Opening post. My response: I think some clarification is in order. The thesis in question is this: (T1) If S believes that p, then S believes that the probability of p is >0.5. It seems reasonable in many contexts. E.g. I believe that the Earth is round, and I believe that the probability that the Earth is round is >0.5. One might ponder what kind of probability that is: prior probability? Clearly not. So we ought to add a clause about what evidence we're calculating, intuitively perhaps, the probability given (T2) If S believes that p, then S believes that the probability of p is >0.5 given the evidence available to S. This amendment seems to fix the unclearness about evidence and probabilities. Now, as this is a categorical prop. we can look for counter-examples. First some further clarification is in order. The thesis is still ambiguous. The ambiguity is about what meaning is to be ascribed to the “if...then...” part. Is it a material or a logical implication? We can clarify it like this (T3) S believes that p logically implies that S believes that the probability of p is >0.5 given the evidence available to S. (T4) S believes that p materially implies that S believes that the probability of p is >0.5 given the evidence available to S. Now obviously (T3) is much stronger than (T4) and so it is more probably false. The difference with counter-examples in relation to (T3) and (T4) is that counter-examples for (T3) only need to be logically possible to work, but they need to be actual against (T4).
Re: Beliefs and probabilities 1
Re: Beliefs and probabilities 1
Re: Beliefs and probabilities 1
Opening post. My response: I think some clarification is in order. The thesis in question is this: (T1) If S believes that p, then S believes that the probability of p is >0.5. It seems reasonable in many contexts. E.g. I believe that the Earth is round, and I believe that the probability that the Earth is round is >0.5. One might ponder what kind of probability that is: prior probability? Clearly not. So we ought to add a clause about what evidence we're calculating, intuitively perhaps, the probability given (T2) If S believes that p, then S believes that the probability of p is >0.5 given the evidence available to S. This amendment seems to fix the unclearness about evidence and probabilities. Now, as this is a categorical prop. we can look for counter-examples. First some further clarification is in order. The thesis is still ambiguous. The ambiguity is about what meaning is to be ascribed to the “if...then...” part. Is it a material or a logical implication? We can clarify it like this (T3) S believes that p logically implies that S believes that the probability of p is >0.5 given the evidence available to S. (T4) S believes that p materially implies that S believes that the probability of p is >0.5 given the evidence available to S. Now obviously (T3) is much stronger than (T4) and so it is more probably false. The difference with counter-examples in relation to (T3) and (T4) is that counter-examples for (T3) only need to be logically possible to work, but they need to be actual against (T4).