Well, I don't know about you, but I value my skin highly, and prefer it not to have warts. Nevertheless, I don't confuse my skin with my soul.
By the way, linguistic determinism is not just about syntax. If it is to be a limiting factor, it must be about a language as a whole, including phonology, morphology, semantics, pragmatics, lexicon, and if you're exceptionally lucky, a culture. As someone who liked to play football when I was younger, I can vouch for the fact that I did a lot of non-linguistic thinking when running down the field deciding how to fake out the pass coverage. I certainly don't believe in the strong Whorf-Sapir hypothesis. And as to whether J proves or disproves your point, much of that language is ultimately derived from mathematics, and even in that realm the algebraicists will disagree with the geometers over how much linguistics has to do with mathematical thought.
But what really has me curious is why you quote Carter's Compass in your signature but refuse to let me apply it to Perl 5. :-)