[FOM] Type-Occurrence-Token

Charles Parsons parsons2 at fas.harvard.edu
Sat Sep 24 17:02:44 EDT 2005

At 6:10 PM +1000 9/23/05, A.P. Hazen wrote:
>[In response to John Corcoran's most recent posting.]
>     Charles Parsons has written, somewhere, of the "obscure notion" of
>an OCCURRENCE.  Put on hold any doubts you might have about the
>type/token distinction.  (If you don't have any nervousness about
>THAT distinction, go read David Kaplan's "Words" ["Aristotelian
>Society Supplementary Volume" 1990, pp. 93-199], or maybe Peter
>Simons's "Token Resistance" ["Analysis" (the philosophy journal of
>that title, not the math or psychotherapy ones!) v. 42 (1992), pp.
>195-203].  But for the length of this posting, assume the type/token

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.

What he suggests is, of course, not an explanation of the notion of 
occurrence but a way of eliminating it, evidently provided that one 
takes formal expressions as sequences.

Charles Parsons

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