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Table of Contents
Application To Scalometry
Origin of monsters
Read here pertinent facts about someone whose work is critical to a proper comprehension of scale.
Imre Lakatos (1922 –1974) was a Hungarian philosopher of mathematics and science, a student of Popper known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes.
Lakatos attempted to reconcile Kuhn’s work with falsificationism by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsificationism.
Karl Popper defined a “research programme,” an idea fine-tuned by his student Imre Lakatos, to describe domains of productive scientific thought such as Darwin’s theory of evolution.
In this view, a ‘theory’ is really a succession of of slightly different theories and experimental techniques developed over time, that all share a common hard core; such a collection is called the research programme. Scientists working within a given research programme shield the core from falsification behind a protective belt of auxiliary hypotheses. The question of whether a worldview is true of false is replaced by the question of whether one research programme is progressive or degenerating. A progressive research programme is characterized by growth, prediction of novel facts, more precise predicitions etc. In contrast, a degenerative program is marked by a lack of growth; its auxiliary belt does not lead to novel predicitions that are later verified.
Lakatos’s view is very different to that of Kuhn. By replacing the notion of the paradigm with the notion of the research programme with a hard core and auxiliary belt, Lakatos legitimizes the action of scientists to keep expanding the auxiliary belt in order to hold on to the hard core of the research programme as far as possible. This is a rational process. More importantly, when a paradigm shift does occur, the shift occurs from a degenerative research programme to a more progressive one; hence the paradigm shift is rational, not irrational as seemed to be suggested by Kuhn.
Lakatos' contribution to the philosophy of science was an attempt to resolve the perceived conflict between Popper's falsificationism and the revolutionary structure of science described by Kuhn. Popper's theory as often (inaccurately) reported implied that scientists should give up a theory as soon as they encounter any falsifying evidence, immediately replacing it with increasingly 'bold and powerful' new hypotheses. However, Kuhn described science as consisting of periods of normal science in which scientists continue to hold their theories in the face of anomalies, interspersed with periods of great conceptual change. Popper acknowledged that excellent new theories may be inconsistent with apparently empirically well supported older theories. For example, he pointed out in Objective Knowledge (at page 200) that "in Newton's theory Kepler's laws are only approximately valid – that is, strictly invalid – if we take into account the mutual attraction between the planets", so that (in precise terms) Newton's theories were inconsistent with Kepler's third law. However, whereas Kuhn implied that good scientists ignored or discounted evidence against their theories Popper regarded counter evidence as something to be dealt with, either by explaining it, or eventually modifying the theory. Popper was not describing actual behaviour of scientists, but what a scientist should do. Kuhn was mostly describing actual behaviour.
Lakatos sought a methodology that would harmonize these apparently contradictory points of view, a methodology that could provide a rational account of scientific progress, consistent with the historical record.
For Lakatos, what we think of as a 'theory' may actually be a succession of slightly different theories and experimental techniques developed over time, that share some common idea, or what Lakatos called their ‘hard core’. Lakatos called such changing collections 'Research Programmes'. The scientists involved in a programme will attempt to shield the theoretical core from falsification attempts behind a protective belt of auxiliary hypotheses. Whereas Popper was generally regarded as disparaging such measures as 'ad hoc', Lakatos wanted to show that adjusting and developing a protective belt is not necessarily a bad thing for a research programme. Instead of asking whether a hypothesis is true or false, Lakatos wanted us to ask whether one research programme is better than another, so that there is a rational basis for preferring it. He showed that in some cases one research programme can be described as progressive while its rivals are degenerating. A progressive research programme is marked by its growth, along with the discovery of stunning novel facts, development of new experimental techniques, more precise predictions, etc. A degenerating research program is marked by lack of growth, or growth of the protective belt that does not lead to novel facts.
Lakatos claimed that he was extending Popper's ideas, which had themselves developed over time. He contrasted Popper, the crude falsificationist, who existed only in the minds of critics and followers who had not understood Popper's writings, Popper1, the author of what Popper actually wrote, and Popper2, who was supposed to be Popper as reinterpreted by his pupil Lakatos, though many commentators believe that Popper2 just is Lakatos. The idea that it is often not possible to show decisively which of two theories or research programmes is better at a particular point in time whereas subsequent developments may show that one is 'progressive' while the other is 'degenerating', and therefore less acceptable, was a major contribution both to philosophy of science and to history of science. Whether it was Popper's idea or Lakatos' idea, or, most likely, a combination, is of less importance.
Lakatos was following Pierre Duhem's idea that one can always protect a cherished theory (or part of one) from hostile evidence by redirecting the criticism toward other theories or parts thereof. (See Confirmation holism and Duhem-Quine thesis). This difficulty with falsificationism had been acknowledged by Popper.
Falsificationism, (Popper's theory), proposed that scientists put forward theories and that nature 'shouts NO' in the form of an inconsistent observation. According to Popper, it is irrational for scientists to maintain their theories in the face of Nature's rejection, yet this is what Kuhn had described them as doing. But for Lakatos, "It is not that we propose a theory and Nature may shout NO rather we propose a maze of theories and nature may shout INCONSISTENT". This inconsistency can be resolved without abandoning our Research Programme by leaving the hard core alone and altering the auxiliary hypotheses. One example given is Newton's three laws of motion. Within the Newtonian system (research programme) these are not open to falsification as they form the programme's hard core. This research programme provides a framework within which research can be undertaken with constant reference to presumed first principles which are shared by those involved in the research programme, and without continually defending these first principles. In this regard it is similar to Kuhn's notion of a paradigm.
Lakatos also took the view that a research programme contained 'methodological rules', some that instruct on what paths of research to avoid (he called this the 'negative heuristic') and some that instruct on what paths to pursue (he called this the 'positive heuristic').
Lakatos claimed that not all changes of the auxiliary hypotheses within research programmes (Lakatos calls them 'problem shifts') are equally as acceptable. He took the view that these 'problem shifts' can be evaluated both by their ability to explain apparent refutations and by their ability to produce new facts. If it can do this then Lakatos claims they are progressive. However if they do not, if they are just 'ad-hoc' changes that do not lead to the prediction of new facts, then he labels them as degenerate.
Lakatos took the view that if a research programme is progressive, then it is rational for scientists to keep changing the auxiliary hypotheses in order to hold on to it in the face of anomalies. However, if a research programme is degenerate, then it faces danger from its competitors: it can be 'falsified' by being superseded by a better (i.e. more progressive) research programme. This is what he says is happening in the historical periods Kuhn describes as revolutions and what makes them rational as opposed to mere leaps of faith (as he considered that Kuhn took them to be).
Application To Scalometry
Following Lakatos, we seek
Monster taming and monster barring
Origin of monsters
Henri Poincaré first used the word monster, 1906, “Logic sometimes breeds monsters.” mathematical monsters serve simply to provide counter-examples to further possible improvements.
Lakatos named it monster-barring, where the monster is deemed as out of scope of the assertion. But one can reasonably take the opposite position that the monster has not ceased to exist thereby, only that one has somehow hidden from it in this way.
Bartley 1976 “On Imre Lakatos,” in Essays in Memory of Imre Lakatos ed. Robert Cohen et al, Boston, D. Reidel, 1976 pp. 37-38. Accessed on Google books.
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