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.

Inversion

Inversion involves using the opponent’s argument against them by reversing the direction of their reasoning. That is, their argument is turned on its head. If we reach a dubious or absurd conclusion (see reductio ad absurdum) then we have reason to assume the original argument is suspect.

For example, Shamoo Shabang is opposed to embryonic stem cell research. She says: You can't destroy an embryo as each is a "potential life".

Her friend Olive Olivers responds by pointing out: The basics of biology tell us that there are many stages in the development of life. Given this, it seems rather arbitrary to say the "potential" begins with fertilisation.

She goes on to invert Shamoo's argument by heading in the other direction: Before fertilisation we have the "potential life" of each sperm and ovum (each of them, potentially, could fuse and start off the whole process). If we follow the "potential life" reasoning we ought to attribute them this moral status too. This is patently absurd.

She has given a reason to assume the "potential life" argument is suspect.

Of course, Shamoo understands inversion also, and inverts Olive's inversion: If I granted that argument any validity, then surely we can go the other way? Concluding that there is no point at which we can attribute "potential life" to a gestating human, and as a consequence award no moral status to any unborn child? Clearly, you'd agree, that's an abhorrent position.

In using embryonic stem cells as an example, it is worth noting that people who hold the "potential life" view follow a deontological ethic, as opposed to a consequentialist ethic (which tends to be argued by those in favour of research using embryonic stem cells). There are advantages and disadvantages, as there are philosophical and practical problems, with both ethical systems. Since the dawn of moral philosophy, both types of ethics, as argued by all their various proponents, either lack credibility (due to some of their conclusions), or are not self-consistent (have internal contradictory aspects). Given people are arguing about embryonic stem cell research from incompatible a priori positions, a conclusion satisfactory to both sides may never be reached.

Examples of Inversion:

• Syllogistic sophisms
  
• Will you "contractually government register our relationship(s)" with me?