Doesn't quantum physics undermine the laws of logic that we use to prove the existence of God?
Comments
Greg made a point in the video that has general applicability. Even for the Copenhagen interpretation (which he unnecessarily allowed, might pose some problems for the laws of logic). Namely that Quantum Mechanics along with everything else, requires that the laws of logic be true.
Here's another way to see this:
The Copenhagen interpretation implies the Equations of Quantum Mechanics. (Otherwise, how is it an interpreation of QM?)
The Equations of Quantum Mechanics imply the Axioms and Theorems of Mathematics. (Otherwise, how are they equations?)
The Axioms and Theorems of Mathematics imply the Laws of Logic (Otherwise, how are they axioms and theorems?)
The only reputable philosopher I know of who has ever questioned logic in light of QM is Hilary Putnam. (Quine, in his (in)famous Two Dogmas of Empiricism also gives a nod to Putnam.)
Putnam's point was that the way we use the words "not", "either-or", "both-and", "neither-nor", "is" and so forth in everyday life might not be the most convenient way of speaking in discussions of Quantum Physics.
Now, it's perfectly true that the marks "or", "and" and the rest have the meaning they have only because English speakers have adopted a convention that they should have the meaning they have. We could, for example, decide to all stop speaking English and start speaking Pig Latin only. In that case, the symbol "not" would have no meaning. It would be replaced by the symbol "otnae". But we could also replace the operator-terms of logic in our old way of speech with terms that do not have any direct mapping to terms in our new convention of speech. And that's what Putnam was suggesting.
Putnam was right to appeal to convenience. That's often the reason we change conventions. We could, for example, eliminate the operator terms "not", "and", "or" in terms of the single operator "nor". The reason we don't is that it would be horribly inconvenient to do so.
It's well worth noting that very few people have been inclined to follow Putnam's lead and use the terms of logic differently or to introduce new terms for a new QM-savvy logical parlance. So I don't think Putnam is right about the greater convenience of a putative QM-talk. Part of the problem also is that Putnam was never entirely clear about what this new way of speaking would be.
Where we get into real trouble is when we confuse the way of words with the way of things. Suppose that, for whatever reason, we did change our terminology so that "and" meant something different. In that case, it might turn out that there is nothing contradictory in saying "Grass is green and grass is not green."
Would that problematize our old friend, the Law of Contradiction?
No. Of course not. We're speaking a different language both when we make our claim about the color of grass, and when we say "There can be no proposition, A, such that 'A and not-A' is true" The old way of expressing the Law of Contradiction no longer expresses the Law of Contradiction.
Under our old way of speaking, the expression of the Law of Contradiction had a certain meaning. That meaning would be expressed differently in the new speech. The meaning might just be expressed differently in a single correlated expression. But it is also possible that the meaning would be distributed over a number of expressions, or lumped together with something else in a single expression.
I think a lot of the "intimidation" of QM can be negated if we still to the very basic laws of non contraditiction.
For instance...the effects of what is really going on in any so called "quantum leap" is not really understood by anyone that I know of. However....we do not NEED to know every aspect of what is driving the phemonenon. What we DO know..(because of the laws of non contradiction)...it that it is NOT caused by "nothing"...which is what the atheist crowd would like to put forward as the "cause". There most certainly IS a cause for this phenomenon...and we just need to relax when bombarded by all this idea of QM giving evidence of no God Creator being needed. Treat that idea as pure bluster because thats what it is...just like evolution.
Yes...you are correct. Dawkins tries the same stunt all the time when he says he only uses "science" when he comes to his conclusion of no God..."logically". How does he KNOW that there is no God?...Why...just it obvious...so there!
If Dawkins would stop faoming at the mouth over how "unreasonable" religious explanations are, give up on the mantra, and just admit that the true causes of physical penomenon HAVE to have some kind of CausER behind them...he would begin to be rational.
Yes scripture is always right.... which means little to the hard core skeptic. If the atheist used only logic...he wouldn't BE an atheist.
This quantum physics diversion came up in the Craig/Krauss debate. When Krauss brought it up I couldn't help but think that it was an argument to undercut all arguments. Still, I know far less about QP than I should; can anyone recommend a primer for someone who's never taken a physics class?
WisdomLover, you bring up something I've been irritated about regarding language. An On The Media bit from July wrote this: "In February 2010, the last living speaker of Boa died, and with her, the logic, culture, and history of the ancient people." Now I can understand how culture and history are lost by this, but logic? Now, I'm a monoglot with only a hint of Spanish and a few books worth of linguistics in me, but that doesn't sound right. It seems that "logic" is being used where "semantics" would have been appropriate. Though, this is yet another area where I could use some learning.
Quantum Physics is a fancy name to label the physics of really small stuff, like sub-atomic particles (electrons, photons, etc). This is in contrast to really big stuff like planets, cars, and people. Newtonian mechanics is adequate to explain these interactions for most situations.
We have to remember that QP is just another scientific model to explain the observed phenomena. It is a human construct but reality may be very different. This is the nature of all science.
One example of a contradiction apparent in QP is the particle/wave duality of light. Under certain experimental conditions, light can behave like either a particle or a wave. These observations are totally contradictory to each other. The law of non-contradiction says it can't be both, except it is both!
The only thing this tells us is that our scientific models of light fail to adequately explain reality.
I am not a physicist, but do remember a few things from my 2nd year Introduction to Quantum Mechanics class.
I find most people do not understand it.
A QUANTUM LEAP DOES NOT MEAN A HUGE LEAP. It means that it moves from state A to State B, without any intermediary state.
Now that is out of the way, even though the logic required to work in that field is using different assumptions than in the macroscopic realm, physicists can predict things with a high degree of precision using mathematics. It is not a realm where everything is totally random and the laws of large numbers mean that all these quantum "randomness" averages out to the sort of thing we expect in classical mechanics when we get up to the level most of us deal with.
In my experience, if someone brings up Quantum Mechanics it is for one of two reasons. 1- To point out some subtle point that might need to be considered 2- To baffle with BS, hoping that you won't know enough to find the mistake.
There is the issue of the wave particle duality of light as well. However this does not contradict the laws of logic in the sense that light has never been shown (at least by any current experiment) to demonstate both properties at the same time and in the same sense. This is precisely what the law of non contradiction states about A and non A. Also scientists do not use non logic or illogic to determine or probe quantum mechanical laws they use mathematics which is about as logical as it gets. Even the idea of questioning the reliability of logic uses logic. In otherwords we are ironically trying to find out whether logic is as logical as we think it is and are using logical arguments to do so. Fascinating.
Greg is spot on--QM depends critically on the same laws of logic we use to argue for the existence of God.
Pick up any textbook on QM. You will find logic employed to convey the foundations of QM, and logic applied to demonstrate that the equations of QM adequately explain the experimental results.
It's reasonable to consider that quantum physics follows the same laws that macrophysics follows. (Or it is rather more correct to say that macrophysics follows the same laws that quantum physics follows.) The reason that odd behavior is observed at the quantum level is because quantum objects exist by virtue of the laws that also govern their behavior. These laws are essentially temporal distortions. We don't think we observe them macroscopically because we don't know what we are looking at in light of our constituent parts. We only observe their collective behavior.
Therefore, if we can observe anything that has philosophical import it is that existence is contingent on substantial form rather than substance being contingent on existential form.
In the expression, "There can be no proposition, A, such that 'A and not-A' is true" A is the bound variable of a universal quantification.
Any letter or other symbol would do. The variable, A, ranges over all propositions. If you like, here is the same claim without letters: "There can be no proposition that can be both true and false".
Or did you mean to be asking what I think a proposition is? If that's it, then I think a proposition is a certain kind of meaning of utterances.
It is a meaning that can bear truth value. So utterances like "Wow!" and "Dude, where's my car?" have a meaning, but that meaning is not a proposition, since neither of those meanings bear truth value.
And it is a meaning that is fully ramified by the context of utterance. So that if you say "It's raining" in Des Moines, Iowa and I say "It's raining" in Hoboken, New Jersey, we have not uttered the same proposition (even though we've uttered the same sentence), since the context of utterance is different.
Yeah, I think "It's raining" uttered in the same context in which "It is not raining" was uttered would be ruled out.
But I think Trent is wrong in saying "I don't need to wear my raincoat" and "I need to water the lawn" are logically ruled out. There might be other reasons for those things to be true. Maybe I'm in a raincoat advertisement where I need to wear my raincoat (even though it's not raining). And maybe I'm deliberately trying to kill my lawn.
You're not trying to sneak me toward an argument that Shrödigner's cat provides some kind of counter-example to the law of contradiction are you?
Because "The cat is alive" and "The cat is dead" are not logically contradictory (though they are contrary). "The cat is alive" and "the cat is not alive" are. "The cat is dead" and "the cat is not dead" also are.
And it is utterly true that the cat cannot be both alive and not alive at the same time. If the cat is alive, then the box has been opened, and the cat has been observed to be alive. If the cat is not alive, then either the box has been opened and the cat found dead, or the box has not been opened and the cat is neither alive nor dead, but in a superposition of alive and dead eigenstates. Before the box is opened, the cat is neither dead nor alive. After the box is opened the cat is either alive or dead.
There's no tension of QM and logic to be found here.
I'm not sure I know what you mean when you ask what work the law of contradiction does.
I think you are right to see that it is already implied in the definitions that we use to speak about truth, falsehood and all the rest. That shows its foundational nature. If A implies B, then not-B implies not-A. So if everything we say seems to imply the law of contradiction, were that principle false, then nothing we say could be true.
If you like, the 'work' that the law of contradiction does (and here I'm talking about the meaning behind the words that express it) is that it is one of the foundation blocks of all thought. It is a sine qua non of all rational endeavor.
Thanks Jesse. Good question. Though you could have come up with more ways to denigrate your second option.
Reality seems to be describable. Maybe it actually is. I don't know. Give a point to 'reflections of reality'.
So we find it useful to make statements - utterances intended to describe a state of affairs. Give a point to conventions evolved social just.
It seems like what you are saying is that the fact that the world is describable - that you can make statements about it - requires an explanation, and a 'transcendental' one at that. Correct?
Is that what is really behind all these demands to 'ground the laws of logic' - you really want an explanation for why the world is describable?
I can imagine a world where making statements was not useful. I just did. And now you have too. Maybe in that world y'all would require a 'grounding for the laws of illogic'.
We have seen that the LNC is contained in the terms used to state it.
That's the grounding of it. Let there be no more demands for grounding the laws of logic - at least not for the LNC.
If you want to modify the demand for grounding that's fine. You can even say the modified demand is what you meant in the first place. I don't mind. But I need to know clearly what that demand is and that it is the final the end point.
(I would think you would want to know the end point too.)
Please understand. I don't want to chase you around the playground indefinitely.
Bottom line: if these definitions are not accurate reflections of an underlying reality then I fail to see how they are useful.
As to your main point, that the law of noncontradiction is properly grounded in the definitions of 'statement' and 'negation', I owe you the honesty that I'm not convinced. But at this point, I'd need to go back and re-read the initial challenge to frame the present discussion.
Is this the starting point here where you said that you don't believe in self-attesting propositions?
"I can imagine a world where making statements was not useful. I just did."
No, Ron. You uttered the words "a world where making statements was not useful". That's not the same as imagining a world where statements are not useful. To imagine something is to construct a mental image of it (thus imagine). If you've constructed a mental image of that world, you should be able to describe that image. If you can describe the image, then it turns out that statements are useful after all.
"And now you have too."
Nope. I can't do it. I can't do it anymore than I can imagine a round square.
As for the Law of Contradiction,* what exactly do you think people are asking for when they ask for a grounding for it? I'm pretty sure that the fact that every proposition implies the law of contradiction (and every other logical truth) in no way renders the request problematic.
No one is looking for a ground for it as if it were some sort of brute contingency (as the existence of the world is). The grounding question for logic is not metaphysical, but, I suspect, epistemological.
You might try looking at it through Cartesian glasses. Descartes, in his first Meditation, considered four scenarios:
A scenario where we are created by an Omnipotent Evil Demon
A scenario where we are created by a less-than omnipotent being
A scenario where nothing creates us.
A scenario where we are created by an Omnipotent Benevolent God.
In all four cases he found that we have good cause to doubt all of our mental processes, even those that only involve the application of the laws of logic. Descartes reasoned in the remainder of the Meditations that only in scenario 4 is any confidence in our mental processes recoverable.
Thus the foundation of logic turns out to be the existence of a Benevolent God, not because the thesis "God exists" implies the laws of logic. (Of course it does...and so does its opposite.) Instead, it is because the only basis for our ability to reliably use logic is the existence of God.
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*-BTW, I'm not sure why people call it the law of non-contradiction...that's not what Aristotle called it. Who first called it the Law of Non-Contradiction I wonder?
Is your line of thinking similar to what Greg mentioned on the radio a few weeks ago regarding reading and a belief in authors? (One can read while denying authors exist, but no one could read at all if authors didn't exist!)
I didn't hear that show, so I can't be sure. The short description you've given in your post sounds like authors are a metaphysical foundation for written words.
But the existence of written words is a contingent fact of the world. It is quite true that there are such words, but it need not have been true. The fact that it is true calls for some sufficient reason to explain its truth.
No logical truth will fall into the same category. Logical truths are implied by anything and everything. The fact that they are true does not immediately call for a sufficient reason to explain their truth.
What does call for an explanation is the fact that we can use logical truths reliably to construct proofs.
I think you can start (and finish) right here, at the beginning of Chapter 1 of Methods of Logic, 3rd edition, by W.V. Quine.
The peculiarity of statements which sets them apart from other linguistic forms is that they admit of truth and falsity, and may hence be significantly affirmed and denied. To deny a statement is to affirm another statement, known as the negation or contradictory of the first. To deny 'The Taj Mahal is white' is to affirm 'The Taj Mahal is not white'. Note that this negation is opposed to the original not as black to white, but as nonwhite to white; it counts as true in every case except the case of whiteness.
The commonest method of forming the negation of statements in ordinary language is by attaching 'not' (or 'does not', etc.) to the main verb, as in the foregoing example. But if the verb is governed by 'sometimes' or 'always', the negation is formed rather by substituting 'never', or 'not always'. If the statement is compound and thus has no main verb, its negation has to be phrased more elaborately; e.g., 'It is not the case both that . . . and that . . .'. But, despite such irregularities of ordinary language, a little care suffices for constructing a clear negation of any given statement, the guiding consideration being simply this: the negation is to count as false if the given statement is true, and the negation is to count as true under any and all circumstances under which the given statement is false.
The LNC, “opposite assertions cannot be true at the same time”, is right there in the negation is to count as false if the given statement is true, and the negation is to count as true under any and all circumstances under which the given statement is false.
"The fact that they [logical truths] are true does not immediately call for a sufficient reason to explain their truth."
"What does call for an explanation is the fact that we can use logical truths reliably to construct proofs."
Does that mean RonH is barking up the wrong tree?
If I raised the challenge to our friend that logical truths had to be grounded, then I apologize for the ensuing wild goose chase (but I don't recall having raised that challenge).
Either way, we're back to this: RonH's brain, having evolved from random processes, makes statements that cannot be in any sense labeled true, but they are merely 'useful' (whatever that means).
By the way, RonH, I do appreciate your taking the time to thoroughly answer my questions here, even digging up your logic textbook. I was not a philosophy major, so the discussions here have posed to me a steep learning curve (well worth the effort).
No Jesse, I don't think you did raise that challenge. On the other hand, I can't blame Ron for the effort he's made. The question of grounding is always ambiguous, and ipso facto tricky. The question always arises: What kind of grounding?
Ron has argued, correctly, that the laws of logic don't need to be grounded logically. The only problem is that I don't think that anyone was really saying that they did.
I think the issue for logic is how it came to pass that the laws of logic can be reliably put to use. And in that sense it's really as much a question about us as it is about logic. Now the opposing views come directly into contact: Time+chance (Descartes' no-creator scenario) vs. Creation by a Benevolent God.
Greg made a point in the video that has general applicability. Even for the Copenhagen interpretation (which he unnecessarily allowed, might pose some problems for the laws of logic). Namely that Quantum Mechanics along with everything else, requires that the laws of logic be true.
Here's another way to see this:
The only reputable philosopher I know of who has ever questioned logic in light of QM is Hilary Putnam. (Quine, in his (in)famous Two Dogmas of Empiricism also gives a nod to Putnam.)
Putnam's point was that the way we use the words "not", "either-or", "both-and", "neither-nor", "is" and so forth in everyday life might not be the most convenient way of speaking in discussions of Quantum Physics.
Now, it's perfectly true that the marks "or", "and" and the rest have the meaning they have only because English speakers have adopted a convention that they should have the meaning they have. We could, for example, decide to all stop speaking English and start speaking Pig Latin only. In that case, the symbol "not" would have no meaning. It would be replaced by the symbol "otnae". But we could also replace the operator-terms of logic in our old way of speech with terms that do not have any direct mapping to terms in our new convention of speech. And that's what Putnam was suggesting.
Putnam was right to appeal to convenience. That's often the reason we change conventions. We could, for example, eliminate the operator terms "not", "and", "or" in terms of the single operator "nor". The reason we don't is that it would be horribly inconvenient to do so.
It's well worth noting that very few people have been inclined to follow Putnam's lead and use the terms of logic differently or to introduce new terms for a new QM-savvy logical parlance. So I don't think Putnam is right about the greater convenience of a putative QM-talk. Part of the problem also is that Putnam was never entirely clear about what this new way of speaking would be.
Where we get into real trouble is when we confuse the way of words with the way of things. Suppose that, for whatever reason, we did change our terminology so that "and" meant something different. In that case, it might turn out that there is nothing contradictory in saying "Grass is green and grass is not green."
Would that problematize our old friend, the Law of Contradiction?
No. Of course not. We're speaking a different language both when we make our claim about the color of grass, and when we say "There can be no proposition, A, such that 'A and not-A' is true" The old way of expressing the Law of Contradiction no longer expresses the Law of Contradiction.
Under our old way of speaking, the expression of the Law of Contradiction had a certain meaning. That meaning would be expressed differently in the new speech. The meaning might just be expressed differently in a single correlated expression. But it is also possible that the meaning would be distributed over a number of expressions, or lumped together with something else in a single expression.
Posted by: WisdomLover | September 19, 2011 at 06:03 AM
I think a lot of the "intimidation" of QM can be negated if we still to the very basic laws of non contraditiction.
For instance...the effects of what is really going on in any so called "quantum leap" is not really understood by anyone that I know of. However....we do not NEED to know every aspect of what is driving the phemonenon. What we DO know..(because of the laws of non contradiction)...it that it is NOT caused by "nothing"...which is what the atheist crowd would like to put forward as the "cause". There most certainly IS a cause for this phenomenon...and we just need to relax when bombarded by all this idea of QM giving evidence of no God Creator being needed. Treat that idea as pure bluster because thats what it is...just like evolution.
Posted by: vic | September 19, 2011 at 07:09 AM
If due to QM you say there is not God, aren't you using logic to say that there is no logic and hence no God?
"I will catch the wise in their craftiness."
Scripture is always proved right.
Posted by: kpolo | September 19, 2011 at 07:57 AM
Yes...you are correct. Dawkins tries the same stunt all the time when he says he only uses "science" when he comes to his conclusion of no God..."logically". How does he KNOW that there is no God?...Why...just it obvious...so there!
If Dawkins would stop faoming at the mouth over how "unreasonable" religious explanations are, give up on the mantra, and just admit that the true causes of physical penomenon HAVE to have some kind of CausER behind them...he would begin to be rational.
Yes scripture is always right.... which means little to the hard core skeptic. If the atheist used only logic...he wouldn't BE an atheist.
Posted by: vic | September 19, 2011 at 08:51 AM
This quantum physics diversion came up in the Craig/Krauss debate. When Krauss brought it up I couldn't help but think that it was an argument to undercut all arguments. Still, I know far less about QP than I should; can anyone recommend a primer for someone who's never taken a physics class?
WisdomLover, you bring up something I've been irritated about regarding language. An On The Media bit from July wrote this: "In February 2010, the last living speaker of Boa died, and with her, the logic, culture, and history of the ancient people." Now I can understand how culture and history are lost by this, but logic? Now, I'm a monoglot with only a hint of Spanish and a few books worth of linguistics in me, but that doesn't sound right. It seems that "logic" is being used where "semantics" would have been appropriate. Though, this is yet another area where I could use some learning.
Posted by: Don | September 19, 2011 at 10:40 AM
Another thought: could the idea that quantum physics breaks logic signify a sort of post-modernism for science?
Posted by: Don | September 19, 2011 at 12:24 PM
Quantum Physics is a fancy name to label the physics of really small stuff, like sub-atomic particles (electrons, photons, etc). This is in contrast to really big stuff like planets, cars, and people. Newtonian mechanics is adequate to explain these interactions for most situations.
We have to remember that QP is just another scientific model to explain the observed phenomena. It is a human construct but reality may be very different. This is the nature of all science.
One example of a contradiction apparent in QP is the particle/wave duality of light. Under certain experimental conditions, light can behave like either a particle or a wave. These observations are totally contradictory to each other. The law of non-contradiction says it can't be both, except it is both!
The only thing this tells us is that our scientific models of light fail to adequately explain reality.
I hope that helps :-)
Posted by: Sam Hight | September 19, 2011 at 12:48 PM
I am not a physicist, but do remember a few things from my 2nd year Introduction to Quantum Mechanics class.
I find most people do not understand it.
A QUANTUM LEAP DOES NOT MEAN A HUGE LEAP. It means that it moves from state A to State B, without any intermediary state.
Now that is out of the way, even though the logic required to work in that field is using different assumptions than in the macroscopic realm, physicists can predict things with a high degree of precision using mathematics. It is not a realm where everything is totally random and the laws of large numbers mean that all these quantum "randomness" averages out to the sort of thing we expect in classical mechanics when we get up to the level most of us deal with.
In my experience, if someone brings up Quantum Mechanics it is for one of two reasons. 1- To point out some subtle point that might need to be considered 2- To baffle with BS, hoping that you won't know enough to find the mistake.
Posted by: Trent | September 19, 2011 at 02:04 PM
There is the issue of the wave particle duality of light as well. However this does not contradict the laws of logic in the sense that light has never been shown (at least by any current experiment) to demonstate both properties at the same time and in the same sense. This is precisely what the law of non contradiction states about A and non A. Also scientists do not use non logic or illogic to determine or probe quantum mechanical laws they use mathematics which is about as logical as it gets. Even the idea of questioning the reliability of logic uses logic. In otherwords we are ironically trying to find out whether logic is as logical as we think it is and are using logical arguments to do so. Fascinating.
Posted by: Damian | September 19, 2011 at 02:15 PM
It is also very predictable, using logic, when it will act in either way.
Posted by: Trent | September 19, 2011 at 02:22 PM
Greg is spot on--QM depends critically on the same laws of logic we use to argue for the existence of God.
Pick up any textbook on QM. You will find logic employed to convey the foundations of QM, and logic applied to demonstrate that the equations of QM adequately explain the experimental results.
Posted by: Jesse | September 19, 2011 at 03:38 PM
Still, I know far less about QP than I should; can anyone recommend a primer for someone who's never taken a physics class?
I'd recommend these two books:
Quantum Reality by Nick Herbert
The Quantum World by Kenneth Ford
Posted by: Sam | September 19, 2011 at 09:40 PM
It's reasonable to consider that quantum physics follows the same laws that macrophysics follows. (Or it is rather more correct to say that macrophysics follows the same laws that quantum physics follows.) The reason that odd behavior is observed at the quantum level is because quantum objects exist by virtue of the laws that also govern their behavior. These laws are essentially temporal distortions. We don't think we observe them macroscopically because we don't know what we are looking at in light of our constituent parts. We only observe their collective behavior.
Therefore, if we can observe anything that has philosophical import it is that existence is contingent on substantial form rather than substance being contingent on existential form.
Posted by: Jim Pemberton | September 21, 2011 at 07:29 AM
WL,
What do you mean by "proposition A"? What does the A represent?
In particular, do you mean to exclude anything?
RonH
Posted by: RonH | September 23, 2011 at 05:41 PM
Ron-
In the expression, "There can be no proposition, A, such that 'A and not-A' is true" A is the bound variable of a universal quantification.
Any letter or other symbol would do. The variable, A, ranges over all propositions. If you like, here is the same claim without letters: "There can be no proposition that can be both true and false".
Or did you mean to be asking what I think a proposition is? If that's it, then I think a proposition is a certain kind of meaning of utterances.
It is a meaning that can bear truth value. So utterances like "Wow!" and "Dude, where's my car?" have a meaning, but that meaning is not a proposition, since neither of those meanings bear truth value.
And it is a meaning that is fully ramified by the context of utterance. So that if you say "It's raining" in Des Moines, Iowa and I say "It's raining" in Hoboken, New Jersey, we have not uttered the same proposition (even though we've uttered the same sentence), since the context of utterance is different.
Posted by: WisdomLover | September 24, 2011 at 01:22 AM
Good.
So, suppose we're sitting at the kitchen table and you say, "It's raining".
Is there any proposition you mean to implicitly but definitely rule out by saying that?
RonH
Posted by: RonH | September 24, 2011 at 06:26 AM
How about "It is not raining."?
or "I don't need to wear my raincoat"? or "I need to water the lawn."?
Posted by: Trent | September 24, 2011 at 06:53 AM
Yeah, I think "It's raining" uttered in the same context in which "It is not raining" was uttered would be ruled out.
But I think Trent is wrong in saying "I don't need to wear my raincoat" and "I need to water the lawn" are logically ruled out. There might be other reasons for those things to be true. Maybe I'm in a raincoat advertisement where I need to wear my raincoat (even though it's not raining). And maybe I'm deliberately trying to kill my lawn.
You're not trying to sneak me toward an argument that Shrödigner's cat provides some kind of counter-example to the law of contradiction are you?
Because "The cat is alive" and "The cat is dead" are not logically contradictory (though they are contrary). "The cat is alive" and "the cat is not alive" are. "The cat is dead" and "the cat is not dead" also are.
And it is utterly true that the cat cannot be both alive and not alive at the same time. If the cat is alive, then the box has been opened, and the cat has been observed to be alive. If the cat is not alive, then either the box has been opened and the cat found dead, or the box has not been opened and the cat is neither alive nor dead, but in a superposition of alive and dead eigenstates. Before the box is opened, the cat is neither dead nor alive. After the box is opened the cat is either alive or dead.
There's no tension of QM and logic to be found here.
Posted by: WisdomLover | September 24, 2011 at 09:56 AM
WL,
Yes "It is not raining" is the one and only.
Your counterexamples for Trent's other suggestions are right. So they are out.
And, if you don't mean to exclude "It is not raining" when you say it is then you're not saying anything.
So to make this abstract again: when you say "A" you mean to implicitly and definitely exclude what? Not A.
Now that we know this, what work is there for the law of non-contradiction to do?
From the above, the LNC is contained in this notion of a proposition that you have to define before you can state the LNC.
For this reason, I wonder why we need the LNC.
What do you think?
RonH
Posted by: RonH | September 24, 2011 at 10:26 AM
What's your point RonH?
Posted by: Jesse | September 24, 2011 at 01:10 PM
Ron-
I'm not sure I know what you mean when you ask what work the law of contradiction does.
I think you are right to see that it is already implied in the definitions that we use to speak about truth, falsehood and all the rest. That shows its foundational nature. If A implies B, then not-B implies not-A. So if everything we say seems to imply the law of contradiction, were that principle false, then nothing we say could be true.
If you like, the 'work' that the law of contradiction does (and here I'm talking about the meaning behind the words that express it) is that it is one of the foundation blocks of all thought. It is a sine qua non of all rational endeavor.
Posted by: WisdomLover | September 24, 2011 at 01:42 PM
Jesse,
The point is: By the time you've defined the terms required to state the LNC, you've grounded it.
RonH
Posted by: RonH | September 24, 2011 at 01:51 PM
So you're saying the law of noncontradiction is self-evident.
Posted by: Jesse | September 24, 2011 at 01:58 PM
More that it's part of the definitions of statement and negation.
Posted by: RonH | September 24, 2011 at 02:01 PM
Uh huh. And are those definitions reflections of reality or just evolved social conventions?
Posted by: Jesse | September 24, 2011 at 02:03 PM
Thanks Jesse. Good question. Though you could have come up with more ways to denigrate your second option.
Reality seems to be describable. Maybe it actually is. I don't know. Give a point to 'reflections of reality'.
So we find it useful to make statements - utterances intended to describe a state of affairs. Give a point to conventions evolved social just.
It seems like what you are saying is that the fact that the world is describable - that you can make statements about it - requires an explanation, and a 'transcendental' one at that. Correct?
Is that what is really behind all these demands to 'ground the laws of logic' - you really want an explanation for why the world is describable?
I can imagine a world where making statements was not useful. I just did. And now you have too. Maybe in that world y'all would require a 'grounding for the laws of illogic'.
RonH
Posted by: RonH | September 24, 2011 at 03:52 PM
Is it an accurate reflection of reality that "we find it useful to make statements"?
Posted by: Jesse | September 24, 2011 at 06:21 PM
We have seen that the LNC is contained in the terms used to state it.
That's the grounding of it. Let there be no more demands for grounding the laws of logic - at least not for the LNC.
If you want to modify the demand for grounding that's fine. You can even say the modified demand is what you meant in the first place. I don't mind. But I need to know clearly what that demand is and that it is the final the end point.
(I would think you would want to know the end point too.)
Please understand. I don't want to chase you around the playground indefinitely.
Posted by: RonH | September 25, 2011 at 08:02 AM
Bottom line: if these definitions are not accurate reflections of an underlying reality then I fail to see how they are useful.
As to your main point, that the law of noncontradiction is properly grounded in the definitions of 'statement' and 'negation', I owe you the honesty that I'm not convinced. But at this point, I'd need to go back and re-read the initial challenge to frame the present discussion.
Is this the starting point here where you said that you don't believe in self-attesting propositions?
Posted by: Jesse | September 25, 2011 at 10:47 AM
"I can imagine a world where making statements was not useful. I just did."
No, Ron. You uttered the words "a world where making statements was not useful". That's not the same as imagining a world where statements are not useful. To imagine something is to construct a mental image of it (thus imagine). If you've constructed a mental image of that world, you should be able to describe that image. If you can describe the image, then it turns out that statements are useful after all.
"And now you have too."
Nope. I can't do it. I can't do it anymore than I can imagine a round square.
As for the Law of Contradiction,* what exactly do you think people are asking for when they ask for a grounding for it? I'm pretty sure that the fact that every proposition implies the law of contradiction (and every other logical truth) in no way renders the request problematic.
No one is looking for a ground for it as if it were some sort of brute contingency (as the existence of the world is). The grounding question for logic is not metaphysical, but, I suspect, epistemological.
You might try looking at it through Cartesian glasses. Descartes, in his first Meditation, considered four scenarios:
- A scenario where we are created by an Omnipotent Evil Demon
- A scenario where we are created by a less-than omnipotent being
- A scenario where nothing creates us.
- A scenario where we are created by an Omnipotent Benevolent God.
In all four cases he found that we have good cause to doubt all of our mental processes, even those that only involve the application of the laws of logic. Descartes reasoned in the remainder of the Meditations that only in scenario 4 is any confidence in our mental processes recoverable.Thus the foundation of logic turns out to be the existence of a Benevolent God, not because the thesis "God exists" implies the laws of logic. (Of course it does...and so does its opposite.) Instead, it is because the only basis for our ability to reliably use logic is the existence of God.
=================================
*-BTW, I'm not sure why people call it the law of non-contradiction...that's not what Aristotle called it. Who first called it the Law of Non-Contradiction I wonder?
Posted by: WisdomLover | September 25, 2011 at 01:38 PM
WL,
Is your line of thinking similar to what Greg mentioned on the radio a few weeks ago regarding reading and a belief in authors? (One can read while denying authors exist, but no one could read at all if authors didn't exist!)
Posted by: Jesse | September 25, 2011 at 02:56 PM
Jesse-
I didn't hear that show, so I can't be sure. The short description you've given in your post sounds like authors are a metaphysical foundation for written words.
But the existence of written words is a contingent fact of the world. It is quite true that there are such words, but it need not have been true. The fact that it is true calls for some sufficient reason to explain its truth.
No logical truth will fall into the same category. Logical truths are implied by anything and everything. The fact that they are true does not immediately call for a sufficient reason to explain their truth.
What does call for an explanation is the fact that we can use logical truths reliably to construct proofs.
Posted by: WisdomLover | September 25, 2011 at 10:37 PM
Jesse,
I think you can start (and finish) right here, at the beginning of Chapter 1 of Methods of Logic, 3rd edition, by W.V. Quine.
The LNC, “opposite assertions cannot be true at the same time”, is right there in the negation is to count as false if the given statement is true, and the negation is to count as true under any and all circumstances under which the given statement is false.
Grounding.
RonH
Posted by: RonH | September 26, 2011 at 04:16 AM
WL,
As you wrote,
"The fact that they [logical truths] are true does not immediately call for a sufficient reason to explain their truth."
"What does call for an explanation is the fact that we can use logical truths reliably to construct proofs."
Does that mean RonH is barking up the wrong tree?
If I raised the challenge to our friend that logical truths had to be grounded, then I apologize for the ensuing wild goose chase (but I don't recall having raised that challenge).
Either way, we're back to this: RonH's brain, having evolved from random processes, makes statements that cannot be in any sense labeled true, but they are merely 'useful' (whatever that means).
Posted by: Jesse | September 26, 2011 at 05:06 AM
By the way, RonH, I do appreciate your taking the time to thoroughly answer my questions here, even digging up your logic textbook. I was not a philosophy major, so the discussions here have posed to me a steep learning curve (well worth the effort).
Posted by: Jesse | September 26, 2011 at 05:41 AM
No Jesse, I don't think you did raise that challenge. On the other hand, I can't blame Ron for the effort he's made. The question of grounding is always ambiguous, and ipso facto tricky. The question always arises: What kind of grounding?
Ron has argued, correctly, that the laws of logic don't need to be grounded logically. The only problem is that I don't think that anyone was really saying that they did.
I think the issue for logic is how it came to pass that the laws of logic can be reliably put to use. And in that sense it's really as much a question about us as it is about logic. Now the opposing views come directly into contact: Time+chance (Descartes' no-creator scenario) vs. Creation by a Benevolent God.
Posted by: WisdomLover | September 26, 2011 at 06:39 AM
Thanks for your responses.
I hope to have (my own) time later to say more.
Posted by: RonH | September 26, 2011 at 07:04 AM
I guess I don't really need to.
Posted by: RonH | September 28, 2011 at 04:16 PM