If you have not read my Introduction to Logic, you may want to do so.

The basic structure of a logical argument is in the form of
IF antecedent THEN consequent. Essentially, this states that if a certain condition (or set of conditions, which may include assumptions and facts) is TRUE, then the consequent will ALSO be true. As a corollary, if the consequent is FALSE, the antecedent must ALSO be false.

For example
IF all dogs are black THEN my dog is black.

I have a dog which is white!
Therefore, all dogs are black is NOT TRUE. It is still possible that some dogs are black, so do not err (which is easily done in English!) and say all dogs are not black. The fact is that NOT all dogs are black, leaving room for non black dogs, which is different from saying there exist NO black dogs.

Another example,
If the Bible is true THEN there is only one way to Heaven.
You believe there are multiple ways to Heaven.

Both of these statements can be true. That doesn’t prove or disprove the assumption. The fact that you believe there are multiple ways to Heaven indicates simply that you deny the Antecedent, rather, you deny that the Bible is True. Again, this doesn’t affirm or deny biblical truth, the analogy only exhibits that any person who denies there is one way to Heaven must also deny the Bible is true. To do otherwise is illogical and inconsiste. So the assumption I made is that “if the bible is true then there is only one way to heaven.” You could certainly say that the bible can be true and there be more than one way to heaven, but we’d have a different argument. We would have to argue about whether there are parts of the Bible that clearly teach a single way to Heaven, and I’d have to prove that you couldn’t believe the Bible AND multiple ways to Heaven or you’d have to prove the bible’s claims are not exclusive.

Here is an example that is more complex.
If it is not raining and it is a Saturday in the summer, you will see a baseball game.

This doesn’t appear like a simple IF p THEN q, statement; but look closer:
If [it is not raining] AND [it is a Saturday] AND [it’s the summer] THEN [baseball game].

This may be more complex, but we can see that the entire thought: [it is not raining] AND [it is a Saturday] AND [it’s the summer] is equivalent to “p” or the antecedent. Thus we know that if ALL 3 of these conditions is true, then we’ll see baseball. If there is no baseball, then we know that AT LEAST one of these conditions failed, but we do not necessarily know which one or how many failed to be true. For the sake of our basic rules for argument, we are not going to delve into any more complexity.

Logical Fallacies

Now we’ve learned how to develop a logical argument and how to understand if it is valid or not. We’ve learned that there are certain situations where we can deduce previously unknown things by applying some rules of logic. That if we can deny the consequent of a logical statement, that we can then also deny the antecedent. (if p then q, THEN ^q-> ^p), or else, if we can say that the logical consequent of a particular antecedent, (assumption or axiom) is FALSE, then the antecedent must also be false. Now let’s looks at a list of logical fallacies (falsehoods) that people are victim to frequently. Be ready to spot these, they MUST always exist (a logical fallacy that is, not necessarily one from this short list) when someone is wrong or else, they must have a wrong assumption.

How can I put this…if someone has a logically valid argument that still results in an absurdity or obvious falsehood, the antecedent (assumptions) must be wrong. If multiple assumptions are made then AT LEAST one assumption must be wrong. Suffice to say many people will refer to their logic when you try to show their assumption is senseless or contradictory. Get used to this if you want to argue for the side of truth. Be aware that if you are in an argument and you are right, it will be impossible for your opponent to avoid using a logical fallacy or faulty assumption. Helping people, often spectators to the debate, understand this is the only chance to win them over with kindness and love.

There are several logical fallacies committed throughout the world of “debate” (sometimes better known as “the web” :-)), I want to outline the ones I think are most popular. Spotting them is often easy when they are understood. Not committing them is another story, or sometimes defending that you haven’t committed them is hard too. Convincing others 1) that they’ve committed a logical fallacy and 2) that their argument is illogical or uses faulty reasoning is sometimes impossible. Again, if someone refuses to follow rules of sound logic then arguing with them is a waste of time. This is when you will employ a technique described later called “Don’t Answer.”

Ad Hominem – Probably the most worthless (and sadly, most common) of all methods of debate I see, this argument gets its name from the Latin, meaning “toward the man.” This is the practice of attacking the person’s character with whom you are debating rather than the idea you are trying to prove or disprove. E.G., If I state that homosexuality is a sin and someone tells me,”You’re a bigoted homophobe!” This statement is an example of an ad hominem attack. It is logically irrelevant to whether homosexuality is a sin if the person making the statement is bigoted or homophobic. This is easily discerned by replacing the speaker with someone anonymous. So imagine the statement you are seeing refuted is written on a piece of paper with no indication as to who the author is. Now…you can see clearly that it is not relevant whether the person is who wrote it. If it is disprovable, truly, it must be some other way than by attacking the speaker!

Affirming the consequent. This is a common practice as well. This is committed when you have a standard “If p then q” argument. The mistake made here is noticing the truth of q, and then assuming that p must be true as well. If p then q implies that if p is true, then q will also be true; it does not imply that if q is true that p is true. q can be true with or without p. for example, “If evolution is true, we’d expect to see a lot of commonalities among life forms.” “We do see a lot of commonalities among life forms,” therefore, evolution is true. Affirming the consequent (we see commonalities) is fallacious if you deduce that it affirms the antecedent (evolution is true), for there could be other explanations for commonalities. Christians can commit this logical fallacy as well (and do), so study them and be aware!

Begging the question. This fallacy is the problem of assuming that which you are trying to prove is true, in order to prove that which you are trying to prove is true. It is not a proof of anything except that your assumption is consistent with itself and other known truth. This can be a value argumentative tool, not for proof though, but for exhibiting that your assumption is consistent with known truth. Often circular reasoning comes into play. This is the reason that all false assumptions can be used in logically valid statements.
Observe: If all dogs are green and I have a dog whose color I haven’t observed then my dog must be green.

This statement is logically sound, or valid. Even if you know it is not the case that your dog is green, that doesn’t invalidate this argument. It just shows that it is not true that all dogs are green. The point is that if you presuppose all dogs are green, then you will declare every dog “green” because you’ve already presupposed this. It doesn’t matter if a dog really is green; you will see it that way because you’ve already decided all dogs are green.

Appealing to an artificial authority: We must appeal to an authority when making claims; the alternative is essentially to appeal to ourselves as “THE” authority. Clearly this won’t be a way to win too many arguments. If you think about it, the fact someone is disagreeing with you already shows they do not believe you are an authority on the topic. You must appeal to another, (in fact, higher) authority. So assuming we must, how do you know if you are appealing to an artificial authority? Let me offer two examples to explain this:

Example 1: I ask my ex-roommate Bob about a legal matter. He refers to the Constitution of the United States to answer the question (either directly or in essence). Bob has appealed to an authority that is not artificial. In matters involving United States justice system, the Constitution is the ultimate authority as well as being a valid (non-artificial) authority. For Bob to tell me what I’ve done is wrong, based on a clear understanding of the Constitution, is valid, and he is within rational logical principles to do so.

Example 2: I asked a lady a few weeks ago where she gets her standard for morality. She agreed that, for example, murder is wrong. When I asked her how she could make such a claim, she cited the fact that it was what she was taught growing up by her family and “the culture” she’s in. I asked her how she could be sure that they were right, and she didn’t know. The fact is that an individual’s parents and cultural upbringing are not and cannot be an authority on human morality. It can be seen clearly from person to person that different ideas of morality will come out of these groups and will be contradictory. A case in point is that it would be just as easy to find a family that teaches their children that sex outside of marriage is wrong as it would be to find a family that will tell their children it is not wrong. It may “feel good” to appeal to your parents, upbringing, religion or community when determining morals, but it is not a valid argument for absolute truth. Keep in mind, just because a person cannot validly explain where they get their morals doesn’t mean the morals they hold to are wrong, it just means they do not have a valid logical argument to explain them.

Obviously, true morality must come from a higher source than society. Of course, if you are morally relativistic or believe truth is relative you do not agree with the previous statement, but that doesn’t matter because by your own admission, you really don’t have the right to tell me I’m wrong, nor can you prove it because you don’t believe in “right” and “wrong.”

Appealing to majority: The fact that any number of people hold a particular belief is irrelevant logically to the validity or truthfulness of the belief. It may be compelling data to encourage you to consider it, but it is not a proof. For example, “Most scientists believe in evolution” is not a valid logical argument for proving “evolution is true.’ It just means that a number of scientists that hold that belief. This is easy to refute because you only have to find a single instance in history where the “majority” was wrong. See “The Holocaust,” and laws prohibiting blacks from having the same rights as whites for examples.