Thomas Nagel writes a review of Alvin Plantinga’s recent book, Where the Conflict Really Lies, which James Beebe has also nicely reviewed here at Prosblogion.
Nagel’s review is well-written and charitable. He covers much territory by summarizing large swathes of Plantinga-philosophy in succinct paragraphs, all without sacrificing accuracy. (He even appears to have carefully read footnotes from Plantinga’s other works.) His only objection seemed to be that Plantinga does not consider naturalist theories of mental content. Plantinga doesn’t cover them in this book, but he deals with a number of them in a recent PPR paper.
So, as one very familiar with Plantinga’s work, I was impressed with Nagel’s review.
In Where the Conflict Really Lies, which James Beebe has nicely reviewed, Alvin Plantinga discusses nomological necessity, the necessity had by physical laws. As he (and everybody else) points out, propositions like
2) Every sphere made of gold is less than 1/2 mile in diameter
are true and universal. However, there is a clear sense in which (2) is not necessary in the sense required for lawhood (the sort of necessity we call ‘nomological necessity’). On the other hand, the proposition that no object can increase from a velocity less than the speed of light to a velocity more than the speed of light is nomologically necessary. Also, it does not seem that this proposition is necessary in the broadly logical or metaphysical sense; the law seems contingent.
How are we to understand nomological necessity? Plantinga suggests:
But numbers and sets themselves make a great deal more sense from the point of view of theism than from that of naturalism. Now there are two quite different but widely shared intuitions about the nature of numbers and sets. First, we think of numbers and sets as abstract objects, the same sort of thing as propositions, properties, states of affairs and the like… On the other hand, there is another equally widely shared intuition about these things: most people who have thought about the question, think it incredible that these abstract objects should just exist, just be there, whether or not they are ever thought by anyone. Platonism with respect to these objects is the position that they do exist in that way, that is, in such a way as to be independent of mind… But there have been very few real Platonists, perhaps none besides Plato and Frege, if indeed Plato and Frege were real Platonists (and even Frege, that alleged arch-Platonist, referred to propositions as gedanken, thoughts). It is therefore extremely tempting to think of abstract objects as ontologically dependent upon mental or intellectual activity in such a way that either they just are thoughts, or else at any rate couldn’t exist if not thought of. (287-288)
I am inclined to think that there are numbers and that they are abstract objects, but I don’t have the second intuition that they must be thought. Is there something I’m missing? I do have the intuition that contingently existing objects must have a cause for their existence, but I don’t have the intuition that abstract objects must be thought, which, if they exist, necessarily exist.
Maybe somebody could help motivate this intuition for me? Or is this intuition not very widely shared (contra Plantinga’s remark)?