[FOM] Fact and opinion in F.O.M.

[Michael Lee Finney]

> Joe Shipman wrote:

> Then your question becomes whether there exist any non-arithmetical facts.

I am puzzled as to why this is even a question. What about results in
Topology, or Knot Theory? Or in logic. Surely "p & q -> p" should be
considered a "fact"? None of these are arithmetical consequences.

And if the criteria for a fact is that no set of axioms exclude it, then are
there really any facts at all?

Even if the above examples are modeled in ZFC, that does not make them a
consequence of ZFC. At best you could say they are a consequence of ZFC plus
additional axioms. Since you could negate any one or all of those additional
axioms or an axiom of ZFC itself, you would always have a potentially proposed
system where any given statement is false.

I don't think you can restrict any proposed set of axioms based on
"agreement", "seriously proposed", etc. That criteria just shifts in the wind.
Just as with non-Euclidian geometry, there was no "permanent disagreement" for
hundreds of years -- and then there was -- which, over time, changed to a
new agreement.

Nor can you restrict it to arithmetical facts, or systems which can be
modelled in ZFC or even just ZF. What about set theories which replace the
axiom of regularity (such as Azcel's systems)? Some of those have been shown
to be consistent if and only if ZFC is consistent. And they contain "facts"
that disagree with ZFC. And those systems have been seriously proposed as
replacements for ZFC.

At best you can say that a "fact" is something that follows from a specific
set of axioms. And an "opinion" is a belief that something "should" be true,
even if it is independent of that set of axioms, such as the axiom of choice.
Facts and opinions in political discourse are an entirely different kettle of
fish. Almost all "facts" in that arena are really opinions -- often very
strongly held opinions -- but nonetheless opinions and not facts.

I would also argue that people of good will can and are in permanent
disagreement about "facts". The gun control "debate" is one such area. What is
a fact for one side is viewed as an incorrect or ignorant opinion by the other
side (not taking a side here). There are many areas like this -- especially
where public policy is concerned -- where people of good will have
irreconcilable differences about the "facts" of the debate.

Michael Lee Finney