# [FOM] Type-Occurrence-Token

Charles Silver silver_1 at mindspring.com
Sun Sep 25 08:05:04 EDT 2005

```Charles Parsons wrote:
> I don't recall having written that. However, I was struck years ago
> by a statement in Benson Mates' logic textbook, that the notion of
> occurrence is "woolly". It's very likely that I have mentioned this
> in conversation or lectures.
>
> I have now located the passage. Mates writes,
>
> Probably the confusion [about free and bound occurrences of variables
> - CP] is further increased by the unclarity that surrounds the notion
> of _occurrence_. Only reluctance to introduce additional complexity
> prevents us from abandoning this woolly notion and defining instead a
> ternary relation 'alpha is bound at the nth place in phi', where
> 'alpha' takes variables as values, 'phi' formulas, and 'n' positive
> integers. Such a definition would obviate all talk about
> 'occurrences', but it is rather involved.
>
> _Elementary Logic_, 2d ed., OUP 1972, p. 49.

A little earlier in Mates's book (p.41), leading up to free and
bound occurrences, he has an exercise I always got
a kick out of.   The problem is to put quotation marks in the
right places in the following statement:
---
The song A-sitting On a Gate is called Ways and Means although
its name is The Aged Aged Man, which in turn is called Haddock's
Eyes.
---
It's a fun exercise, but I thought it more than a little perverse to
include such a tricky exercise for beginners so early in the book.

Concerning some of the same and related issues, Boolos
develops some interesting new ideas in his: "Quotational Ambiguity,"
in "Logic,...," (pp. 392-405)

Charlie Silver

```