[FOM] impredicative definitions/paper announcement

[Nick Nielsen]

Arnon Avron wrote:

> a predicativist is first of all a mathematician who finds as vague
> and possibly meaningless the notion of an ``arbitrary subset of S"
> in case $S$ is an infinite collection...  Thus "arbitrary" subsets of N
> (say) are mystic objects that only an infinite
> mind (whatever this means) can identify, and belief in their existence
> is exactly this: a sort of religious belief.

Do you think that there is a relation between the idea of an arbitrary
subset of S where S is an infinite collection and the difficulty of
generating pure randomness in algorithmic information theory?

Is not an arbitrary set a set selected randomly?

In so far as we can define pure randomness, but it is difficult to
realize (generate) randomness in practice, are we not confronting a
limitation like that typical of non-constructive thought generally
speaking, as when the existence of a given x can be demonstrated, but
little or nothing more can said of x?

What is the difference, if any, between the arbitrary and the random?

Nick