As far as I can see, that’s just an acknowledgement that we can’t know anything for certain—so we can’t be certain of any ‘laws’, and any claim of certainty is invalid.
I was arguing that any applied maths term has two types of meanings—one ‘internal to’ the equations and an ‘external’ ontological one, concerning what it represents—and that a precise ‘internal’ meaning does not imply a precise ‘external’ meaning, even though ‘precision’ is often only thought of in terms of the first type of meaning.
I don’t see how that relates in any way to the question of absolute certainty. Is there some relationship I’m missing here?
The quote is getting at a distinction similar to yours. It’s from the essay Geometry and Experience, published as one chapter in Sidelights on Relativity (pdf here).
A different quote from the same essay goes:
On the other hand it is certain that mathematics generally,
and particularly geometry, owes its existence to the need which was
felt of learning something about the relations of real things to one
another. The very word geometry, which, of course, means earth measuring, proves this. For earth-measuring has to do with the
possibilities of the disposition of certain natural objects with respect
to one another, namely, with parts of the earth, measuring-lines,
measuring-wands, etc. It is clear that the system of concepts of
axiomatic geometry alone cannot make any assertions as to the
relations of real objects of this kind, which we will call practically rigid bodies. To be able to make such assertions, geometry must be
stripped of its merely logical-formal character by the co-ordination
of real objects of experience with the empty conceptual frame-work
of axiomatic geometry.
As far as I can see, that’s just an acknowledgement that we can’t know anything for certain—so we can’t be certain of any ‘laws’, and any claim of certainty is invalid.
I was arguing that any applied maths term has two types of meanings—one ‘internal to’ the equations and an ‘external’ ontological one, concerning what it represents—and that a precise ‘internal’ meaning does not imply a precise ‘external’ meaning, even though ‘precision’ is often only thought of in terms of the first type of meaning.
I don’t see how that relates in any way to the question of absolute certainty. Is there some relationship I’m missing here?
The quote is getting at a distinction similar to yours. It’s from the essay Geometry and Experience, published as one chapter in Sidelights on Relativity (pdf here).
A different quote from the same essay goes: