[FOM] Understanding universal quantification

[Giuseppina Ronzitti]

Neil Tennant wrote:

> On Sat, 22 Feb 2003, Giuseppina Ronzitti wrote:
>
> > The proof-theoretic approach to the understanding of the meaning of
> > quantification rests thus on not constructive tools and therefore does
> > not seem  a viable means to eliminate ontological commitments.
>
> Could you please explain your use of the word "thus" in this passage?
>
> Neil Tennant

>From a classical point of view, of course there is no problem concerning
ontological commitments, the question does not arise at all. From a
(generic) constructive point of view the situation seems to be as follows.
One just understands the use of inference rules and says nothing about
'existence' of domain of quantification,   but 'understanding' inference
rules is understanding some proof theoretic techniques
and proof theoretic techniques are committed to the existence of big
totalities. Thus ...

Of course, one can claim that 'understanding inference rules' has nothing to

do with the understanding of proof theoretic techniques and results. That
person should offer an explanation of what does it mean 'understanding
inference rules' (just applying them ?).

G.Ronzitti