A reply to new Zeno
appeared in Analysis v.60, #2 (April 2000)S. YabloI. A new Zeno paradox has been devised that looks at first sight rather more challengingthan the old ones. It begins like so:A man decides to walk one mile from A to B . A god waits in readiness to throw up awall blocking the man's further advance when the man has travelled 1/2 mile. Asecond God (unbeknownst to the first) waits in readiness to throw up a wall of hisown blocking the man’s further advance when the man has travelled 1/4 mile. Athird God etc. It is clear that this infinite sequence of mere intentions (assuming thecontrary to fact conditional that each God would succeed in executing his intensionsif given the opportunity) logically entails...that the man will be arrested at point A; hewill not be able to pass beyond it, even though not a single wall will in fact bethrown down in his path (Bernardete 1964: 259).So far this is just a surprising result. But a contradiction ensues if we stipulate -- whatseems anyway implicit in the original set-up -- that the man does not stop unless a barrier isput in his way. Now we can infer from the fact that no walls are thrown down that heeventually makes it to B, and so in particular makes it past A . So he both does and doesn'tprogress beyond A.Borrowing from Priest (1999), we can see the paradox as disclosing an unexpectedinconsistency between some innocent-looking assumptions. Suppose that object α isgliding in from the left along an infinite number line, with A and B at the x =0 and x =1marks respectively. The Gods are waiting to set up their walls if α goes anywhere to the