It just hit me how puzzling Platonism is. There are infinitely many abstract objects. These objects are really real, and their existence seems not to be explained by the existence of concreta, as on Aristotelianism. Why is there this infinitude of objects?
Of course, we can say that this is just a necessary fact. And maybe it’s just brute and unexplained why necessarily there is this infinitude of objects. But isn’t it puzzling?
Augustinian Platonism, on which the abstract objects are ideas in the mind of God, offers an explanation of the puzzle: the infinitely many objects exist because God thinks them. That still raises the question of why God thinks them. But maybe there is some hope that there is a story as to why God’s perfection requires him to think these infinitely many ideas, even if the story is beyond our ken.
I suppose a non-theistic Platonist could similarly hope for an explanation. My intuition is that the Augustinian’s hope is more reasonable.
8 comments:
Alex
Actually, the only thing that is puzzling is the existence of necessary objects. Once we accept that necessary objects exist, there is nothing puzzling about saying that necessarily there is this infinitude of objects.
A non-theistic Platonist can argue that the infinitude of objects is due to the fact that the (Platonic) world is perfect, IOW that the perfection of the world "requires" that infinitely many objects exist. After all, if perfection didn't require infinitely many objects, then God would not be required to think infinitely many ideas to be perfect either.
I suppose one could have a metaphysical principle on which the Platonic world needs to be perfect. But the Platonic world isn't a *thing*: it is a plurality of things. I find principles embodied in individual substances more comprehensible.
Alex
I think you have it backwards. If necessary objects can exist, the Platonic world is perfect because it contains all (possible) necessary abstract objects. If there are infinitely many possible abstract objects, the Platonic world necessary contains all of them. It's not that the Platonic world "needs" to be perfect, and the same holds for God. God doesn't "need" to be perfect, God is perfect because He "contains" all (possible) abstract objects.
The Platonic world can be seen as a set, so it is not a plurality of things any more than a mind containing an infinitude of ideas is a plurality of things.
For the record, I am not a Platonist myself.
Oh. I read your "is due to the fact" as offering an explanation. I guess it wasn't.
It is a deep question, though, whether God's perfection is explanatory of God's specific attributes.
Alex
I think the real deep question is how exactly necessity can be explanatory.
My "is due to the fact" is an explanation iff (the) necessity (of abstract objects) counts as an explanation, just as "God is necessary" would count as an explanation for why there is a God and what exactly this God is.
In general "p is necessary" is not an explanation of p. Otherwise, we get a ridiculous regress:
0 = 0 because Nec(0=0) because Nec(Nec(0=0)) because Nec(Nec(Nec(0=0))).
There might be some special cases where "p is necessary" is an explanation of p.
Alex
If the necessity of abstract objects doesn't count as an explanation, perfection doesn't count as an explanation either, because God's specific attributes are necessary for God's perfection. So, we get P (God's perfection) = S(God's specific attributes)
because Nec(P=S) because Nec(Nec(P=S) etc.
So, we get back to my original point, which is that what is puzzling is the existence of necessary objects and I should add, what it means for something to be necessary.
Hi Alex,
There are abstract objects because there are no universal properties (i.e., properties held by everything that exists).
Take the property of being a concrete object. This property is not universal, so there is at least one thing that is not concrete. That is, there is at least one abstract object.
Further - by applying a number of plausibly true principles for obtaining new abstract objects from given ones - it follows that there are infinitely many abstract objects.
Now, you might wonder why there are no universal properties? Well, for that I would like to refer to my "semantic argument":
Short version: http://gjerutten.nl/SemanticArgumentSpecialVersion_ERutten.pdf
Full version: http://gjerutten.nl/SemanticArgument6.pdf
Best,
Emanuel
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