The Rules of Logic Part 2: Good vs. Bad Arguments

Posted on January 27, 2015 by Fallacy Man

The core of any debate is the arguments being used. To win a debate, you must show that your arguments are good, and your opponents arguments are bad. It sounds simple, but most people struggle to distinguish good and bad arguments. More often than not, these terms are used subjectively, resulting in widespread disagreement about whether an argument is good or bad. In reality, these terms are completely objective, and it is possible to know and demonstrate for sure whether an argument is good or bad.

There are three criteria for an argument to be good (note: I am dealing with deductive arguments here).

  1. It contains only true premises.
  2. It does not contain any logical fallacies.
  3. The conclusion follows necessarily from the premises (technically, if #3 is violated, it’s a non-sequitur fallacy, so its redundant with #2, but it’s such an important point that I included it as its own criterion).

Any argument which does not meet all three criteria is a bad argument. If an argument is good, then you MUST accept its conclusion. If an argument is bad, then you MUST reject the argument. This is an important distinction. If the argument is good, then the conclusion must be true, but if the argument is bad, the conclusion may or may not true, all that you can conclude is that the argument itself does not work. For example:

  1.  All men are mortals
  2. Socrates is a man
  3. Therefore, Socrates is a mortal.

This is a good argument. All the premises are true, there are no logical fallacies, and the conclusion follows necessarily from the premises. Socrates MUST be a mortal, there are no other possibilities. This is not an opinion, it’s a logical certainty. The following argument is, however, bad:

  1. All men are mortals
  2. Socrates is a mortal
  3. Therefore, Socrates is a man.

This argument doesn’t work, because the conclusion does not follow necessarily from the premises (in technical terms this argument commits a fallacy known as affirming the consequent). The fact that Socrates is a mortal does not automatically mean that he is a man. Notice, however, that even though the argument does not work, the conclusion is actually true, we just can’t use this argument to get to that conclusion. That isn’t always the case, however. Consider:

  1.  All men are mortals
  2. Trogdor (my pet gecko) is a mortal
  3. Therefore, Trogdor is a man.

Now the problem with the argument is even more obvious because the conclusion is not true. This brings me to the restatement of a very important point. If someone demonstrates that one of your arguments is bad, you MUST reject the argument. From this example, it should be obvious that a bad argument tells you nothing about the conclusion, and continuing to use an argument that you know is bad is ridiculously foolish.

There is one and only exception to the rule that you reject a bad argument, not its conclusion. This occurs when the argument is absolutely essential to your opponents position. Under that condition, demonstrating that the argument is bad also demonstrates that the conclusion is wrong, but that is a fairly rare occurrence.

Note: what I have just described applies only to deductive arguments. These are the most common and most powerful types of arguments because they show what absolutely must be true. Other types of arguments, like inductive arguments, show what is probably true, not what must be true. So for an inductive argument to be good, it must contain only true premises, have no logical fallacies, and the conclusion must be the most likely outcome of the premises. So for inductive arguments, you accept the conclusion as the most likely answer, not as the definite answer. However, it is still logically invalid to reject that conclusion unless you can demonstrate that a premise is false, a fallacy has been committed, or another answer is more likely.

Other posts on the rules of logic:

 

 

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The Rules of Logic Part 1: Why Logic Always Works

Posted on January 27, 2015 by Fallacy Man

An Introduction to Logic

In debates, I often find that people are unwilling to accept the rules of logic, and they make foolish comments like, “well you’re entitled to your opinion.” In reality, the rules of logic are like the rules of mathematics. They are an inherent and immutable property of existence, not opinions. Just as 2+2 always equals four, the rules of logic are always true and must always be followed. To illustrate, the most basic rule upon which all other rules rely is known as the Law of Noncontradiction. It states that something cannot be A and not A simultaneously. In other words, two mutually exclusive things cannot exist simultaneously. For example, you cannot have a circular triangle, because a circle, by definition, has no straight lines and no corners, and a triangle, by definition, has three straight lines and three corners. An object cannot simultaneously have zero corners and zero lines and three corners and three lines. That’s not an opinion, it’s an immutable property. If you reject the rules of logic, then you have just acknowledged the possibility of a triangular circle, and, in fact, all rational thought disintegrates. You see, we all inherently and intuitively know that the rules of logic work, and we apply them in our daily lives, we just don’t often think about them in technical terms. For example, suppose that your fuel gauge shows that you are low on gas, and you know that your fuel gauge works, what do you conclude? Obviously, you will conclude that you are low on fuel, but why did you reach that conclusion? Without you even knowing it, your brain did the following:

  1. My fuel gauge is designed to tell me how much fuel I have
  2. I know that my fuel gauge works
  3. My fuel gauge says that I am low on fuel
  4. Therefore I am low on fuel.

That’s plain and simple deductive logic. If, however, you deny the laws of logic, and claim that they are just opinions, then you have just denied that syllogism. In other words, if the rules of logic don’t work, then the fact that your fuel gauge works and is currently showing that you’re low on fuel does not mean that you are low on fuel. Cause and effect relationships operate because of the rules of logic. So, if you deny the rules of logic, then you deny cause and effect.

I mentioned earlier that the rules of logic are like the rules of math. In fact, they aren’t just like math, math relies on them. For example, anyone who has taken geometry has probably been introduced to proofs. These are simple logical syllogisms. For example,

  1. The sum of the angles of any triangle equal 180 degrees
  2. For triangle ABC, angle A = 90
  3. For triangle ABC, angle B= 45
  4. Therefore, for triangle ABC, angle C = 45

Notice, the conclusion is made absolutely necessary by the premises. If 1–3 are true, then 4 absolutely must be true. Angle C cannot be anything other than 45. That is logic. It’s not an opinion, it is an inherent property of the universe that absolutely must be accepted. If you reject the rules of logic, then you must also reject the rules of mathematics.

Do Christians Have to Follow the Rules of Logic?

It may seem odd that I am singling Christians out in a blog about science, but on scientific issues like climate change and evolution, I often find that Christians are hesitant to accept logical arguments and often respond to them with statements like, “Logic is just man’s wisdom, but God is higher than man, therefore we shouldn’t trust man’s logic and should rely on God instead.” I want to address this argument, because I encounter it frequently, and it often seems to be an underlying reason for rejecting science. To be clear, I’m not going to enter into a debate about theism or atheism, rather I am simply going to address the issue of whether or not a belief in God somehow makes you exempt from the rules of logic.

First, this argument is obviously dependent on the belief that God is actually real. So the argument is predicated on faith, which is problematic to say the least (again, I’m not telling you what to believe, but you should be aware that this argument is based on a premise which cannot be proved, which means that it is going to be completely unconvincing to anyone who does not share your faith). Nevertheless, for the sake of argument, let’s assume for a second that Christians are right, and God does actually exist. If he is real, then he, like everything else, must be bound by the laws of logic. I can prove that via that law of non-contradiction. Consider the following hypothetical dialogue between two Christians:

1. (Christian 1) “Can God do anything evil?”
2. (Christian 2) “No”                                                                                                                              3. (Christian 1) “Why not?
4. (Christian 2) “Because his inherent nature is perfectly good.”
5. (Christian 1) “Why does his inherent nature prevent him from doing anything evil?”
6. (Christian 2) “Because, it’s impossible to be perfectly good and do something evil.”

Does #6 look familiar? It’s an affirmation of the law of non-contradiction. If God was not bound by the laws of logic, then he could be evil and perfectly good simultaneously, but every Christian agrees that he cannot do anything evil, therefore if he exists, he must be bound by the laws of logic (note: this is also the appropriate response to creationists’ absurd and ad hoc allegation that logic would not exist without God, clearly it would since, if he exists, he must be bound by it).

What I have just argued often makes Christians irate because they see this as an assault on God’s omnipotence, but that is only because they misunderstand the concept of omnipotence. Philosophers universally agree that “the ability to do anything” is a terrible definition for omnipotence. The most widely accepted definition is, “The ability to do anything logically possible if one wanted to.” The reason for this definition becomes obvious if we return to the example of a triangular circle. No matter how powerful a being might be, he wouldn’t be able to make a triangular circle because it’s not logically possible for such an object to exist.

So, in short, even an omnipotent being would have to be bound by the laws of logic, and would not be capable of doing anything that is not logically possible. Therefore, claims that we should not follow the laws of logic because, “they are just opinions,” or “they are man’s wisdom,” or “all things are possible with God,” are silly and invalid. The laws of logic always hold true and must always be followed in all rational conversations and debates, regardless of your religious beleifs.

Other posts on the rules of logic:

 

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