Edward of London proposes the following triad
O1. The proposition ‘Bill is looking for a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is looking for a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.
as a nominalistic equivalent to my
W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.
Edward imposes the following contraint on aporetic polyads: "The essence of an aporetic polyad is that any proper subset of statements (including the singleton set) should be consistent on its own, and only the whole set being inconsistent." I accept this constraint. It implies that nothing can count as an aporetic polyad if one of its limbs is self-contradictory.
My definition runs as follows. An aporetic polyad is a set S of n self-consistent propositions (n>1) such that (i) any n-1 members of S, taken in conjunction, entail the negation of the remaining member; (ii) each member of S has a strong claim on our acceptance. Edward's constraint follows from this definition. For if any member is self-inconsistent, then it cannot have a strong claim, or any claim, on our acceptance.
If I understand Edward, he is urging two points. His first point is that my formulation of the triad is inept because (W1), unlike (O1), is self-contradictory. If this charge sticks, then my formulation does not count as an aporetic polyad by my own definition. His second point is that his version of the triad has a straightforward and obvious solution: reject (O2).
Reply to the First Point. There is nothing self-contradictory about 'We sometimes think of the nonexistent.' As I made clear earlier, this is a datanic, not a theoretical, claim. On this score it contrasts with the other two limbs. It is meant to record an obvious fact that everyone ought to grant instantly. Because the fact is obvious it is obviously self-consistent. So if Edward denies (W1), then it is not profitable to to continue a discussion with him.
All I can do at this point is speculate as to why Edward fails to get the point. I suppose what he is doing is reading a theory into (W1), a theory he considers self-contradictory. But (W1) simply records a pre-theoretical fact and is neutral with respect to such theories as Meinong's Theory of Objects. Suppose I am imagining a winged horse. If so, then it would be false to say that I am imagining nothing. One cannot simply imagine, or just imagine. It follows that I am imagining something. We are still at the level of data. I have said nothing controversial. One moves beyond data to theory if one interprets my imagining something that does not exist as my standing in a relation to a Meinongian nonexistent object. That is a highly controversial but possible theory, and it is not self-contradictory contrary to what Edward implies. But whether or not it is self-contradictory, the main point for now is that
1. BV is imagining a winged horse
Is neutral as between the following theory-laden interpretations
2. BV (or a mental act of his) stands in a dyadic relation to a Meinongian nonexistent object.
and
3. BV is imagining winged-horse-ly.
The crucial datum is that one cannot just imagine, or simply imagine. We express this by saying that to imagine is to imagine something. But 'imagine something' needn't be read relationally; it could be read adverbially. Accordingly, to imagine Peter (who exists) is to imagine Peter-ly, and to imagine Polonious (who does not exist) is to imagine Polonious-ly. I am not forced by the crucial datum to say that imagining involves a relation between subject and object; I can say that the 'object' reduces to an adverbial modification of my imagining.
So even if the relational reading of (1) were self-contradictory — which it isn't – one is not bound to interpret (1) relationally. Now (1) is just an example of (W1). So the same goes for (W1). (W1) is obviously true. He who denies it is either perverse or confused.
Reply to the Second Point. One can of course solve Edward's triad by denying (O2). But the real question is whether one can easily deny the distinct proposition (W2). I say no. For one thing, the alternatives to saying that intentionality is a relation are not at all appetizing. All three of the limbs of my triad lay claim to our acceptance, and none can be easily rejected – but they cannot all be true. That is why there is a problem.
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