Sunday, January 31, 2010


Stirring the hornet's nest part II

In response to bogus claims from the audience that Gödel's Ontological Argument is circular, I articulated the most basic form a premise would take in modal logic (related to the topic at hand), i.e., if God exists, then he exists necessarily. The audience, in unison, shouting back "IF God exists..." to which I replied, "YES IF, that's the form mathematical arguments take. In mathematics we define an object and then seek to prove it exists." I was trying to show them that a premise of the form "If P then necessarily P" is legitimate and not "circular." The following is excerpted from this article:

"If God exists, then it is necessary that he exists."

In this example, "necessary" has narrow scope, that is, its scope is restricted to the proposition's consequent, rather than the whole proposition. The proposition claims that if God does in fact exist, then His existence is a necessary one. This is a special claim about God which is not true of other things; for instance, it is thankfully not the case that if Osama bin Laden exists then he necessarily exists. If the scope of the modality were broad, then the proposition would say that it is necessarily the case that if God exists then He exists. While this is true, it is true of everything including Osama bin Laden.

In these two examples it is clear what the scope of the modality is, but in other sentences it is not clear whether the modality has a broad or narrow scope. The modal scope fallacy occurs when this amphiboly is exploited.

The audience was hopeless, however, and accused me of being an obtuse creationist. I refer the interested reader to my previous comments on Dawkins' fan club, wherein I combat similar inanity. Also, I refer the interested reader here for what a mathematician (i.e., "Tarski") who publishes research and does not accept Gödel's Ontological Argument wrote in response to an pretentious atheist who was similarly clueless in asserting that the argument is transparently circular.

"Tarski" in brief:

There is a difference between saying that Gödel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

To be continued...

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