I normally don’t link to Crooked Timber posts because I assume most people here are reading them already, but Daniel Davies’s post on The War On (some kinds of) Theory is so good I have to break that rule. Here’s just one of the money quotes.
[I]n the construction of arguments of this kind, there are certain kinds of mistake which it is fearfully easy to make. Its easy to spot particular benefits and miss the fact that their counterparts are costs elsewhere in the system. To come up with arguments which, if true, would imply that people systematically allowed others to impoverish them without changing their behaviour. To miss the fact that your model requires the build-up of debts forever that never get repaid. Etc, etc. The bestiary of really bad economic commentary is full of all sorts of logical howlers. And the good thing about building mathematical models is that, in general, it acts as a form of double-entry book-keeping, to make sure that, if youve followed the rules of the game, your economic argument will not have any of these most common and most egregious flaws. It doesnt mean that it wont be bad or misleading for other reasons, of course, but it does mean that youll at least be saying something that makes sense, if only to other experts.
Exactly the same kind of defence can be given for the use of jargon, and for technical work, in philosophy. There’s a reason that you can’t find easy holes in any argument by, say, Tim Williamson. It’s because the formalism he’s using either up-front or on his notepad is designed to catch little holes. Well maybe that’s not the best example, because Tim being Tim there’s a possibility he could catch plenty of those in his head. But in general it’s true that the very same things that raise barriers to entry can, when used properly, mean avoiding the very errors that it is the business of philosophy to expose.