LINGUIST List 13.1396

Sat May 18 2002

Disc: Last Post: Falsifiability vs. Usefulness

Editor for this issue: Karen Milligan <karenlinguistlist.org>

Directory

1. H.M. Hubey, Re: 13.1379, Disc: Next to Last Posting/Falsifiability/Usefulness
2. Denis Bouchard, Falsifiability II

Message 1: Re: 13.1379, Disc: Next to Last Posting/Falsifiability/Usefulness

LINGUIST List wrote:


> From: Robert Whiting <whitingcc.helsinki.fi>
> Subject: Re: 13.1354, Disc: Falsifiability vs. Usefulness
>
> >That is certainly not possible. P + ~P =1 always. If P=0,
> >and ~P=0, then we'd have P+~P=0 which is not possible.
>
> This is only true of existential categorical propositions. Here
> is the rule (sometimes known as the rule of existential falsity):
>
> If a categorical proposition implies but does not presuppose
> the existence of entities to which its subject or predicate
> or their contradictories apply, then it is false if any of
> these terms is empty.
>
> What this means is that if X is presupposed to exist, then
> of (1) X is P and (2) X is ~P, either (1) or (2) must be true and
> the other false. But if X is not presupposed to exist then there
> is the possiblity (3) X does not exist, and if (3) is true then
> both (1) and (2) are false. (Unless, of course, (1) and (2) are
> existential statments about X.)

The only people who deny The Law of the Excluded Middle
(e.g. P + P' =1) are the intuitionists. Their view is that if you
prove P is false then you have still not proven that P' is true.
They want a proof that P' is true. They want constructive proofs.

What you are referring to is not in propositional calculus but
in predicate calculus usually, and it refers to the problems of
logic. Any statement about a non-existent object is true e.g.
what I wrote about the case of P=0 and Q=0 in P=>Q.

The reason why this works out is because, again, logic is biased
towards truth, and only the counterexample disproves a [general]
statement. For example, the statement "All submarines longer than
one mile long are pink" is true, because there are no submarines
longer than 1 mile long. This can also be understood quite easily
in terms of the "counterexample". In other words, since there are
no submarines longer than a mile, nobody can find one of them
and show that there is one that is not pink. You can see the explanation
in my book, The Diagonal Infinity, World Scientific, Singapore, 1999.



- 
M. Hubey

hubeyhmail.montclair.edu
http://www.csam.montclair.edu/~hubey

Now consider falsifiability. Dan says that "neither analysis has been
falsified" in my example. He seems to have in mind something like what
Lakatos (1970) calls "naive falsification", as his second criticism
indicates: "Bouchard has...overlooked a large part of linguistics
history in which hypotheses have been abandoned and gone back to time
and time again, even after having been supposedly falsified.... But
this just means that falsifiability is nonlethal to hypotheses,
i.e. that it can always be circumvented, which makes it less than
useful."

Dan seems to attribute to me a notion of falsification according to
which a hypothesis is dead forever once the facts say NO to it. But no
serious scientist takes this approach to falsification nowadays. Naive
falsification is based on the wrong premiss that facts are out there,
solid and undeniable, and that a fact may constitute a counterexample
to a theory. But facts do not interact with the propositions of
theories, only other propositions do--in this case, factual
propositions. Naive falsification requires that there be a clear,
natural borderline between theoretical propositions and factual
propositions. But there isn't. The demarcation is a question
of decision: it can and does vary as progress is made.

Since falsification is about the confrontation of propositions, not of
facts and propositions, a falsified theory in this sense is an
instance of inconsistency between propositions. As Lakatos puts it,
nature never shouts NO, it just says INCONSISTENT. Crucially, any
proposition, theoretical or factual, may turn out to be incorrect and
be the cause of the inconsistency. In sophisticated falsification, an
unfalsifiable theory is one with propositions that cannot be shown to
be inconsistent in some respect.

Sophisticated falsifiability throws a different light on Dan's comment
about the history of linguistics. If proposition P1 has been abandoned
in the past because it was inconsistent with P2, and we later realize
that P2 is inconsistent with P3 and P2 is the culprit, then we can
come back to P1 without contradicting sophisticated falsification.

Let us now return to the examples. My first example illustrates a case
in which the incorrect proposition creating the inconsistency is a
theoretical proposition. The problem with ST is that it is consistent
with the theoretical proposition stating that the basic order is
SHC,but also with the proposition that it is CHS,and so on for all
possible basic orders. But these basic universal orders are mutually
inconsistent: they can't all be universal. ST is consistent
with inconsistent propositions: so it is wrong, falsified. Note that
here, the inconsistent propositions are theoretical, not factual: so
the theory is falsified even if no "fact" contradicts it.

My second example is a case in which some of the incorrect
propositions creating the inconsistency are theoretical and some are
factual. The theory with SHC and ST is consistent with the factual and
theoretical propositions which describe L, but it is also consistent
with the propositions which describe anti-L. However, these two sets
of propositions are not consistent, so the theory with SHC and ST is
falsified.

Falsifiability fosters progress because it drives scientists to look
for inconsistencies between the propositions of their theory and as
many other propositions as they can, including potential observational
propositions (predicting new "facts"), and it forces scientists to
correct these inconsistencies, to come up with a better theory.

Far from only telling us negative things, sophisticated falsifiability
gives us good indications whether a statement is worth believing in,
worth trying, worth following. Falsifiability is very helpful,
particularly in aiding us avoid some misguided applications of
usefulness in linguistics.

Denis Bouchard