Wednesday, 6 September 2017

Popper’s Falsification Principle and Second-order Statements

Are Second-order Statements Heterological or Homological?

In the following I'll discuss two well-known statements: Karl Popper’s Falsification Principle and what I call the Relativist Claim.

Such statements can be taken as either homological or heterological in nature. A heterological predicate, statement or sentence is one that doesn't apply to itself. The statements to be considered may well fall into this category.

For example, the statement

All truth-claims are relative.”

may not be self-applicable. 

Alternatively, statements can be taken as homological in nature. A homological statement is one that applies to itself. So, for example, the claim that “All truth-claims are relative” may - or even must - itself be relative to context, speaker, etc.

However, the relativist claim “All truth-claims are relative” may be heterological That is, a meta-statement which isn't self-applicable.

Why is that?

Possibly because such statements aree second-order (or metalinguistic) in nature.

For example, take the relativist claim again. That claim is about the first-order statements within its domain which aren't themselves (generally speaking) about truth-claims. Instead they're about objects, events, facts, observations, etc. in the world. Of course such second-order (or metalinguistic) statements can themselves be related to yet higher-order (metalinguistic) frameworks.

Nonetheless, who's to say that those who formulate such meta-statements deny that they have the property of being related to frameworks? They may concede their own status vis-à-vis higher metalinguistic languages. They may also concede that their very own statements are self-applicable. That is, they may concede (or admit) their own self-referentiality or homologicality.

However, Thomas Nagel (in his The Last Word), for example, has said that the relativist claim must itself be a victim of relativity if it's true (or if it's to be taken as true). And if that’s the case, Nagel also argues, then why should we pay it any attention whatsoever? As Nagel himself puts it (though about 'subjectivism', not relativism):

To put it schematically, the claim 'Everything is subjective' must be nonsense, for it would itself have to be either subjective or objective. But it can't be objective, since in that case it would be false if true. And it can't be subjective, because then it would not rule out any objective claim, including the claim that it is objectively false.”

Though isn’t this to assume that Nagel himself can escape from relativity and that the relativist claim can't escape from relativity (i.e., by claiming second-order status)?

Karl Popper’s Falsification Principle

Popper’s statement has been used against - to take only two examples - Freud’s claims as well as against the claim that there may be - or are - infinite universes. Indeed it's now almost a commonsense theory, especially when used by those who're scientifically-minded. However, until Charles S. Peirce formulated his related theory of “fallibilism” (in late 19th century), such ideas were very rarely discussed. Nevertheless, the history or etiology of this theory - and the way Popper himself may have elaborated upon it elsewhere - is of no concern here. The theory is taken as it stands - as a single statement that is, possibly, self-referential or homological in nature.

Popper’s Falsification Principle states that all theories must be open to (possible) falsification. The obvious question now is:

Can Popper’s Falsification Principle itself be falsified? Is it falsifiable in principle?

If it can actually be falsified, then isn't the statement invalid or simply false? If it's falsifiable in principle, then it may simply be self-defeating rather than false. If it can’t either be falsified or it isn't falsifiable in principle, then isn't it self-contradictory?

Not only that. If Popper’s theory can be falsified, this may well imply that there are indeed other theories that can't be falsified or which aren’t even falsifiable in principle. More clearly, if Popper’s statement were actually falsified (though, again, Popper demanded falsifiability in principle, rather than an actual falsification), there may - by implication - be theories that are in principle irrefutable or unfalsifiable. On the other hand, if Popper’s theory weren't falsifiable, then it would be exempting itself from its own universal claim. Again, in order for Popper’s theory to be falsifiable in principle it may need to accept - or even entail - the existence of a theory (or theories) that's not falsifiable in principle. How else would the falsification theory itself be either falsifiable in principle or actually falsified?

If these non-falsifiable and non-falsified theories actually exist, then Popper’s theory would perhaps be either useless and/or self-defeating.

If Popper’s theory can be falsified (rather than it being simply falsifiable in principle), then that would mean that it's false. And if it's false, then what it claims is false. And it claims that all true (or genuine) theories must be falsifiable in principle. Therefore if what the theory claims is actually false, then it's also false that all true (or genuine) theories must be – or are - falsifiable in principle. So Popper loses on both counts. If his theory isn't falsifiable in principle, then it can be seen as self-contradictory. On the other hand, if it can be actually falsified, then what it claims isn't true.

Nevertheless, is it correct to argue that if Popper’s Falsification Principle can't itself be falsified, then it must be invalid, self-contradictory or self-defeating? According to Popper himself (though not, however, according to the theory itself), no theory is ever completely certain or valid. Therefore Popper might have happily accepted the limited applicability of his own theory (despite its universal nature). Of course Popper’s principle can be given a kind of absolutist, axiomatic or normative status. If Popper had done so, then he might have allowed his theory an escape which is denied to all other scientific or philosophical theories. He might have therefore allied himself with, say, theologians or non-naturalistic metaphysicians.

The case against the Falsification Theory is similar in certain ways to the case against the relativist claim; as well as against the Testability/Verifiability Principle of the (early) logical positivists.

For example, the claim that “All truth-claims are relative or contextual” may itself be relative or contextual. Similarly, if all of Popper's genuine theories are falsifiable in principle, then the Falsification Theory must itself be being falsifiable in principle. (Again, if it's a theory of the same type as the theories within its domain!) If it can be - or is - actually falsified, then it may have limited (or no) validity or use. Similarly, relativists claim (or do they?) that the relativist claim isn't itself relative or contextually-mediated because it's second-order. Though if it were relative or contextually-mediated (or if it did claim for itself such a status), then it may either be of no use and/or be of self-defeating in nature (as Nagel argued above). On the other hand, if the relativist claim is itself a claim that's relative or contextually-mediated, then it's no more - or less - valid or useful than any other theory of truth.

In any case, perhaps relativists don't really offer us a concept or theory of truth. That is, if the relativist claim is second-order, then (just like Verificationist Principle), it may also be normative, stipulative, prescriptive, etc.

To recapitulate a little.

Popper argued that theories and hypotheses must allow the possibility of their own falsification or refutation; though not – obviously - their actual falsification or refutation. Is Popper’s theory of falsifiability or refutability itself falsifiable or refutable in principle? If it isn't, then it may be self-contradictory. If it can actually be falsified, then it may be self-defeating.

For instance, if Popper’s theory of falsifiability can be falsified (or even if it's only falsifiable in principle), this would entail the possibility - or even the actuality - that there are other theories which can't be falsified or even be falsifiable in principle. In other words, in order for Popper’s theory to be open to being shown to be false (i.e., to be falsifiable in principle), then other theories may - or must - be unfalsifiable in principle. On the other hand, if Popper’s theory isn't falsifiable in principle, then Popper might have been exempting it from his own universal statement about all other theories. (Of course, the Falsification Principle may not be a member of its own domain. That is, it may not belong to itself.) In order for Popper’s principle to be falsifiable itself, it may need to accept - or even entail - the existence of at least one theory that isn't actually falsified or falsifiable in principle.

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