philosophy-of-mathematics

  1. What is the difference (if any) between the concepts of natural numbers and finite cardinals?

  2. Is Euclid's syllogistic approach to proving mathematical theorems logically insufficient?

  3. Criticisim of Hilbertian Formalism

  4. “Without the assumption of the existence of uniformities there can be no knowledge.”

  5. can we reason about logic?
  6. What are the philosophical consequences of employing computers to do science and mathematics?

  7. What would be gained philosophically if logicism succeeds?

  8. Quantified Logic and Unquantified Modal Logic
  9. If mathematical platonism is true, is mathematics then a discovery?

  10. Is it certain that aliens exist in an infinite universe?

  11. To what extent can the invention of zero in India as a number be tied to Buddhist philosophy, if at all?

  12. Does Poppers theory of Falsification apply to mathematics?
  13. Is getting 100 Heads in a row from a fair coin a miracle or not?
  14. How "concrete" is mathematics, even when it's formal, rather than natural science?

  15. Proof that the rules of logic are true
  16. Can there only be one success in an infinite amount of trials?

  17. Can other "sciences" be applications of mathematics?
  18. Does Quine's dissolution of the Analytic/Synthetic distinction challenge mathematical realism?

  19. Can a problem be solved if there exists no solution for it in any context?

  20. Are analogies between ethics and mathematics philosophically coherent?

  21. Do mathematical entities transcend duality and cause/effect?
  22. What are the philosophical implications of category theory?
  23. Motivations for Mathematical Platonism

  24. Introduction to science philosophy
  25. Why didn't Newton pursue philosophy?

  26. Philosophy and Reading: Towards Math, and Physics

  27. What is the number 2?
  28. The hanging judge

  29. Is Mathematics considered a science?

  30. What are the "undefinable numbers" in real analysis and philosophy?
  31. Why can/should we conclude that something is true without proving it?

  32. What current foundational theories of mathematics are considered to be the state-of-the-art?
  33. Philosophers that would be of particular interest to engineers/designers?

  34. What did Poincaré mean by intuition of pure number?
  35. What is the philosophical ground for distinguishing logic and mathematics?

  36. Implications of a discovered mathematics
  37. Are numbers real?

  38. What is the difference between a probability and a possibility?

  39. What are computable numbers, and what is their philosophical significance?

  40. What does mathematical constructivism gain us philosophically?
  41. Where did Gödel write that first-order logic is the "true" logic?

  42. Some questions on Graham Priest's remarks about Russell's solution of paradoxes
  43. How do we learn math and science?
  44. What is the relation between proof in mathematics and observation in physics?

  45. What is the relation between calculus and Aristotle's view of infinite divisibility?
  46. Mathematics and René Descartes

  47. Is the fine-structure constant a physical number?
  48. Methods for testing the posibility of some action?
  49. What is the difference between science and mathematics?
  50. Given proofs of A → B and A, when do we get a proof of B?
  51. What makes something mathematics?
  52. What are some arguments for the golden ratio making things more aesthetically pleasing?

  53. What is the role of the a priori nature of time in intuitionism?
  54. Can every assumption be stated mathematically?

  55. What was the impact of the discovery of non-euclidean geometry on Kantian thought?

  56. The shadow of a tree

  57. Does pure mathematics express something about objects?

  58. What is the difference between concepts of number and natural number?
  59. Higher-order probability

  60. Is Logic Empirical?
  61. Putnam's argument against the possibility of nominalising 'distance-statements' in "Philosophy of Logic" (1972)
  62. According to Aristotle, can knowledge of geometry exist outside of particular subjects?

  63. Are there kinds of arithmetic that are decidable despite the Gödel theorem?

  64. If we assume logic is correct, does it imply that our consciousness proccesses real information?
  65. Is it generally taken that the thesis of Kant's first antinomy fails?

  66. Hilbert Grand Hotel vs. Cantor: Can we postpone the solution into infinity?

  67. When do descriptions of objects qualify as "known" vs "unknown"?

  68. Can an idea lack simplicity?
  69. Foundations of logic and reasoning in natural languages

  70. Is Aristotle's resolution of Zeno's paradoxes vindicated by motion in the intuitionistic continuum?

  71. Is Platonism required to accept transfinite set theory?

  72. Can the truth of statements cause the truth of other statements?
  73. Do transfinite sets have practical applications?
  74. On Mastering Topics of a Certain Difficulty

  75. What are the useful outcomes of denying the Continuum Hypothesis?
  76. How does Frege's definition of number solve the Julius Caesar problem?
  77. Quine - Two dogmas of empiricism - status of mathematics
  78. What sources discuss Russell's response to Gödel's incompleteness theorems?

  79. Is this a lucky person or an unlucky person?

  80. What meaning should we ascribe to infinite sets?

  81. FOL - Functions that don't apply to all elements in the domain of discourse

  82. Is the system of Mathematics derivative from the corporeal nature of experience?

  83. At what order of logic do we have a unique model of the natural numbers?
  84. What was Leopold Kronecker's philosophical view which guided his mathematics?

  85. Is mathematics a language?
  86. How should one interpret modern mathematics if one doesn't believe in infinity?

  87. How many numbers does it take to describe conscious reality?

  88. What is the nature of proof in mathematics?

  89. What were the 'costs' in completeness in formulating ZFC in first-order logic?

  90. Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor in a letter to Dedekind?
  91. How do we know if a mathematical proof is valid?
  92. Is there any justification for the existence of sets?
  93. Downward causation and unpredictable pattern formation in cellular automata
  94. What was Cantor's philosophical reason for accepting the infinite but rejecting the infinitesimal?

  95. Is mathematics founded on beliefs and assumptions?
  96. The opposite of 'x'
  97. Alternatives to Axiomatic Method

  98. Does mathematical proof require faith

  99. Are Geometries True?

  100. What is a better way to describe the "arbitrary" nature of the value of pi?