## Wednesday, May 30, 2012

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Thanks for the detailed comments. However, note the principle behind my point, namely your objection that I can't see what's obvious. I replied that if it were really obvious, you could explain it in a simple and obvious way. Now you say it cannot be reduced to a 'sound bite', i.e. a clear and simple explanation. So you concede my point, no?

I hate the term 'sound bite', by the way. I often have it thrown at me on Internet discussions when I ask for clarity or a simple argument. A 'sound bite' is not a clear and simple and reasoned explanation at all. Rather, a mixture of sloganeering, argument by distant analogy etc.

Dr Vallicella,

I don't think the argument as stated works. First of all, (9) seems too strong. Every circular definition is indeed such that the crucial term occurs on both sides, but the converse is not true. There are valid definitions of this sort --- I will call them implicit definitions. Compare

D1. Let x be a number such that x + 7 equals 10.
D2. Let TallestMan denote a man such that for every other man m, TallestMan is taller than m.

The above can of course be restated in a non-implicit form. Just as a valid argument can instantiate an informally fallacious argument form, a valid definition can instantiate a prima facie circular form. Here is a an example

D3. Let yellow be the colour of the sun.

This is as straight a definition as there ever was. Now we may ask, in a similar way that you ask about existence, whether the sun is yellow or not? By definition the sun is yellow, so (D3) is equivalent to

D3'. Let yellow be the colour of the yellow sun.

Now, following your line of thought we declare (D3') circular and (D3) together with it. Surely this is wrong; (D3') is in fact not circular. Note that 'yellow' in 'yellow sun' gives redundant information and does not pick out the yellow sun from other non-yellow suns. The latter would indeed be circular. Similarly, 'existing' in 'existing individual' is redundant under the thin theory.

It seems to me the argument reduces to asking the thin theoretist to give an account of truthfulness of claims like 'sun exists'. In other words, it reduces to the the problem of the existence of haecceity properties.

Thanks, Jan, but I am having a hard time following you. I would deny that (D1) is a definition. How can you define a variable? 'x' is a variable.

(D2) if a definition is plainly circular.

The sun is not yellow by definition. It is an empirical fact that it is yellow, although I wouldn't say it is yellow . . .

Consider these definitions:

X is a necessary being =df x exists in all possible worlds
X is an impossible being =df X exists in no possible world
X is a contingent being =df X exists in some but not all possible worlds
X is a possible being =df X exists in at least one possible world
X is an actual being =df X exists in the actuial world.

The last two are plainly circular. The other three are also circular, though less obviously so.

Now does pointing out this circularity constitute an objection to the definitions? It does if the project it to reduce the modal to the nonmodal. But it does not if one is simply setting forth equivalences.

Bear in mind that the thin theorist's project is to reduce existence to instantiation. This is why the circularity I exposed constitutes an objection to the theory.

Bill,
Why would Ed accept the premise 6?
Couldn't Ed still say: "the distinction between non-existent objects and existent objects is simply non-sense". There is no such a thing that instantiate a concept but fail to exist because "to instantiate" means "to exist"

Dr Vallicella,

Small 'x' is a name of some natural number. Perhaps I should have used 'X'. Dealing with individuals introduces an additional layer of difficulty, so I will reformulate (D2) to

D2 (definition of the word 'dyhrogen'). Let dyhrogen be the chemical element such that for every other element e, the atomic number of dyhrogen is lower than that of e.

(D2) is clearly logically equivalent to

D2'. Let dyhrogen be the element with least atomic number.

I will now set up a fork. Either both of (D2) and (D2') are circular, or both are non-circular, or exactly one is. If both are, then (D2') in particular is circular. This however contradicts your (9), because the defined term does not occur on the right side. Moreover, it is clear it is non-circular as one may take it as a definition of hydrogen.

If both are non-circular, (9) is false again because the defined term occurs on both sides in (D2).

If exactly one is circular, then logical equivalency is not circularity-preserving, which your argument implicitly assumes (you take the thin theoretist's definition, find another one logically equivalent to it that you deem circular, and conclude the original definition is circular).

Which is your poison of choice?

As for (D3), it was meant as a definition of 'yellow'. Replacing 'yellow' with 'shmellow' will make it clearer. Then, by definition of shmellow, sun is of shmellow colour. My point that one can introduce the defined term on the right hand side and then remove it by purely logical analysis stands. In other words, (D3) and (D3') are logically equivalent. This reintroduces the fork.

Arash,

Actually, Ed did accept something like (6) in an earlier thread.

In any case, no reasonable person could say that the distinction between existent and nonexistent objects is nonsense.

(a) The circularity argument introduced by Bill above is presumably against a thin theorist that offers an account of what ‘exist’ *means* in terms of instantiation. Such a thin theorist will, in my opinion, accept (somewhat modified versions of): (1), (2), (3), (4), (5), and (7). He will reject for one reason or other the rest of the propositions appearing in the above argument. In particular, a thin theorist will reject (6) and (8). Also he most likely will challenge the unnumbered proposition between (3) and (4). I will begin with the later.

(b) The unnumbered propositions states: “We now ask whether a exists, does not exist, both, or neither. These are the only options.”

According to the thin theorist there is only one option in light of (1)-(3): namely, the option that a exists. After all, (3) stipulates that ‘a’ shall denote the individual which instantiates *F*. (2) says that *F* is the sort of concept that is instantiated by individuals such as a, if *F* is instantiated at all. And so *F* is instantiated by the individual object a. And, finally, (1) says that existence and instantiated mean the same thing. It then follows that a exists. The other options are excluded because they include that a does not exist.

(c) A thin theorist ought to reject (6) because (6) would make no sense in light of the thin theorist’s view expressed in (1). If ‘exists’ *means the same as* ‘being instantiated’ and since ‘means the same as’ is symmetrical, then any object that fails to exist also fails to be instantiated, and vise versa. In light of (1), Meinongian nonexistent objects make no sense.

(d) Why reject (8)? First, it should be clear that (8) does not follow from (7) alone. Since (8) involves the intensional ‘means the same as’ whereas (7) involves the much weaker material conditional, the later cannot entail the former.

Second, the official account of the thins (according to this version) is expressed by (1). But notice that (1) all by itself does not entail anything about whether or not Fs exist or for that matter whether any individuals exist. If (1) is true at all, then it will be true in a world in which no individuals exist at all, for it only asserts what the concept *exists* means. Moreover, (1) does not include the term ‘exists’ on the RHS. Therefore, (1) alone does not entail (8).

What (1) entails instead is the biconditional:

(1*) An F exists if and only if the concept *F* is instantiated.

Since (3) stipulates that ‘a’ shall denote an individual object that instantiates *F*, it entails:

(3*) The concept *F* is instantiated by a.

(1*) and (3*) together (with some minor tinkering) entail:

(i) a exists.

So (i) is not presupposed by (1) and since (8) is neither entailed by (1) nor by a combination of premises acceptable to the thins, I am not sure how the above argument proves that this version of the thin-conception is circular (i.e., how it proves (11)).

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