Re: Impredicativity in Rosennean parlance

[Torkel Franzen <***>]

Judith Rosen says:

>Would you argue that there is absolutely no analogy or metaphor
>involved in the modeling relation, in science (as it currently exists,
>today)?

  On the contrary, I quite accept that anything is analogous to
anything else, when suitably regarded. I myself prefer writings that
do not include metaphorical invocations of relativity, incompleteness,
or uncertainty in the technical sense, but this is chiefly a matter of
taste. My essential carping concerns statement that have the
appearance of making factual claims about non-metaphorical
matters. Thus, you commented:

>Hilbert apparently believed that impredicativities were not
>formalizable.

This is not a metaphorical statement, but a statement about what
Hilbert apparently believed; hence his actual views and statements
become relevant.

Similarly, looking at the comment beginning

>In this sense, syntactic or algorithmic systems, or formalizable 
>systems, are extremely weak in entailment: ....

a reader might be led to believe that these remarks apply to formal
systems as understood in logic. It is then a relevant question in what
sense, and on what grounds, it might be held that "almost every why
question about what is in the system cannot be answered from within
the system". Again, the statement that
  
  Within a short time, however, Goedel proved his celebrated
  Incompleteness Theorem, which in effect show that syntactic rules
  captured only an infinitesimal part of "real" mathematics--in effect
  that Church's Thesis was false, even in this realm.

gives the impression of making a factual statement about the
incompleteness theorem, about mathematics, and about Church's Thesis.