Isn't your claim about probabilities logically inconsistent?

I don't think 0<p<1 is true, the probability of logical tautologies is 1. The probability that a bachelor is not married and never has been is 1.

nothing is impossible, and nothing is absolutely sure. this is obviously wrong. The proposition a="at exactly 3am at the exact GPS locations my house there spontaneously appeared a big chunk of pure gold" clearly has $P(a)=0$, at least and very much so in hindsight.

@AnoE a very unlikely quantum tunneling event!? ;o)

@Anoe your statement about gold in your house is quite naive. It is possible that a plane with gold falls over your house, it's possible a friend gives you a surprise, it's possible an animal leaves it, it's possible that it's hidden behind a wall and an earthquake suddenly throws it in your hands, etc. The probability is small, but it's NEVER zero. Empirically, p is never 0 or 1. The probability that a coin breaks in the middle, and each side falls visible over the table is not zero. The probability you win the lottery is not zero, even if you try ten times and win nothing.

@DikranMarsupial logical tautologies are not empirical facts, read the answer. 0<p<1 occurs empirically, not logically (metaphysically, rationally). Rationally, p=0 or 1 is not a problem. Empirically, you can ask Schroedinger to change the cat with a bachelor in a superposition of being married and single states, even I can think of a mechanism to do that. Or you might apply the scientific method, measure the married state of the bachelor and get two false positives among three measurements (and then, you will write a successful paper, not joking). Probability of error is never 0 in science.

@DikranMarsupial somewhere I've read that in some country, a man can be (legally) married, while for taxing purposes he is (also legally) considered a bachelor because he doesn't live with his wife. Sounds correct. Voilà, a married bachelor in practice (while here, there's clearly a logical error, empirically, this works. Apparently, lawyers have the right to break the rules of logic).

@RodolfoAP logical impossibilities don't occur in reality either, if something is a logical tautology, then they can't happen any other way in reality. This is because they are statements about logic and they only apply if the definitions in reality match those used in the logic. In the bachelor example, the definition of a bachelor has been altered so that a married bachelor is no longer a logical impossibility.

Also Schrodinger's cat is only a thought experiment, it isn't what would actually happen. A cat is far too large an object to be in quantum superposition, so effectively it would be the observer. As for measurement error, if you think you have observed something logically impossible and don't try to eliminate the possibility of measurement error, you are acting irrationally.

Talking of gold, any gold that does make a surprising appearance in @AnoE 's house will definitely have an atomic number of 79... is knowing this an empirical discovery, or a purely formal definition of a symbol in the English language? If you go with the latter, consider this: the Earth did not necessarily have a moon, but it certainly had one yesterday.

@DikranMarsupial I don't see the point on rebating an idea that dates from 1700 (see David Hume). If you want to believe that 100% and 0% probabilities exist, good for you! Congratulations! You know the future! Science doesn't. In science, there are no unquestionable predictions (not even statements) in the full body of science. Regarding Schroedinger's cat, it does not work for macro bodies, correct, but I've assumed you would consider the idea. You don't need to put a fat guy inside the box. Just a quantum particle in superposition, as the indicator married/non-married.

@rodolfoap, maybe let's return to the question from OP. It seems like he is talking on a quite different level (more conceptual etc.) from what we are discussing in this comment stream, and I just don't see how this answer is related to his question (and sorry for starting so much confusion with my comment by not wording/thinking it out to standards).

@RodolfoAP I note you provide no real responses to the counter arguments I provided and just try and make it personal. The only way that logical consistency does not apply to the real world is because of problems with natural language. The inconsistency disappears with the appropriate change of wording. This is nothing to do with knowing the future, that is just rhetorical hyperbole/straw man.

"Just a quantum particle in superposition, as the indicator married/non-married" this is sort of the point, in the quantum realm, it isn't a contradiction for particles to be in superimposed states, that is how the quantum world is (as far as we know).

"In science, there are no unquestionable predictions (not even statements) in the full body of science. " I think this clarifies the disagreement. When has science ever made predictions about logically impossible events in the real world? E.g. faster than light travel is not a logical impossibility, it is just a corollary of particular set of theories. Science doesn't hold any theories as being certain, so it isn't a logical impossibility for reality, just when conditioned on that theory.

@DikranMarsupial "logical(...) events in the real world" is an oxymoron. Either an event is logical (e.g. A->B, A) or either an event is empirical ("real") (e.g. it rains). Relativity formulae are logical facts, where 0≤p≤1, so, logically, 100% probability is OK. In "reality", 0<p<1, so, 100% probability is impossible, independently of what formulae say. This occurs because reality is far, far, far more complex that logical abstractions. You should avoid mixing logic (mind) and reality (senses), they are two different realms. Read the answer carefully.

"Read the answer carefully." making the discussion personal again. There are correspondence between reality and logic. We get that when we use words to describe what we see. When we describe something that is logically impossible, it means the words we used do not map correctly onto reality because logical impossible things can't happen in reality. 2+2=5 doesn't happen in reality, if it happens in our descriptions it is an error in the descriptions (e.g. redefinition of terms).

Haha, sorry this is fun, no personal intentions. 2+2 is not always 4 in reality. If you have a weighing device that displays weights rounded to the Kg, without decimals, and you weigh an object of 2.33 kg, you'll get "2Kg". Put another of the same weight on the device, and you'll get "5Kg". So, logically, "2+2=4", but empirically, in this case, "2kg+2kg=5kg". And THIS IS NOT THE ONLY CASE! In reality, the weighing device could have bad batteries, no decimals, exhaust springs, bad calibration, etc. In other words, the empirical probability of 2kg + 2kg measuring 4kg is not 100%.

Let us continue this discussion in chat.