We've all heard of logical fallacies - those errors of reasoning that can lead to unreliable conclusions but which seem convincing to someone motivated to believe. There is a complete taxonomy of fallacies, and some people rejoice in observing them in the wild, like bird watching.
But there are just three particular fallacies I want to discuss here. One is a subset of Red Herring fallacies, called the Fallacy of Relative Privation. Red Herrings generally are a response to a position that instead of addressing the evidence for the position or the arguments that connect the evidence to the position's conclusion, simply changes the subject. For example:
"How about cancer, huh? Pretty bad stuff, am I right?"
"How DARE you minimize the suffering of people with heart disease!"
We've all seen exchanges like this in internet comments sections, and we can all recognize that the respondent is an irrational person. The first person has evidence which leads him to conclude that cancer is a bad thing, and the second person disagrees on the basis that something else exists which they perceive as being just as bad or worse. This Fallacy of Relative Privation leads the respondent to the unreliable conclusion that the first statement is somehow incorrect.
Another of my favourite fallacies is the Fallacy of Four Terms Via an Equivocation Error. Cool name, huh? The Four Terms refers to the fact that a classical syllogism has exactly three terms, not four; and slipping in a fourth (or fifth or sixth) term invalidates it. Basically, it states:
If A = B, and if B = C, then A = C.
But if we introduce a fourth term, we get:
If A = B, and C = D, then A = D. Or A = E. Or G = H.
This reasoning is clearly flawed.
What makes a Four Terms fallacy hard to spot is the addition of an Equivocation Error, i.e. you disguise the fact that B and C are not actually the same thing. While almost impossible to do using mathematical notation, it's pretty easy using the good ol' English Language. A great example is attributed to Lewis Carroll:
If we accept that nothing is better than Eternal Bliss,
and that a Ham Sandwich is better than nothing,
then a Ham Sandwich is better than Eternal Bliss.
Clearly. Fun Fact: This syllogism was not found in an early draft of the Koran.
The equivocation error is that nothing is not the same thing as nothing. Get it? No?
Then let us rewrite the syllogism as follows:
Given: the set of things greater in value than Eternal Bliss is empty.
Given: a Ham Sandwich is greater in value than any Empty Set.
Therefore, a Ham Sandwich is greater in value than the set of things that are greater than Eternal Bliss.
This exposes the fallacy, since it is not Eternal Bliss that a Ham Sandwich is greater than, rather the set of things greater than Eternal Bliss, which happens to be an empty set, since we have accepted (without evidence as it turns out) that Eternal Bliss is the greatest possible thing.
Therefore, if someone offers you the choice of a Ham Sandwich, or Everything that is Greater than Eternal Bliss, you take the ham sandwich, without question. Because the other thing is an empty set; in other words, nothing.
But if given the choice of a ham sandwich or Eternal Bliss, then you have to start asking for evidence of the existence of both Eternal Bliss AND this alleged ham sandwich.
This leads us to the relationship between arguments and evidence. An argument is just a way of drawing a continuous line between the evidence and some conclusion. A fallacious argument is like a broken line: the conclusion is not necessarily connected to that evidence.
But it should be recognized that there can be any number of lines (arguments) connecting the evidence to a conclusion. If one line is broken, that does not exclude the possibility of some other solidly connected line
This leads me to the third fallacy I wished to discuss: the Fallacy Fallacy. Just because an argument is fallacious doesn't mean that the conclusion is automatically wrong. It just means that the argument is wrong. In other words, the line is broken and the evidence and conclusion are not connected in that particular way. Perhaps by some other way, but not that one. The conclusion could still be right by some other unknown argument or on the back of some different evidence.
However, without at least some kind of evidence, all the greatest arguments in the world are meaningless. The lines leading to a conclusion have to lead back to something. They have to originate somewhere, from some kind of evidence.
I have seen a lot of different arguments for the existence of gods or goddesses. Hell, I invented some of them myself. The fact that I now find all of them in some way fallacious isn't even the most relevant point.
The real point is that there is no evidence that does not support some other, more concordant conclusion that does not require further baseless assumptions, e.g. invoking the supernatural. In many cases, the arguments for theism lead back to nothing - no originating evidence whatsoever.
In spite of the Fallacy of Four Terms via Equivocation, if someone offers you the choice of a ham sandwich or eternal bliss, take the ham sandwich. Lewis Carroll's argument may be dodgy, but the conclusion was still sound: a (real) Ham Sandwich is infinitely better than (nonexistent) Eternal Bliss.