Paola, Avril, Rob, Ed, Rob, (01)
First of all, it is essential to distinguish empirical sciences from
pure mathematics. In empirical sciences, the ultimate test is agreement
of predictions with observations. Mathematics, however, is not an
empirical science. It does not makes any predictions about anything
observable. It is simply a tool that aids the reasoning processes. (02)
First-order predicate calculus, as a pure formalism, is a branch
of mathematics. By itself, it does not make any predictions about
anything observable. But like other versions of mathematics, it
can be used as an aid to reasoning. (03)
But I admit that some people (among whom I am not one) may make
a very strong claim: (04)
First-order logic is the foundation for every possible kind of
reasoning, including all the kinds of reasoning that people make. (05)
There are many examples where people reach correct conclusions
without following the rules of inference that are sanctioned by FOL.
Those cases show that the above claim is false. (06)
However, there are weaker claims that are true: (07)
First-order logic is a systematic abstraction from the resources
of natural languages (i.e., words like 'and', 'or', 'not', 'if',
'then', 'some', and 'every', and the syntax for connecting them).
FOL is often used to display and clarify the structure of *many*
arguments that people use. (08)
You can find abundant examples of arguments presented in all branches
of science, engineering, business, philosophy, and even politics that
can be cast in the form of an FOL proof. Those examples confirm the
above observation. (09)
PDM> ... if we want to advance scientific knowledge 'as a whole',
> we need to stop dismissing outright what cannot be translated to
> FOL as quackery, (010)
I agree. My only claim is that people around the world, in all
cultures, *often* use arguments that can be cast in FOL form.
Even you, in some of your emails, use arguments that can be
cast in the form of FOL. (011)
That is all I am claiming. (012)
AS> Logical thinking should indeed be accommodated, but the role
> of logic is only instrumental. (013)
That is what I was claiming: logic is an aid to thought, but it
is not intended to be a theory of how people think. (014)
PDM> there are still strong formalist tendencies going on in philosophy,
> and I think they are too strong. Logical thinking should indeed be
> accommodated, but the role of logic is only instrumental. (015)
I have been saying that for years, and so have my favorite logicians:
C. S. Peirce, A. N. Whitehead, and L. Wittgenstein. See the following
article: (016)
http://www.jfsowa.com/pubs/signproc.htm
Signs, Processes, and Language Games (017)
RF> [Kuhn] p. 167
> The very existence of science depends upon vesting the power
> to choose between paradigms in the members of a special kind of
> community. (018)
EB> I'm not sure that this is the essence of science, but it is
> certainly true that good science owes much to the peer review process.
> And Paola is correct in her accusation that that process produces both
> false positives and false negatives from time to time. Any science
> has its fads, and their success inevitably depends on their partial
> truth and their ability to resolve some known problems. The peer
> process will often reward fad-consistent work, and denigrate
> "revolutionary" work that is inconsistent with the fad. (019)
I agree with those points, but I'd add that similar issues apply
to every community or organization from a nuclear family up to
the largest business corporations and governments. (020)
The communities can be highly effective when there are appropriate
checks and balances and empirical tests against reality. But in
any community, things sometimes get unbalanced when the people in
power abuse their power or fail to perform the necessary checks
and tests. In those cases, it's time for some kind of corrective
action -- protest, divorce, lawsuit, strike, revolution, etc. (021)
EB> At the same time we must realize that every quack thinks himself
> a revolutionary -- this exploder has seen a few examples -- but
> there are hundreds of quacks for every real revolutionary. The
> peer process weeds out the quacks with high reliability. In return
> for preventing the cluttering of the literature with the works of
> 99 goats, we must forgive that process for its occasional sacrifice
> of a lamb. (022)
I agree that peer review (and more generally review by the community,
which could be family, colleagues, customers, voters, etc.) is
necessary. But it's also important to have an ombudsman, appeal
process, or safe haven that can enable the lambs or goats to
get a second chance. (023)
EB> As to funding scientific research, the sad fact is that you have
> to kiss a lot of frogs to find a prince. Some funding managers are
> better at choosing more promising frogs, but the ratio of princes
> to funded frogs is still very low. (024)
RF> [Kuhn] p. 158
> The man who embraces a new paradigm at an early stage must often do
> so in defiance of the evidence provided by problem-solving. He must,
> that is, have faith that the new paradigm will succeed with the many
> large problem that confront it, knowing only that the older paradigm
> has failed with a few. A decision of that kind can only be made on
> faith. (025)
Yes. Sometimes the lambs and goats do have a better idea, and it's
important to provide some options for them. (026)
RF> [Kuhn] p. 159
> Though the historian can always find men -- Priestley, for instance
> -- who were unreasonable to resist for as long as they did, he
> will not find a point at which resistance becomes illogical or
> unscientific. At most he may wish to say that the man who continues
> to resist after his whole profession has been converted has ipso
> facto ceased to be a scientist. (027)
Priestly did make important contributions. He discovered oxygen, but
he continued to call it 'dephlogisticated air'. Lavoisier gave the
death blow to the phlogiston theory by his very precise measurements
of the weight gains and losses during the process of burning. Until
then, one could reasonably advocate the old theory. (028)
Unfortunately, Lavoisier was on the receiving end of a death blow
in the French Revolution. Priestly was an English "dissenter"
who celebrated Bastille day in 1791, but an English mob burned
down his house, and he decided to move to Pennsylvania. (029)
So sheep and goats are often sacrificed, one way or another. (030)
John (031)
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