I don't really know what you mean by "conjecture", but I thought apriori was implied by positing it as a linguistic construct. "Fundamental" doesn't imply empiricism at all. All of apriori knowledge for a language is a set of all sets of coherent statements: the outer set represents a set of implied axioms required to make the statements cohere. Recursion just broadens the complexity of the statements you can express, but it's fundamentally a concept that arises from language and can be evaluated for coherency (like all other apriori concepts).
Edit: added a definition of apriori knowledge.
Edit2: to put this another way, nobody is arguing that recursion doesn't exist. Or that it is empirically-derived. No, it's a useful construct to show certain relations.
Edit3: added a sentence
Edit4: The extent to which our own grammars are inherently recursive vs this being culture or technology is irrelevant to identifying the concept of recursion as an apriori, linguistic concept.
Edit5: i suppose you might also be referring to the idea that we naturally process recursion. I mean, we clearly, evidently do; whether or not that's inherent to being human is a separate question entirely. Hell in the free software world there's a whole recursive acronym meme that taps into some part of our brain and tickles it.
Edit: added a definition of apriori knowledge.
Edit2: to put this another way, nobody is arguing that recursion doesn't exist. Or that it is empirically-derived. No, it's a useful construct to show certain relations.
Edit3: added a sentence
Edit4: The extent to which our own grammars are inherently recursive vs this being culture or technology is irrelevant to identifying the concept of recursion as an apriori, linguistic concept.
Edit5: i suppose you might also be referring to the idea that we naturally process recursion. I mean, we clearly, evidently do; whether or not that's inherent to being human is a separate question entirely. Hell in the free software world there's a whole recursive acronym meme that taps into some part of our brain and tickles it.