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Under the Bayesian school of thought, probability represents our degree of belief and is ultimately subjective. There is no a priori reason I can't assign a pr

by glial 8y ago

Under the Bayesian school of thought, probability represents our degree of belief and is ultimately subjective. There is no a priori reason I can't assign a probability to the existence of God, since the probability reflects my belief about God's existence. Evidence lets us update our beliefs, and therefore our probabilities. While I have no issue at all with assigning a probability to the inconsistency mathematics, the value I'd assign varies with the branch and mathematics. For Zermelo–Fraenkel set theory, for example, I'd assign a probability very very very close to 0, but not equal to zero (because to be equal to zero, I'd need a proof).

joe_the_user 8y ago
The inconsistency of math was a trick question. It doesn't matter what probability you assign to it since if math is inconsistent, all numbers are equal!
- coldtea 8y ago
  >since if math is inconsistent, all numbers are equal! That doesn't follow.
  - clickok 8y ago
    It does, insofar as you can express anything meaningful in an inconsistent system. A formal system being inconsistent implies being able to prove some statement A, and also its converse ~A. If both A and ~A are true, then we can prove that every other statement in this system is also true. A quick proof: 1. A 2. A v B 3. ~A & A v B 4. B We start with A. The union (logical-or) of true statement (here A) and any other statement (say B) is a true statement, thus A v B. Then we introduce another true statement, ~A, via logical-and to get ~A & (A v B), which simplifies (disjunctive syllogism) to just B. So we have proved B, but B was arbitrary. It could be anything, including the statement that x = y for x and y two ostensible non-equal numbers.
    - coldtea 8y ago
      See here for examples why such inconsistency doesn't disqualify math in toto: https://plato.stanford.edu/entries/mathematics-inconsistent/ https://plato.stanford.edu/entries/mathematics-inconsistent/

by glial 8y ago

joe_the_user 8y ago

The inconsistency of math was a trick question. It doesn't matter what probability you assign to it since if math is inconsistent, all numbers are equal!

coldtea 8y ago
>since if math is inconsistent, all numbers are equal! That doesn't follow.
- clickok 8y ago
  It does, insofar as you can express anything meaningful in an inconsistent system. A formal system being inconsistent implies being able to prove some statement A, and also its converse ~A. If both A and ~A are true, then we can prove that every other statement in this system is also true. A quick proof: 1. A 2. A v B 3. ~A & A v B 4. B We start with A. The union (logical-or) of true statement (here A) and any other statement (say B) is a true statement, thus A v B. Then we introduce another true statement, ~A, via logical-and to get ~A & (A v B), which simplifies (disjunctive syllogism) to just B. So we have proved B, but B was arbitrary. It could be anything, including the statement that x = y for x and y two ostensible non-equal numbers.
  - coldtea 8y ago
    See here for examples why such inconsistency doesn't disqualify math in toto: https://plato.stanford.edu/entries/mathematics-inconsistent/ https://plato.stanford.edu/entries/mathematics-inconsistent/