In his book Metaphysics: A Contemporary Introduction (2006) , Michael J. Loux tackles the problem of “modal notions” in Chapter 5 – notions such as possibility, impossibility, and necessity – as well as empiricist objections to how we can know them. He makes a key distinction between de dicto modality (which has to do with the modality of a proposition) and de re modality (which has to do with a thing’s possessing some attribute contingently or necessarily/essentially).
Historically speaking, empiricists have been deeply suspicious about the epistemic status of modal claims. David Hume once argued that only those claims which can be (1) traced back to sense experience or which (2) result from relations between ideas based on that experience can could as knowledge. But since sense experience only tells us what is – not what must, might, or can’t be – it follows that modal knowledge is simply a matter of the definitions we create in language and the conceptual entailments of those definitions. So, for example, if we define the idea of “bachelor” as being an “unmarried male,” then bachelors possess the property of being unmarried necessarily, not contingently. Thus, modal claims are definitionally true, not empirically based. [Note: in the 20th Century, Saul Kripke argued in favor of the empirical discovery of modal truths, such as “Necessarily, water is H2O.”]
Another more obscure objection came from analytic philosophy of language in the 1940’s and 50’s. This view rejected modal notions because they were not amenable to the extensional form (see pp.178-180) which statements must have in order to be serious candidates for philosophical consideration. This can be dubbed the objection from extensionality. Later advances in modal logic tended to ease the extensionality problem through the development of a neo-Leibnizian logic of possible worlds where statements can have various truth values in different worlds (de dicto), and entities can exist or have properties in various worlds (de re). Philosophers of the neo-Leibnizian bent claim that possible worlds logic (PWL), while seemly odd and obscure at first, is deeply routed in our pre-philosophical intuitions: we intuitively sense that things might have been otherwise, and that these modal properties are the basis for the modal statements we make.
Now, philosophers still debate about what kind of ontology is required by modal logic. The Platonist school contends that “possible worlds” are causally effete abstract entities that exist is much the same way that Plato saw the Forms existing in some ideal realm beyond concrete material objects. By contrast, the Nominalist school reduces the modal to the non-modal. For example, in David Lewis’ nominalism, he reduces modal properties to sets of concrete objects and modal propositions to sets of real (but non-actual) worlds!
I will do more blog posts on Platonism and Lewis’ nominalism in the future, but in the meantime my questions are these: which view do you, the reader, gravitate to? Would you say that modality is an irreducibly abstract feature of the world (like the Platonist affirms) or can it be reduced to concrete particulars (like the Nominalist affirms)? Are there any alternatives to both of these views which are explanatorily superior?
 Michael, J. Loux, “The Necessary and the Possible” Chapter 5, in Metaphysics: A Contemporary Introduction (2006).