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Is it OK to argue that what is hugely more likely to occur is in fact the case?

There seems to be a class of paradox that relies on the idea that what we think is the case is in fact much much less likely to occur by chance than some other scenario, usually highly counter-intuitive, the suggestion being that we should reject the former is in fact the case. e.g. Boltzmann brains:

The paradox states that if one considers the probability of our current situation as self-aware entities embedded in an organized environment versus the probability of stand-alone self-aware entities existing in a featureless thermodynamic "soup", then the latter should be vastly more probable than the former.

Another example may be the idea, and I'm sorry but I forgot who to cite, that we're not alive for so much of the existence of the universe, reality, that it makes no sense, and the odds are we alive for more of it than we think.

Or perhaps the idea that the universe or multiverse is so huge that the odds are that our minds will repeat or re-occur someplace else.

Is this a class of paradox?

  • It is better now. I assume we are talking about heuristic reasoning here, not mathematics. Then it is reasonable to downrate scenarios that require unlikely events if an alternative is at all possible, think of catastrophes and saltations once used to "explain" evolution. This does not mean that they did not happen at all (in rare cases we know they did), but "extraordinary claims require extraordinary evidence" rule applies. Paradox and fallacy are two different things. When something factual "seems" unlikely we have a paradox, the argument for why it is unlikely, or likely, may be a fallacy. – Conifold Mar 14 '17 at 21:00
  • @Conifold that's quite helpful actually, think I do make that mistake. I guess there's no fallacy general to all paradoxes of this type, else they would not be called paradoxes hah – anon Mar 14 '17 at 21:06
  • @Conifold are these bad explanations of evolution (not sure what you refer to?) unlikely in the same way as the Boltzmann claim that we are not really brains? something that is a fluke (that i am not a Boltzmann brain) need not have little evidence for it. right? also is the following wrong? A has 1/3 chance. If A then B. So B has at least a 1/3 chance. – anon Mar 14 '17 at 22:31
  • Sorry, I do not understand what "in the same way" or "something that is a fluke need not have little evidence for it" mean. Saltations are certainly less likely than regular mutations since multiple genes have to be altered at once. The probability claim is technically right under ironclad inference, but such ironcladness rarely applies in empirical contexts, for heuristic inference it might be less due to the uncertainty of the inferring. – Conifold Mar 14 '17 at 22:45
  • @Conifold this is obviously not a helpful discussion in this format, as i'm clearly failing to communicate. i just mean that what really was unlikely (smith winning the lottery) can happen. – anon Mar 14 '17 at 23:12

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