Recently I got into a discussion with my friend concerning sizes of lexicons of different languages. He stated something about Japanese having considerably more words than English. (The exact languages don't matter, my point is about assessing the size of a lexicon)
My friend's opinion was based in a big part on the difference between sizes of dictionaries which seem inadequate to me as no dictionary provides the whole lexicon. (AFAIK)
I am very sceptical about any specific assessments of the number of language's words, but I have only my common sense to support that. It appears to me that the difficulty behind that task is based on the impossibility in determining which lexemes to consider "alive", being actively a part of the language at a certain point in time, and which to consider archaic and no longer productive nor being part of the language at this certain point in time. The other difficulties, in my view, would appear in deciding whether a certain recently borrowed word is already a part of the lexicon as a proper loanword or merely a temporal influence that is very likely to fade in usage after a couple of years . One would also have to strictly determine which specific dialect of the language is to be analised. And then it overlaps with the perennial struggle in delimitation within languages and lects.
All these problems seem to be mere manifestations of the most basic and obvious fact of language being in constant change. That inherent feature of natural languages, in my opinion, doesn't allow for any accurate estimations of the size of lexicon.
Can you provide any literature on that topic ? Or maybe there are some loopholes in my thought process or a consensus in linguistics that I am simply not aware of ?
Even if there was a method of producing a safe assessment, would the margin of error of these assessments allow to state that "Language X has more extensive vocabulary than Language Y" ?