Infinit analyses?

Dave Chalmers agrees that any concept can be explicitly analyzed by an infinite conjunction of application-conditionals. But he wants to restrict 'explicit analysis' to finite analyses. That certainly makes sense, but I doubt that there are any concepts for which the application-conditionals cannot be determined by finite means. For example, I think it will usually suffice to partition the epistemic possibilities into, say, 50 zillion cases and specify the extension in each of these cases. Admittedly, I can't prove that, but the fact that concepts can be learned and our cognitive capacities are limited seem suggestive.

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