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Thursday, October 19, 2006

Schnieder on Leibniz's Law

The January 2006 issue of The Philosophical Quarterly features an interesting article, " 'By Leibniz's Law': Remarks on a Fallacy", by Benjamin Schnieder.

Schnieder makes a convincing case for the view that the following sort of argument is sometimes fallacious.

a is F
b is not F
By Leibniz's Law, a is not identical to b

Leibniz's Law says (roughly) that if a and b have distinct properties, then a is not identical to b. The problem with (A)-style arguments is that the negation in the second premise may be meta-linguistic. Here are a couple of examples of meta-linguistic uses of negation (from Schnieder, p. 45):

I din't trap two mongeese, I trapped two mongooses.

Non-English speaking student: I shall become a great toy for christmas.
English teacher: No, you will not become a toy, you will get one.

In these cases the negation is not used to deny that the thing in question has a property expressed by the predicate, for the predicate does not express a property. Rather, as Schnieder points out, it is used to deny that the predicate "lacks proper usage in English" (p. 45) or does not express the property the speaker intended it to express. For example, I am not denying that I have the property of trapping two mongeese, for there is no such property. Rather, I am saying that 'trapped two mongeese' lacks proper usage. Likewise, the English teacher is not denying that the student has the property of becoming a toy for christmas. Rather, she is saying that 'shall become a great toy for christmas' does not express the property the speaker intended it to express.

Schnieder concludes by considering some arguments from the literature that could perhaps be refuted by arguing that the negation is meta-linguistic, for instance, Nicholas Wolterstorff's argument against taking the kind K to be identical to the property of being K:

The Apple Blossom is the state flower of Michigan
The property of being an apple blossom is not a state flower.
Therefore, The Apple Blossom is not identical to the property of being an apple blossom.

It is arguable that 'the property of being an apple blossom is a state flower' lacks proper usage, and that that is what the negation sign is supposed to indicate.

As I was reading Schnieder's article, I came to think of Kit Fine's case for the non-identity of the statue and the clay. In his case for non-identity Fine appeals to the following sort of argument:

The statue is well made
The clay is not well made
So, the statue is not identical to the clay

Fine even says that predicates such as 'is well made', 'is ugly', 'is Romanesque', 'is insured', and so on may apply to the statue, but the "correct and proper" application of the predicates prevents them from applying to the clay. So, it isn't simply that it is false to say 'the clay is ugly', on Fine's view. It is meaningless to say it. So, when we say 'the clay isn't ugly', Schnieder or anyone sympathetic to his view could argue that the negation is meta-linguistic. If it is, then arguably Fine's non-identity argument does not go through.


Mike said...

I've wondered similarly about familiar metaphysical identicals. Here I don't want to deny the identity, but deny the inference by LL to their having the same properties.

1. the property of being H2O = the property of being water.
2. the property of being H2O is a chemical property.
3. But the property of being water is not a chemical property.

Or, so it seems to me. But then consider the platitude that normative properties supervene on descriptive properties. Suppose (wildly) that the moral property 'being wrong' supervenes on the descriptive property 'failing to maximize utility'. The former property is a normative property. The latter property is not. LL doesn't seem to govern these inferences or, if it does, then these are not identicals.

Aidan said...

I haven't thought this through, but the other obvious place this might come up is in discussions of Evan's analysis note on vague objects. I'll need to think about that later though.

Brit Brogaard said...

Hi Mike,
Interesting! Which assumption are you denying in the arguments? LL? Or the applicability of LL? If the latter, why is LL inapplicable in these cases, I wonder?

Brit Brogaard said...

Hi Aidan,
Yes, that seems like an interesting possibility.

Suppose it is vague whether a = b.
Then b has the property of being a thing x such that it is vague whether x = a.
It is not vague whether a = a.
So, it is not the case that a has the property of being a thing x such that it is vague whether x = a.
By Leibniz's law, a is not identical to b.

Perhaps we can deny 'a does not have the property of being a thing x such that it is vague whether x is identical to a' on the grounds that the negation is metalinguistic (?).

Mike said...


I've been tempted to the (um, daring?) conclusion that LL does not apply in every case where identicals stand in an interesting supervenience relation. Similar problems seem to arise with the property of seeing red and the property of being in physical state R. There seems to me no reason why the physical state R should not be very similar to the physical state B, though seeing red nothing like seeing blue. And we get a slightly more complicated worry for LL.

Brit Brogaard said...

That seems right to me. So, that could also be what is going on in the case of the statue and the lump.

Mike said...

How many solutions are there to lumple & goliath?

1. LL is true and they are identical.
2. LL is true and they are contingently identical.
3. LL is true and they are non-identical spatially coincident objects.
4. LL is not true and they are identical.
5. ?

Brit Brogaard said...

5. LL is true, but it does not apply here, and they are identical.

Maybe that's it. Moreover, in case 2, LL will be indexed to times or regions.