The example of such an unthinkable or unimaginable thing for a person could be non-existence, therefore argument against existence seems to be so absurd. Aren't we calling such things axioms or postulates?

  • Not clear... The text speaks of an "an unthinkable or unimaginable thing", in which case how we can "name" an unthinkable thing ? – Mauro ALLEGRANZA Sep 18 '19 at 7:36
  • While the title is more convoluted : "a statement that is unthinkable/ unimaginable for a person to not be the case" that sounds like (but I may be wrong) that a person cannot fail to think... – Mauro ALLEGRANZA Sep 18 '19 at 7:37
  • I meant: A statement that is unthinkable or unimaginable for a person to not be the case. – TKN Sep 18 '19 at 7:59
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    In other words: We argue that something is the case and we cannot imagine any possible case in which the it is not the case. My question is than: How do we call such a statement for which it is unthinkable for a person to not be the case? – TKN Sep 18 '19 at 8:03
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    Obviously not a postulate: we can imagine for Euclid's fifth postulate to not be the case (and we have imagined it...). – Mauro ALLEGRANZA Sep 18 '19 at 8:06

Such a thing is not in general an axiom or postulate. Such an idea can be complex and non-foundational. Humans may not be able to actually imagine that there are countably many Real numbers. But to get to that point requires a lot of leverage. No one would consider that an axiom.

More formally, very few such things are axioms. For if you had two or more ideas that cannot be imagined to be false, their combination would also be such a thing. The combination of two axioms is never an axiom.

I think that what you are after are simply necessary propositions, statements in the modality of "must", the content of the standard modal logic selected by the 'box' operator, facts true in all possible worlds (however one chooses to name this content.)

If you mean a specific person, and not a general person, this is the variant of that modality where the relevant attached context for necessity (or set of possible worlds, or visibility filter on the possible worlds (again depending on your model of a modal)) is determined by that individual's mental configuration rather than by "natural" possibility.

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