Should We Trust Reason? A Brief Defense of the Laws of Logic

April 7, 2015 By Khuitt

Shortly after launching my blog, the point of which is to pursue truth through reason, I was told by some friends that I trust reason too much. These friends were both fellow philosophy majors, and they have had a few more courses than I have, so I was intrigued and ready to listen to what they had to say. The reason they gave for distrusting reason was the usual one, the laws of logic cannot be justified. I kicked this idea around in my mind for a while, but never really made much progress.

A short time later I was in a discussion on Facebook and I responded to a friend’s question about whether or not he should be able to defend everything he believes (I think the answer is that he should be able to do so). Eventually, I mentioned the laws of logic and my friend replied by asserting that I was saying that we should ground our beliefs in the laws of logic, while I gave no justification for the laws of logic themselves. In other words, my friend wanted a justification for the laws of logic which he assumed I was taking for granted. After all, many people do seem to take the laws of logic as foundational principles that cannot be supported or questioned, so I can see why he would assume that I would be no different.
I, however, think that with careful consideration, the laws of logic can be proven to be true. I am probably a little too bold to take on such a topic in a blog post, but here goes nothing.

There are three laws of logic:

1. The law of identity: Something is equal to itself
2. The law of non-contradiction: Two contradicting statements cannot both be true
3. The law of the excluded middle: Either something is true or it is false

In order to justify all three laws, I think it is important to start with the law of non-contradiction.
That is because the opposite statement is self-defeating which means we can deduce the law of non-contradiction via argumentum ad absurdum.

Consider the following premises:

1. Two contradicting statements can both be true.
2. “No two opposing statements can both be true” is the contradiction of Premise 1.
3. If Premise 1 is true then the statement “No two opposing statments can both be true” is true. (By applying Premise 1 to itself)
4. The statement “No two opposing statements can both be true” is false if its contradiction (premise 1) is true (applying the statement to itself)
5. Premise 1 is true (Assumed)
6. Premise 2 is false (Premise 4)
7. Premise 1 is therefore false because it would only be true if its own contradicting statement could be true. Its contradiction is false (Premise 6), therefore Premise 1 is false.

In other words, the possibility of contradictory truths disqualifies itself because its own contradiction cannot be true. Because two truths cannot contradict themselves, we can say that no two contradictory statements can be true, and the law of non-contradiction is justified. 

We have the law of non-contradiction is true, so we can now apply it to the other laws of logic and our job just got a whole lot easier. 

Let’s use the law of non-contradiction to prove the law of identity.
The law of identity would say that something is itself. If the law of identity is not true, then something is not itself. Something obviously has to be something, otherwise it would be nothing. Something cannot be nothing, because that would be a contradiction and we have already shown the law of non-contradiction to be true. Something must then be something, and we must now talk about something in particular that we will call P. P must be itself. If P is not P then somebody simply got confused and wrongly labeled something P (perhaps a lower-case q). This would simply be an error in judgment, and it has no bearing on the law of identity. So P is P, but if the law of identity is false then P is P and not P at the same time. This would be a contradiction, and since we have already demonstrated the truth of the law of non-contradiction we know that two contradicting statements cannot both be true. Therefore, P is either rightly labeled P and is itself, or P never was P and is not P but is still itself. If it was not itself, then it would simply be something else that was itself. If it was not anything, then it would simply be nothing at all. Since something cannot be itself and not itself at the same time, the law of identity is true given the falsity of the opposite. 

This brings us to the final law of logic which is the law of the excluded middle. This law is very similar to the law of non-contradiction in that it simply says that P is either P or not P and it cannot be both. In other words, I am either reading this sentence, or I am not. I cannot be doing both at the same time (I dare the reader to try). The law of the excluded middle is not hard to prove after we have proven non-contradiction. If I said that you are both reading and not-reading this sentence at the same time, then I would be contradicting myself. Since I am contradicting myself, both statements cannot be true, and there is no middle ground (except in the possible sense that you are reading this sentence and not paying attention, but that is not the kind of middle ground we are talking about).

Since there is no middle ground in contradictory statements in that a statement is either true or false (A statement cannot be true along with its contradictory statement), the law of the excluded middle is proven.

The keystone of this entire argument is the law of non-contradiction. If the law of non-contradiction is proven false then the other two laws fall with it. However, the law of non-contradiction can be proven true, and along with it the other two laws. Therefore, we do not have to assume the laws of logic are true. We simply have to think about them a little bit. Because the laws of logic can be justified, we can continue to trust our reason as long as it is properly applied. The proper application of reason, rather than the merit of reason itself, is where the fun is really at.

#logic #reason #philosophy )


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