circularity of possibility defined over possible worlds

Question

I have just checked similar questions that have been asked(and answered) before but I am still confused. How is it that the notion of possibility defined over as being True in some possible world not a circular definition? I mean if we assume that I need to explain some alien race that does not have a conception of the notion of possibility , it seems as though an explanation of it over some 'possible' world does not do the trick. Is this circularity dismissable? (Do you know of any papers that discuss such issues?) Thanks in advance

Answer 1

"Possible worlds" must be read as a façon de parler (manner of speech).

See Kripke semantics:

A Kripke frame or modal frame is a pair (W,R), where W is a set, and R is a binary relation on W. Elements of W are called nodes (or worlds) and R is known as the accessibility relation.

See: Saul Kripke, A Completeness Theorem in Modal Logic, JSL (1959).

The same in E.Zalta, Basic Concepts in Modal Logic:

A standard model M for a set of atomic formulas shall be any triple (W;R;V) satisfying the following conditions:

1. W is a non-empty set,

2. R is a binary relation on W, [...]

Remark: For any given model M, we call W the set of worlds in M, R the accessibility relation for M.

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See also: John Divers, Possible Worlds, Routledge (2002).

Answer 2

In complement to the other answer, I would say that there's indeed a circularity if you think of the semantics as some kind of exhaustive definition for the terms "possible" and "necessary". But you can also think of it as an exposition of the structure associated with these terms, without thinking that this structure exhaust the meaning of these terms. It just make these terms more "graspable" by indicating the rules that govern their use. You could have the same difficulty with most fundamental mathematical concepts. For example, it's not clear that a model of natural numbers in set theory is an exhaustive definition of "natural number" rather than an exposition of their structure. In principle, something else could have the same structure, which would indicate that there's a one-to-one mapping with natural numbers, not that they're numbers. Intuitively speaking, I would be tempted to say that something else is required for a structure to actually represent natural numbers, or modalities, which has to do with how the structure is practically applied (counting...). But in this respect, there are different kinds of numbers (Cardinal/ordinal) just as there are different kinds of modalities (logical, epistemic, metaphysical...) which all imply different meanings of "possible"and "necessary", even though the semantics is the same.

In the case of metaphysical modalities, some philosophers solve this issue by assuming that either "possible" or "necessary" is a primitive, non-analysable term.