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Ideas for 'Parmenides', 'Plato on Parts and Wholes' and 'The Barcan Formula and Metaphysics'

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4 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
     Full Idea: The Barcan Formula and its converse gives expression to the most straightforward way of combining modal operators with classical quantification.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
     Full Idea: The Barcan Formulas are a threat to 'actualism' in modal metaphysics, which seems regrettable since the Formulas are validated by standard modal logics, but clash with the plausible and attractive actualist view (that there are no merely possible things).
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
     A reaction: He notes that the Barcan Formulas 'appear to require quantification over possibilia'. So are you prepared to accept the 'possible elephant in your kitchen'? Conceptually yes, but actually no, I would have thought. So possibilia are conceptual.
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
     Full Idea: In accordance with the Barcan Formula we assume that if it is possible that Wittgenstein should have had a child, then something or other is possibly Wittgentein's child.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §5)
     A reaction: Put like this it sounds unpersuasive. What is the something or other? Someone else's child? A dustbin? A bare particular? Wittgenstein's child? If it was the last one, how could it be Wittgenstein's child while only possibly being that thing?
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology began as a nominalist revolt against the commitments of set theory [Harte,V]
     Full Idea: Historically, the evolution of mereology was associated with the desire to find alternatives to set theory for those with nomimalist qualms about the commitment to abstract objects like sets.
     From: Verity Harte (Plato on Parts and Wholes [2002], 1.2)
     A reaction: Goodman, for example. It is interesting to note that the hardline nominalist Quine, pal of Goodman, eventually accepted set theory. It is difficult to account for things by merely naming their parts.