Since Taleb delights in make his mathematical writing as opaque as possible, it's a useful read in just to know exactly the claims that Taleb is making in his paper.
In regards to Nate Silver's forecasts more generally? I don't know - it's hard to get past the tone of his arguments to understand what his actual disagreement is.
Dear @aubreyclayton, I'm genuinely interested in seeing how you arrived at this conclusion. Would you kindly share the proof, or at least explain the logic behind it. Thank you.
If that's foreign to you, you might be interested in this write-up I did about election-forecasting in which I considered the same example, just in discrete time rather than continuous time: http://nautil.us/issue/70/variables/how-to-improve-political...
The basic idea is that if you increase the volatility of a random-walk process, say by making the step-sizes larger, that won't actually make the probability of finishing above where you started any less (or more) volatile. The higher volatility means that from any given starting point your final resting place is more dispersed, but you're also more likely to range farther from home as you go. The two effects exactly cancel. Taleb's critique misses the second part of that.