What exactly are the three laws of logic? Is there a word for it?

[Fanghur]

Does anyone know what exactly the three laws of logic - Identity, Non-Contradiction and Excluded Middle - are? To be clear, I am not referring to the statements, but rather the 'things' that those statements are referring to? What do you call something which all of existence is contingent on?

 

Is there even a word for what they are? Or does it fall into the category 'they simple ARE'?

[Ophiolite]

These are the Laws of Thought. Wikipedia has articles on non-contradiction, excluded middle and identity.

 

A google search on the three together returns many links - almost half a million. You may find something more relevant to your questions there.

 

As someone struggling to be considered even a neophyte in the field I find the Standford Exncyclopedia of Philosophy invaluable for both overview and quite detailed exposition on matters philosophical.

[Fanghur]

I know what the three laws of logic are and what they say. What I am not certain about is what they actually are; what is their nature? They aren't physical, they aren't material, they aren't conceptual because they would apply even if no minds existed, they are completely non-contingent on anything whatsoever because they would apply even to absolute nothingness if such a thing existed. So what would be a word that describes their nature? Does one even exist?

[ydoaPs]

Does anyone know what exactly the three laws of logic - Identity, Non-Contradiction and Excluded Middle - are? To be clear, I am not referring to the statements, but rather the 'things' that those statements are referring to? What do you call something which all of existence is contingent on?

 

Is there even a word for what they are? Or does it fall into the category 'they simple ARE'?

There's really no such thing as "laws of logic", but I think you're referring to three tautologies of bivalent sentential logic that people think are special for some reason. That would be pv~p, p=p, and ~(p&~p) (which is actually the same as pv~p).

 

they aren't conceptual

Yes, they are.

because they would apply even if no minds existed

No, they wouldn't. Logics are invented, not discovered. Sentential logic is just the one that most closely approximates how thoughts relate to each other.

[ydoaPs]

Actually, now that I think about it, all three of those propositions are equivalent.

[Ophiolite]

I agree with ydoaPs's first post, but assuredly not his second.

 

The word you are looking for is immaterial. I am confident you will disagree, but that would be a mistake.

[Prometheus]

Logics are invented, not discovered.

 

Now this interesting. So if we were to say something like an object cannot be black all over and white all over at the same time, it would be something we invented rather than discovered? It is difficult though to imagine that without minds that this would not be the case. I assume i am missing something?

 

Also i have heard mathematical objects have been said to have an existence independent of the mind (Platonic). I have also heard it said that mathematics is a form of logic. If these are true would it not suggest that logics are discovered rather than invented? Are they true?

[ydoaPs]

Now this interesting. So if we were to say something like an object cannot be black all over and white all over at the same time, it would be something we invented rather than discovered? It is difficult though to imagine that without minds that this would not be the case. I assume i am missing something?

Logics are indeed invented. The one most people know about is an approximation of how ideas (and, thus our descriptions of the macroscopic world) relate to one another. There are cases when it fails to accurately describe reality. For instance, take the spin of an electron. It can act like it is spinning clockwise, or counterclockwise. We can, however, make it so that it acts like it is spinning clockwise and counterclockwise at the same time. That is, if we say p:the electron is spinning clockwise, we get p&~p which is a contradiction in classical bivalent logic.

 

Also i have heard mathematical objects have been said to have an existence independent of the mind (Platonic).

That's been dead since Plato.

I have also heard it said that mathematics is a form of logic.

Mathematics and logics are formal systems, but mathematics aren't logics and logics aren't mathematics. You can, however, build mathematical systems using second order quantified logics in conjunction with set theory.

 

I agree with ydoaPs's first post, but assuredly not his second.

 

The word you are looking for is immaterial. I am confident you will disagree, but that would be a mistake.

~pvp is the same thing as p->p (they're contrapositives of each other). p=p is (p->p)&(p->p) which is the same as p->p which is ~pvp. ~(p&~p) is the same as (via De Morgan's rule) ~pvp.

[PeterJ]

Aristotle's logic works fine for QM. It just needs to be applied properly. It rarely is.

 

Usually people take some apparent contradiction - wave/particle, x-spin/y-spin etc - and assume that A's laws apply to them before confirming that they would in fact conform to A's definition for a true contradiction. This causes havoc in philosophy and some trouble in physics. It leads Heisenberg to the view that A's logic must be modified for physics. Actually it just needs to be applied more carefully than usual.

 

As to what the laws are, they are a formal description of how people naturally think, and all animals so it seems, or the ideal to which their thinking process aspires.

[Ophiolite]

.

As to what the laws are, they are a formal description of how people naturally think, and all animals so it seems, or the ideal to which their thinking process aspires.

 

This would imply that people think logically. Do oyu have any evidence to support this?

 

As to an ideal of thinking process, my most effedtive work is achieved when I ignore, or outright reject non-contradiction.

[ydoaPs]

Aristotle's logic works fine for QM.

No, it doesn't. Aristotle's logic doesn't even work for beliefs, necessity, or time. Not all logics are created equal.

As to what the laws are, they are a formal description of how people naturally think

It most certainly is not. Humans suck at doing logic naturally.

.

 

This would imply that people think logically. Do oyu have any evidence to support this?

No, because it's false.

[Fanghur]

There's really no such thing as "laws of logic", but I think you're referring to three tautologies of bivalent sentential logic that people think are special for some reason. That would be pv~p, p=p, and ~(p&~p) (which is actually the same as pv~p).

 

Yes, they are.No, they wouldn't. Logics are invented, not discovered. Sentential logic is just the one that most closely approximates how thoughts relate to each other.

Wait a minute, let me get this straight. You're saying that, hypothetically, if the universe were exactly the way it is not but with the sole exception being that there were no minds, then the law of identity wouldn't apply? A rock in that mind-less universe wouldn't be a rock? That something wouldn't be what it is and not be what it isn't? That's absurd.

 

And just for the record, I am NOT arguing TAG and I think Matt Slick is a complete idiot. So please nobody get the impression that I'm doing that. The laws of identity, non-contradiction and excluded middle are NOT logic. They are the foundations which make logic possible. To say that because logic is conceptual therefore the 'logical absolutes' are also conceptual is a fallacy of division.

Edited February 20, 2013 by Fanghur

[ydoaPs]

Wait a minute, let me get this straight. You're saying that, hypothetically, if the universe were exactly the way it is not but with the sole exception being that there were no minds, then the law of identity wouldn't apply? A rock in that mind-less universe wouldn't be a rock? That something wouldn't be what it is and not be what it isn't? That's absurd.

 

And just for the record, I am NOT arguing TAG and I think Matt Slick is a complete idiot. So please nobody get the impression that I'm doing that. The laws of identity, non-contradiction and excluded middle are NOT logic.

Read by posts again.

They are the foundations which make logic possible. To say that because logic is conceptual therefore the 'logical absolutes' are also conceptual is a fallacy of division.

There is no such thing as "logical absolutes".

[Prometheus]

Logics are indeed invented. The one most people know about is an approximation of how ideas (and, thus our descriptions of the macroscopic world) relate to one another. There are cases when it fails to accurately describe reality. For instance, take the spin of an electron. It can act like it is spinning clockwise, or counterclockwise. We can, however, make it so that it acts like it is spinning clockwise and counterclockwise at the same time. That is, if we say p:the electron is spinning clockwise, we get p&~p which is a contradiction in classical bivalent logic.

 

 

Similar to Schrodinger's cat which can be both alive and dead, though by logic this should be impossible? Interesting.

 

What use in logic then, if empiricism can be found to contradict it? Is it to be regarded only as a pragmatic tool?

 

That's been dead since Plato.

 

The opening of this entry would seem to suggest that the topic is still debated.

[ydoaPs]

Similar to Schrodinger's cat which can be both alive and dead, though by logic this should be impossible? Interesting.

 

What use in logic then, if empiricism can be found to contradict it? Is it to be regarded only as a pragmatic tool?

There's no such thing as capital L Logic. You need to use the logic suited to the task. For example, the standard example of logical syllogism (All men are mortal. Socrates is a man. Therefore, Socrates is moral) is invalid on standard sentential logic. You need to use a more powerful logic (first order quantified logic) for it to be valid.

[Fanghur]

Read by posts again.There is no such thing as "logical absolutes".

First of all, what we refer to them as is unimportant. Even though Matt Slick's argument is completely flawed and fallacious, the term he coined for Identity, Non-Contradiction and Excluded Middle, namely 'logical absolutes', strikes me as an appropriate one, therefore I will use that term to save time.

 

I did read your posts; you said that the three 'logical absolutes' WERE conceptual and would NOT apply if no minds exist. Those assertions are both flawed and, in the case of the latter, nonsensical. It is true that our mathematical depiction of what those laws mean is conceptual; the statements "A = A", "A ≠ NOT A", and however one would mathematically depict the law of excluded middle, could not exist if we didn't create them. However, to say that because we have a concept in our minds of the three logical absolutes, the logical absolutes themselves are therefore conceptual is a logical fallacy. It is analogous to saying "I have a concept of an apple, therefore apples are conceptual". And to say that the logical absolutes ARE logic is another logical fallacy; it is saying "because logic is conceptual, the foundations upon which logic is based are also conceptual."

 

Now if this is not what you actually meant, then could you please clarify?

[ydoaPs]

First of all, what we refer to them as is unimportant. Even though Matt Slick's argument is completely flawed and fallacious, the term he coined for Identity, Non-Contradiction and Excluded Middle, namely 'logical absolutes', strikes me as an appropriate one, therefore I will use that term to save time.

Giving examples is not the same thing as defining. Guess what, they're just three forms of the same tautology. It's not even special, since all theorems are tautologies. Citing three equivalent forms of the same proposition in no way tells us what a "logical absolute" is.

I did read your posts; you said that the three 'logical absolutes' WERE conceptual and would NOT apply if no minds exist. Those assertions are both flawed and, in the case of the latter, nonsensical.

Uninterpreted, logic is just manipulation of meaningless symbols. Given the standard interpretation, it's called "PROPOSITIONAL Calculus" and, as the name suggests, is about propositions. In a world with no minds, there are no propositions. So, yeah, logic doesn't exist if there are no minds.

 

The only thing logic has to do with is how ideas structurally relate to one another. That's it. Nothing more.

[Fanghur]

Giving examples is not the same thing as defining. Guess what, they're just three forms of the same tautology. It's not even special, since all theorems are tautologies. Citing three equivalent forms of the same proposition in no way tells us what a "logical absolute" is.

Uninterpreted, logic is just manipulation of meaningless symbols. Given the standard interpretation, it's called "PROPOSITIONAL Calculus" and, as the name suggests, is about propositions. In a world with no minds, there are no propositions. So, yeah, logic doesn't exist if there are no minds.

 

The only thing logic has to do with is how ideas structurally relate to one another. That's it. Nothing more.

Yes, but what I am referring to the three logical absolutes are NOT logic. If no minds existed in the universe, what we know of as being a rock WOULD still be a rock, and would still not NOT be a rock. Therefore the ontological nature of the three tautologies would STILL apply to that universe. That is what the three tautologies are really saying. Otherwise you are essentially arguing for a solipsistic universe in which nothing exists unless someone observes it, and that is nonsense.

[ydoaPs]

Yes, but what I am referring to the three logical absolutes are NOT logic.

That's because there's no such thing as a "logical absolute".

[Fanghur]

That's because there's no such thing as a "logical absolute".

Fine, call it whatever you want then. Please address my objections rather than correcting my terminology.

[imatfaal]

If a tree falls in a forest, and there is no one around, is it a tree? Badly mangling a quote of Bishop Berkeley which he never actually said in the first place.

 

You seem to be positing a toy universe which by definition contains everything, everyone and everything, which we are commenting on from our universe which also by definition contains everything, everyone, and everytime; yet you find the idea of a solipsism absurd - surely the only way your toy universe could exist is purely within one's own mind? What is ontology without the presumption of a mind to study the nature of being?

[Fanghur]

If a tree falls in a forest, and there is no one around, is it a tree? Badly mangling a quote of Bishop Berkeley which he never actually said in the first place.

 

You seem to be positing a toy universe which by definition contains everything, everyone and everything, which we are commenting on from our universe which also by definition contains everything, everyone, and everytime; yet you find the idea of a solipsism absurd - surely the only way your toy universe could exist is purely within one's own mind? What is ontology without the presumption of a mind to study the nature of being?

I quite honestly have no idea what you mean. A solipsist is someone who believes that they are the only thing in existence and everything else is just a figment of their imagination; ie. they believe that reality is subjective rather than objective. That is what I said was absurd.

Edited February 21, 2013 by Fanghur

[imatfaal]

I quite honestly have no idea what you mean. A solipsist is someone who believes that they are the only thing in existence and everything else is just a figment of their imagination; ie. they believe that reality is subjective rather than objective. That is what I said was absurd.

 

"if the universe were exactly the way it is not but with the sole exception being that there were no minds," and yet you are commenting on that universe and the nature of its ontology. The universe is everything - yet you are starting your argument with a universe lacking any interrogator or observer; further you are then making observations and questioning ideas within that universe.

 

How can you possibly be considering doing that without acknowledging it must be a purely imaginative speculative entity residing entirely within your consciousness? If the universe is merely a speculation, clearly unreal and totally contained within an individual's conception can you not see the parallels with solipsism?

[ydoaPs]

Fine, call it whatever you want then. Please address my objections rather than correcting my terminology.

You still seem to be missing what logic is about. Logic isn't about rocks, trees, or gods; it's about ideas. What's more, it's not even about the content of the ideas (you'll need probability theory for that)-it's just about the structure. Logic is the calculus of how ideas relate to each other. That's it. It has absolutely nothing to do with anything in the universe other than ideas.

 

That being said, logics aren't absolute. There are cases where basic bivalent sentential logic is inadequate. It doesn't work for QM, since it is bivalent and reality on the quantum level isn't. That is, our ideas about reality will be contradictions in sentential logic if they accurately describe the QM world.

 

 

It doesn't work for most of English (or any natural language, for that matter). It can't handle adjectives, verbs, or quantities (which is why we usually use first order quantified predicate logics rather than simple sentential logics). It also can't hand what we call "modalities"-things like tense, causal connection, belief, necessity/contingency, and moral obligation.

 

There is nothing "absolute" about logics. When one doesn't work, we make a new one.

[Fanghur]

You're right, there is nothing absolute about LOGIC. What I am talking about, though, is NOT logic. They are fundamental properties of existence itself which the three tautologies I mentioned are our representations of. If those weren't properties of existence, logic would not work, because truth statements would be impossible to make. I have made that point several times already and yet you keep going back to logic and making the same fallacy of division over and over again. Where is the disconnect here?

 

And by the way, just because we are unable to perceive order at the quantum level does not necessarily mean that it truly is completely devoid of a consistent nature. To make an analogy, if you have a repeating sequence of random numbers a googleplex figures long, it does indeed have an underlying order and is not truly random, but it would be impossible for us to perceive the underlying structure of the sequence. I have always felt that quantum mechanics may operate in an analogous way.