Why don't they teach them logic at these schools?
For those of you hyper-familiar with C. S. Lewis, you will no doubt recognize that quote. It comes from The Lion, the Witch, and the Wardrobe, the speaker is Professor Digory Kirke, and the audience is Peter and Susan. Peter and Susan have just shown that they do not quite buy Sherlock Holmes's statement that, "Whenever you have eliminated the impossible, whatever remains, however improbable, must be the truth." The Professor is lamenting their ignorance.
What's so great about logic? Why should anyone use logic? Of what value is it? Now in the following arguments (and I mean the word in its logical sense, as in debate, not altercation), I'm going to make a few rather large assumptions. The most important assumption I'm going to make is that you, the reader, believe there are absolute truths that man can know. In today's postmodern world, this is certainly an unwarranted assumption. I'll only reply that if you believe there are no absolutes, haven't you just uttered an absolute? I mean, are you saying that there is no absolute truth except for the truth that there is no absolute truth? Certain it is that the statement, "There is no absolute truth" is making a universal, absolute claim. Thus you have contradicted yourself.
The next assumption I'm going to make is what is called the Law of Non-contradiction. It goes like this: A cannot be A and not-A at the same time and in the same respect. This seems inherently obvious to many people (because I believe God has built this into our brains), but its implications many people seem unwilling to accept. As a rather trivial example, consider the statements, "I see at least one car,” versus "I do not see any cars whatsoever." These two statements might both be true, but they can't both be true at the same time, with the same speaker. Either you see a car or you don't. On a much more important and far less trivial note, consider the following statements: "Jesus said, I am the way, the truth, and the life. No one comes to the Father except through me." Here Jesus is claiming that He is the only road to salvation. Now Islam says that their religion is the only true religion. These two religions are making simultaneous claims that they are absolutely the only way to salvation (as defined by each group separately!). Can they both be true? Well, I believe the Law of Non-contradiction says they cannot both be true. Either Jesus is the way, or He isn't. But you can't have it both ways.
If you accept these assumptions, that there are absolute truths, and the Law of Non-contradiction, then you are forced to accept quite a few more things. This may sound like a bad thing, and it would be, unless these new things are true. And I believe they must be, because of where I believe logic comes from. Logic comes from God. He gave it to us, as a tool (merely a tool!) to discover truth. God knows everything, but He has commanded us to fill the earth and subdue it, and this is one way in which we subdue the earth. God is above logic. I don't mean that He is illogical, but that He created it. He certainly lives by it Himself, but He is not restrained by it. The Bible gives us logic. You can find instances of nearly every kind of reasoning you can think of somewhere in the Bible. Paul's writings are perhaps the best place to find them.
One disclaimer, and it is an important one: logic will not guide you into all truth. It is simply not possible to take a set of assumptions and reason your way into all knowledge. Many people have tried this. However, Kurt Goedel actually proved that you can't do this. This is not to say that you can't get quite a bit of truth this way: you can. And I claim that if you take the Bible as your Great Assumption, and you apply logic back to the Bible, then you will get an awful lot of truth, certainly enough to live by.
Because the Bible uses logic, it becomes acceptable, even advisable for us to use it. What are the ramifications of this?
Well, perhaps that questions is best answered by listing a few fallacies (fallacies are errors in reasoning, things that go against logic.)
The great granddaddy of them all is the ad hominem (Latin for "against the man") fallacy. This fallacy says that what a person says is not true because of what he is. The textbook example of this fallacy is the alcoholic speaking out against alcoholism. Some one would object, saying that because he is an alcoholic, what he says about alcoholism is not true. I would be tempted to say rather that because he is an alcoholic, what he says about alcoholism might be especially valuable. Actually, there are two kinds of ad hominem. The example above is termed "ad hominem circumstantial.” So because of the circumstances surrounding this man, what he says is not true. The other kind of ad hominem is called "ad hominem abusive." This is just name-calling. Politicians seem to be rather adept at using this fallacy. Again, name-calling does not have anything directly to do with the argument at hand.
One huge application of this fallacy, or perhaps I should say knowledge of this fallacy, is the idea that you can attack an argument without attacking someone who holds that argument. The number of times I have run into people who, when you attack their way of thinking, assume you are attacking them, is astronomical. It really is very tiring to have to continue to explain that no, I'm not attacking you. It's much the same as in the martial arts, when you do sparring. You are not literally attacking the other person. You are sham-attacking them (though perhaps you do attempt some degree of realism) for the purposes of making them a better person. So if I attack someone's argument, I am not attacking the person.
Another quite common fallacy is the "post hoc ergo propter hoc" fallacy. The Latin there means "after the fact, therefore because of the fact." This fallacy says since I brush my teeth every morning very early, and after that the sun rises, therefore my brushing causes the sun to rise. So the idea here is that just because one event follows another in time does not mean that the earlier event causes the later event.
As Dorothy Sayers once said, "Indeed, the practical utility of Formal Logic today lies not so much in the establishment of positive conclusions as in the prompt detection and exposure of invalid inference." Yes, logic is one way we can discover positive truth. But the exposure of a falsehood is just as important, and is where logic perhaps excels.
I would encourage you to study logic. If you want to know where to begin, I'd say there are a number of places. You could take a course at one of your local colleges, most of which offer at least one course in it. You could get Copi and Cohen, which while expensive, is definitely worth it. Once you get into logic a bit, you might want to do some symbolic logic. For that I would highly recommend
Language, Proof, and Logic. These would certainly get you started.
So on to the world of clear thinking!
What's so great about logic? Why should anyone use logic? Of what value is it? Now in the following arguments (and I mean the word in its logical sense, as in debate, not altercation), I'm going to make a few rather large assumptions. The most important assumption I'm going to make is that you, the reader, believe there are absolute truths that man can know. In today's postmodern world, this is certainly an unwarranted assumption. I'll only reply that if you believe there are no absolutes, haven't you just uttered an absolute? I mean, are you saying that there is no absolute truth except for the truth that there is no absolute truth? Certain it is that the statement, "There is no absolute truth" is making a universal, absolute claim. Thus you have contradicted yourself.
The next assumption I'm going to make is what is called the Law of Non-contradiction. It goes like this: A cannot be A and not-A at the same time and in the same respect. This seems inherently obvious to many people (because I believe God has built this into our brains), but its implications many people seem unwilling to accept. As a rather trivial example, consider the statements, "I see at least one car,” versus "I do not see any cars whatsoever." These two statements might both be true, but they can't both be true at the same time, with the same speaker. Either you see a car or you don't. On a much more important and far less trivial note, consider the following statements: "Jesus said, I am the way, the truth, and the life. No one comes to the Father except through me." Here Jesus is claiming that He is the only road to salvation. Now Islam says that their religion is the only true religion. These two religions are making simultaneous claims that they are absolutely the only way to salvation (as defined by each group separately!). Can they both be true? Well, I believe the Law of Non-contradiction says they cannot both be true. Either Jesus is the way, or He isn't. But you can't have it both ways.
If you accept these assumptions, that there are absolute truths, and the Law of Non-contradiction, then you are forced to accept quite a few more things. This may sound like a bad thing, and it would be, unless these new things are true. And I believe they must be, because of where I believe logic comes from. Logic comes from God. He gave it to us, as a tool (merely a tool!) to discover truth. God knows everything, but He has commanded us to fill the earth and subdue it, and this is one way in which we subdue the earth. God is above logic. I don't mean that He is illogical, but that He created it. He certainly lives by it Himself, but He is not restrained by it. The Bible gives us logic. You can find instances of nearly every kind of reasoning you can think of somewhere in the Bible. Paul's writings are perhaps the best place to find them.
One disclaimer, and it is an important one: logic will not guide you into all truth. It is simply not possible to take a set of assumptions and reason your way into all knowledge. Many people have tried this. However, Kurt Goedel actually proved that you can't do this. This is not to say that you can't get quite a bit of truth this way: you can. And I claim that if you take the Bible as your Great Assumption, and you apply logic back to the Bible, then you will get an awful lot of truth, certainly enough to live by.
Because the Bible uses logic, it becomes acceptable, even advisable for us to use it. What are the ramifications of this?
Well, perhaps that questions is best answered by listing a few fallacies (fallacies are errors in reasoning, things that go against logic.)
The great granddaddy of them all is the ad hominem (Latin for "against the man") fallacy. This fallacy says that what a person says is not true because of what he is. The textbook example of this fallacy is the alcoholic speaking out against alcoholism. Some one would object, saying that because he is an alcoholic, what he says about alcoholism is not true. I would be tempted to say rather that because he is an alcoholic, what he says about alcoholism might be especially valuable. Actually, there are two kinds of ad hominem. The example above is termed "ad hominem circumstantial.” So because of the circumstances surrounding this man, what he says is not true. The other kind of ad hominem is called "ad hominem abusive." This is just name-calling. Politicians seem to be rather adept at using this fallacy. Again, name-calling does not have anything directly to do with the argument at hand.
One huge application of this fallacy, or perhaps I should say knowledge of this fallacy, is the idea that you can attack an argument without attacking someone who holds that argument. The number of times I have run into people who, when you attack their way of thinking, assume you are attacking them, is astronomical. It really is very tiring to have to continue to explain that no, I'm not attacking you. It's much the same as in the martial arts, when you do sparring. You are not literally attacking the other person. You are sham-attacking them (though perhaps you do attempt some degree of realism) for the purposes of making them a better person. So if I attack someone's argument, I am not attacking the person.
Another quite common fallacy is the "post hoc ergo propter hoc" fallacy. The Latin there means "after the fact, therefore because of the fact." This fallacy says since I brush my teeth every morning very early, and after that the sun rises, therefore my brushing causes the sun to rise. So the idea here is that just because one event follows another in time does not mean that the earlier event causes the later event.
As Dorothy Sayers once said, "Indeed, the practical utility of Formal Logic today lies not so much in the establishment of positive conclusions as in the prompt detection and exposure of invalid inference." Yes, logic is one way we can discover positive truth. But the exposure of a falsehood is just as important, and is where logic perhaps excels.
I would encourage you to study logic. If you want to know where to begin, I'd say there are a number of places. You could take a course at one of your local colleges, most of which offer at least one course in it. You could get Copi and Cohen, which while expensive, is definitely worth it. Once you get into logic a bit, you might want to do some symbolic logic. For that I would highly recommend
Language, Proof, and Logic. These would certainly get you started.
So on to the world of clear thinking!
posted by Adrian C. Keister @ 9:03 AM
1 Comments
1 Comments:
Kurt Goedel (it's really Go(umlaut)del) proved two things. The first thing he proved was the Completeness of First Order Logic. The First-Order-ness refers to the ability to quantify over objects, but not over properties. So, for example, I can say for all dogs, they have four legs. I have quantified over all dogs. But I have only used one property, that of having four legs. Completeness, I believe, refers to the fact that any logically valid well-formed formula in first-order logic is provable. Actually, this is called semantic completeness. There are other kinds. The second, much more important theorem that Goedel proved was the Incompleteness of Second-Order logic. Second-order refers to the idea of quantifying over properties. So here I could say (though in most cases it would be nonsense), that for all conceivable properties, the person Evan has each one. Note that second-order does not rule out first order. We have extended first-order logic. So first-order is a subset of second-order. You really want second-order logic eventually, because first-order is a little bit too unwieldy. So Goedel's Incompleteness Theorem is about second-order logic, and it says that there are logically valid well-formed formulae in second-order logic that are not provable. And in fact, there are infinitely many such formulae.
There's what Goedel said.
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