[FOM] Type-Occurrence-Token (Slightly edited version of a message I sent Prof. Corcoran)
Mark Steiner
marksa at vms.huji.ac.il
Thu Sep 22 16:28:03 EDT 2005
Wittgenstein, in Remarks on the Foundations of Mathematics IV, 39 says
39. The proposition 'a = a', 'p if and only p', "The word 'Bismarck' has 8
letters", "There is no such thing as reddish-green", are all obvious and are
propositions about essence: what have they in common? They are evidently
each of a different kind and differently used. The last but one is the most
like an empirical proposition. And it can understandably be called a
synthetic a priori proposition.
It can be said: unless you put the series of numbers and the series
of letters side by side, you cannot know how many letters the word has.
(See also VI, 36 on the number of sounds in the words Plato, Daedalus,
OBEN.)
What Wittgenstein means by a "synthetic a priori" proposition, in my
opinion, is an empirical propositions which has been "hardened into a rule."
In this sense arithmetic propositions are synthetic a priori. We can use
7+5=12 to predict the result of counting because it is based on an
underlying regularity. At the same time, it functions as a rule, since it
is an arbiter of CORRECT counting.
"'Bismark' has 7 letters" according to Wittgenstein is either an empirical
proposition or a rule which gives the identity of the word 'Bismark'. But
the rule is supervenient on the regularity of counting.
It would seem then that Wittgenstein has a version of the occurrence/token
distinction, according to which it is identical to (or perhaps replaced by)
the distinction between an experiment and a priori in mathematics, or
between an empirical proposition and a mathematical rule.
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