There is a clear sense in which every intentional mental state 'takes anIn other words, he clearly regards as valid the inference from (A) to (B) below:
accusative,' 'is of or about an object.' That object could be called the
intentional object. Accordingly, whether I want a three-headed dog or a
one-headed dog, my wanting has an intentional object.
(A) Bill wants a three-headed dog
(B) Bill’s wanting has an intentional object
This is the crucial step in the argument for ‘intentional object’, and it is clearly faulty. Look at the verbs of sentences (A) and (B). Sentence (A) contains the verb ‘wants’. Sentence (B) contains the verb ‘has’. These are different types of verb, and of course the whole problem began with important logical differences between ‘intentional’ verbs such as ‘wants’, ‘thinks about’, ‘is looking for’ and so on, and other verbs such as ‘owns’, ‘works in’, ‘is to the left of’ and so on. Both realist and nominalist agree that ‘Bill wants a three-headed dog’ is consistent with ‘no dog is three-headed’, and therefore does not imply ‘some dog is three-headed’. And they also agree that ‘Bill lives in a house in the desert’ is inconsistent with ‘no house is in the desert’, and therefore does imply ‘some house is in the desert’.
With that agreed, it is unreasonable for the realist to argue from (A) to (B). The verb ‘has’, which connects ‘Bill’s wanting’ and ‘an intentional object’ doesn’t look like an intentional verb. It is a verb of posession like ‘owns’. Thus it is inconsistent with ‘no object is intentional’, and therefore does imply ‘some object is intentional’. Similarly for the argument given by Peter Lupu where he says “Bill defines whatever it is that they [intentional states] are about, or are of, or directed towards by the term 'intentional object'. “ But the sentence
(B’) Bill’s wanting is directed towards an object
also contains a verb ‘is directed towards’ which is not obviously an intentional verb. The nominalist will challenge both of these inferences, on the grounds that (A) does not imply the existence of anything at all apart from Bill and his mental states, whereas (B) and (B’) do imply the existence of something apart from Bill’s and his mental states, and on the grounds that ‘whatever is implied by the consequent is implied by the antecedent’.
Note that this nominalist line of reasoning is purely logical. It starts with something that both sides agree on – namely that the logic on ‘intentional verbs’ is different from ‘non-intentional verbs’, and that what the logical properties of ‘wants’ may be different from the logical properties of ‘has’. Then the nominalist simply points out that a crucial step in the realist’s argument depends on the assumptiont that the logical properties of ‘wants’ are not different from the logical properties of ‘has’.