Gardner’s Misstep

In carnap, critical rationalism, empiricism, experiments, fallibilism, gardner, holism, justificationism, popper, the ancient greeks, wittgenstein on 28/06/2011 at 10:33 am

Martin Gardner wrote A Skeptical Look at Karl Popper back in 2001. I decided to give it a read then put down some provisional comments …

I believe that Popper’s reputation was based mainly on this persistent but misguided efforts to restate common-sense views in a novel language that is rapidly becoming out of fashion. Consider Popper’s best known claim: that science does not proceed by “induction”—that is, by finding confirming instances of a conjecture — but rather by falsifying bold, risky conjectures. Conformation, he argued, is slow and never certain. By contrast, a falsification can be sudden and definitive.

Popper said, time and again, that confirmations do not exist and falsifications were never definitive. This is completely–absolutely–different from what Gardner asserts. Such a mistake is excusable only for a first year undergraduate. Has Gardner actually read what Popper had to say? I hope so, but if that is the case, Gardner is such a satisfied follower of Carnap (see below) that he cannot see beyond the tip of his nose. Thus, Gardner softens Popper’s critique of inductive theories of science (confirmation is “slow,” rather than nonexistent) so far that I can only shrug my shoulders.

There are many objections to this startling claim [that there is no such thing as induction]. One is that falsifications are much rarer in science than searches for confirming instances. Astronomers look for signs of water on Mars. They do not think they are making efforts to falsify the conjecture that Mars never had water.

First, rarity speaks nothing of the logical asymmetry between corroboration and refutation. Second, the example is pure poppycock: finding water on Mars corroborates the existential statement “There is water on Mars at location F,” which is perfectly permissible. One need only present water existing on Mars in much the same way one need only present a black swan or a white raven. Existential statements, understood as basic statements or protocol statements that can be intersubjectively tested, are the bread and butter of science, even according to Popper.

While scientists may not have intended to refute the theory that “Mars never had water,” I’m sorry to disappoint Gardner by pointing out that this is exactly what occurred. Adopting an existential statement as true, be it “This here is a black swan,” “A white raven is flying over Bristol at time t,” or “There is water on Mars at location F,” refutes an infinite number of incompatible theories.

Falsifications can be as fuzzy and elusive as confirmations.

Yes. This is true–but the falsifiability of theories != falsifying theories. Gardner does not understand this simple distinction (see below for further comments). People have written dozens of articles confusing the two, but that does not excuse Gardner’s childish mistake.

Astronomers are not trying to falsify it; they are looking for confirmations.

A fisherman may look for fish and find buried treasure. The intent of the fisherman is ancillary to the fisherman’s success.

Falsification may be based on faulty observation. A man who claims he saw a white crow could be mistaken or even lying. As long as observation of black crows continue, it can be taken in two ways; as confirmations of “all crows are black,” or disconfirmations of “some crows are not black.” Popper recognized — but dismissed as unimportant — that every falsification of a conjecture is simultaneously a confirmation of an opposite conjecture, and every conforming instance of a conjecture is a falsification of an opposite conjecture.

Gardner is striking in his ineptitude. First, note that we begin with only the logical structure:

If an existential statement e is true, does it deductively entail that universal statement p that is compatible with existential statement e is true or false? No! Then existential statement e serves no purpose for deciding if compatible universal statement p is true or false.

Does it deductively entail that universal statement q that contradicts the existential statement e are true or false? Yes: it deductively entails that the universal statement q is false! Then existential statement e serves a purpose for rejecting incompatible theory q.

Then we move on to methodological rules: if an individual S decides to adopt existential statement e as true, then–all things being equal, and putting the set of auxiliary hypotheses h aside for the moment–we reject incompatible theory q.

Does that mean scientists could be wrong in their decision to adopt an existential statement? Auxiliary hypotheses h or initial conditions i could be mistaken! Our universal statement p + auxiliary hypotheses h + initial conditions i may predict, for instance, that on the evening of October 25, 1946, at the meeting of the Cambridge Moral Sciences Club, Ludwig Wittgenstein had precisely three shillings in his pocket, yet if were the case that Wittgenstein did not have precisely three shillings in his pocket, the auxiliary hypotheses h or initial conditions i could be mistaken, rather than the universal statement. However, it is comparatively easier for a group of scientists to agree–provisional though this agreement may be–over the location of a needle on a dial or the numbers on a readout than to agree on theories.

Lastly, even though “every falsification of a conjecture is simultaneously a confirmation of an opposite conjecture, and every conforming instance of a conjecture is a falsification of an opposite conjecture,” that does not make confirmation perform any epistemic duty. Gardner first must address the problem of induction and the logical asymmetry between confirmations and refutations before we take a refutation of a theory to hold any epistemic weight as simultaneously a corroboration of its negation (other than the most banal: “There exists at least one X that is Y”).

For Popper, what his chief rival Rudolf Carnap called a “degree of confirmation”—a logical relation between a conjecture and all relevant evidence—is a useless concept. Instead, as I said earlier, the more tests for falsification a theory passes, the more it gains in “corroboration.” It’s as if someone claimed that deduction doesn’t exist, but of course statements can logically imply other statements.

Far from it–Popper made a mistake to spend so much time on corroboration, for corroborations give no evidential support to theories that go beyond what is assumed. Corroborations don’t have any epistemological significance, but it may prove methodological significance when choosing between two surviving theories.

Scholars unacquainted with the history of philosophy often credit popper [sic] for being the first to point out that science, unlike math and logic, is never absolutely certain. It is always corrigible, subject to perpetual modification. This notion of what the American philosopher Charles Peirce called the “fallibilism” of science goes back to ancient Greek skeptics, and is taken for granted by almost all later thinkers.

Poor, poor scholars–Popper was indebted to Peirce and the Presocratics, and made this debt public throughout his life. I do not understand why Gardner wrote such a paragraph. And yet, most people do not take fallibilism seriously, for unlike Popper, they think that when sufficient reasons are unavailable, insufficient reasons can carry any weight. It would be like, when a bucket is unavailable, asking for a sieve to carry water more than a few steps!

I am convinced that Popper, a man of enormous egotism, was motivated by an intense jealousy of Carnap. It seems that every time Carnap expressed an opinion, Popper felt compelled to come forth with an opposing view, although it usually turned out to be the same as Carnap’s but in different language. Carnap once said that the distance between him and Popper was not symmetrical. From Carnap to Popper it was small, but the other way around it appeared huge. Popper actually believed that the movement known as logical positivism, of which Carnap was leader, had expired because he, Popper, had single-handedly killed it! (bolding mine)

I do not care if Popper was a megalomaniac and a ponce–I do not care about intentions; I care about whether he was correct or incorrect. Motives speak only to distinguishing a murder from a manslaughter, not a better or worse theory of scientific practice. If I may psychoanalyze Gardner as he psychoanalyzes Popper, I conjecture that Gardner, a man who does not understand some basic philosophical problems, was motivated to write such a hack piece by his intense–nay, mad!–devotion to Carnap.

Popper’s great and tireless efforts to expunge the word induction from scientific and philosophical discourse has utterly failed. Except for a small but noisy group of British Popperians, induction is just too firmly embedded in the way philosophers of science and even ordinary people talk and think.

I agree that our language is theory-laden, but does that make our natural use of language correct? Take a synthetic example: if grass were in fact grue and not green, then our language would have been mistaken! Or take the embedded concepts about gender, race, or the rights of animals: all have come under revision in the past two hundred years. Gardner, if he should have access to a time machine, wouldn’t have (one thinks!) called such expansions of the social circle to be for naught. Even the most embedded concepts may, over time, change when confronted with criticism. Appealing to natural language might have worked in Oxford during the 50’s, but Wittgenstein’s philosophy has aged as poorly as a pear.

Confirming instances underlie our beliefs that the Sun will rise tomorrow, that dropped objects will fall, that water will freeze and boil, and a million other events. It is hard to think of another philosophical battle so decisively lost.

Gardner must know nothing of the distinction between the psychological problem of induction and the logical problem of induction. Gardner assumes that Hume’s psychological solution was correct, which neglects all the work done in psychology in the past two hundred years (Selz, Bühler, &c.).

In sum, Gardner is woefully unprepared to address Popper’s criticism of inductivist or justificationist accounts of science.


  1. Reblogged this on Quantum Prana – The Dark Matter Guitar and commented:
    Trying to make my own opinion on this debate. What do you people think?

  2. The author of this blog has clearly failed to read (or understand) Gardner.

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