3 ms·

I recall hearing this adage from a philisopher of mathematics a few years ago, and it has really stuck with me. To me, this seems like the source of much unprod

by rocqua 7y ago

I recall hearing this adage from a philisopher of mathematics a few years ago, and it has really stuck with me. To me, this seems like the source of much unproductive disagreement. It highlights on one hand the value of Baysian theory (for it can break the stalemate). On the other hand, it highlights an uncomfortable truth for science. Two reasonable people with different experiences (and hence different priors) can interpret the same evidence in wholly different ways. Hence, there is not a clear-cut criterion for 'conclusive' evidence.

nabla9 7y ago
How does Bayesian thinking hep with this??
- deleted 7y ago
  [deleted]
- rocqua 7y ago
  When you have an proof that A -> B and indications that A is true, you have two choices: - Accept that B is also true - Accept that A is false despite the indications. In a Bayesian way of thinking you compare which of these has a higher prior and pick that one. (Glossing over the fact that 'accept X is true' is not quite a Bayesian thing to say)
  - nabla9 7y ago
    That changes nothing because you assume A has higher prior and the other guy assumes -B has higher prior. When someone rejects the premise priors, you Bayesian reasoning does not help.
    - rocqua 7y ago
      It helps explain the paradox that the same evidence leads to differing conclusions.
      - danharaj 7y ago
        What you described is not essentially different. It's the same phenomenon with {0, 1} (classical) and [0,1] (bayesian). What makes bayesian reasoning interesting is its dynamics, how does evidence change beliefs? But does it even make sense to talk about posteriors associated with classical deduction?
        gwern 7y ago
        It's hard to say how Bayesian reasoning really works with classical logic (which is true of all statistical approaches), but you can set up plausible Bayesian models where you do get 'backfire' or 'polarization' effects in which people update in different directions based on the same observation because of the different models/priors they hold: https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarization.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarizatio...
        rocqua 7y ago
        I was thinking of Bayesian here as a contrast to Frequentist, not as a form of logic with uncertainty.
taneq 7y ago
> Two reasonable people with different experiences (and hence different priors) can interpret the same evidence in wholly different ways. I don't understand how this could possibly be otherwise? Thinking about it more, the problem lies in the juxtaposition of "two reasonable people with different experiences" and "the same evidence", since the evidence you're evaluating is always really the sum total (or distillate, at least) of all evidence you've ever seen. You can't just give someone a new fact in a vacuum and ask them to evaluate it without letting the entire rest of their experience affect that evaluation.

by rocqua 7y ago

nabla9 7y ago

How does Bayesian thinking hep with this??

deleted 7y ago
[deleted]
rocqua 7y ago
When you have an proof that A -> B and indications that A is true, you have two choices: - Accept that B is also true - Accept that A is false despite the indications. In a Bayesian way of thinking you compare which of these has a higher prior and pick that one. (Glossing over the fact that 'accept X is true' is not quite a Bayesian thing to say)
- nabla9 7y ago
  That changes nothing because you assume A has higher prior and the other guy assumes -B has higher prior. When someone rejects the premise priors, you Bayesian reasoning does not help.
  - rocqua 7y ago
    It helps explain the paradox that the same evidence leads to differing conclusions.
    - danharaj 7y ago
      What you described is not essentially different. It's the same phenomenon with {0, 1} (classical) and [0,1] (bayesian). What makes bayesian reasoning interesting is its dynamics, how does evidence change beliefs? But does it even make sense to talk about posteriors associated with classical deduction?
      - gwern 7y ago
        It's hard to say how Bayesian reasoning really works with classical logic (which is true of all statistical approaches), but you can set up plausible Bayesian models where you do get 'backfire' or 'polarization' effects in which people update in different directions based on the same observation because of the different models/priors they hold: https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarization.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarizatio...
      - rocqua 7y ago
        I was thinking of Bayesian here as a contrast to Frequentist, not as a form of logic with uncertainty.

taneq 7y ago

> Two reasonable people with different experiences (and hence different priors) can interpret the same evidence in wholly different ways. I don't understand how this could possibly be otherwise? Thinking about it more, the problem lies in the juxtaposition of "two reasonable people with different experiences" and "the same evidence", since the evidence you're evaluating is always really the sum total (or distillate, at least) of all evidence you've ever seen. You can't just give someone a new fact in a vacuum and ask them to evaluate it without letting the entire rest of their experience affect that evaluation.