## 4/08/2010

### Is 'is' ambiguous?

One of the essential components of modern logic is the view, standardly attributed to Frege and Russell, that 'is' is ambiguous: 'is' has the senses of
(i) identity (Mark Twain is Samuel Clemens; in other words, Mark Twain = Samuel Clemens),
(ii) predication (Mark Twain is an author), and
(iii) existence (Mark Twain is; in other words, Mark Twain exists), and
(iv) class inclusion (Authors are artists).

After grading a batch of logic problem sets, I'm wondering whether (i) and (ii) really are ambiguous; more specifically, how the senses of identity and predication fare with respect to the standard ambiguity tests. As I've mentioned several times before on this blog, one of the most widely-accepted ambiguity tests is the conjunction-reduction (or 'no crossed readings') test. The basic idea can be illustrated by an example: 'Alice has a bat' can mean she has a flying pet or a new baseball bat; 'Bob has a bat' has the same two possible readings, with Bob instead of Alice. However, 'Alice and Bob have bats' cannot mean that one has a baseball bat, and the other has a pet flying mammal.

'Mark Twain is Samuel Clemens' has a true reading, and
'Mark Twain is a famous author' has a true reading.
But what about 'Mark Twain is Samuel Clemens and a famous author'?
This sounds zeugmatic to me, confirming the Frege-Russell view of 'is' as ambiguous. However, many of my logic students wrote something analogous to this on their most recent problem set, when asked to translate a particular sentence of first-order logic into English. Student responses to logic problem sets are probably some of the worst data imaginable for this kind of question, but it did make me wonder whether my observations about 'is' in English are very theory-laden, ruined by years of logic and logically-inspired philosophy. What do other folks think about 'Mark Twain is Samuel Clemens and a famous author'?

At 8/4/10,  Kenny said...

"Mark Twain is named Samuel Clemens" should be a clear use of the "is" of predication. But it sounds just as bad to me to say "Mark Twain is named Samuel Clemens and a famous author".

But maybe we can do this with an example in the plural, and with single-word predicates rather than phrases. (I'm using single-word predicates in case the problem is some restriction involving long phrases, and I'm using plurals so that we can get good readings of conjoined "is" of identity.)

The murderers are tall and blond.

The murderers are John and Mary.

*The murderers are tall and Mary.

I have to say the latter one as "The murderers are a tall person and Mary".

At 11/4/10,  Greg Frost-Arnold said...

Hmm. That's a good point about 'Mark Twain is named 'Sam Clemens' and a famous author' -- I share your reaction that it is as marked (or nearly as marked) as the original.

This led me to think about other cases. What do you make of
'MT is identical to SC and a famous author'?

Also, does the order matter?
'Mark Twain is a famous author and named "Samuel Clemens".'
or
'Mark Twain is a famous author and identical to Samuel Clemens'.
I can't say why, but this order does not sound as strange to my ear.

At 14/4/10,  Anonymous said...

It depends on what your definition of 'is' is.

As I have said before.

Sincerely, Bill C.

At 19/4/10,  Rafal Urbaniak said...

One stance on this was taken by Lesniewski, who clearly saw a distinction between two singular terms flanking an is' and the situation where you have a singular term on the left and a predicate on the right. Still, he used only one predication copula, epsilon (read as is' or is one of'), just saying that the truth-conditions of atomic formulas are more elaborate. He took a \epsilon b' to be true when exactly one object falls/is referred to by a, and at least one object is referred to/falls under b, and the object referred to by a is among the objects to which b refers. He also had only one category of name variables, in which he put together empty names, singular terms, plural terms and predicates. So the following he'd read as true (mind you, his first language, Polish, has no articles, so his intuitions might've been different from yours):

Socrates is Socrates
Socrates is Plato's most famous teacher [`Plato's most famous teacher' is meant as a singular term here]
Socrates is (a) philosopher
Plato's most famous teacher is Socrates
Plato's most famous teacher is a philosopher

I reckon he'd also take to be true:

Socrates is Plato's most famous teacher and a philosopher

Cicero is Tullius and a philosopher

(I do have to admit, the last case sounds slightly unusual, but probably not more unusual than the idea that one should use material implication to represent conditionals).