Criticism of Karl Popper
in Martin Gardner's
Are Universes Thicker Than Blackberries?

W.W. Norton & Company, 2003

Martin Gardner (1914-2010) for many years wrote regular columns for Scientific American magazine and then The Skeptical Inquirer on science and mathematics. No less than sixty-five books by him are listed in this new book, which collects columns from The Skeptical Inquirer, Scientific American, and other venues. Gardner was thus in the stratosphere of prolific science writers with the likes of the late and beloved Issac Asimov. If anything, Gardner seems better at the hard details of matters, especially in mathematics, than Asimov.

The second essay in Gardner's book, "A Skeptical Look at Karl Popper" [pp.12-18], is a sharp, even a somewhat personal and dismissive, critique of Karl Popper's philosophy of science. Gardner is a well informed writer, but the personal dimension of his criticism seems in part to follow from his relationship with and admiration for Rudolf Carnap, one of the principal exponents of Logical Positivism in its heyday -- and on my short list for the worse philosopher in history. Gardner's experiences of classes with Carnap and in transcribing and editing taped lectures into one of Carnap's books are recounted in the essay following the one on Popper ["Rudolf Carnap, Philosopher of Science," pp.19-22].

The sum of Gardner's critique seems to be that induction exists in science, induction as a form of logic is real, Popper's dismissal of it was a mistake, and anything of value that Popper did say about science wasn't really any different, and was less well put or confused, than what other philosophers of science, like Carnap, already were saying. And Popper wasn't a nice man.

The central issue is thus induction. Gardner never does refer to the Problem of Induction by name, though he obviously has it in mind. His sole reference to Hume, the great debunker of induction, is deceptive. All he says is, "David Hume's famous question was 'How can induction be justified?'" [p.13]. Unfortunately, we don't know from this essay that Hume did not simply ask a question and leave it at that. Readers of Hume will hardly find the question, but they will easily find the answer:  Induction cannot be objectively justified by reason. We come closer to getting this message in a separate essay in Gardner's book, "Some Thoughts About Induction" [pp.23-28], where, however, Hume is still somewhat misrepresented. Gardner does say "David Hume considered this question and concluded that induction has no logical justification" [p.25], but then goes on to say, "Induction works, they [Hume and John Stuart Mill] said, because nature is orderly" [ibid.]. Hume would say no such thing, since the regularity or orderliness of nature is known, or not known, in no different a way than any particular law of nature. It is not induction but simply habit, or "custom," which leads us to expect that nature is regular or similar causes will continue to produce similar effects. Nature itself provides no assurance that this is so, unless it is human nature, which fosters the habits, that does.

Since Gardner has softened or misdirected Hume's conclusions, perhaps this is why he doesn't appreciate Popper's point. Yet the rest of Gardner's essay on induction is honest and informative enough, since he does understand that the confirmation of predictions made by a theory, at the best, increases the probability that a theory is true, but then we cannot even say by how much. He mentions that Carnap hoped that it would be possible to state the degree of confirmation with a quantified probability [p.27]. Citing Popper that such a quantification is not possible, Gardner admits in a backhanded way that no such quantification has been achieved. Indeed, for such a quantification one would have to know, perhaps, the percent of the logical space of phenomena that is covered by particular confirmations. That the extent of the logical space is not known is simply a way of restating the Problem of Induction:  we do not know how much confirmation is necessary before the falsity of a theory is precluded.

If Gardner is comfortable with induction because he accepts that nature is orderly, as advocated by Mill and his pseudo-Hume, he should admit that this would have to be a postulate of science, and, gasp, a synthetic a priori proposition. In other words, metaphysics. Rudolf Carnap, however, would not have touched this with a ten-foot pole. Gardner recounts how Carnap used to erase without comment the remnants of Plato and Aristotle from his University of Chicago blackboard, symbolically trashing the "stale and meaningless" metaphysics that the "notorious" likes of Mortimer Adler had left (rather rudely, indeed) from the previous class [pp.19-20]. Gardner mentions how he saw Carnap arguing with Bertrand Russell over metaphysical realism, whether there is a world really out there. Russell evidently wasn't too bothered by such an assertion, but Carnap recoiled from it [p.20]. Indeed, this is Humean skepticism. Gardner only sees skepticism as the endorsement of the fallible and corrigible nature of knowledge -- something that goes "back to ancient Greek skeptics, and is taken for granted by almost all later thinkers" [p.15]. Greek Skepticism, however, denied that there was knowledge, not just that it was infallible; and this is only "taken for granted" by later thinkers who happen to be an Anglo-American tradition derived from Hume's own skepticism. The result seems to be that Gardner is a theoretical skeptic but a practical metaphysician, not unlike Hume, but with less self-awareness, consciousness, and justification.

With complacency about induction, Gardner can easily miss Popper's point. Indeed, he is a bit confused about that point, and even about the nature of induction that Popper is addressing. It is all too easy in this debate to redefine "induction" as something that it isn't and then upbraid critics for making a mistake. It is a bad sign when Gardner begins his "look" at Popper by saying that according to him science proceeds by "falsifying bold, risky conjectures" [p.12]. This is a distortion that betrays a misunderstanding. Scientific theories subject to falsification do not have to be "bold" or "risky" conjectures, but simply universal propositions. All universal propositions, according to Popper, are like conjectures, in that they are about more things (usually) than are subject to inspection. This is true. This is also what induction, in its classical meaning since Aristotle, is about:  the derivation of universal propositions from the experience and observation of particulars. Gardner, at the very least, blurs the distinction between universals and particulars. Thus, he cites the theory that "there are Earth-sized planets" around other stars [p.14]. This may indeed be a scientific theory and a conjecture, but it is a particular (or an existential) proposition, not a universal. The truth condition for existential propositions is that at least one individual satisfies them. This is not what induction is about, or ever has been.

Since Gardner himself accuses Popper of redefining induction and reintroducing it surreptitiously [pp.13 & 14-15], it is best to be clear about what induction was originally supposed to be. The basic idea is that the observation of sufficient particular individuals or events leads to an inductive generalization, by which a universal proposition is derived and justified. Thus, we see the sun rise every day and generalize that the sun will simply continue to rise. Since Aristotle understood the Problem of Induction, he realized that it did not really justify the universal. The universal was only justified by its own self-evidence, apprehended by "mind" (noûs); and such an apprehension indeed consisted of grasping the universal essence (ousía) that subsisted in the events themselves. Now, Hume's skepticism strikes at two points. He agrees with Aristotle that induction does not justify the universal, which thinkers like Carnap and Gardner do not sufficiently appreciate, and he denied that there is a real, universal essence apprehended by the mind in nature. Hume is a Nominalist. Carnap was certainly a Nominalist also. The opposite of Nominalism is Realism, but since "realism" is now commonly used to mean the assertion that the world, or mathematics, and not just universals, exists, it is more common to hear classical Realism called "Essentialism." Popper, as well as Wittgenstein and countless others today, reject Essentialism. Does Gardner? Probably. But if he accepts the regularity of nature as a postulate of science, and is also a realist, he is advancing on perilous ground, with nothing but Rationalists or Kant ahead.

Overlooked by Hume, and most thereafter, is the problem with the other side of Aristotle's view of induction. While Aristotle wisely perceived that induction was not justifying, it remained fundamental to his theory that universal propositions were discovered and derived through it. A feature of this is still conspicuous in Francis Bacon:  if induction is the means of discovery for scientific theories, then the mind must be kept blank and unprejudiced, purged, in Bacon's words, of the "Idols" that would skew and bias its impartial receptivity. Hume still took this so seriously that he denied that anyone could have ideas that were not about the objects of experience -- or that science would ever be able to discover much more than it already had. Subsequently, for a century after Dalton's introduction of the atomic theory in chemistry, serious scientists and philosophers questioned whether such a theory could be more than a convenience when atoms could not be perceived.

Today no one worries about this. The Aristotelian view of induction as a means of discovery has been destroyed by the combined critique of Popper, Wittgenstein, and the deconstructionists. More than anything else, this is what took down the view of science by Carnap and the Logical Positivists. It is not that they maintained it all that explicitly, and it really could not last without Essentialism, but it was part of the heritage of Hume, which the Positivists tended to presuppose rather uncritically. It certainly goes unremarked by Gardner, as might be expected. Where the Positivists implicitly relied on it was in the theory of meaning that they had inherited from Hume:  not just propositions, but concepts, needed to be justified; and they were justified for Hume and the Positivists by tracing them back to an empirical datum. The Positivists called this the "cash" value of the concept and agreed with Hume that concepts without an empirical antecedent were without meaning. This notion, however, makes it possible to confuse discovery with justification, since now an inductive means of discovery is used as the form of justification for the use of certain concepts. This, perhaps, makes it possible to confuse discovery and justification to the extent that Hume's rejection of inductive justification can be accepted, even while another sense of inductive justification is smuggled in, as it was by Hume himself [note].

Where Gardner appears to have in mind that induction, somehow, still justifies scientific knowledge, something no careful thinker since Aristotle had really believed, it was thus probably the remaining role of the means of discovery that provided a sense of justification hovering in the background. Real skepticism now, however, goes deeper than Hume's, rejecting induction as both discovery and justification, along with Essentialism. In its simplest form, this produces the nihilism referenced by Gardner [p.17] as a form of "irrationalism" (including Thomas Kuhn's philosophy of science, which to many academics outside of the sciences, and especially in English and literature departments, is the philosophy of science).

Induction fails as a means of discovery both from some simple reflections and from an examination of the history of science (or of philosophy, since philosophers like Descartes, who also wanted to start with a blank mind, were unable to do so). People had been observing nature carefully for centuries, but it was the imagination, not observation, that produced the Copernican revolution -- which had poor to no observational evidence behind it at the time. Indeed, the only real argument for Copernicus was that his system was simpler than the old astronomy -- a preference based on Ockham's Razor, something that Gardner himself [p.28] apparently regards as more or less a postulate of science, like the orderliness of nature. Einstein conducted thought experiments, not real experiments, in developing Relativity. The structure of the benzine ring was seen in a dream. And so forth. In hermeneutical terms, any set of observations (any "text") in principle can be explained by a large number, perhaps an infinite number, of different theories. Thinking of a particular theory is a matter of inspiration and genius. Most people can look at the same data and conceive of no theories whatsoever. The strongest deconstructionist nihilism is simply that theories have nothing to do with any supposed structure in the data, which itself is interpreted in whatever ways necessary to support the theory.

Gardner also references Popper in the irrationalist camp with the deconstructionists, but this is absurd. While Popper does also reject Essentialism and induction as discovery and justification, he is a realist who a fortiori must endorse some form of essentialist Realism, with the important qualification, which is the main point, that the laws of nature (or essences) cannot be directly or intuitively apprehended, as Aristotle would have thought. They are thus derived, not from induction, but from the imagination, the very thing that Hume had said (in the inductive discovery vein) could not diverge from the "ideas" given in experience.

Gardner certainly knows of the difference between discovery and justification, as well as between universals and particulars, and he would probably assent with the consensus that induction is not the means of discovery that Aristotle and others since have thought. If he does assent, and agrees with Hume about justification and Essentialism, then the grounds of his dismissal of Popper are reduced to the thin reed that induction is responsible for some unquantifiable degree of probability that accrues with each confirmation. Carnap only hoped, vainly, that this could be pinned down. In its absence, Gardner's objections to Popper are busted. Popper's claim that confirmation of predictions, and so successful corroboration of a theory, does not prove the theory and cannot contribute a quantifiable degree of probability of the theory being true [p.13] is really conceded by Gardner, although more clearly in his induction essay than in his Popper essay (where it would undercut the condescension) [note].

Gardner considers the case of the Higgs field in physics to claim that confirmation is on the same ground as falsification, that the observation of the field would confirm the theory but falsify the views of those (like Roger Penrose) that there is no Higgs field. However, the Higgs field is not going to be observed as some particular object, like a new extra-solar planet. Instead, the Higgs field theory makes certain predictions, especially for the existence of unique new particles, the Higgs bosons. If particles are observed, and the Higgs theory is the only one around to predict anything of the sort, then this would tend to confirm the theory, but without, of course, any certainty. The same observation, however, will falsify opposing views, e.g. "There are no Higgs bosons," because particulars can falsify universals -- and the contradictory of a particular/existential is a universal. This does not amount to a criticism of Popper -- it is just a truth of logic. On the other hand, Galileo's observation of Venus, and the Michelson-Morely experiment, falsified and, especially in retrospect, decisively took down Ptolemaic astronomy and Newtonian physics, respectively, because they contradicted the predictions of those theories. While Gardner doesn't think that falsification happens very often, and may be right, and is willing to muddle falsification with some quasi-hermeneutic objections, it is logically decisive and sharp in a way that induction can never be. Which is the point.

Gardner's confusion of particulars and universals continues with the following cut:  "If Popper bet on a certain horse to win a race, and the horse won, you would not expect him to shout, 'Great! My horse failed to lose!'" [p.14]. Popper's "theory" about the horse race, that a certain horse would win, is not a universal. If the horse wins, it wins. A particular proposition, in the absence of a confirming observation of the particular, can only be falsified by the universal. This is going to be extraordinarily difficult, unless, of course, the universe of individuals being considered is limited, as in the actual horses participating in a horse race. Falsification by a universal, however, can occur where the universal is itself a theory. Thus, the theories of the Higgs field and recent theories of "Supersymmetry" in particle physics all predict new particles, as Paul Dirac originally predicted magnetic monopoles. None of these things has ever been observed. Similarly, attempts to unite the strong nuclear reaction with electromagnetism and the weak interaction were long predicting the decay of the proton. In the absence of confirmation, doubt begins to build, though the defense of the Higgs field is that the particles may be too massive to be created by present particle accelerators. With the protons, none were ever observed to decay in experiments where they should have. So this is an anomaly that tends to falsification. When rival theories make predictions that are confirmed, and their predictions contradict those of the unconfirmed ones, then the doubtful theories are eliminated.

Gardner's statement that most scientists "are inductivists who seek positive confirmation" [p.14], uses a word that really means nothing, "inductivists," simply to say that most scientists either look to see if the predictions of their theories are correct, just as Popper would say, or they are observational experts who compile data that may or may not fit some theory or another. The latter would be an inductive project if induction were the Aristotelian means of discovery, which the consensus, probably including Gardner, pretty much holds it isn't. If induction means to Gardner, "whatever scientists do," then "inductivists" can still mean something. But this would beg the question; and it is Popper rather than Gardner who seems to be addressing what induction has meant historically, and the rough handling it received at the hands of Hume, not to mention the extension of the critique more recently.

Gardner's "Addendum" ads an extra barb:

Popper's favorite example of a theory that cannot be falsified was Freudian analysis. This is surely wrong. Adolf Grünbaum, in The Foundations of Psychoanalysis (1984) shows clearly that psychoanalysis not only can be falsified, but that in fact it already has been. [p.18]

Are there still Freudian analysts? Or, more particularly, were there when Popper was writing? Certainly. Gardner even mentions them (cf. Bruno Bettelheim, pp.188-194). So would they have considered Freudian psychoanalysis falsified? Indeed no. That is what Popper was talking about:  those who refused (or still refuse, like Marxists) to accept the falsification of the technique/theory. Did they have reasons for not accepting falsifying evidence? Yes. We are all familiar with psychobabble reasons for rejecting criticism:  "resistance" or "denial" on the part of the critic (Marxists can reject evidence or arguments from "class enemies" or those afflicted with "false consciousness"). The deconstructionists now have systematized protection from falsification with the claim and practice that any contrary evidence can be explained away. Where this doesn't actually work very well, they use the technique that has always worked:  ignore the evidence. Since they believe that knowledge is only about power, they can even justify such a practice (following, as it happens, the Marxists).

The "Addendum" makes another mistake, citing Harry White, who complained about Gardner's original column, that Popper claimed that "a theory has no cognitive content unless it can be falsified" [p.17]. No, it was the Positivists who liked to say that unverifiable theories were meaningless or had "no cognitive content." Popper did not have a theory of meaning, only a theory of scientific knowledge. If something cannot be falsified, it is not therefore meaningless, only not a part of science. Indeed, a theory must have meaning before we can recognize whether it is confirmed, falsified, or even falsifiable. Whether White made this mistake, or only Gardner in rendering the point, I do not know.

Popper doesn't help his case against people like Gardner in two respects:  (1) If a probability theory is ever possible to quantify the degree of confirmation of a scientific theory, this will be a scientific theory like any other, and thus will be the fruit, not of induction, but of mathematical imagination, to be confirmed (probabilistically) or falsified (deductively) like any other theory. It will be neither produced nor justified by induction. Not wanting to give an inch on probability, Popper perhaps misses the chance to use this point. And (2) Popper doesn't have a very good theory on the epistemology of particular/existential statements describing experience. He says they are "caused" by experience, which really strips them of epistemic force. But Gardner's critique overlooks such a problem and so takes no advantage of it.

Gardner accuses Popper of an "enormous egotism" that was simply "motivated by an intense jealousy of Carnap" [p.16]. This seems strange. Why should Popper be jealous of Carnap any more or less than any other famous Positivist or, for that matter, someone like Wittgenstein? If Carnap really had some tremendous individual achievement, jealousy might be an issue, but Popper lived to see Logical Positivism vanish with phlogiston. By the time Popper died, it had been a good thirty years since anyone would have had reason to be jealous of Carnap or his school, while Popper, although obviously no favorite of Gardner or others still clinging to a confused Positivist conception of induction, continued to possess a substantial, if not actually universal, following. The jealousy really seems to go the other way around; as Gardner has to admit, "Carnap's reputation is not as high now as it was then" [p.22], he can only hope that "more younger philosophers of science will surely discovery the greatness of his contributions and his influence" [ibid.]. How personal this gets seems to come out in how Gardner quotes with some glee the statement by David Papineau that "Popper was a monster, a moral prig" [p.16]. I don't know to what extent anything of the kind was true, but it does seem like scraping the bottom of the barrel in what is supposed to be a brief intellectual critique.

Criticism of Karl Popper in Anthony O'Hear's An Introduction to the Philosophy of Science

Philosophical Vienna

Philosophy of Science

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Criticism of Karl Popper in Martin Gardner's
Are Universes Thicker Than Blackberries?, Note 1

Exactly what induction meant to Hume is well revealed in his low expectations for scientific discovery:

These ultimate springs and principles are totally shut up from human curiosity and enquiry. Elasticity, gravity, cohesion of parts, communication of motion by impulse; these are probably the ultimate causes and principles which we shall ever discover in nature. [An Enquiry Concerning Human Understanding, Section IV, Part I, p. 26, L.A. Shelby-Bigge, editor, Oxford University Press, 1902, 1972, p. 30, boldface added]

Elsewhere he denies we shall ever know, for instance, what it is that makes bread suitable for nutrition. The possibility of detailed knowledge of atomic structures, leading to proteins and vitamins, is inconceivable to Hume. Why? Because we don't see such things. Induction from experience is about what we see. The theory of atoms requires an imaginative leap to the unseen. Hume actually denies that the imagination can produce something that is not already in perception. It is not hard to imagine that quantum events, which are unlike anything in experience, would have been been particularly indigestible to Hume. The uneasiness of some scientists with atomic theory (e.g. Ernst Mach) continued through the 19th century, with no more basis than doubt about the legitimacy of knowledge about the unseen.

Why Hume expected so little from science is well worth taking into account, since it reveals the narrow character of the inductive discovery process he describes and its lack of correspondence or relevance to the modern practice of science, even in Hume's own day. But if it is imagination, not induction, from which scientific theories are derived, we are talking about Popper, not any traditional form of inductivism. But if induction is neither discovery nor justification, it is nothing.

Gardner's confusion about induction comes out in a reference he makes in another book to Mach:

Although philosophy may have played a positive role in the work of Einstein, Heisenberg, and others, it has, in [physicist Steven] Weinberg's opinion, done more harm to science than good. Particularly baleful, he argues, was an early, crude version of positivism that prevented many eminent physicists from regarding unobservable entities as "real." The most flagrant example was the refusal of the Austrian physicist Ernst Mach, who had so strong an influence on Einstein, to admit the reality of atoms or to accept the unobservable fields of general relativity. [Weird Water & Fuzzy Logic, "Will Science Discovery Everything?" Prometheus Books, 1996, p.255 -- this was a review of Weinberg's book, Dreams of a Final Theory]

Mach's judgment was not based on "an early, crude version of positivism," but simply on the traditional Aristotelian and Baconian meaning of induction. The later, sophisticated version of Positivism, which rejected words as meaningless if they did not have empirical "cash" value, was the last gasp of the ancient principle. Gardner's own nostalgia for Rudolf Carnap helps prevent progress beyond this.

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Criticism of Karl Popper in Martin Gardner's
Are Universes Thicker Than Blackberries?, Note 2

While the degree of confirmation cannot be quantified, there are cases where we feel that a theory has been proven for all practical purposes. Thus, Gardner says elsewhere, as Carl Sagan used to say, that Darwin's theory of Evolution by natural selection has been confirmed to a degree that renders it essentially a fact rather than just a "theory." I tend to agree with them. This is a matter of some interest because various people hotly dispute that Evolution has been properly confirmed, or has even avoided falsification. "Creationists" and recent advocates of "intelligent design" deny that conventional readings of the fossil record, or naturalistic interpretations of nature, are sufficient as scientific theories.

If a generalization from individuals becomes a matter of certainty, it can be because of "complete induction," i.e. examining all the individuals in questions, or, more abstractly, all the possibilities. Thus, if we wonder whether there were any ruling Queens of France, as there were Queens of England (e.g. Queen Elizabeth I, Queen Anne, etc.), all we have do is examine the list of the rulers of France. No women. A similar question, however, about Roman Emperors leads to a problem. From Augustus to 476, there are no ruling women; but the line of Emperors at Constantinople, extending to 1453, contains three women who ruled, beginning with Irene. Complete induction, therefore, can be a matter of defining the relevant individuals.

In science, when there is a theory that explains the facts well and really has no conceivable rival, this amounts to something like the abstract equivalent of complete induction, at least given the present state of understanding. Evolution by natural selection is in this category. Arguments against Evolution are to be discounted because usually they do not even amount to scientific arguments, or adduce relevant scientific evidence. The recent arguments for "intelligent design" involve a number of errors. The idea that natural systems cannot independently develop the level of organization that they have is contradicted by easily identifiable cases of self-organizing natural systems. The most conspicuous of these is the grammar of natural languages, which develops and changes without any intentional design or control. Why this all is possible in nature is a good question, but it is more a metaphysical than a scientific question, and the existence of a personal Deity is by no means necessary for such a explanation. Platonism, with a transcendent World of Forms, could handle the problem just as easily as theism.

More importantly, a theory of "intelligent design" implies, and is intended to imply, an intelligent Designer. Since such a Designer would be, and would be intended to be, a transcendent object, it would suffer from the drawbacks of all transcendent objects, namely, that they give rise to Antinomies:  contradictions that arise when any attempt is made to develop a rational theory of them. This is what Kant called "dialectical illusion," and it is one of the reasons why Kant did not think that speculative and theoretical metaphysical knowledge of the transcendent was possible.

Also, we expect that such a Designer would be omnipotent, but this characteristic renders all scientific inquiry unnecessary. Whatever we wish to explain in nature, it can be explained directly by the omnipotence of God. The sky is blue because God wants it to be blue and can make it be that way. Because God represents overkill for any explanation, scientific inquiry is necessarily naturalistic, which means only natural causes are considered. If, in the end, no natural explanation is possible, then supernatural ones are left, but this is a last resort only when the human imagination has certifiably run out of all explanations. There is really no way to know this, and, in any case, the supernatural explanations cannot be made rationally coherent anyway, as already noted. Therefore, supernatural or transcendent explanations are of no practical value in science.

The advocates of "intelligent design" sometimes accuse the scientific community of "methodological naturalism," as though this is a grave fault. Guilty as charged, but it is no fault:  it is the essence of science. In Kantian terms, phenomena are conditioned realities that can only be rationally explained in deterministic terms. If there is a God, or any other transcendent object (souls, karma, the Dharma, Nirvana, Forms, etc.), they are unconditioned realities, for which there is no rational understanding (as Buddhism actually says of Nirvana). Naturalism thus must be the method of science, or inquiry will simply be terminated in a rationally arbitrary fashion.

With complete induction, there is much in science that seems beyond doubt. This, however, does not solve the Problem of Induction or refute Popper's claim than science uses falsification rather than verification. Complete induction as an abstract matter, indeed, fits better with a coherence theory of truth rather than a correspondence theory. Gardner, properly, regards a correspondence theory as all but self-evident. Evolution, however, is not to be considered a "fact" because we are able to independently examine external reality, but just because nothing else in science, or in philosophy of science, contradicts or problematizes it. There is thus no rational alternative -- given our present state of understanding, which is the whole present system of human knowledge. Truth isn't coherence, but our manner of knowing is limited by coherence. This makes a kind of certainty in science possible, when a real Cartesian certainty may not be.

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