Inductivism

Inductivist endorsement Francis Bacon, articulating inductivism in England, is often falsely stereotyped as a naive inductivist. Near 1740, David Hume, in Scotland, identified multiple obstacles to inferring causality from experience. Hume noted the formal illogicality of enumerative induction—unrestricted generalization from particular instances to all instances, and stating a universal law—since humans observe sequences of sensory events, not cause and effect. Perceiving neither logical nor natural necessity or impossibility among events, humans tacitly postulate uniformity of nature, unproved. Later philosophers would select, highlight, and nickname Humean principles—Hume's fork, the problem of induction, and Hume's law—although Hume respected and accepted the empirical sciences as inevitably inductive, after all. Immanuel Kant, in Germany, alarmed by Hume's seemingly radical empiricism, identified its apparent opposite, rationalism, in Descartes, and sought a middle ground. Kant intuited that necessity exists, indeed, bridging the world in itself to human experience, and that it is the mind, having innate constants that determine space, time, and substance, and thus ensure the empirically correct physical theory's universal truth. Thus shielding Newtonian physics by discarding scientific realism, Kant's view limited science to tracing appearances, mere phenomena, never unveiling external reality, the noumena. Kant's transcendental idealism launched German idealism, a group of speculative metaphysics. While philosophers widely continued awkward confidence in empirical sciences as inductive, John Stuart Mill, in England, proposed five methods to discern causality, how genuine inductivism purportedly exceeds enumerative induction. In the 1830s, opposing metaphysics, Auguste Comte, in France, explicated positivism, which, unlike Bacon's model, emphasizes predictions, confirming them, and laying scientific laws, irrefutable by theology or metaphysics. Mill, viewing experience as affirming uniformity of nature and thus justifying enumerative induction, endorsed positivism—the first modern philosophy of science—which, also a political philosophy, upheld scientific knowledge as the only genuine knowledge. Inductivist repudiation Nearing 1840, William Whewell, in England, deemed the inductive sciences not so simple, and argued for recognition of "superinduction", an explanatory scope or principle invented by the mind to unite facts, but not present in the facts. John Stuart Mill rejected Whewell's hypotheticodeductivism as science's method. Whewell believed it to sometimes, upon the evidence, potentially including unlikely signs, including consilience, render scientific theories that are probably true metaphysically. By 1880, C S Peirce, in America, clarified the basis of deductive inference and, although acknowledging induction, proposed a third type of inference. Peirce called it "abduction", now termed inference to the best explanation, IBE. The logical positivists arose in the 1920s, rebuked metaphysical philosophies, accepted hypotheticodeductivist theory origin, and sought to objectively vet scientific theories—or any statement beyond emotive—as probably false or true as to merely empirical facts and logical relations, a campaign termed verificationism. In its milder variant, Rudolf Carnap tried, but always failed, to find an inductive logic whereby a universal law's truth via observational evidence could be quantified by "degree of confirmation". Karl Popper, asserting since the 1930s a strong hypotheticodeductivism called falsificationism, attacked inductivism and its positivist variants, then in 1963 called enumerative induction "a myth", a deductive inference from a tacit theory, explanatory. ==Scientific methods==

From the 17th to the 20th centuries, inductivism was widely conceived as scientific method's ideal. Even at the 21st century's turn, popular presentations of scientific discovery and progress naively, erroneously suggested it. The 20th was the first century producing more scientists than philosopherscientists. Earlier scientists, "natural philosophers," pondered and debated their philosophies of method. Inductivism Inductivism infers from observations of similar effects to similar causes, and generalizes unrestrictedly—that is, by enumerative induction—to a universal law. Inferring the relation A to B implies the relation B to A'' supposes, for instance, "If the lamp is broken, then the room will be dark, and so the room's being dark means the lamp is broken." Even if B holds, A could be due to X or Y or Z, or to XYZ combined. Or the sequence A and then B could be consequence of U—utterly undetected—whereby B always trails A by constant conjunction instead of by causation. Maybe, in fact, U can cease, disconnecting A from B. Disconfirmation A natural deductive reasoning form is logically valid without postulates and true by simply the principle of nonselfcontradiction. "Denying the consequent" is a natural deduction—If A, then B; not B, so not A—whereby one can logically disconfirm the hypothesis A. Thus, there also is eliminative induction, using this Determination At least logically, any phenomenon can host multiple, conflicting explanations—the problem of underdetermination—why inference from data to theory lacks any formal logic, any deductive rules of inference. A counterargument is the difficulty of finding even one empirically adequate theory. Still, however difficult to attain one, one after another has been replaced by a radically different theory, the problem of unconceived alternatives. A hypothesis can be tested only conjoined to countless auxiliary hypotheses, mostly neglected until disconfirmation. Deductivism In hypotheticodeductivism, the HD model, one introduces some explanation or principle from any source, such as imagination or even a dream, infers logical consequences of it—that is, deductive inferences—and compares those with observations, perhaps experimental. In Popperian hypotheticodeductivism, sometimes called falsificationism, although one aims for a true theory, one's main tests of the theory are efforts to empirically refute it. ==Inductivist reign==

Francis Bacon introduced inductivism—and Isaac Newton soon emulated it—in England of the 17th century. In the 18th century, David Hume, in Scotland, raised scandal by philosophical skepticism at inductivism's rationality, whereas Immanuel Kant, in a German state, deflected Hume's fork, as it were, to shield Newtonian physics as well as philosophical metaphysics, but in the feat implied that science could at best reflect and predict observations, structured by the mind. Kant's metaphysics led to Hegel's metaphysics, which Karl Marx transposed from spiritual to material and others gave it a nationalist reading. Auguste Comte, in France of the early 19th century, opposing metaphysics, introducing positivism as, in essence, refined inductivism and a political philosophy. The contemporary urgency of the positivists and of the neopositivists—the logical positivists, emerging in Germany and Vienna in World War I's aftermath, and attenuating into the logical empiricists in America and England after World War II—reflected the sociopolitical climate of their own eras. The philosophers perceived dire threats to society via metaphysical theories, which associated with religious, sociopolitical, and thereby social and military conflicts. Bacon In 1620 in England, Francis Bacon's treatise Novum Organum alleged that scholasticism's Aristotelian method of deductive inference via syllogistic logic upon traditional categories was impeding society's progress. Admonishing allegedly classic induction for inferring straight from "sense and particulars up to the most general propositions" and then applying the axioms onto new particulars without empirically verifying them, In Bacon's inductivist method, a scientist, until the late 19th century a natural philosopher, ventures an axiom of modest scope, makes many observations, accepts the axiom if it is confirmed and never disconfirmed, then ventures another axiom only modestly broader, collects many more observations, and accepts that axiom, too, only if it is confirmed, never disconfirmed. Yet ultimately, as applied, Bacon's term axiom is more similar now to the term hypothesis than to the term law. In Bacon's estimation, during this repeating process of modest axiomatization confirmed by extensive and minute observations, axioms expand in scope and deepen in penetrance tightly in accord with all the observations. But, as Bacon provides no clear way to frame axioms, let alone develop principles or theoretical constructs universally true, researchers might observe and collect data endlessly. Geocentric were both Aristotelian physics and Ptolemaic astronomy, which latter was a basis of astrology, a basis of medicine. Nicolaus Copernicus proposed heliocentrism, perhaps to better fit astronomy to Aristotelian physics' fifth element—the universal essence, or quintessence, the aether—whose intrinsic motion, explaining celestial observations, was perpetual, perfect circles. Yet Johannes Kepler modified Copernican orbits to ellipses soon after Galileo Galilei's telescopic observations disputed the Moon's composition by aether, and Galilei's experiments with earthly bodies attacked Aristotelian physics. Galilean principles were subsumed by René Descartes, whose Cartesian physics structured his Cartesian cosmology, modeling heliocentrism and employing mechanical philosophy. Mechanical philosophy's first principle, stated by Descartes, was No action at a distance. Yet it was British chemist Robert Boyle who imparted, here, the term mechanical philosophy. Boyle sought for chemistry, by way of corpuscularism—a Cartesian hypothesis that matter is particulate but not necessarily atomic—a mechanical basis and thereby a divorce from alchemy. In 1666, Isaac Newton fled London from the plague. Newton became the exemplar of the modern scientist, and the Newtonian research program became the modern model of knowledge. Supposedly, Newton maintained that toward his gravitational theory, he had "framed" no hypotheses. For Hume, humans experience sequences of events, not cause and effect, by pieces of sensory data whereby similar experiences might exhibit merely constant conjunction—first an event like A, and always an event like B—but there is no revelation of causality to reveal either necessity or impossibility. and interpreted enumerative induction to be among the mind's unavoidable customs, required in order for one to live. Rather, Hume sought to counter Copernican displacement of humankind from the Universe's center, and to redirect intellectual attention to human nature as the central point of knowledge. Hume proceeded with inductivism not only toward enumerative induction but toward unobservable aspects of nature, too. Not demolishing Newton's theory, Hume placed his own philosophy on par with it, then. Though skeptical at common metaphysics or theology, Hume accepted "genuine Theism and Religion" and found a rational person must believe in God to explain the structure of nature and order of the universe. Still, Hume had urged, "When we run over libraries, persuaded of these principles, what havoc must we make? If we take into our hand any volume—of divinity or school metaphysics, for instance—let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion". Kant Awakened from "dogmatic slumber" by Hume's work, Immanuel Kant sought to explain how metaphysics is possible. Reasoning that the mind contains categories organizing sense data into the experiences substance, space, and time, Kant thereby inferred uniformity of nature, after all, in the form of a priori knowledge. Kant's synthetic a priori, then, buttressed both physics—at the time, Newtonian—and metaphysics, too, but discarded scientific realism. This realism regards scientific theories as literally true descriptions of the external world. Kant's transcendental idealism triggered German idealism, including G F W Hegel's absolute idealism. Positivism Comte In the French Revolution's aftermath, fearing Western society's ruin again, Auguste Comte was fed up with metaphysics. As suggested in 1620 by Francis Bacon, Human knowledge had evolved from religion to metaphysics to science, explained Comte, which had flowed from mathematics to astronomy to physics to chemistry to biology to sociology—in that order—describing increasingly intricate domains, all of society's knowledge having become scientific, whereas questions of theology and of metaphysics remained unanswerable, Comte argued. Comte considered, enumerative induction to be reliable, upon the basis of experience available, and asserted that science's proper use is improving human society, not attaining metaphysical truth. Later, concluding science insufficient for society, however, Comte launched Religion of Humanity, whose churches, honoring eminent scientists, led worship of humankind. Mill commended Comte's positivism. Mill noted that within the empirical sciences, the natural sciences had well surpassed the alleged Baconian model, too simplistic, whereas the human sciences, such ethics and political philosophy, lagged even Baconian scrutiny of immediate experience and enumerative induction. Similarly, economists of the 19th century tended to pose explanations a priori, and reject disconfirmation by posing circuitous routes of reasoning to maintain their a priori laws. the five principles whereby causal laws can be discerned to enhance the empirical sciences as, indeed, the inductive sciences. In the 20th, America led. Via the solar eclipse of May, 29, 1919, Einstein's gravitational theory, confirmed in its astonishing prediction, apparently overthrew Newton's gravitational theory. This revolution in science was bitterly resisted by many scientists, yet was completed nearing 1930. Not yet dismissed as pseudoscience, race science flourished, overtaking medicine and public health, even in America, with excesses of negative eugenics. In the 1920s, some philosophers and scientists were appalled by the flaring nationalism, racism, and bigotry, yet perhaps no less by the countermovements toward metaphysics, intuitionism, and mysticism. mathematics, logic, and physics, and sought to lend humankind a transparent, universal language competent to vet statements for either logical truth or empirical truth, no more confusion and irrationality. Staking it at the analytic/synthetic gap, they sought to dissolve confusions by freeing language from "pseudostatements". And appropriating Ludwig Wittgenstein's verifiability criterion, many asserted that only statements logically or empirically verifiable are cognitively meaningful, whereas the rest are merely emotively meaningful. Further, they presumed a semantic gulf between observational terms versus theoretical terms. Altogether, then, many withheld credence from science's claims about nature's unobservable aspects. Thus rejecting scientific realism, many embraced instrumentalism, whereby scientific theory is simply useful to predict human observations, or meaningless. Pursuing both Bertrand Russell's program of logical atomism, which aimed to deconstruct language into supposedly elementary parts, and Russell's endeavor of logicism, which would reduce swaths of mathematics to symbolic logic, the neopositivists envisioned both everyday language and mathematics—thus physics, too—sharing a logical syntax in symbolic logic. To gain cognitive meaningfulness, theoretical terms would be translated, via correspondence rules, into observational terms—thus revealing any theory's actually empirical claims—and then empirical operations would verify them within the observational structure, related to the theoretical structure through the logical syntax. Thus, a logical calculus could be operated to objectively verify the theory's falsity or truth. With this program termed verificationism, logical positivists battled the Marburg school's neoKantianism, Husserlian phenomenology, and, as their very epitome of philosophical transgression, Heidegger's "existential hermeneutics", which Carnap accused of the most flagrant "pseudostatements". Popper asserted that although exemplary science is not dogmatic, science inevitably relies on "prejudices". Popper accepted Hume's criticism—the problem of induction—as revealing verification to be impossible. Popper accepted hypotheticodeductivism, sometimes termed it deductivism, but restricted it to denying the consequent, and thereby, refuting verificationism, reframed it as falsificationism. As to law or theory, Popper held confirmation of probable truth to be untenable, Logical positivism, Popper asserted, "is defeated by its typically inductivist prejudice". Problems Having highlighted Hume's problem of induction, John Maynard Keynes posed logical probability to answer it—but then figured not quite. Bertrand Russell held Keynes's book A Treatise on Probability as induction's best examination, and if read with Jean Nicod's ''Le Probleme logique de l'induction'' as well as R B Braithwaite's review of that in the October 1925 issue of Mind, to provide "most of what is known about induction", although the "subject is technical and difficult, involving a good deal of mathematics". Rather than validate enumerative induction—the futile task of showing it a deductive inference—some sought simply to vindicate it. Feigl posed it as a rule, thus neither a priori nor a posteriori but a fortiori. In such mission, Carnap sought to apply probability theory to formalize inductive logic by discovering an algorithm that would reveal "degree of confirmation". Kurt Gödel's incompleteness theorem of 1931 made the logical positivists' logicism, or reduction of mathematics to logic, doubtful. Some, including logical empiricist Carl Hempel, argued for its possibility, anyway. ==Early criticism==

During the 1830s and 1840s, the French Auguste Comte and the British J S Mill were the leading philosophers of science. Debating in the 1840s, J S Mill claimed that science proceeds by inductivism, whereas William Whewell, also British, claimed that it proceeds by hypotheticodeductivism. Whewell proposed recognition of "the peculiar import of the term Induction", as "there is some Conception superinduced upon the facts", that is, "the Invention of a new Conception in every inductive inference". Rarely spotted by Whewell's predecessors, such mental inventions rapidly evade notice. Later philosophers gave Peirce's abduction, and so on, the synonym inference to the best explanation, or IBE. Many philosophers of science later espousing scientific realism have maintained that IBE is how scientists develop approximately true scientific theories about nature. ==Inductivist fall==

After defeat of National Socialism via World War II in 1945, logical positivists lost their revolutionary zeal and led Western academia's philosophy departments to develop the niche philosophy of science, researching such riddles of scientific method, theories, knowledge, and so on. The movement shifted, thus, into a milder variant better termed logical empiricism or, but still a neopositivism, led principally by Rudolf Carnap, Hans Reichenbach, and Carl Hempel. Neopositivism became mostly maligned, In 1958, Norwood Hanson's book Patterns of Discovery subverted the putative gap between observational terms and theoretical terms, a putative gap whereby direct observation would permit neutral comparison of rival theories. Hanson explains that even direct observations, the scientific facts, are laden with theory, which guides the collection, sorting, prioritization, and interpretation of direct observations, and even shapes the researcher's ability to apprehend a phenomenon. Meanwhile, even as to general knowledge, Quine's thesis eroded foundationalism, which retreated to modesty. Revolutions The Structure of Scientific Revolutions, by Thomas Kuhn, 1962, was first published in the International Encyclopedia of Unified Science—a project begun by logical positivists—and somehow, at last, unified the empirical sciences by withdrawing the physics model, and scrutinizing them via history and sociology. The scientists reinterpret ambiguous data, discard anomalous data, and try to stuff nature into the box of their shared paradigm—a theoretical matrix or fundamental view of nature—until compatible data become scarce, anomalies accumulate, and scientific "crisis" ensues. Kuhn's ideas were rapidly adopted by scholars in disciplines well outside of the natural sciences, where Kuhn's analysis occurs. Kuhn's thesis in turn was attacked, however, even by some of logical empiricism's opponents. Reinforcing Quine's assault on logical empiricism, Kuhn ushered American and English academia into postpositivism or postempiricism. Popper's demarcation principle of falsifiability, instead of verifiability, grants a theory the status of scientific—simply, being empirically testable—not the status of meaningful, a status that Popper did not aim to arbiter. Popper found no scientific theory either verifiable or, as in Carnap's "liberalization of empiricism", confirmable as highly probable, and found unscientific, metaphysical, ethical, and aesthetic statements often rich in meaning while also underpinning or fueling science as the origin of scientific theories. such as ones conventionally predicted to fail. ==Postpositivism==

At 1967, historian of philosophy John Passmore concluded, "Logical positivism is dead, or as dead as a philosophical movement ever becomes". Logical positivism, or logical empiricism, or verificationism, or, as the overarching term for this sum movement, neopositivism soon became philosophy of science's bogeyman. Kuhn's influential thesis was soon attacked for portraying science as irrational—cultural relativism similar to religious experience. one "incapable of being inferred either from experience or from other logical principles, and that without this principle, science is impossible". And yet in 1963, Karl Popper declared, "Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure". Popper's 1972 book Objective Knowledge opens, "I think I have solved a major philosophical problem: the problem of induction". Some have argued that although inductive inference is often obscured by language—as in news reporting that experiments have proved a substance is safe—and that enumerative induction ought to be tempered by proper clarification, inductive inference is used liberally in science, that science requires it, and that Popper is obviously wrong. There are, more actually, strong arguments on both sides. In a 1965 paper now classic, Gilbert Harman explains enumerative induction as a masked effect of what C. S. Peirce had termed abduction, that is, inference to the best explanation, or IBE. Philosophers of science who espouse scientific realism have usually maintained that IBE is how scientists develop, about the putative mind-independent world, scientific theories approximately true. Thus, calling Popper obviously wrong—since scientists use induction in effort to "prove" their theories true By now, enumerative induction has been shown to exist, but is found rarely, as in programs of machine learning in artificial intelligence. Yet sheer enumerative induction is overwhelmingly absent from science conducted by humans. Although much talked of, IBE proceeds by humans' imaginations and creativity without rules of inference, which IBE's discussants provide nothing resembling. Still, Popper has been the only philosopher of science often praised by scientists. the verificationists—that is, the logical positivists—became identified as pillars of scientism, allegedly asserting strict inductivism, as well as foundationalism, to ground all empirical sciences to a foundation of direct sensory experience. Logical empiricists indeed conceived the unity of science to network all special sciences and to reduce the special sciences' laws—by stating boundary conditions, supplying bridge laws, and heeding the deductivenomological model—to, at least in principle, the fundamental science, that is, fundamental physics. And Rudolf Carnap sought to formalize inductive logic to confirm universal laws through probability as "degree of confirmation". And neopositivists did not seek rules of inductive logic to regulate scientific discovery or theorizing, but to verify or confirm laws and theories once scientists pose them. Practicing what Popper had preached—conjectures and refutations—neopositivism simply ran its course. So its chief rival, Popper, initially a contentious misfit, emerged from interwar Vienna vindicated. For Feyerabend, the sham of inductivism was pivotal. At persistent claims that faith in induction is a necessary precondition of reason, Feyerabend's 1987 book sardonically bids Farewell to Reason. Research programmes Imre Lakatos deemed Popper's falsificationism neither practiced by scientists nor even realistically practical, but held Kuhn's paradigms of science to be more monopolistic than actual. Lakatos found multiple, vying research programmes to coexist, taking turns at leading in scientific progress. A research programme stakes a hard core of principles, such as the Cartesian rule No action at a distance, that resists falsification, deflected by a protective belt of malleable theories that advance the hard core via theoretical progress, spreading the hard core into new empirical territories. Corroborating the new theoretical claims is empirical progress, making the research programme progressive—or else it degenerates. But even an eclipsed research programme may linger, Lakatos finds, and can resume progress by later revisions to its protective belt. In any case, Lakatos concluded inductivism to be rather farcical and never in the history of science actually practiced. Lakatos alleged that Newton had fallaciously posed his own research programme as inductivist to publicly legitimize itself. Research traditions Lakatos's putative methodology of scientific research programmes was criticized by sociologists of science and by some philosophers of science, too, as being too idealized and omitting scientific communities' interplay with the wider society's social configurations and dynamics. Philosopher of science Larry Laudan argued that the stable elements are not research programmes, but rather are research traditions. Inductivist heir By the 21st century's turn, Bayesianism had become the heir of inductivism. ==Notes==