[gjm11]

I believe the following is a reasonably accurate but more explicit paraphrase.

1. Philosophers have sometimes attempted to deal with the big questions they face by giving big grandiose answers. ("Heroic remedies for intellectual difficulties".)

2. What actually appears to be more effective in producing genuine solutions to hard problems is simply very careful and clear thinking. ("Greater care and accuracy".)

3. Careful and clear thinking isn't really a special subject all to itself: it's just what one should be doing in every field of study, and when systematized and taken very far it turns into science and mathematics.

4. So maybe it's a mistake to think of philosophy as a separate field of activity with special methods, because the most effective way of dealing with philosophical problems is just to apply the same methods of thinking that are useful everywhere, and especially those of science.

5. Why might we have thought otherwise? Perhaps because a lot of philosophical topics were formerly within the purview of theology, and a distinctive philosophical method seemed necessary only by contrast with the even more unhelpful methods of theology.