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A Roadblock for Theories of the Trinity

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Here’s an argument that poses a problem for developing a theory of the Trinity:

  1. For polytheism to be true is for it to be the case that there is an x and there is a y such that (i) x is god (i.e., the predicate “god” applies to x), (ii) y is god (i.e., the predicate “god” applies to y), and (iii) x is not identical to y. In other words, there are at least two gods
  2. The Son is god (i.e., the predicate “god” applies to the Son)
  3. The Father is god (i.e., the predicate “god” applies to the Father)
  4. The Son is not identical to the Father

    Therefore, via conjunction introduction and existential generalization on (2), (3), and (4):

  5. There is an x and there is a y such that (i) x is god (i.e., the predicate “god” applies to x), (ii) y is god (i.e., the predicate “god” applies to y), and (iii) x is not identical to y
  6. Therefore, polytheism is true

Question: why hasn’t anyone rejected (2) and (3) and introduced a non-distributive plural predicate “(are) god” that applies to a plurality of things taken together without applying to any of them individually (or understood “god” to be a “multigrade” predicate that can be used in such a way)?

Compare: Jones, Smith, and Mary are such that they are carrying the casket, but none of them is individually such that they are carrying the casket.

This needn’t incur an ontological commitment to a fourth divine thing (a “group”) so long as plural logic is irreducible to singular logic.

NOTE: I submitted this draft post unintentionally, but since it already generated some discussion in the comments, I decided to leave it up.

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