Originally posted by DoctorScribbles
Under your view, I can conclude that all coins land heads under 50% of the time. For example, any coin could warp mid-flight and become a double-tailed coin, since we can't be certain that the laws of physics preclude this. This is no different than your analysis that frogs jump to Jupiter with a positive probability since we can't be certain of the laws that indicate that they can't.
Everything about probabilities follows from:
(i) A probability is a surjection from an event space to the interval [0,1];
(ii) The probability of the union of every event in the event space is 1;
(iii) If two elements of the event space are disjoint, then the probability of their union is the sum of their probabilities.
Let's modify these, creating the PSPPF (Potentially Strawmanular Pawnokeyhole Probability Formalisation):
PSPPF(i) A probability is a surjection from an event space to the interval (0,1];
PSPPF(ii) The probability of the union of every event in the event space is 1;
PSPPF(iii) If two elements of the event space are disjoint, then the probability of their union is the sum of their probabilities.
These are obviously inconsistent or incomplete (either P({...}) is positive, violating (iii) or undefined, violating (i)).