I vote for Francis Bacon.
The standard answer gives the honor to René Descartes.
Descartes’s claim to the title is based primarily on his epistemology — specifically his method of doubt. The method of doubt is both a challenge to previous, more authoritarian epistemologies and a re-invigoration of a skepticism that exercises philosophers to this day.
Bacon’s reputation is also based in epistemology — his re-introduction and expansion of inductive methods. His empiricism is also a challenge to authoritarian epistemologies and grounds much of the scientific method used by investigators to this day.
How do we decide matters such as who should be considered the founder or father of modern philosophy? Let me propose four criteria.
1. Influence on academic philosophy. Descartes’s skeptical challenges have generated a huge literature in academic philosophy. Yet a huge literature has also been generated developing empirical methods in philosophy of science along lines established by Bacon. My call: a tie between Descartes and Bacon, absent a quantitative measure of the literature.
2. Influence on philosophy as used by all thinkers. Baconian epistemology has been internalized by most modern intellectuals (especially in the sciences and social sciences) and is part of their normal professional practice, and the more sophisticated inductive methods are explicitly used as guiding principles. The hardcore Cartesian skeptical challenges are rarely used outside academic philosophical discussions. My call: Bacon.
3. The positive and the negative. Descartes’s legacy is essentially negative. He digs philosophy into a skeptical hole from which many haven’t escaped. Bacon’s legacy is essentially positive. He provides tools many have used to develop new knowledge. Clearly there is still much truth to C. P. Snow’s “two cultures” thesis, in which much of the humanities is skeptical and pessimistic while much of the sciences is progressive and optimistic. My call: Absent a quantitative measure of the literature, a tie between Descartes and Bacon.
4. Chronology. Bacon’s key works were published in the first quarter of the 17th century: The Proficience and Advancement of Learning (1605), The Wisdom of the Ancients (1619), Novum Organum (1620), and The New Atlantis (1626). Descartes’s key works were written in the second quarter of the 17th century, and some were not published until the third quarter: Rules for the Direction of the Mind (1628; published posthumously in 1684), Discourse on Method (1637), Meditations on First Philosophy (written in 1641, published in 1647), and Principles of Philosophy (1644). My call: Bacon.
So by simple philosophy math, Bacon wins by two.
Before we revise the textbooks, let me ask: Are there other criteria we should consider?