Readers who've heard that philosopher Karl Karl Popper is somewhat of an expert in epistemology should find much to savour, if not much on which to agree, in two related and masterful pieces.
First, while Popper is often taken to be a pre-eminent defender of both science and liberty, in two articles, Nicholas Dykes shows that as a defender of either, Popper's thought is seriously deficient: 'Debunking Popper: A Critique of Karl Popper's Critical Rationalism,' [25-page PDF] and the much longer, 'A Tangled Web of Guesses: A Critical Assessment of the Philosophy of Karl Popper' [39-page PDF].
Popper's whole notion that science consists of "conjecture and refutation" is shown by Dykes to be both internally contradictory and a position that opens the door wide to subjectivism, to "consensus science," and ultimately to the post-modern bullshit of Thomas Kuhn and his paradigm shifts; and Popper's idea that science may be distinguished from non-science primarily by the virtue of "falsifiability" is seen to be important, but on its own woefully insufficient as an an essential defining characteristic by which to winnow the bold from the bullshit.
Popper is worth reading, says Dykes -- "full of valuable insights, astute observations, and stimulating, sometimes inspiring prose" -- but in the end the Philosopher's Stone of explaining and defending science eluded him. Dykes concludes by suggesting, albeit briefly, what Popper missed, and what might have made his project complete.
Popperians offended by the demolition might at least take comfort in Diana Hsieh's point: "Of course, Dykes knock-down arguments don't just apply to Popper, but also to the similar ideas in Kant and Hume and others in the history of philosophy." (And they might also reflect, as Diana has, that Popper's flawed philosophical base makes him a less than worthwhile advocate for liberty.)
The second piece, which I'd strongly recommend reading in conjunction with Dykes' piece, is David Harriman's account of Induction and Experimental Method. Harriman is both philosopher (in the Objectivist tradition) and a physicist at Caltech, so this is a topic on which he is eminently qualified to write. The piece is a chapter of his forthcoming book on the subject:
[It] examines the key experiments involved in Galileo’s kinematics and Newton’s optics, identifies the essential methods by which these scientists achieved their discoveries, and illustrates the principle that induction is inherent in valid conceptualization.Modern science began with Galileo, he says, in particular with Galileo's methodology.
The scientific revolution of the 17th century was made possible by the achievements of ancient Greece... The modern scientist views himself as an active investigator, but such an attitude was rare among the Greeks. This basic difference in mindset—contemplation versus investigation—is one of the great divides between the ancient and modern minds. Modern science began with the full development of its own distinctive method of investigation: experiment. Experimentation is “the method of establishing causal relationships by means of controlling variables.” The experimenter does not merely observe nature; he manipulates it by holding some factor(s) constant while varying others and measuring the results. He knows that the tree of knowledge will not simply drop its fruit into his open mind; the fruit must be cultivated and picked, often with the help of instruments designed for the purpose.Scientific investigation and philosophical induction, argues Harriman, are characterised not just by falsification (as Popper would have it), but by by a clear understanding of identity, causality (ie., identity in action), and above all of the importance of integration. It is these three that skeptics like Hume never understood, and would-be scientific defenders like Popper needed to learn.
Cognitive integration is the very essence of human thought, from concept-formation (an integration of a limitless number of concretes into a whole designated by a word), to induction (an integration of a limitless number of causal sequences into a generalization), to deduction (the integration of premises into a conclusion). An item of knowledge is acquired and validated by means of grasping its relation to the whole of one’s knowledge. A thinker always seeks to relate, grasp hidden similarities, discover connections, unify. A conceptual consciousness is an integrating mechanism, and its product—knowledge—is an interconnected system, not a junk heap of isolated propositions. Galileo integrated his knowledge not only within the subject of physics but also between physics and the related science of astronomy...The precision necessary for scientific induction is mathematical, says Harriman.
While discussing concept-formation, Ayn Rand explained that “perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.” She ended the discussion with a challenge to the skeptics: Those who deny the validity of concepts must first prove the invalidity of algebra... A concept can function as a green light to induction only if it is defined precisely—and, in physical science, the required precision is mathematical... The cognitive integration necessary to validate a high-level generalization in physics is made possible only because the discoveries and laws are formulated in quantitative terms. Thus progress requires that the key concepts be defined in terms susceptible to numerical measurement. Such measurement is both the primary concern of the mathematician and the primary activity of the experimentalist.
Thus induction in physics is essentially dependent on two specialized methods. Experimentation provides the entrance into mathematics, and mathematics is the language of physical science.
It's impossible to recommend this highly enough. (Unfortunately, the full paper is only available to subscribers to The Objective Standard -- which is partly why I've quoted here as much as copyright allows -- but as I've said before, subscription to this quarterly is worth every penny.)