I'm well aware of the fantastic advances in medicine, mathematics, astronomy, and philosophy (broadly defined) during this time period. However, as a budding scientific researcher, I'm interested in gaining more perspectives on the philosophy of science.
Discussion of philosophy of science in the Muslim world during the (esp. Umayyad, Abbasid, and Cordoba) Caliphates has always eluded me. As it is often taught in American universities and as it is discussed in American scientific discourse, the philosophy of science is focused upon Western and certainly more modern thought.
If anyone could mention any texts/thinkers/debates that exemplify or characterize strands of thought on this topic I would be really grateful!
Interesting question - this is fresh on my mind as Islamic thought came up briefly in another thread.
There's an edited collected by George F. Hourani called Essays on Islamic Philosophy and Science, which is a useful introduction. It is weighted more toward philosophy than science, and it's a couple of decades old, but it could offer you some interesting starting points.
The only other book I've read on the subject is George Saliba Islamic Science and the Making of the European Renaissance. I think Saliba overstates his case somewhat, but the early chapters do a good job of discussing science during the Caliphates.