The funniest thing is that the deductive logic partisans don't even seem to realize that logicians utilize math all the time for just this reason. The philosophers of math out there aren't German idealists or post-structuralists, after all!
I shared this with stickman, which I think readers will appreciate:
"This past fall I was at a conference with Richard Freeman and I was talking to him after dinner. He told me something I think you'd like.
He said that whenever you see anything by him where the math is extremely dense, he's probably talking about something he's not very confident about or that he fully understands yet. He said that when he starts to think about a problem he writes it all down formally. As he continues to work through it the math becomes more elegant and readable and he is able to focus on the key elements of the model. When you come across a paper of his that is easily readable it's usually a more mature idea. He's fully digested the insights from the math so he can express the intuition in words, and he's also had the opportunity to clean up the model a little. But he only gets there by thinking the models through several times and trying to figure out the intuition behind the model."