## Thursday, May 31, 2012

### A sound bite for circularity

Maverick has just posted a reply to my request for what he calls a ‘sound bite’ on his argument for circularity. Before I comment, a brief aside on my dislike of the term ‘sound bite’. In philosophy, particularly ‘Internet philosophy’, I frequently encounter it when I ask for a clear and concise explanation of or argument for the opponent’s position. “You can’t reduce my argument to a sound bite”. Well in that case I am not interested in the  opponent’s  argument, for it is not an argument at all. I suspect the underlying reason is a fear that the position really is incoherent, or that the underlying argument is invalid. There should be an informal fallacy ‘The Sound Bite fallacy’ named after it. And in any case I do not want a ‘sound bite’, which is simply a short slogan summarising a position or attitude such as ‘This was their finest hour’, often little more than a cliché. Note also my previous post, where I argued that the ‘circularity objection’ is actually more complex and difficult than Maverick originally implied, and that it is unfair to say I am being disingenuous, when I claim I fail to understand it.  I feel he has now conceded that it is somewhat more complicated and less obvious than he originally suggested.

But anyway: Maverick has now given a pretty clear outline of his argument, which I copy verbatim below.

1. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated.'
2. If a first-level concept such as *F* is instantiated, then it is instantiated by an individual.
3. Let the arbitrary constant 'a' denote an individual that instantiates *F.*
4. By LNC, a cannot both exist and not exist.
5. By LEM, a must either exist or not exist.
6. If a does not exist, i.e., if a is a Meinongian nonexistent object, then the link expressed in (1) between existence and instantiation is broken.
Therefore
7. If *F* is instantiated, then *F* is instantiated by an individual that exists.
Therefore
8. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'
9. A definition (analysis, account, theory, explanation) is circular iff the term to be defined occurs in the defining term.
10. 'Exists' occurs both in (8)'s definiendum and its definiens.
Therefore
11. The thin theory is circular.

Is it valid? Well, my first point is that the argument is even more complex than this, by reason of premisses (7) to (10). Consider the following, obviously invalid argument:

(1a) ‘Bachelor’ means the same as ‘unmarried man’.
(2a) (From 1a, definition) Every bachelor is an unmarried man.
(3a) Every bachelor is a bachelor who is an unmarried man.
(4a) ‘Bachelor’ means the same as ‘bachelor who is an unmarried man’.
(5a) ‘Bachelor’ occurs in the definiendum and the definiens of (4a)
(6a) The definition of ‘bachelor’ is circular.

What’s wrong with it? Well, from the fact that a definition occurs somewhere in the argument it doesn’t follow that whatever we derive from the definition can itself be turned into a definition. The universal proposition (3a) above is perfectly true and follows from the original definition, but it doesn’t follow that we can turn any old universal proposition into a definition. So the move to (4a), which turns the universal proposition into a definition, is blatantly fallacious.

Likewise, even if I grant the truth of the universal proposition corresponding to Maverick’s (7) above, i.e. “any F that exists is an F instantiated by an individual that exists”, it doesn’t follow that you can turn this into something that looks like a definition. Quite obviously not. In particular, Bill needs to avoid the charge that he has reintroduced the term ‘exist’ in (7) in much the same way that ‘bachelor’ has been reintroduced in (3a).

David Brightly said...

>> In particular, Bill needs to avoid the charge that he has reintroduced the term ‘exist’ in (7) in much the same way that ‘bachelor’ has been reintroduced in (3a). <<

Very nicely put.

Anthony said...

>> The universal proposition (3a) above is perfectly true and follows from the original definition, but it doesn’t follow that we can turn any old universal proposition into a definition.

First of all, what special properties are needed in order to turn a universal proposition into a definition?

Secondly, do you agree with 8? Not whether or not it is a definition, but whether or not "On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'"?

I would say that neither 1. nor 8. is a definition. Whereas, in your example (1a) is a definition, and (4a) is not. I'll explain why after I hear your critique.

Edward Ockham said...

>>First of all, what special properties are needed in order to turn a universal proposition into a definition?

I'm not sure. My only argument is that it is clear that the universal proposition above is not a definition. Another example would be 'every human has skin'. At the very least, the defining expression has to include every essential property of the thing defined, and must not repeat any property in a superfluous way.

>>Secondly, do you agree with 8? Not whether or not it is a definition, but whether or not "On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'"?

If the 'that exists' bit is superfluous, i.e. is already embedded in 'an individual', then it's not a proper definition.

Anthony said...

>> If the 'that exists' bit is superfluous, i.e. is already embedded in 'an individual', then it's not a proper definition.

8 does not claim to be a definition. 9/10 claims that it is a definition. Therefore I'd say the problem is with 9/10, not with 8.

>> I'm not sure. My only argument is that it is clear that the universal proposition above is not a definition.

So, "I don't know how to define it, but I know it when I see it, and that isn't it"?

Anyway, I said I'd explain, so here goes. A definition is a reduction of a concept into logically prior concepts. So "bachelor" is reduced to the concepts of "unmarried" and "man". But "exists" and "is instantiated", on the thin theory, seem to exist on the same level. So this is not a definition, it is just a synonym, for something which is undefined. The thin theory seems to be that *there is no definition*. Which is fine, if that's what is being said, since it is correct.

Edward Ockham said...

>>8 does not claim to be a definition.

Clearly Bill means that it does. See his first statement, (1) above.

Apart from a quibble, I agree with the other point you make. It needs to be established that 'exists' is not already embedded in 'an individual'.

Anthony said...

>> Clearly Bill means that it does.

Fair enough. He does make this clear with 9/10.

>> See his first statement, (1) above.

(1) doesn't claim to be a definition either.

If the theory is that 'An F exists' is defined as 'The concept *F* is instantiated.'...

...Well, first of all, I thought we defined words, not sentences.

Anyway, I agree with you that this is not a good argument. Though, he warned you beforehand that his argument was too complicated to be reduced to a single blog post.