Ideas from 'Platonistic Theories of Universals' by J Hoffman/G Rosenkrantz [2003], by Theme Structure

[found in 'The Oxford Handbook of Metaphysics' (ed/tr Loux,M /Zimmerman,D) [OUP 2005,0-19-928422-9]].

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2. Reason / B. Laws of Thought / 6. Ockham's Razor
Entities can be multiplied either by excessive categories, or excessive entities within a category
                        Full Idea: There are two ways that entities can be multiplied unnecessarily: by multiplying the number of explanatory categories, and by multiplying the number of entities within a category.
                        From: J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 4)
                        A reaction: An important distinction. The orthodox view is that it is the excess of categories that is to be avoided (e.g. by nominalists). Possible worlds in metaphysics, and multiple worlds in physics, claim not to violate the first case.
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
'There are shapes which are never exemplified' is the toughest example for nominalists
                        Full Idea: The example which presents the most serious challenge to nominalism is 'there are shapes which are never exemplified'.
                        From: J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 3)
                        A reaction: To 'exemplify' a shape must it be a physical object, or a drawing of such an object, or a description? If none of those have ever existed, I'm not sure what 'are' is supposed to mean. They seem to be possibilia (with all the associated problems).
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalists are motivated by Ockham's Razor and a distrust of unobservables
                        Full Idea: The two main motivations for nominalism are an admirable commitment to Ockham's Razor, and a queasiness about postulating entities that are unobservable or non-empirical, existing in a non-physical realm.
                        From: J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 3)
                        A reaction: It doesn't follow that because the entities are unobservable that they are non-physical. Consider the 'interior' of an electron. Neverless I share a love of Ockham's Razor and a deep caution about unobservables.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete
                        Full Idea: There are four models of the ontological status of possible worlds: conceptualist (mental constructions), combinatorial (all combinations of the actual world), abstract worlds (conjunction of propositions), and concrete worlds (collections of concreta).
                        From: J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 4)
                        A reaction: [the proponents cited are, in order, Rescher, Cresswell, Plantinga and Lewis] They dismiss Rescher and Cresswell, both of whom seem to me more plausible than Plantinga or Lewis. 'Possible' can't figure in the definition. Possible to us, or in reality?