappling with the question, what if the rules of logic and mathematics are not immutable but subjective or specific to our incarnation of reality?

That's impossible. If you were to argue, "The rules of logic are subjective" that statement itself actually presupposes the Law of Noncontradiction and the Law of Excluded Middle. In denying the objectivity/reality of Logic, it actually must use Logic itself, thus it is self-referentially incoherent. The Medieval Islamic philosopher Avicenna once humorously wrote (well, I at least hope he intended this to be humorous!):

"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."

In Michael Frayn's book The Human Touch he makes the statement:

Logic is just a system we have made up, not an inherent condition of the natural world.

Is this true? Is logic changeable?

Again, no for any denial of the laws of logic must use them in doing so. It's an absurd argument Frayn makes in his book - which is startlingly "out of touch". Jerry Fodor recently ripped it to shreds in the London Review of Books and even his wasn't its most damning criticism.

In another thread I saw the following statement:

I don't quite know how knowing something about events inside a system from outside of the system is on the same level of impossibility as a logical impossibility. There cannot be a square circle, a rational root of a prime number or the simultaneous existence of an irresistible force and an immovable object. These are logical impossibilities..

Is this true? Could a being outside our own manisfestation of material reality not create such logical impossibilities?

I can see that here many readers of this post would begin to state that logic and mathematics were immutable. That there indeed could not exist a rational root of a prime number and these are objective truths.
This leads on to the question, how may one prove it? Bearing in mind that any proof of the immutability of logic must have its basis in logic. The question is, how can immutable logic prove istelf to objectively exist?

Why should it have to? Is it really so odd or intellectually taxing to accept: A=A; ~(P and ~P); and P v ~P that they need to be empirically falsified? Anyway, they couldn't be even if we insisted on it. They are indemonstrable because anyone who wishes to deny them uses them in denying them, thus begging the question and if anyone wished to prove them, he would have to use them in doing so, and this would be circular. Thus, they are literally undeniable first principles of reasoning. The fact that they cannot be empirically verified/falsified in no way detracts from their truth.

If we then decide that, possibly, logic is not immutable then where does this leave us? Can we ever make a metaphysical argument without firstly assuming that mathematics and logic are immutable?

More than that, we could not even formulate rational sentences which could be impregnated with propositions to analyze, reflect on, etc. All communication and rational thought would be impossible.

[Bugmaster]

I really don't think rules like "that thing is not like that other thing" are our way of thinking, therefore they must be universal. I think they are universal so that is the way we have to think.

Sure, this is possible, but why do you think so ? In other words, can you logically prove that this is the case, or can you offer some evidence for why this is overwhelmingly most likely the case ?

But are you saying neural cannot comprehend a position like "that thing there is not like that thing there" or fuzzy logic cannot comprehend that thing there is 100% not like that thing there".

Of course not; clearly, we can comprehend it with our brains, which are made of neural networks. I was merely pointing out that other ways of thought are at least possible; because some of them exist right here on our own planet. In fact, our own brains do not think logically at the lowest level; logic is an abstraction that we've built (or, rather, evolution has built for us) on top of neural networks. It's conceivable that, on some other planet, evolution has worked differently.

[Bugmaster]

That's impossible. If you were to argue, "The rules of logic are subjective" that statement itself actually presupposes the Law of Noncontradiction and the Law of Excluded Middle. In denying the objectivity/reality of Logic, it actually must use Logic itself, thus it is self-referentially incoherent.

All you've proven is that it's impossible to use logic to prove that logic is false. This does not mean that logic is necessarily true; nor does it prove that logic is necessarily universal. By analogy, I can't use Euclidean geometry to measure angles on a hyperbolic surface, but that doesn't mean that hyperbolic surfaces don't exist, or that all surfaces are flat -- at least, not necessarily so.

[Furrowed Brow]

Sure, this is possible, but why do you think so ? In other words, can you logically prove that this is the case, or can you offer some evidence for why this is overwhelmingly most likely the case ?

Well no. But that is the point about formal logical. You can prove a conclusion follows from a premise, but you cannot prove an axiom. They are taken to be self evidently true, because we are unable to comprehend how they might possibly be false. The 'unable to comprehend' not being contingent on finding out some new knowledge that will improves our comprehension.

I was merely pointing out that other ways of thought are at least possible; because some of them exist right here on our own planet.

Well yes. Lets take fuzzy logic as one example. This kind of logic offers more than true/false logic of the propositional or predicate calculi. However even fuzzy logic has a limiting case. At the extremes something can be 100% true, or 100% false. Thus true/false are the limiting conditions of fuzziness. Rather than being contradicted, or found to be irrelevant, the rules of logic that apply to true/false propositions are subsumed into a larger set of rules as the limiting conditions. They just can’t be shaken off - which is what we would expect if they are universal.

In fact, our own brains do not think logically at the lowest level...

You’ll need to expand on that point. I’m not sure what you have in mind.

...logic is an abstraction that we've built (or, rather, evolution has built for us) on top of neural networks. It's conceivable that, on some other planet, evolution has worked differently.

I can agree evolution has built brains that are well suited to thinking logically. No problem putting the question that way. And I can agree that when we try to express the rules of logical in formal notation - then this is an abstraction. And I can agree different kinds of brains could use different types of physical processes to think through problems. However, if they are using the rules of the predicate calculus or fuzzy rules, we could quickly learn how they think - because these rules have a generality/universality. To really surprise us they’d have to be using a form of logic we have never thought of before, and could never understand. If that were the case then we would probably not recognise that they were thinking beings; though their existence would prove that logic was not universal.

[achilles12604]

That's impossible. If you were to argue, "The rules of logic are subjective" that statement itself actually presupposes the Law of Noncontradiction and the Law of Excluded Middle. In denying the objectivity/reality of Logic, it actually must use Logic itself, thus it is self-referentially incoherent.

All you've proven is that it's impossible to use logic to prove that logic is false. This does not mean that logic is necessarily true; nor does it prove that logic is necessarily universal. By analogy, I can't use Euclidean geometry to measure angles on a hyperbolic surface, but that doesn't mean that hyperbolic surfaces don't exist, or that all surfaces are flat -- at least, not necessarily so.

Once again I am forced to agree with a non-theist. In my recent experiences I am discovering that Logic itself is in the eye of the beholder. Logic is based on preconceptions of what is true. Preconceptions are extreamly subjective.

For example a man walks into a public park and promptly shoots another man in the head killing him. He is of course arrested and sent to prison. We would say that his actions were totally illogical.

But what if the first man was from the future and knew that the second man was about to set off a nuclear device in down town Tokyo? Now his actions seem much more justified. Our preconception of what we think happened was incorrect. Thus our logic was not incorrect as far as we were concerned, but it was flawed in a larger picture.

Applying this to our forum here, miracles are a violation of the natural. They are a "logical impossibility" for a non-theist. However they are totally logical for a theist because the theist has a different preconception about the laws of the universe and of nature.

So both people using logical analysis can come to totally opposite conclusions. Hence, logic is subjective.

[Furrowed Brow]

For example a man walks into a public park and promptly shoots another man in the head killing him. He is of course arrested and sent to prison. We would say that his actions were totally illogical.

But what if the first man was from the future and knew that the second man was about to set off a nuclear device in down town Tokyo? Now his actions seem much more justified. Our preconception of what we think happened was incorrect. Thus our logic was not incorrect as far as we were concerned, but it was flawed in a larger picture.

I have something else in mind when using the word logic than how you are using it here. Trying to fit an interpretation of someone's behavior into an explanatory framework that makes sense is not what I have in mind. So I would substitute the word "illogical" as you use above with the word "unreasonable".

The rules of logic are empty of content. They are a syntax that determine whether a conclusion follows from a premise in a systematic way. These rules can be coded into a formal language, and they have the kind of self evidence that one also sees in mathematics e.g. "1 + 1 = 2". So if someone insisted "1 + 1 = 3" we would say they are not thinking straight, or do not understand what they are saying. Now if someone said they could prove "1 + 1 = 3" we might think they were joking. But if they are serious and write down a bunch of notation to prove their point, they would then either prove they do not understand "1 + 1 = 2"; or we would not understand how the proof could possibly be valid, because they would be thinking in a totally different way to us.

[LightGrenade04]

That's impossible. If you were to argue, "The rules of logic are subjective" that statement itself actually presupposes the Law of Noncontradiction and the Law of Excluded Middle. In denying the objectivity/reality of Logic, it actually must use Logic itself, thus it is self-referentially incoherent.

All you've proven is that it's impossible to use logic to prove that logic is false. This does not mean that logic is necessarily true; nor does it prove that logic is necessarily universal.

What I've shown is that Logic is literally undeniable regardless of the linguistic group, geographic location, or anything else involved. What you do when you deny it is effectively saw off the very branch you're sitting on. Using Reason to prove there is no Reason is simply a nonsensical and meaningless endeavor and it doesn't cast any doubt whatsoever on the truth - more than that the necessary truth - of the first principles of reason.

By analogy, I can't use Euclidean geometry to measure angles on a hyperbolic surface, but that doesn't mean that hyperbolic surfaces don't exist, or that all surfaces are flat -- at least, not necessarily so.

That's a false analogy, Logic is the study of proper reasoning itself, nothing is more foundational or self-evident. Thus, the very truth value of the thesis of this thread - that Logic is merely a projection of human minds - is necessarily determined by the very rules of it purports to deny. It is, itself, necessarily either true or false. To suggest otherwise is a literally meaningless proposition even if it can be expressed in a grammatically correct sentence.

[LightGrenade04]

Once again I am forced to agree with a non-theist. In my recent experiences I am discovering that Logic itself is in the eye of the beholder. Logic is based on preconceptions of what is true. Preconceptions are extreamly [sic] subjective.

And we are to assess your assertion here as either true or false, are we not?

For example a man walks into a public park and promptly shoots another man in the head killing him. He is of course arrested and sent to prison. We would say that his actions were totally illogical.

But what if the first man was from the future and knew that the second man was about to set off a nuclear device in down town Tokyo? Now his actions seem much more justified. Our preconception of what we think happened was incorrect. Thus our logic was not incorrect as far as we were concerned, but it was flawed in a larger picture.

All this thought experiment proves, if anything, is that we the observers of this action drew a false conclusion about the behavior of the first man. It's wildly fallacious to say, "Well, guess we were wrong about that guy. Looks like the patterns, structures, and inferences of reasoning I used in drawing that conclusion are really just illusions generated by the hive-mind of humanity". The very point you're trying to make with this analogy actually depends on the objectivity of the laws you're trying to do away with.

Applying this to our forum here, miracles are a violation of the natural. They are a "logical impossibility" for a non-theist. However they are totally logical for a theist because the theist has a different preconception about the laws of the universe and of nature.

Again, I think there's some significant confusion here. Miracles are not "logical" or "true" for the theist and "illogical" or "impossible" for the non-theist. The possibility and/or actuality of miracles does not depend on any human mind. They either exist or they don't. The non-theist says, "Miracles are impossible" the theist says, "Miracles are not only possible, they've actually happened"; the theist and the non-theist cannot both be right in this. Their propositions are mutually exclusive. One of them is wrong.

So both people using logical analysis can come to totally opposite conclusions. Hence, logic is subjective.

That's a a total non sequitur. Disagreement between people does not render the very fact of reasoning itself with its rules and structures to be subjective qualities. The simple fact of our disagreement doesn't collapse reality into solipsism (and solipsism actually is the consequence entailed by your thesis here). I don't really think you entirely grasp what you're saying here; if you're right, then you wouldn't still be trying to defend your thesis. It's impossible to be wrong on your view.