FOM: second-order logic is a myth

Vladimir Sazonov sazonov at
Wed Feb 24 17:30:41 EST 1999

Stephen G Simpson wrote:
> Perhaps I expressed myself in a misleading way.  Robert Black 23 Feb
> 1999 17:22:56 thinks I'm a formalist, but I'm not one.


> The remarks in my original `second-order logic is a myth'
> posting (22 Feb 1999 16:16:41) were certainly not intended as an
> attack on the standard `Platonist' or realist view of sets, `the
> intended interpretation' of second-order quantifiers in terms of
> arbitrary subsets of the domain of individuals, etc.  I actually favor
> the `Platonist' or realist view in many contexts.

In which contexts? Are there contexts in which you do not favor 
this view?


> When I said that second-order logic is a myth, this was simply my
> provacative way of making the point that the study of V_2 as a whole
> is fruitless and hopelessly intractable.  (I'm apologize if some
> people were confused or offended by this formulation.)

I was and still am confused.

Does not this (i.e. "fruitless and hopelessly intractable")
actually mean that the set of second-order validities V_2 is
meaningless (if considered outside ZFC or any other
[first-order] formal system which describes in its own way
the set of "all" subsets of arbitrary set)? 

Is not this a counteradvertisement of your own Platonism?

I realize that "logically" speaking this is not a contradiction.  
But, anyway, this looks rather strange. 

Vladimir Sazonov

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