ackien

I've also had luck with only storing results for only a very small subset of the productions of a grammar.

What you've shown is that that particular number (0.0178.../the length of the pencil in metres) is describable. This isn't the same as showing every real number is describable. There are some numbers which are not the length of anything (in metres), or the mass of anything (in kilograms), or the square root or sin of anything. You could try to capture more numbers by using descriptions like "the length of this pencil in feet" and other made-up units of measurement, but you'll never describe them all.

>To sum up: probabilities are (a) true or false, (b) regardless of what I believe about this probabilities. Estimated probabilities (c) depend on the prior knowledge of the mind in question. Moreover, (d) the fact that the probability is X is a fact about my mind.

I'm not sure why you then go on to say that probability is neither objective nor subjective, and that probability has traits of both (which seems somewhat like a contradiction), rather than conclude that there are two different kinds of probability: objective probability and subjective probability ('probabilities' and 'Estimated probabilities' as you even differentiate yourself). (And then there is the other interpretation of the question of whether objective probability even exists at all or wether the world is deterministic.)

The bystander effect/Genovese syndrome: http://en.wikipedia.org/wiki/Bystander_effect

Perhaps the effect is quite different when there is just one other bystander, as opposed to a whole crowd of them.