If you think that none of these have anything to do with each other, you’re not thinking like a philosopher. In fact, each represents a form of hypothesis confirmation.
To illustrate, take the following hypothesis:
1. All ravens are black.
From this follows that
2. All non-black things are non-ravens.
These two statements are logically equivalent–they must be, since each is the contrapositive of the other.
When a black raven is seen, the hypothesis that “all ravens are black” is confirmed. Similarly, when any non-black object is seen, and it is not a raven, statement (2) that “all non-black things are non-ravens” is supported. Then, by extension, statement (1) is also supported. By this logic, every green apple or white tennis shoe is confirmation tat all ravens are black.
Such a conclusion is, of course, counterintuitive, and an apparent paradox. Many philosophers, however, say that no paradox exists, and that each green apple and goldfish does support the hypothesis that all ravens are black. The logic only seems stranger to us than a black raven supporting the hypothesis than all ravens are black because there are so many more non-black things in the universe than ravens, and thus the confirmation from a non-black non-raven is much smaller in merit than that of seeing a black raven. In fact, the number of non-black things in the universe is either infinite or very large, the degree by which a non-black object supports the hypothesis that all ravens are black is infinitesimal.
The problem may not be so easily resolved, however, for a green apple equally supports the statement that all ravens are white. This new contradiction leads us to examine confirmation in more depth.
The only way to prove for certain that all ravens are black is to check every raven in the universe and show that each is black: simply finding a very large number of black ravens is insufficient. After all, just like swans were assumed to be white without contradictions until black swans were discovered in Australia, so somewhere in the universe, a non-black raven might exist.
A simpler instance to search the universe for is a non-black raven. If just one is found, the hypothesis is immediately disproved.
But what if we hypothesized that “all centaurs are green”? Then our search would return zero non-green centaurs, and we must conclude that all centaurs are indeed green.
There is really only one situation in which there is a simple answer to “all Xs are Ys”: if there is only one X. So, if we ever discover the Loch Ness Monster (of which there is only one), it will be very easy to test hypotheses.
Do all Loch Ness Monsters eat ice cream for breakfast? Well, just sneak up to Nessie’s breakfast time and check out what she eats. If you see a nice bowl of ice cream, well, it seems all Loch Ness Monsters eat ice cream for breakfast.