Objections to Platonism

Pears’ Argument Against Platonism

1. (Premise) Platonism explains “green” being applicable to a by a’s instantiating greenness.
2. (Premise) To explain something about the applicability of “green” in terms of greenness is circular.
3. (Premise) To explain circularly is pointless.
4. Therefore, Platonism does something pointless.

Field’s Epistemological Argument Against Mathematical Platonism (from SEP, s.v. “realism”)

1. Platonic realism is committed to the existence of acausal objects and to the claim that these objects, and facts about them, are independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on (in short to the claim that these objects, and facts about them, are language- and mind-independent).
2. Any causal explanation of reliability is incompatible with the acausality of mathematical objects.
3. Any non-causal explanation of reliability is incompatible with the language- and mind-independence of mathematical objects.
4. Any explanation of reliability must be causal or non-causal.
5. There is no explanation of reliability that is compatible with both the acausality and language- and mind-independence of mathematical objects

Therefore,

6. There is no explanation of reliability that is compatible with platonic realism.

The Multilocation Argument

1. (Premise) A universal is wholly present wherever it is instantiated.
2. (Premise) Nothing can be wholly present in two different places at the same time.
3. Therefore, a universal is not instantiated in more than one place at the same time. (1 and 2)
4. (Premise) If there are any universals at all, then dogness is a universal which is instantiated in more than one place at the same time.
5. Therefore, there are no universals. (3 and 4)

Alternative to (1): A universal is a scattered object.

Ryle’s Regress of Instantiation (=Exemplification) Relations

• Donagan thinks this can be escaped by denying that there is a relation between x and redness when x is red. Whether x is red or not, there is x and there is redness, and that is all that is there.
• But doesn’t this give up on the Russellian principle that the basic ingredients in sentences must correspond to something real? We say that x has the property of redness—shouldn’t there be something that corresponds to that “has”?

Alternate Languages

1. (Premise) If we could have a language as expressive as English but which did not involve predication, we would not need universals.

2. (Premise) We can have such a language.

3. Therefore, we do not need universals.

Donagan denies (1).

Tropes

• The big problem with Platonism is the problem of how the concrete things in the world are related to the universals—what the relation of instantiation is.
• One solution is to reduce the puzzling instantiation relation to a parthood relation: the universals are parts of the things that instantiate them, and that’s what makes the things instantiate them. But then the same thing ends up being a part of many widely separated things.
• One might then solve that problem by supposing that instead of universals, we have tropes which are exactly alike.