Puzzle for Dave!

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Across
  1. 1. Mathematician Augustus, known for laws involving conjunction, disjunction, and negation
  2. 6. NBA star Bryant
  3. 7. Truth in a logic
  4. 8. Freddie Mercury's family religion
  5. 10. Assume not in this proof by
  6. 11. Worlds A and B, playing tennis
  7. 14. Mathematician Kurt
  8. 15. Essences of all things, according to Plato
  9. 16. Belief system that there exist true contradictions
  10. 18. Logician Graham, or an ecclesiastical officer
  11. 20. It is, indeed, itself
  12. 22. All alone in a set
  13. 23. Purportedly wrote the first ontological argument
  14. 24. Modal operator for possibility
  15. 26. Big Bang Theory character, or eponym of the K modal logic
  16. 30. Relating to knowledge
  17. 31. Dave's Fall 2020 lectures were often accompanied by this outside the window activity
  18. 32. It follows
  19. 34. Aristotle's example to examine the problem of future contingents
  20. 35. In January 2020, UBC cancelled classes due to this
  21. 36. Non-violence (Sanskrit)
  22. 37. Dharma is a basis for Hinduism, Buddhism, Sikhism, and this philosophy
  23. 42. Christian saint of Hippo
  24. 43. "Logical Syntax of Language" author
  25. 45. All else being equal
  26. 46. Having no limit
  27. 47. It is proved
  28. 49. Philosopher Frege, known for arithmetic proofs
  29. 50. A conditional logic, or an average grade
Down
  1. 2. Kind of silk made from wild silk moths
  2. 3. Validity plus truth
  3. 4. "Be Here Now" author, aka Richard Alpert
  4. 5. Modal operator for necessity
  5. 9. What is common between two sets
  6. 12. Logician Ed, or Dave's Ph.D. supervisor
  7. 13. Mathematician Alan, known for halting problem proof
  8. 17. You can make the pit stop, or not
  9. 19. A modal world, chatting to itself
  10. 21. A school of Jewish mysticism
  11. 25. He shares the paradox with Russell
  12. 27. When one makes an announcement, it becomes common
  13. 28. When two sets join up
  14. 29. Logician Dave, who teaches at UBC
  15. 32. Plato's allegory of perception
  16. 33. Anything follows from a contradiction
  17. 38. Start with the base case
  18. 39. A gut feeling, or -ism, a logic that seeks proof
  19. 40. It's a problem if you strengthen it
  20. 41. First form of logic we learn
  21. 44. An argument in which one of the premises is left unstated
  22. 48. It's sound. but is it...