Isn’t it always the case when a catalogue is published that new specimens are found straight away as people begin to use it. I’m in the process of updating a catalogue for a particular series of the coins of Carausius and whilst I am checking against significant public and private collections I know new ones will turn up after it is published.
It’s because we’re dealing with an unknown total population. We know what does exist and we may predict what should exist but we don’t know what could exist. We’re dealing with a sample population and therefore we cannot, for certain, prove a hypothesis, only disprove it. I can’t remember my lectures so well but it may be called deductive reasoning (or possibly inductive reasoning).
The example I was given at university, a number of years ago now, was that we could come up with a hypothesis “all swans are white”. We can test this by observation and indeed the hypothesis will hold true until the first black swan is observed.
An example in the coin world is could be the Gallic usurpers. In the 19th century the hypothesis “the Gallic usurpers that issued coins are Postumus, Laelianus, Marius, Victorinus, plus Tetricus I and II” was thought to be true. There was no indication that it was not and all the data from hoards and site finds corroborated it. In 1900 we finally knew with certainty that the hypothesis was not true because a coin of Domitianus II was found. So, we now include him in the hypothesis of the list of Gallic usurpers that issued coins which we will only know for certain not to be true when a new usurper is found. As we are dealing with an unknown total population the hypothesis itself can never be proved true.