Reasons Given By Lewis
Lewis backs modal realism for a variety of reasons. First, there doesn't seem to be a reason not to. Many abstract mathematical entities are held to exist simply because they are useful. For example, sets are useful, abstract mathematical constructs that were only conceived in the 19th century. Sets are now considered to be objects in their own right, and while this is a philosophically unintuitive idea, its usefulness in understanding the workings of mathematics makes belief in it worthwhile. The same should go for possible worlds. Since these constructs have helped us make sense of key philosophical concepts in epistemology, metaphysics, philosophy of mind, etc., their existence should be uncritically accepted on pragmatic grounds.
Lewis believes that the concept of alethic modality can be reduced to talk of real possible worlds. For example, to say "x is possible" is to say that there exists a possible world where x is true. To say "x is necessary" is to say that in all possible worlds x is true. The appeal to possible worlds provides a sort of economy with the least number of undefined primitives/axioms in our ontology.
Taking this latter point one step further, Lewis argues that modality cannot be made sense of without such a reduction. He maintains that we cannot determine that x is possible without a conception of what a real world where x holds would look like. In deciding whether it is possible for basketballs to be inside of atoms we do not simply make a linguistic determination of whether the proposition is grammatically coherent, we actually think about whether a real world would be able to sustain such a state of affairs. Thus we require a brand of modal realism if we are to use modality at all.
Read more about this topic: Modal Realism
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