The Instigator
NKaloms
Pro (for)
Losing
0 Points
The Contender
philochristos
Con (against)
Winning
6 Points

Can we use logic to prove logic?

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Post Voting Period
The voting period for this debate has ended.
after 2 votes the winner is...
philochristos
Voting Style: Open Point System: 7 Point
Started: 8/31/2017 Category: Philosophy
Updated: 4 months ago Status: Post Voting Period
Viewed: 514 times Debate No: 103745
Debate Rounds (3)
Comments (5)
Votes (2)

 

NKaloms

Pro

I have read that many philosophers (Gorgias, C.S. Lewis, and others) believe that logic cannot be proved, and that we must assume (have faith in) that logic just works. I find this extremely interesting. At first I was distressed at this thought, for how can we know for certain that anything is certain if can't know that logic is certain. I wrestled with this for a while until I came to an interesting conclusion. The statement that "we cannot know anything for certain, including logic" is in fact a logical statement. That very statement uses logic.

I propose the following argument: Logic CAN prove logic because every statement is a logical statement. Any conclusion that you come to uses logic, including the conclusion that "we cannot know anything for certain, including logic."
Even if you come to an untrue/illogical conclusion, you still used logic to get to that conclusion (even if that conclusion is faulty).
Any attack on the laws of logic or the certainty of logic uses logic.

I'd truly like to see if anyone can disprove this. I genuinely want to know if I can be proven wrong because I don't understand how I can come to this conclusion while more intelligent philosophers disagree with me. I'm either doing something wrong, misunderstanding what they actually said, or I'm in fact correct and they are wrong, which I find extremely unlikely.

If nothing is self-evident, nothing can be proved. There are some premises that can't be reached as conclusions. - C.S. Lewis
To prove that anything is true you need some truth to start with. - C.S. Lewis
philochristos

Con

Thank you for coming to tonight's debate. Since I am Con, I will argue that we cannot use logic to prove logic.

My argument is this: If I use logic to prove logic, then I am assuming the very thing I'm trying to prove, which is circular reasoning. Circular reasoning is a fallacy and doesn't prove anything.

There are a number of things my opponent said that I agree with and some that I disagree with. I agree with my opponent when he says that "every statement is a logical statement." After all, anything I say that's meaningful must, by necessity, exclude it's negation. The statement, "My dog barks," would be a meaningless statement if it did not exclude as true the statement, "My dog does not bark." So every statement assumes the law of non-contradiction.

But how does that work out as a proof for logic? I suppose one could construct the following syllogism:

1. If the law of non-contradiction is not true, then no statement has meaning.
2. Some statements do have meaning.
3. Therefore, the law of non-contradiction is true.

But this argument is invalid precisely because it assumes what it's trying to prove. If the law of non-contradiction were not true, then neither premise would be meaningful. So the mere statement of the premises assumes already that the law of non-contradiction is true. Since the conclusion is hidden in each premise, the whole argument is question-begging.

So the fact that every statement is a logical statement does not show that you can use logic to prove logic. Rather, it proves that one must assume logic before they can make any meaningful statement. The fact that every statement is a logical statement supports my view, not Pro's. Proofs require premises, but logic must be in place before premises can have meaning. So logic must be presupposed before anything at all can be proved.

Since logic must be presupposed before anything can be proved, logic itself cannot be arrived at through a proof.

Where I disagree with Pro is when he says that if logic could not be proved, then we must simply "have faith in" logic. He seems to draw the conclusion that if we could not prove logic, then "We cannot know anything for certain, including logic." None of the philosophers Pro cites ever draw that conclusion. It doesn't follow that if logic can't be proved that it therefore can't be known.

But whether logic can be known or not is irrelevant to this debate, so I won't bother disproving Pro's inference.
Debate Round No. 1
NKaloms

Pro

Thank you philochristos for accepting my debate. Before I begin, I would just like to say that although it may be irrelevant whether logic can be known or not, I would gladly put it in here anyway. My reason for starting this debate was to see if I was wrong or not in my conclusion. To be completely honest, I don't care if I win or lose, I just want to know if I was wrong or not. So, I'm sorry if I seem like a disappointment because I won't defend my position completely, but as I stated before, my entire reason for creating this was to see if I was wrong. I will ask a question however. You said that " It doesn't follow that if logic can't be proved that it therefore can't be known." So I ask you, how can logic be known to be absolutely certain/completely true beyond a shadow of a doubt, without logic?

Once again, sorry if I disappoint, but I'm more concerned with discovering the truth about this. Any other debate I'd love to argue without conceding my position (unless I obviously lose of course).

So to clarify I'll put my question down here:
You said that " It doesn't follow that if logic can't be proved that it therefore can't be known." So I ask you, how can logic be known to be absolutely certain/completely true beyond a shadow of a doubt, without logic?
philochristos

Con

I understand my opponent's desire to have a discussion around logic and how we know it apart from proof, but this is a debate format, and I did enter this to debate. I don't want to be rude or inconsiderate, though, so here's what I'll do. For the sake of Pro and for the readers, I'll divide this post up into two parts. The first part will be arguments relevant to this debate. The second part will be an informal discussion with Pro that should not be considered when it comes time to debate.

Part 1: The debate

Pro appears to concede that whether logic can be known or not isn't relevant to the question of whether we can use logic to prove logic. Then he spends the rest of the time on the subject of whether and how logic can be known. Since how we know logic isn't relevant, I'm gong to ignore that here and reserve all discussion for Part 2.

Pro does not attempt to defend his argument against my rebuttal. Nor does Pro attempt to rebut my argument. That leaves Pro's case undefended and my case unrefuted.

Part 2: The discussion

You asked, "how can logic be known to be absolutely certain/completely true beyond a shadow of a doubt, without logic?"

There are two kinds of knowledge--a priori and a posteriori. A priori knowledge is knowledge we have that was inferred from some prior item of knowledge. A posteriori knowledge is knowledge that is not inferred from some prior item of knowledge. If we know anything at all, then all of our knowledge must fit under one category or the other.

It is not possible for all knowledge to be a priori because that would lead to an infinite regress. For every item of knowledge we had, there would have to be some prior item of knowledge, ad infinitum. Since none of us knows an infinite number of things, and none of us are capable of making an infinite number of inferences, our knowledge must begin with a priori knowledge. In other words, there's a foundation of a priori knowledge upon which all other knowledge is derived.

Since a priori knowledge is not inferred from anything prior, it is not arrived by a process of logical reasoning. Rather, it is known immediately upon reflection. In other words, once we contemplate it, we know it. Philosophers call this "knowledge by intuition."

There are different kinds of a priori knowledge, though. Some of it we know immediately upon reflecting on our own mental states. For example, if you are feeling pain, you know you are feeling pain simply by feeling it. You're immediately aware of your subjective feeling of pain. Likewise, if you're thinking of a number between 1 and 10, you know immediately which number you're thinking of just because you're thinking of it. So one kind of a priori knowledge is first person private knowlege of your own mental states. You can have certainty about these items of knowledge because they are incorrigible.

Another kind of a priori knowledge is synthetic a priori knowledge. This includes things like, "My senses are giving me true information about the world," or "The future will resemble the past." With these items of knowledge, we don't have certainty. What makes them a priori is that they seems to just be built into us. They are the assumptions we use to learn about the world around us. Without assuming the future will resemble the past, for example, it would be impossible to learn anything from experience. The fact that nature has behaved a particular way in the past wouldn't tell us anything about how we should expect nature to behave in the future. No scientific experiment in a lab could tell you anything about how things behave outside the lab. But this principle, which philosophers call "the uniformity of nature," can't be proved. One might be tempted to say we have shown it to be true or to work in the past, but if we say that it is therefore true from now on, then we are begging the question by assuming the very thing we're trying to prove. These items of knowledge are not things we can know without absolute certain the way we can know the content of our own thoughts, feelings, and perceptions. They are not incorrigible, and they are not necessary truths. It's at least possible that the external world does not exist at all and that all of our perceptions occur strictly in the mind without corresponding to anything outside of our minds.

The third category of a priori knowledge is knowledge of necessary truths that we rationally grasp. These include things like "Two and two make four," and that "The opposite angles formed by intersecting lines are equal." It also includes the laws of logic. We know these things by rational intuition. That is, by simply understanding them, we immediately recognize that they are true. We are able to "see" the necessity of them and the impossibility of their not being true. This knowledge, too, appears to be just built into us. We grasp it merely by reflecting on it. But while it is possible for an individual to know these things with absolute certainty by rationally seeing it with vivid clarity, that doesn't mean every individual can know these things with the same degree of certainty. After all, some people can't always apprehend the necessity behind these truths. One example is the Pathagorean theorem. This theorem states a necessary truth that with inward reflection, one can rationally grasp that it is a necesary truth. Once it is grasped, it is known with necessity. But not everybody can see it. For years, I didn't see it. I believed it because I trusted all my teachers, everybody else was using it, and I seemed to get good grades when I used it. But I didn't understand why it was true. I had to wrestle with it for a while. But once I saw it, I knew it with absolute certainty. That's the way it is with logic. Logic can be known with absolute certainty merely by reflecting on it and "seeing" the necessity of it.

Most people believe in logic without even realizing it because they never think about it. They just assume it. Whenever anybody says anything and expects to be understood, they are using logic. Whenever anybody reasons, they are using logic. Some people do it better than others, but everybody does it. Even eastern philosophers who claim to deny logic continue to use logic every day of their lives.

The closest anybody has ever come to proving logic was when Aristotle argued that without the law of non-contradiction, there could be no significant speech or action. If there is no logic, then nothing you say or do has any meaning. Without the law of non-contradiction, there's no difference between walking and not walking. There's no difference between your dog barking and your dog not barking. But strictly speaking, Aristotle wasn't proving logic. He was merely illustrating logic. He was showing that since everybody speaks and acts, everybody knows and uses logic. Rather than proving logic, he was proving that we dont need to prove logic. It's something we already know a priori.


Debate Round No. 2
NKaloms

Pro

Thank you philochristos for bearing with me and my curiosity. I will concede my argument here and in the future I will make sure to make an opinion poll instead of a debate.
philochristos

Con

Alrighty then! That concludes tonight's debate/discussion. Thank you for coming.
Debate Round No. 3
5 comments have been posted on this debate. Showing 1 through 5 records.
Posted by canis 4 months ago
canis
Logic does not exist... Without it, (our creation of it).. We would not know what exist.
Posted by NKaloms 4 months ago
NKaloms
Awesome. Thanks you guys for clearing that up. Hope to talk to you guys in the future.
Posted by philochristos 4 months ago
philochristos
Be careful, Surgeon, or people might think you just proved the law of non-contradiction. :-)
Posted by Surgeon 4 months ago
Surgeon
No we cannot use logic to prove logic, but it is not all bad news....that is because logic is at the foundation of knowledge (it is axiomatically true). In order to deny logic you must first use it, thus the denial of logic is self-refuting (and commits the fallacy of the stolen concept).

Consider the statement "the law of non-contradiction is false". If that statement is true then contradictions are possible. If contradictions are possible then the law of non-contradiction can be true and false in the same way, at the same time. If that is true then the law of non-contradiction is not false. Thus the attempt to dsiprove it refutes itself.
Posted by vi_spex 4 months ago
vi_spex
cause implies effect, effect implies effect.. no cause no effect and vice versa
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by Nd2400 4 months ago
Nd2400
NKalomsphilochristosTied
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Total points awarded:03 
Reasons for voting decision: Since pro, didn't really have a argument, just wanted to ask a question, con won this debate.
Vote Placed by dsjpk5 4 months ago
dsjpk5
NKalomsphilochristosTied
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Total points awarded:03 
Reasons for voting decision: Concession.