Another way to see it: consider the case where an examiner asks you to choose between three boxes (red, green, blue) one of which contains a diamond.
Normally you would assign 1⁄3 probability to each box of containing the diamond, but you have cleverly slipped a priming cue while talking earlier with the examiner, saying “I love blue skies”, and your experience with priming is such that your probability assignments are now 1/3+epsilon for blue, and 1/3-2*epsilon for each of red and green.
We now have a situation where p(blue) < .5 but where you nevertheless “believe that” the diamond is in the blue box, insofar as that is the box you’d pick.
The verb “believe” expresses what linguists call a modality. I think we should be careful when mixing in the same sentence statements of probability and everyday language modalities, because they belong to different levels of abstraction. (Disclaimer: I am no linguist and claim only basic familiarity with concepts like modalities and the pragmatics of language. But they do seem like awesome tools, that I should learn more about just as I should learn more about probability theory.)
I wouldn’t assume that “I believe X” is the same as “it is more likely than not that X is true”. “I believe” is called an epistemic modality, one that expresses a state of knowledge. An interesting property of epistemic modalities is that they usually weaken whatever statement they are associated with. For instance, “The cat is on the mat” is a nice definite statement. If you told someone, “I believe the cat is on the mat”, they might ask “Oh, but are you sure?”. Paradoxically, even “I’m sure the cat is on the mat” would be taken as expressing less confidence than “The cat is on the mat” without a modal part.
Bruno Latour is fond of pointing out that the construction of scientific knowledge largely involves stripping modalities. You go from “Kahneman (1982) suggests that X”, to “Kahneman has shown that X”, to “It is well established that X”, to “Since X”, and finally you don’t even mention X any longer, it has merged into background knowledge.
You go from “Kahneman (1982) suggests that X”, to “Kahneman has shown that X”, to “It is well established that X”, to “Since X”, and finally you don’t even mention X any longer, it has merged into background knowledge.
Unfortunately, this process can occur even in the absence of any attempt to obtain evidence for X. Sometimes just by accident.
Another way to see it: consider the case where an examiner asks you to choose between three boxes (red, green, blue) one of which contains a diamond.
Normally you would assign 1⁄3 probability to each box of containing the diamond, but you have cleverly slipped a priming cue while talking earlier with the examiner, saying “I love blue skies”, and your experience with priming is such that your probability assignments are now 1/3+epsilon for blue, and 1/3-2*epsilon for each of red and green.
We now have a situation where p(blue) < .5 but where you nevertheless “believe that” the diamond is in the blue box, insofar as that is the box you’d pick.
The verb “believe” expresses what linguists call a modality. I think we should be careful when mixing in the same sentence statements of probability and everyday language modalities, because they belong to different levels of abstraction. (Disclaimer: I am no linguist and claim only basic familiarity with concepts like modalities and the pragmatics of language. But they do seem like awesome tools, that I should learn more about just as I should learn more about probability theory.)
I wouldn’t assume that “I believe X” is the same as “it is more likely than not that X is true”. “I believe” is called an epistemic modality, one that expresses a state of knowledge. An interesting property of epistemic modalities is that they usually weaken whatever statement they are associated with. For instance, “The cat is on the mat” is a nice definite statement. If you told someone, “I believe the cat is on the mat”, they might ask “Oh, but are you sure?”. Paradoxically, even “I’m sure the cat is on the mat” would be taken as expressing less confidence than “The cat is on the mat” without a modal part.
Bruno Latour is fond of pointing out that the construction of scientific knowledge largely involves stripping modalities. You go from “Kahneman (1982) suggests that X”, to “Kahneman has shown that X”, to “It is well established that X”, to “Since X”, and finally you don’t even mention X any longer, it has merged into background knowledge.
Unfortunately, this process can occur even in the absence of any attempt to obtain evidence for X. Sometimes just by accident.