1. NietzscheI wrote back to Fr. Al saying something along the lines of "Wow, apart from Davidson these guys aren't even on the radar for me as possible candidates." So Fr. Al challenged me to post just what are my five favorites. He actually used the word "meme", but that word is so Dawkinsian that I'm not going to use it myself, I will only mention it.
The list that I sent to Fr. Al was this, in chronological order:
1. PlatoSuch lists are inevitably personal in character. The poster at Mormon Philosophy and Theology noted that his list was determined by the thinkers who had "most affected" him, and that has also informed my list; one could go the Time magazine route and try to list the thinkers that one believes to have most affected others, but even that sort of process is influenced by possibly unexamined assumptions and preferences.
3. Saint Anselm
4. Saint Thomas Aquinas
5. Immanuel Kant
Apart from Aristotle there aren't any philosophers of science in my list, in spite of the fact that philosophy of science is one of my own particular interests. This is not because I don't think that there are any truly great philosophers of science (Aristotle actually is one, after all), but rather because few philosophers of science have influenced me in the way that those in my list have. If I were to make a list of just philosophers of science, their names would pale in greatness compared to the five in my overall list, so I won't try to embarrass them by making such a B-list, even though some of them deserve to be so embarrassed.
There are also a lot of realists in my list, in spite of the fact that I am something of an anti-realist, but my anti-realism is confined to certain issues in the philosophy of science. When it comes to metaphysics, I'm a full-blown Thomist, with all the realism that entails.