[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
    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     

More information about the FOM mailing list