[FOM] Frege's error

Hartley Slater slaterbh at cyllene.uwa.edu.au
Sun Jul 17 23:13:09 EDT 2005

Richard Heck misses the mark:

>So what did Frege mean by the remark Carnap recorded? It is, in 
>effect, a remark about the syntax of the system: If F(,) is a 
>two-place function-symbol, then we can form both the expression 
>F(x,y) and the expression F(x,x). Not too much controversial there.

Maybe *that* is not controversial, but I went on to question whether, 
in the case of logical 'functions', unlike mathematical functions, 
(R)(EP)(x)(Rxx iff Px).   I think other people cannot be allowing for 
a premise I have had since 1984 (see my 'Sensible Self-Containment' 
in Philosophical Quarterly for that year, also the more recent items 
referred to before, for example, most immediately to anyone's mouse, 
'A Poor Concept Script' in the Australasian Journal of Logc 

What seems to have gone unnoticed more generally is that the grammar 
of 'x is not in x' has not been construed properly.  For instance, 
there is no paradox with
<x,x> is in {<y,z> | y is not in z} iff x is not in x.
So a relational analysis of the form Rxx works, while a predicative 
analysis of the form Px does not.

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