{"id":1030,"date":"2020-05-29T23:30:11","date_gmt":"2020-05-30T03:30:11","guid":{"rendered":"http:\/\/aristotle2digital.blogwyrm.com\/?p=1030"},"modified":"2020-06-21T15:11:03","modified_gmt":"2020-06-21T19:11:03","slug":"boy-girl-paradox-and-the-language-of-probability","status":"publish","type":"post","link":"https:\/\/aristotle2digital.blogwyrm.com\/?p=1030","title":{"rendered":"Boy-Girl Paradox and the Language of Probability"},"content":{"rendered":"\n

It is odd how the phrasing of a question changes the meaning\nand interpretation of probability-based situations.  Philosophically, we should expect a degree of\nfluidity because when we engage in thinking about and discussing probabilities\nwe wander into the twilight zone of thought. \nClear distinctions between what is known and what can be known, between\nepistemological uncertainty and ontological uncertainty (sometimes called aleatory\nvariability<\/a>), and how and why we know are important if we ever want to\nemerge from the forest of confusion and doubt.<\/p>\n\n\n\n

For a simple example of some of the complexity that can\narise, consider the lowly coin flip. \nImagine you are at a friend\u2019s house and the two of you are arguing over\nwhat movie to watch.  Your friend wants\nto watch Predator<\/em> and you want to\nwatch Alien<\/em>.  You decide to settle the debate on a coin\nflip of the variety where he flips the coin, catches it, mashes it onto his arm\nwith his hand covering it, and then he invites you to call it heads or tails.<\/p>\n\n\n\n

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Assuming the coin is fair, you reckon that there is a\nfifty-fifty chance that you\u2019ll be enjoying Alien tonight while he just has to\ngrin and bear it.  He then flips the coin\nand, as you contemplate the hidden disk upon which all your hopes and dreams\nride (at least as this evening\u2019s movie selection is concerned), you may be\nmoved to say that the probability of heads is 0.5.  But in this you would be wrong.  The probability of the flip coming up heads\nbefore it is tossed is 0.5 (an example of ontological uncertainty) but after\nyou friend has flipped and caught the coin there is a decided outcome.  The correct way of phrasing the situation is\nto say that the probability that you will guess the already selected result is\n0.5 (an example of epistemological uncertainty).  <\/p>\n\n\n\n

Hopefully this simple example has clarified these points a\nbit.  Ontological uncertainty usually\narises when making predictions of physical outcomes of an event with the\ntraditional example being Aristotle\u2019s\nsea battle<\/a>.  Whether a sea battle\nwill happen tomorrow is a statement that cannot have definitive truth value\n(either true or false) and is an example where the law of the excluded\nmiddle<\/a> may be violated. \nEpistemological uncertainty arises when making decisions about the past\noutcome of an event with limited knowledge with a corresponding example being\nwhether the sea battle that happened today was a victory for one side or a\ndefeat.<\/p>\n\n\n\n

It is very easy to get confused on these points, and an excellent example of this controversy was raised by Zach Star in his YouTube video entitled This May Be The Most Counterintuitive Probability Paradox I’ve Ever Seen | Can you spot the error?<\/em> from April 7, 2019.\u00a0 <\/p>\n\n\n\n