An [Ontological?] Argument for Free Will

Greetings,

I'm going to present to you an argument that human beings have free will. I have not seen this argument composed elsewhere, but if you uncover a similar argument from another source, I'd love to hear about it.

Here's how it will work. There are three "sets" of arguments. The first set has 5 premises, and should yield "C1"-- conclusion 1. The second set has 3 premises, and shoudl yielf "C2"-- conclusion 2. C1 and C2 should form an additional argument to yield C3. If you think my argument is wrong, it would be great for you to either attack one of the premises or argue that one of the conclusions do not follow from its respective premises. I'd love to hear your thoughts!

SET 1:
1. Either human beings can freely will or they cannot freely will.
2. If human beings cannot freely will, they either cannot will or they can will without freedom.
3. Human beings can will.
4. If a human being can freely will, we say that such a human being has "free will".
5. If a human being cannot will with freedom, we say that the human being is subject to "determinism".
C1: THUS, human beings either have free will or they are subject to determinism.

SET 2:
1. If human beings are subject to determinism, they perform the actions they perform but do not do so freely.
2. If one performs an action but does not do so freely, they do so because they were compelled.
3. If an entity is compelled to perform the action of evaluating an argument, they did so because they were compelled, regardless of beliefs about the validity of the argument.
C2: THUS, if an entity evaluates this argument to establish its validity, one was not compelled.

SET 3:
C1. Human beings either have free will or they are subject to determinism.
C2. If an entity evaluates this argument to establish its validity, one was not compelled.
C3: THUS, if an entity evaluates this argument to establish its validity, it did so with free will.

So, now we have C3: "If an entity evaluates this argument to establish its validity, it did so with free will". It's a conditional, and I'm fine with that. Let me ask you: did you evaluate my arguments to determine their validity? According to C3, if you cannot, you cannot reject arguments for free will. If you can, you have free will.

What are your thoughts? Is there a problem? Is it convincing, or do you find it lacking in some regard?

Naming Infinity

That's the title of a book by Loren Graham and Jean-Michel Kantor that I finished reading recently. It may be one of the most unusual books I've read, as it focuses on two topics--the mathematics of the infinite and heresy in the Eastern Orthodox Church--that are not typically associated with each other. The story is fascinating and covers the origins of set theory and its early development at the start of the 20th century by French mathematicians. According to the authors, the tendency in France toward positivism and Cartesianism contributed to a bias among French mathematicians against theories that could not be connected to physics. Accordingly, French mathematicians became reluctant to pursue the study of the transfinite. Russia, with its mystical orientation, and particularly what became the Moscow School of Mathematics were a more fertile ground for research in this area. Especially interesting is the role played by Pavel Florensky, a Russian Orthodox monk and mathematician. Florensky represents the link between the Moscow mathematicians, several of them faithful churchgoers, and an obscure sect, the Name Worshippers, within the Russian church. While the authors do not get into the details of the theology of the Name Worshippers, it becomes clear that their beliefs had an effect on the mathematical work of Florensky and perhaps the other Moscow mathematicians. After the revolution and with the growing oppression of the Soviet regime, the overt Christianity that informed these mathematicians' outlooks had to go underground. The exception was the fearless Florensky, who continued to wear his clerical robe even in the presence of leading communists like Trotsky. Florensky ended up in prison camps where he was tortured and eventually killed. The stories and personal travails of many of the other mathematicians are also sad and poignant. But in the midst of totalitarianism, a spirit of faith and mysticism continued to color the Moscow school even in the darkest periods.

The authors are right to conclude modestly that religion does not change mathematics. A Christian mathematician should come to the same conclusions as a positivist mathematician. But the spiritual and philosophical spirit that characterizes a culture can allow ideas to develop that may otherwise be neglected or overlooked. It seems that in this case, at least, it was religion rather than rationalism that proved a more fertile ground for the growth of scientific ideas.