Syllogistic sophisms

Humbug reader Dan sent me this “proof” of the existence of god. He knew it was rubbish, but wasn’t sure why:

Premise: If God didn't exist, there would be no atheists.
Premise: Atheists exist.
Conclusion: Therefore, God exists.

Sometimes dullards people find various versions of such sophistry convincing. For example, here is my version of St. Anselm’s ontological argument for the proof of god:

Premise: I can imagine the greatest being that exists (i.e. god).
Premise: He/she/it would not be the greatest being that I can imagine if he/she/it did not exist.
Conclusion: Therefore he/she/it (i.e. god) exists.

Though on first inspection these constructions might seem convincing, as with all syllogisms, they are based on premises that must be accepted a priori. We can show the flawed reasoning they are based on in a variety of ways.

One method is Reductio Ad Absurdum, whereby I use the same logic and show that an absurd or opposite conclusion is reached. Combined with the technique of Inversion, I am able to do this:

Premise: If atheists exist, there would be no God.
Premise: Atheists exist.
Conclusion: Therefore, there is no God.

I’ve simply followed the identical structure of the initial syllogism and reached the exact opposite conclusion. Both versions are equally valid, provided we accept the premises. But this is the key point with deductive logic; you need to accept the premises and often the premises, as is the case with the above examples, are without merit.

The god/atheist premise is obviously flawed. The existence of god and atheists are independent of each other. But the flaw in St. Anselm's ontological argument is less obvious. The flaw is the fact that this argument presupposes existence is greater (or more perfect) than non-existence. Why? A counter example should make it clear that if anything, not existing is more perfect or “greater” than existing in many (if not all) cases. (And again, this all depends on what one means by “greater”.)

Pick any geometrical figure or mathematical concept and its existence is greater (or more perfect) in your imagination than in reality. The definition of a circle, for example, is the points in a plane that are at a constant distance from a fixed point. This is literally impossible to create. It does not exist in reality and moreover, in theory could not ever be created in reality. I mean this in two ways, at a classical level we cannot do this using current technology (all measurements have inherent limitations due to resolution/precision) and at a quantum level (indeterminacy).

Accepting this premise - that greater, more perfect things exist in the mind rather than in reality (which I’d say is more justifiable than the other) - using St. Anselm’s logic, we get:

Premise: I can imagine the greatest most perfect being that exists (i.e. god)
Premise: Greatest, most perfect things can only exist in the mind that conceives of them
Conclusion: Therefore the greatest being (i.e. god) exists in my mind only

QED.

Back to Reductio Ad Absurdum, but this time using Substitution; unicorns for God and a-unicornists for atheists:

Premise: If unicorns didn't exist, there would be no a-unicornists (people who don’t believe in unicorns).
Premise: A-unicornists exist.
Conclusion: Therefore, unicorns exist.

These word games are so bad they’re not even wrong.

Examples of Reductio Ad Absurdum

The Advocate's premises are shown to be false as, if they are true, an absurd conclusion is reached.

• Syllogistic sophisms
  
• Will you "contractually government register our relationship(s)" with me?
• Professor Peter Singer, Philosopher-Idiotarian

An example: Hesa Cicy maintains that all beliefs are equally valid. For the sake of argument, this would mean that the scientific view of the Origin of the Universe and the Diversity of Life is of equal validity as a Young Earth Creationist view. Whilst this in itself is absurd, and perhaps example enough, his friend Chip Baud shows Hesa Cicy his argument is flawed - by following the premises to their natural conclusion:

If your argument is true - that all beliefs are equally valid, then there is no reason to give any particular belief any greater merit than any other - including your argument. Your argument is self-contradictory and as such, is absurd.