The concept of probability is not as simple as you think

#1
https://aeon.co/ideas/the-concept-of-pro...-you-think

INTRO: . . . Three popular theories analyse probabilities as either frequencies, propensities or degrees of belief. Suppose I tell you that a coin has a 50 per cent probability of landing heads up. These theories, respectively, say that this is:

(1) The frequency with which that coin lands heads;
(2) The propensity, or tendency, that the coin’s physical characteristics give it to land heads;
(3) How confident I am that it lands heads.

But each of these interpretations faces problems. Consider the following case:

Adam flips a fair coin that self-destructs after being tossed four times. Adam’s friends Beth, Charles and Dave are present, but blindfolded. After the fourth flip, Beth says: ‘The probability that the coin landed heads the first time is 50 per cent.’

Adam then tells his friends that the coin landed heads three times out of four. Charles says: ‘The probability that the coin landed heads the first time is 75 per cent.’

Dave, despite having the same information as Charles, says: ‘I disagree. The probability that the coin landed heads the first time is 60 per cent.’

The frequency interpretation struggles with Beth’s assertion. The frequency with which the coin lands heads is three out of four, and it can never be tossed again. Still, it seems that Beth was right: the probability that the coin landed heads the first time is 50 per cent.

Meanwhile, the propensity interpretation falters on Charles’s assertion. Since the coin is fair, it had an equal propensity to land heads or tails. Yet Charles also seems right to say that the probability that the coin landed heads the first time is 75 per cent.

The confidence interpretation makes sense of the first two assertions, holding that they express Beth and Charles’s confidence that the coin landed heads. But consider Dave’s assertion. When Dave says that the probability that the coin landed heads is 60 per cent, he says something false. But if Dave really is 60 per cent confident that the coin landed heads, then on the confidence interpretation, he has said something true – he has truly reported how certain he is.

Some philosophers think that such cases support a pluralistic approach in which there are multiple kinds of probabilities. My own view is that we should adopt a fourth interpretation – a degree-of-support interpretation....

MORE: https://aeon.co/ideas/the-concept-of-pro...-you-think
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#2
(Feb 28, 2019 08:33 PM)C C Wrote: https://aeon.co/ideas/the-concept-of-pro...-you-think

INTRO: . . . Three popular theories analyse probabilities as either frequencies, propensities or degrees of belief. Suppose I tell you that a coin has a 50 per cent probability of landing heads up. These theories, respectively, say that this is:

   (1) The frequency with which that coin lands heads;
   (2) The propensity, or tendency, that the coin’s physical characteristics give it to land heads;
   (3) How confident I am that it lands heads.

But each of these interpretations faces problems. Consider the following case:

   Adam flips a fair coin that self-destructs after being tossed four times. Adam’s friends Beth, Charles and Dave are present, but blindfolded. After the fourth flip, Beth says: ‘The probability that the coin landed heads the first time is 50 per cent.’

   Adam then tells his friends that the coin landed heads three times out of four. Charles says: ‘The probability that the coin landed heads the first time is 75 per cent.’

   Dave, despite having the same information as Charles, says: ‘I disagree. The probability that the coin landed heads the first time is 60 per cent.’

The frequency interpretation struggles with Beth’s assertion. The frequency with which the coin lands heads is three out of four, and it can never be tossed again. Still, it seems that Beth was right: the probability that the coin landed heads the first time is 50 per cent.

Meanwhile, the propensity interpretation falters on Charles’s assertion. Since the coin is fair, it had an equal propensity to land heads or tails. Yet Charles also seems right to say that the probability that the coin landed heads the first time is 75 per cent.

The confidence interpretation makes sense of the first two assertions, holding that they express Beth and Charles’s confidence that the coin landed heads. But consider Dave’s assertion. When Dave says that the probability that the coin landed heads is 60 per cent, he says something false. But if Dave really is 60 per cent confident that the coin landed heads, then on the confidence interpretation, he has said something true – he has truly reported how certain he is.

Some philosophers think that such cases support a pluralistic approach in which there are multiple kinds of probabilities. My own view is that we should adopt a fourth interpretation – a degree-of-support interpretation....

MORE: https://aeon.co/ideas/the-concept-of-pro...-you-think

can a computer toss a coin ?
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#4
IMHO the writer knows rather less about probability than he thinks he does.

Nevin Climenhaga is assistant professor at the Institute for Religion and Critical Inquiry at the Australian Catholic University in Melbourne. His work has been published in the Journal of Philosophy and Mind, among others. He lives in Oakleigh, Victoria.
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