Sorry, still not with you. (I spotted a missing ‘not’ in the first line, but that seems not germane to your criticism.)
1. You syllogistically imply that cost can outweigh utility over time.
Yes. Although I would say it is a statement of fact, rather than a syllogistic implication, on the basis that there is no constraint that would limit the long term cost of a choice to a ceiling equal to, or less than its corresponding utility.
2. You equally syllogistically imply that, to be rational, an action must outweigh or, (I assume) at least equal, its cost over time.
I presume there is an implied “the utility of” just before “an action”. It’s not so much a syllogism as a definition.
3. Therefore rationality = utility/cost.
This is unclear. Do you mean that rationality can be a quantity which, if >1 means one thing, and if <1 another? I’d have written it something like
utility(x)>cost(x) ⇒ rationality(x) = TRUE
Therefore, any action which, over time, costs more than its utility cannot, by your own terms, be rational, Q.E.D.
This seems to me to be a reformulation of 2.
Help me out here.