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

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

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/~hubeyMail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue

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 BouchardMail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue