Jubien’s second argument against propositions concerns the arbitrary procedure by which we distinguish between propositions of the following sort:

i) All dogs are canines.

ii) All canines are dogs.

These propositions have a subextensive relation, which is the relation between properties expressed by ‘all’ (King, 132). However, the mereological fusion of the constituents of these propositions by itself does not differentiate between (i) and (ii), for they both have the same constituents: being a canine, being a dog, and being subextensive. What we must do is take into account the order of these properties with respect to the relation of subextensiveness. His solution may be abstracted as follows: we may take the property of being the property of being x, the property of being y, and subextensiveness to assert that all x’s are y’s. Therefore, by taking the property of being the property of being x we can distinguish which property is subextensive to the other. However, claims Jubien, this account is arbitrary and stipulative, for we could just as well have taken the subextensive property to be the property of being x (while the other is the property of being the property of being y), instead of requiring that it be the property of being the property of being x. Since this appears to show that neither mereological sum has any more claim to being the proposition in question, we are confronted by the Benacerraf dilemma (henceforth B – dilemma). The B – dilemma leaves us with two equally suited entities as propositions with no principled reason to claim one over the other. We may conclude that ontological theories of propositions cannot provide us with an account of what propositions are and hence fail.

Lets extract a logical argument from Jubien’s dialectic:

Lets suppose that z is the mereological sum of the property of being the property of being a dog, the property of being a canine, and subextensiveness. Let us also suppose that z’ is the mereological sum of the property of being a dog, the property of being the property of being a canine, and subextensiveness.

1. z

2. z’

3. if (1), then z is the proposition all dogs are canines (henceforth (i)).

4. if(2), then z’ is the proposition (i).

5. z is the proposition (i).

6. z’ is the proposition (i).

7. (5) & (6)

8. if (7), then there are 2 different mereological sums equally suited to be proposition (i).

9. There are 2 different mereological sums equally suited to be proposition (i).

10. if (9), then there is no principled reason by which we could favour one over the other.

11. There is no principled reason by which we could favour one over the other.

12. If (11), then neither z nor z’ is the proposition (i).

13. Neither z nor z’ is the proposition (i).

14. if (13), then it is not the case that ontological theories of propositions can provide us an account of propositions.

15. It is not the case that ontological theories of propositions can provide us an account of propositions.

King, however, argues against both 3 and 4. What Jubien assumes, for these conditionals to be true, is (a) that propositions are mereological sums of properties, relations, etc (King, 133). Furthermore, it is also assumed that (b) there is only one unique some given parts (King, 133). The problem got started up because these assumptions constrained the account of propositions. They required a distinction between 2 mereological sums so that they could be the two different propositions (i.e. (i) and (ii)). King rejects these assumptions, and argues that his alternative account allows properties to occupy different positions in the proposition. King’s account allows a proposition such as all x’s are y’s to differ from the proposition all y’s are x’s, since these properties (x and y) would occupy different positions in the proposition. King gives the following examples of how this might work: [ALL [x] [y]] for one proposition (such as (i)), and [ALL [y] [x]] for the other proposition (such as (ii)). Jubien’s argument, concludes King, is limited to accounts of propositions which assume both (a) and (b), and that his (King’s) account is immune from Jubien’s argument, since it does not accept (a) and (b) and still accounts for the two different propositions.

Jubien, however, does not hold assumptions (a) and (b) just to make the propositionalist’s life harder. He claims that for an ontological account of propositions to succeed, it must be consistent with our intuitions about propositional constituency, which, as King agrees, include properties and relations. However, the type of propositions he considers are Platonic propositions, that is, propositions that are mind-independent and a-temporal. If, propositions are Platonic propositions, then perhaps we have some reason to believe that (I) the truth value of a proposition is due to the representing nature of its internal constituents themselves, as he argues for in his first objection to ontological propositional accounts. Now, it can be argued (and Jubien seems to argue), that if propositions are Platonic propositions, it cannot be that they received their truth value from something external, since we would be left to wonder if these propositions are merely surrogate accounts. Furthermore, if this worry is warranted, then we must try to account for this internal representing, and perhaps the best way to accomplish this and still be consistent with Platonic intuitions is to accept assumption (II): propositions are mereological sums of properties and relations. However, that this is the best way to accomplish this is left un-argued for here, but at least the possibility is left open.

## 1 comment:

Just in case anyone else saw the apparent invalidity of my argument, the following corrections should bring everything back into valid-land:

Supposing z and z' are the mereological fusions as outlined in the original post,

1. Propositions are the merelogical fusion of properties and relations

2. if (1), then z is a proposition and z' is a proposition.

3. z is a proposition and z' is a proposition.

4. if (3), then z is the proposition all dogs are canines and z' is the proposition all dogs are canines (hencefore (i)).

5. z is the proposition all dogs are canines and z' is the proposition all dogs are canines.

6. if (5), then there are 2 different mereological sums equally suited to be propsotion (i)

...and then the argument would continue on as before, only the numbers designating premises should be altered accordingly.

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