# FOM: second-order logic is a myth

Tim Heap timh at dcs.ed.ac.uk
Wed Mar 10 14:14:12 EST 1999

```Pat Hayes writes:

Pat> In contrast to Silver's intuition, it seems to me that saying
Pat> "for all x..." implies that one has some notion of the extent
Pat> over which that "all" is supposed to reach. If I can't (even
Pat> conceptually) distinguish a Canada goose from a hooting swan,
Pat> then for me to say "All Canada geese..." is impossibly
Pat> vague. (How can we evaluate a proposed counterxample if we can't
Pat> know whether or not is a goose?) The meaning is indeterminate
Pat> until we decide what counts as a Canada goose. But that amounts
Pat> to deciding what is in the set of Canada geese. The point is that
Pat> the criteria which determine the truthvalue of "for all x..", and
Pat> those which make all the x's into a set, are both purely
Pat> extensional; and they coincide; so they are the same.

...but what happens to this argument when you replace "Canada Goose"
with "set"?

tim

```