I'm not convinced that you have a working definition of "property" sufficient to base a deduction upon.
I use the Aristotelean concept, wherein it is important to remember that within Neo-Aristotelean logic metaphysical facts of logic, consistency and existence are facts of reality, inherent to reality and not things separate or merely conceived of. An object which is red (by some measurement) has the property of redness in that sense. Red is something which belongs to the object. Now to take it to formal, axiomatic reasoning a property of is something belonging to a concept, and it is simply a feature or a thing that makes up that concept. To put it more classically, it is 'in the nature' of the object.
As a note, I am such a hard-core anti-Platonist it's kind of funny. People tend to be surprised when I launch a tirade against him if the subject is brought up. Wonderful, writer, though..
I think the argument is essentially that we can rationally make decisions; that rational decisions are basically determined; and therefore, the argument is moot because we are in a position to make free choices that appear deterministic.
This is not my argument. My argument is that, to use a standard model, your brain is a machine made of electrons and following certain processes which may not be predictable but are deterministic according to the way those things are made up. But your brain does in fact rely on a feedback mechanism of sensory, automatic as well as rational, conscious appraisal. That fact is what we experience and feel, and we do indeed make choices. To talk about 'free will' for making 'choices' outside of the reality of what decision making is (the physiology of our minds behaving in a systematic way and resulting in awareness) is to make a categorical error, like talking about the favourite song of nobody. The existence of our brains is what making choices is, and yes it is deterministic, but that does not make it not intentional or willfull. What we intended was inevitable, but it was rational and volitional.
This seems to ignore the fact that people sometimes (usually) make irrational choices.
No, they do not. No act can be irrational, nor can any desire be irrational, these are casual facts. 'Irrationality' can only occur within an idea, wherein our premises, arguments or conclusions are erroneous and thus not in accord with reason. As we do not perfectly and with infinite speed calculate things we are quite capable of holding an opinion that is 'without reason', but even if we adopt this opinion on consciously or unconsciously emotivistic anti-rational reasons our fundamental purpose of the decision is the belief that we will somehow be 'better' or avoid something we don't want to confront by making psychological or thoughtless commitments. Such behavior and choices may be inappropriate for achieving what we desire, but they are not irrational, anymore than a man is 'irrational' for making a mistake on what size of wrench to use.