The Law of Non-Contradiction

@Shaun Connell,

Aristotle used the law of noncontradiction (his formulation from his Metaphysics: "It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect") as one of his first principles, claiming it to be the "most secure" of such principles. Because it is a first principle Aristotle does not see it to be demonstrable, and suggests that anyone who contests the validity of the principle is simply uneducated in analytics. He does provide a "refutative demonstration" () in his Metaphysics, but this relies heavily on his logic, and, to be honest, is not something I'm familiar with at all. Perhaps someone more familiar with Aristotle can explain his "refutative demonstration".

From what I can tell by some quick reading this morning, Aquinas followed Aristotle's thinking: that the law of noncontradiction can only be argued for by showing someone who denies the law to be themselves commited to the law of noncontradiction. Again, my familiarity with Aristotle's defense of the law is shaky to say the least, but if my quick, morning study is accurate, the defense suggested by Aristotle and Aquinas might be fairly difficult to overcome. How is anyone going to tear down the law of noncontradiction and not, in the process, tear down the fundamentals of their initial argument?

@Shaun Connell,

I think everyone should consider that behind every systematic approach to reality is the belief that there is a system, and a universal system at that. All of which begs the question of God. If we were all made by the same hand, from the same plan as it were, there is some reason to expect everything to fit without contradiction into a system of logic, or religion. What if there is no system. What if we were not all created, but each person, species, and kind evolved to a similar enviroment? Does that not account for much non-contradiction and yet ultimately prove nothing. Think of how this concept of non contradiction was applied even to God in the middle ages. Yet, if God created the logical system does God not stand outside of it?

@Fido,

Here is link that should prove helpful:

Aristotle on Non-contradiction (Stanford Encyclopedia of Philosophy)

@Fido,

Fido wrote:

Yet, if God created the logical system does God not stand outside of it?

This classical reasoning stuff is not my strong point, so I'll only venture a question or two... Isn't the "logical system" simply a way for a finite mind to try recognize truth? And if God is simply true, then wouldn't He be the basis for logic, or the answer for which logic ultimately searches for, rather than either creating it or being outside it?

@NeitherExtreme,

NeitherExtreme wrote:

This classical reasoning stuff is not my strong point, so I'll only venture a question or two... Isn't the "logical system" simply a way for a finite mind to try recognize truth? And if God is simply true, then wouldn't He be the basis for logic, or the answer for which logic ultimately searches for, rather than either creating it or being outside it?

What does "God is true" mean? I am not sure what you mean by logical system (and I guess you are not, or you would not place quotes around the word) but logic (classical or not) is the science of inference, which is to say the science which studies and collates the rules for discovering what propositions follow from other propositions, so that if p is true, and q follows from p, then q is true. So, the following is an inconsistent (self-contradictory) set of propositions: (1) p is true; (2) p implies q; and, (3) q is false. So, it is not by logic alone that anyone can discover what it true. I would have to know what is true first, to determine whether some other proposition followed from it, and so is true. If you are already persuaded that God is the answer (to what question?) then why would you have to search for Him? You are already persuaded that you have found Him. Logic is not, I think, like a microscope.

@kennethamy,

kennethamy wrote:

What does "God is true" mean? I am not sure what you mean by logical system (and I guess you are not, or you would not place quotes around the word) but logic (classical or not) is the science of inference, which is to say the science which studies and collates the rules for discovering what propositions follow from other propositions, so that if p is true, and q follows from p, then q is true. So, the following is an inconsistent (self-contradictory) set of propositions: (1) p is true; (2) p implies q; and, (3) q is false. So, it is not by logic alone that anyone can discover what it true. I would have to know what is true first, to determine whether some other proposition followed from it, and so is true. If you are already persuaded that God is the answer (to what question?) then why would you have to search for Him? You are already persuaded that you have found Him. Logic is not, I think, like a microscope.

Thanks for the response! I think that you might have misunderstood my intent... which could very easily have been my fault. I wasn't proposing any sort of argument or statement about the eixstence of God. I was responding to what I understood to be a logical problem presented by Fido. On reading it again, I'm not sure I fully understood his intent...

Anyway, about my questions... I was pondering the nature of logic and how it would apply or not apply to the omiscient, self-existant, prime-reality God represented in Christianity. If such a God existed, how would He relate to logic... As I understand it, logic is one way in which we attempt to understand what is true. But if God would know everything at all times, simply by His nature, He would not need logic to understand it, right? And if such a God did exist, and all that exists exists through Him, then to know what is true in any give situation (the purpose of logic?) would be to know what God is doing. Given the fact that such a God could change even the nature of the physical universe at any given moment, we would have no way of knowing absolutely what is true (including the causes) without knowing His thoughts and actions. Which of course would not be fully possible as long as we have finit minds.

Just some rambling thoughts really. Nothing very consequential IMO one way or the other.

@NeitherExtreme,

First of all, something can not be the same in every respect and be contradictory. This is logical because sameness implies not in contradiction. Logic does not define sameness or contradiction it merely shows the relationship of the two concepts.
I think that expecting the universal system of everything to be logical and non-contradicting is a reasonable expectation, however it is impossible to determine until we know all truth. Things sometimes appear to be in contradiction when really they are in full harmony with the laws of physics/nature. Conflict and competition are not contradiction; they are struggles for equilibrium within the bounds of logic.
Logics purpose is not to originate truth; it is a systematic way of rationalizing from one truth to another or to invalidate a rationale. As Kennethamy said "if p then q. Debate often uses logic but is not necessarily concerned with truth. Up is certainly not down so they define opposing ideas but they are only contradictory if they are both used to describe the same thing.

Doesn't the bible say God is unchanging, the same yesterday, today and tomorrow? And if God is omniscient then he doesn't really think at all he just knows everything at once right? So then He doesn't need logic, and if He is truth then He cannot be contradictory or illogical at all. So if everything exists through God then creation must also be logical and non-contradictory. You don't have to worry about what He is thinking or doing because He and His creation are continually consistent.
The above statement is not what I believe, but it is the logical argument I would use if I did.:eek:

@Shaun Connell,

Thanks Ogden. That makes sense. Though I'm not sure that I'd go so far as to say that He doesn't think, but maybe that He wouldn't have to... And also that everything would be logical, but maybe not from our perspective... To many unknowns to draw any hard and fast conclusions IMO.

@NeitherExtreme,

NeitherExtreme wrote:

Thanks for the response! I think that you might have misunderstood my intent... which could very easily have been my fault. I wasn't proposing any sort of argument or statement about the eixstence of God. I was responding to what I understood to be a logical problem presented by Fido. On reading it again, I'm not sure I fully understood his intent...

Anyway, about my questions... I was pondering the nature of logic and how it would apply or not apply to the omiscient, self-existant, prime-reality God represented in Christianity. If such a God existed, how would He relate to logic... As I understand it, logic is one way in which we attempt to understand what is true. But if God would know everything at all times, simply by His nature, He would not need logic to understand it, right? And if such a God did exist, and all that exists exists through Him, then to know what is true in any give situation (the purpose of logic?) would be to know what God is doing. Given the fact that such a God could change even the nature of the physical universe at any given moment, we would have no way of knowing absolutely what is true (including the causes) without knowing His thoughts and actions. Which of course would not be fully possible as long as we have finit minds.

Just some rambling thoughts really. Nothing very consequential IMO one way or the other.

I cannot see how, if we know that water is H20, or that Quito is the capital of Ecuador, is to know what God is doing. And, even if God can change the state of the universe at any give moment, that does not mean that at this moment, water is not H20. After all, we would have no reason to think that God had, in fact, changed that. And, if he did not, then we would still know it. Perhaps you mean that we could not be absolutely certain that water is H20 because we might be mistaken. And that is true. But, after all, that we might be mistaken does not mean that we are mistaken. And if we might be mistake, we might be correct too. And then we would know. I suspect that you mean by "knowing absolutely" infallible certainty. And, I think that human beings are not infallible. "To err is human". But we should not expect to be infallibly certain (absolutely know) about anything. One thing we have, I think, learned from the rise of empirical science, is that although we do know a lot of things, we can be certain of relatively nothing, since no one can predict when new evidence may not overturn what we think we know. But, then, of course, equally that may not happen. And, in that case, what we think we know we really do know.

@Shaun Connell,

Yeah, like I said, just some wandering of the mind.

I must say it's a bit of a confusing subject as it seems to run all of the problems of epistemology, theology, and logic all together at once.

@NeitherExtreme,

NeitherExtreme wrote:

Yeah, like I said, just some wandering of the mind.

I must say it's a bit of a confusing subject as it seems to run all of the problems of epistemology, theology, and logic all together at once.

I suppose it is the philosopher's job to distinguish them.

@Shaun Connell,

Shaun Connell wrote:

Aristotle explained the principles of non-contradiction, or why, if my memory serves correctly, contradiction is impossible in the abstract reality. Does anyone contest the validity of his argument?

Reading this over again two points come to mind. First. What we think of as reality is really an abstraction of reality. And, what we think of as abstract reality is an abstraction of an abstraction. I doubt that we can develope a unitary view of reality because we cannot conceive of one without contradictions, and what seems true of concepts, forms and ideas is that they are one thing free of contradiction. We may be able to picture white and black, or yin and yang, or an arrow pointing in opposite directions, as these are signs but we cannot really concieve of them as a single thing. I have to wonder of the value of any concept that raises more questions than it answers. So we may be limited in our thinking by the only method we have to think, which is by way of concepts.imo

@Fido,

Fido wrote:

I think everyone should consider that behind every systematic approach to reality is the belief that there is a system, and a universal system at that. All of which begs the question of God. If we were all made by the same hand, from the same plan as it were, there is some reason to expect everything to fit without contradiction into a system of logic, or religion. What if there is no system. What if we were not all created, but each person, species, and kind evolved to a similar enviroment? Does that not account for much non-contradiction and yet ultimately prove nothing. Think of how this concept of non contradiction was applied even to God in the middle ages. Yet, if God created the logical system does God not stand outside of it?

I've come to believe that in distant times the concept of levels of reality was accepted. For some reason it was forgotten and now appears to be coming back.

Quote:

"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." (Avicenna, Medieval Philosopher)

It seems that there are some brave souls who have come to see the limitations of the Law of the Excluded Middle and have begun to appreciate the "Law of the Included Middle." My gut feeling is that this additional direction it opens us to will provide a necessary link to the eventual unification of science and religion. If you'd like to read about the "Law of the Included middle," read this article by a highly regarded scientist.

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