Richard Swineshead was also an English mathematician, logician, and natural philosopher. Alan Turing, a mathematician, logician and computer scientist, linked computing systems to thinking. He was a renowned logician and philosopher. One of her later tutors was the mathematician and logician Augustus De Morgan. PFL is mostly the invention of the logician and philosopher Willard Quine. The philosopher and logician Willard van Orman Quine was born and grew up in Akron. He was a poet, devotee, philosopher, logician and master-teacher (desikan). William of Sherwood () was a medieval English scholastic philosopher, logician, and teacher. Karl Popper approached the problem of indeterminacy as a logician and metaphysical realist. The astrophysicist Edward Arthur Milne and logician John Venn both hailed from Hull. Vidyananda was a "Digambara" Jain logician, scholar and monk in Pataliputra. Descartes submitted his manuscript to many philosophers, theologians and a logician before publishing the "Meditations". Craig was an orthodox logician and an authority on algebraic logic. Carroll was a logician and parodied logic using illogic and inverting logical methods. The theorem was proven by Karl Menger, the next deontic logician.