by Dave Maier
This post started out as one about the mathematical question of whether 1 = 0.9999…, an issue which confuses a lot of people. This confusion shouldn’t be surprising, as it involves infinity; and if you’re not confused about infinity, then you probably don’t understand it. Unfortunately what I had to say about it, at least in the strictly mathematical context, has been said fairly well already by many others, which shouldn’t be surprising either, as I am not a mathematician. (I should have Googled it first and saved myself some time.)
So rather than going through all that stuff again (although we will see some of it soon enough), let me say here at the beginning why it was sticking in my mind in the first place. This will introduce some dramatic tension into an otherwise boring post, as the reader wonders what the heck these things have to do with each other. Like I said: another shaggy dog story to start the new year. (The pictured animal is to be found on the Wikipedia entry for “shaggy dog story” and is identified there as “the archetypical subject of long-winded, pointless stories”.)
So then. I just began reading Charles Taylor’s new book The Language Animal (seriously, I’m on page 6). Taylor has been writing about these things for many years, so his general views are already familiar, but apparently he has a bit more to tell us. His main concern, as he tells us on page ix, is the same as always: to argue that our linguistic capacity is “more multiform than has usually been supposed, [in that] it includes capacities for meaning creation which go far beyond that of encoding and communicating information, which is too often taken as its central form.” In particular, while Taylor allows that contemporary analytic philosophy of language is much more sophisticated than in early modernity, when rationalism and empiricism were the main players on the philosophical stage, “certain […] key assumptions” of that era “have survived into analytic post-Fregean philosophy”.
The reason we need a new book, it turns out, is that while progress has been made on this front, and the objectionable theory has at least been crushed into pieces, it has not yet been entirely pulverized.
