Imre Lakatos

Falsification and the Methodology of Scientific Research Programmes

For centuries knowledge meant proven knowledge — proven either by the power of the intellect or by the evidence of the senses. Wisdom and intellectual integrity demanded that one must desist from unproven utterances and minimize, even in thought, the gap between speculation and established knowledge. The proving power of the intellect or the senses was questioned by the sceptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics. Einstein’s results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge. But few realize that with this the whole classical structure of intellectual values falls in ruins and has to be replaced: one cannot simply water down the ideal of proven truth - as some logical empiricists do — to the ideal of’probable truth’1 or — as some sociologists of knowledge do — to ‘truth by [changing] consensus’.2

History of Science and Its Rational Reconstructions

“Philosophy of science without history of science is empty; history of science without philosophy of science is blind”. Taking its cue from this paraphrase of Kant’s famous dictum, this paper intends to explain how the historiography of science should learn from the philosophy of science and vice versa. It will be argued that (a) philosophy of science provides normative methodologies in terms of which the historian reconstructs ‘internal history’ and thereby provides a rational explanation of the growth of objective knowledge; (b) two competing methodologies can be evaluated with the help of (normatively interpreted) history; (c) any rational reconstruction of history needs to be supplemented by an empirical (socio-psychological) ‘external history’.

Changes in the Problem of Inductive Logic

Publisher Summary This chapter discusses several changes in the problem of inductive logic. There are two main problems of classical empiricism: inductive justification and inductive method. Classical epistemology in general is characterized by its two main problems: (1) the problem of the foundations of—epistemic, that is, perfect, infallible—knowledge (the logic of justification); and (2) the problem of the growth of—perfect, well-founded—knowledge or the problem of heuristic, or of method (the logic of discovery). The classical twin problems of induction were the justification of theories, and the discovery of theories from facts. Carnaps neoclassical solution provides at best a solution of the problem of weak justification. However, it leaves the problem of discovery, the problem of the growth of knowledge, untouched.

Replies to Critics

The arguments my critics produce have made me realise that I fail to stress sufficiently forcefully one crucial message of my paper. This message is that my ‘methodology’, older connotations of this term notwithstanding, only appraises fully articulated theories (or research programmes) but it presumes to give advice to the scientist neither about how to arrive at good theories nor even about which of two rival programmes he should work on.1 My ‘methodological rules’ explain the rationale of the acceptance of Einstein’s theory over Newton’s, but they neither command nor advise the scientist to work in the Einsteinian and not in the Newtonian research programme.

Falsifikation und die Methodologie wissenschaftlicher Forschungsprogramme

Jahrhundertelang verstand man unter Wissen bewiesenes Wissen — bewiesen entweder durch die Kraft der Vernunft oder durch die Evidenz der Sinne. Es galt als ein Gebot der Weisheit und der intellektuellen Redlichkeit, sich unbewiesener Behauptungen zu enthalten und die Kluft zwischen bloser Spekulation und begrundetem Wissen, sogar im Denken, auf ein Mindestmas zu beschranken. Wohl wurde die beweisende Kraft des Verstandes und der Sinne schon vor mehr als zwei Jahrtausenden von den Skeptikern in Frage gestellt, aber sie wurden durch den Triumphzug der Newtonschen Physik mit Verwirrung geschlagen. Einsteins Ergebnisse haben die Situation dann wieder auf den Kopf gestellt, und heute gibt es nur noch wenig Philosophen und Wissenschaftler, die der Ansicht waren, wissenschaftliche Erkenntnis sei oder konnte bewiesenes Wissen sein. Aber fast niemand sieht ein, das damit auch das ganze klassische Gebaude intellektueller Werte zusammenbricht und durch etwas Neues ersetzt werden mus: Man kann das Ideal bewiesener Wahrheit nicht einfach verdunnen — etwa zum Ideal ‚wahrscheinlicher Wahrheit‘2), wie es einige logische Empiristen tun, oder zur ‚Wahrheit aufgrund [wechselnder] Ubereinstimmung‘3), die wir bei einigen Wissenssoziologen finden.

A Renaissance of Empiricism in the Recent Philosophy of Mathematics

According to logical empiricist orthodoxy, while science is a posteriori, contentful and (at least in principle) fallible, mathematics is a priori, tautologous and infallible. It may therefore come as a surprise for the historian of ideas to find statements by some of the best contemporary experts in foundational studies that seem to herald a renaissance of Mills radical assimilation of mathematics to science. In the next section I present a rather long list of such statements. I then go on (in section 2) to explain

PROOFS AND REFUTATIONS (I)

Introduction § 1. A Problem and a Conjecture. §2. A Proof. § 3. Criticism of the Proof by Counterexamples which are Local but not Global. § 4. Criticism of the Conjecture by Global Counterexamples. (a) Rejection of the conjecture. The method of surrender. (b) Rejection of the counterexample. The method of monsterbarring. (c) Improving the conjecture by exception-barring methods. Piecemeal exclusions. Strategic withdrawal. (d) The method of monster-adjustment. (e) Improving the conjecture by the method of lemma-incorp oration. Proof-generated theorem versus naive conjecture.

Preface to this edition

The present edition of Jenkins Fantasias for four, five and six viols is based on British Library manuscripts. Though not a scholarly edition, the parts have been carefully corrected and have been read several times for errors. It is presented with the blessing of Andrew Ashbee who edited the Faber editions of same, and this edition uses his and Meyer’s numbering system so parts may be compared easily. A great deal of credit is due Mr. Ashbee for consulting so many sources and for his immense knowledge of Jenkins and his times. My thanks are due to Atlanta viols players who have helped proof read the website editions: Emily Stevenson, Paul Miller, Marian Burge, Stephen Morris, Greg Armijo, Susan Patterson, Pam Woodcock, Jorg Voss, Brian Bishop and Joyce Clinkscales. Special thanks are due Joyce, Librarian of the Emory Heilbrun Music and Media Library, for her help in obtaining microfilms of the original manuscripts. The present edition is presented in the spirit of the several copyists who felt that Jenkins’s music should be available to as many people as possible, for their immense musical enjoyment and to spread around the genius of the composer John Jenkins. What better way to do this in modern times than by the internet? Martha Bishop, July 2010 Instructions for Printing