Philip David Welch (born 6 January 1954) is a British mathematician known for his contributions to logic and set theory.
After obtaining a BSc in mathematics from University College London in 1975, he attended Exeter College at the University of Oxford, taking an MSc in mathematical logic in 1976 and his DPhil in 1979, under the supervision of Robin Gandy.
He worked as an assistant at the Seminar für Logik at the University of Bonn from 1980 to 1981, then as an SERC Research Fellow at Wolfson College, Oxford, from 1981 until 1983.
He subsequently held a Guest Professorship at the Kurt Gödel Research Center at the University of Vienna (2000–2001) and a Mercator Professorship at the University of Bonn (2001) before returning to Bristol in 2002.
Apart from research articles he is co-author with Aaron Beller and Ronald Jensen of Coding the Universe.