Perhaps one of the least understood arguments in the philosophy of science, Paul Feyerabend's reductio ad absurdum of specific rationalist conceptions of scientific method is at once a subtle critique of rigidity in thinking and an historical study of Galileo's rhetorical strategies in the latter’s discussions of Copernicanism. In this paper we explain the structure of the reductio before considering how Feyerabend applied it.
When Feyerabend first published his Against Method, he was explicit concerning his aim:
My intention is not to replace one set of general rules by another such set: my intention is, rather, to convince the reader that all methodologies, even the most obvious ones, have their limits. The best way to show this is to demonstrate the limits and even the irrationality of some rules which she, or he, is likely to regard as basic. (1975, 32)
He went on to entreat the reader to "always remember that the demonstrations and the rhetorics used do not express any 'deep convictions'" of his. Nevertheless, this work has consistently been described as an attempt to advance and defend the methodological principle "anything goes", so much so that MunÚvar complained that "it should be an embarrassment to the profession that many reviews were completely unable to see the structure of this simple reductio
" (1991, 181). (See Laudan, 1996, for an excellent example of a total misunderstanding that borders on the ridiculous, as well as Newton-Smith, 1981.) As a measure of his exasperation at such empty critiques, Feyerabend’s Science in a Free Society
contains an appendix entitled "Conversations with Illiterates" (1975, 125-218), in which he responded to some of his detractors.
In general, a reductio ad absurdum
is a form of argument in which the proponent may take as given the premises of the opponent while explaining how their acceptance leads to absurd consequences. As a result, one or more premises must be rejected. (This is widely used in mathematics.) The structure of Feyerabend’s reductio
is quite straightforward, notwithstanding its confusion with a positive argument for anarchism: faced with the methodological principles of certain forms of rationalism (or what Feyerabend thought of under this rubric, most notably logical positivism and falsificationism) and so-called paradigmatic instances of these at work in the history of science, Feyerabend sought to show that the same rationalists would have to admit that science has developed in a fashion either contrary to their standards or otherwise in a manner that they would have to characterise as ir
As a result of this rhetorical strategy, Feyerabend was able to explain himself clearly:
'Anything goes' is not the one and only 'principle' of a new methodology, recommended by me. It is the only way in which those firmly committed to universal standards and wishing to understand history in their terms can describe my account of traditions and research practices ... If this account is correct then all a rationalist can say about science (and about any other interesting activity) is: anything goes.
thus took the following form:
- Take the principles of a rationalist methodology for science;
- Consider what the same rationalists propose as a representative example of such a methodology at work in the history of science;
- Note that the decisions made on the basis of a rational methodology should, ceteris paribus, be rational; and
- Demonstrate that an account of this episode in such terms forces us to describe the actions of those purportedly following the rules as irrational or in violation of them.
Before we look at Feyerabend's argument, it is useful to take a simple example of a reductio
at work. If we subscribe to the tenets of dogmatic falsificationism
(or else advocate basing our acceptance and rejection of scientific theories on so-called decisive experiments
) and suppose Einstein's Special Theory of Relativity to have been a step in the right direction with regard to gaining knowledge of our universe, we find that we run into a problem. Falsificationists do not dispute the historical account of 1905, in which the first response to Einstein's paper noted that his theory had already been refuted by Kaufman's experimental results, published in the Annalen der Physik
in that year. The dogmatic falsificationist is thus forced to admit that Einstein should have dismissed his theory as falsified – which, of course, he did not. We are led to the unfortunate position of either arguing that Einstein was irrational (or mistaken, if we wish to be more charitable) in his refusal to give up the special theory (and moreover that we, as good falsificationists, would have rejected it, along with any consequences) – a demand we would probably call absurd – or else accepting that dogmatic falsificationism fails.
Feyerabend preferred to use another – more famous – example from the history of science: Galileo's work on geostaticism. His reductio
consisted in three stages, designed to critique na´ve empiricism, Popper's falsificationism and Lakatos' Methodology of Scientific Research Programmes
in turn – each being an instance of a rationalist approach to science (in the case of the latter two, the most common even today). For the first of these, he considered the famous Tower Argument
, a circumstance relied upon by Aristotelians to discount the possibility of a moving Earth. Its proponents pointed to the fact that a stone dropped from a tower lands at its base. If the Earth was moving, as some supposed, the tower would move with it and hence the stone would drop some distance away. (A variant of the same argument stated that an arrow fired vertically into the air should fall far from the firer, since he or she would have moved along with the earth while the arrow was in flight.) This was an idea everyone could understand and hence served as a powerful refutation of the notion that the Earth moves.
It matters not at this stage whether Galileo was an empiricist or not: in order to undertake a reductio
, we assume that he was and see what follows. What Galileo did was to accept the observations made by those who had tested this theory (that the stone falls at the base) and then appeal to a principle of relativity (often called Galilean relativity
). He asked his readers to imagine two friends throwing a ball to each other while inside a cabin on a ship alongside and then the same situation while the ship was underway, considering whether more (or less) force would be required to throw the ball when the ship was moving. This was also a test that most people could understand and it helped him to explain that there was no difference because any motion of the ship would also be shared by the passengers. That is, whichever direction the ship moved in, the cabin would, too - along with everything inside it.
As a result of this discussion, Galileo was able to demonstrate that the very same "fact" used by the Tower Argument itself - the stone falling at the base - also supported the idea that the Earth was rotating, since any evidence that the geostaticist could appeal to would likewise support the alternative (this is actually an example of underdetermination
by data and the theory-ladenness
of observational terms). The na´ve empiricist has no means of deciding between these two rival theories and hence any
choice made by Galileo would violate this form of empiricism. If our methodology insists that only those decisions made on the basis of evidence can be called rational then Galileo and the Aristotelians alike were irrational to prefer geokineticism or geostaticism respectively. We are thus forced either to give up on calling Galileo's behaviour rational or else admit that na´ve empiricism is inadequate.
of Popper's falsificationism proceeded in a similar way. Copernicus' system predicted magnitudes for both Venus and Mars that were refuted by observations, which led to the same conclusion with regard to dogmatic falsificationism as in the example of Einstein above. Feyerabend considered the sophisticated
version of falsificationism, though, according to which Copernicanism should have excess empirical content over the Ptolemaic model, including the prediction of novel facts that were falsifiable. Unfortunately, Copernicanism was of equal empirical content to its rival (see Kuhn, 1985 and Swerdlow, 1973) and was incompatible with the Aristotelianism of the day. This latter point is an important one to appreciate: Aristotelianism did not merely consist in an astronomical theory concerning the heavens but was an integrated system that applied widely. In particular, Aristotle’s dynamics was a theory of change
, including explanations of generation, corruption, locomotion and qualitative change. The dynamics that Galileo proposed in its stead dealt only with locomotion, which was a decrease in truth-content
(as always, from the perspective of that time
). Thus we find that Copernicanism represented a theory that was falsified, of equal empirical content and of lesser-truth content. As Popperian falsificationists, we are forced again to admit that Galileo was irrational to persist in his studies or that Popper's methodology is flawed.
The last reductio
that Feyerabend attempted – that of Lakatos' much more subtle approach – could not rely on his analysis of Galileo’s behaviour, since Lakatos was in complete agreement (Lakatos and Zahar, 1975; see also Lakatos, 1978). Since Lakatos' methodology was careful to incorporate the lessons of the failure of falsificationism, his classification of research programmes
if they demonstrate excess empirical content that has been confirmed
for the converse) was far better equipped to survive problematic episodes in the history of science. Indeed, Lakatos accepted that a new theory would initially show a loss in empirical content as it took time to become established, and that ad hoc
measures are acceptable insofar as they help the theory avoid falsification and thus give it more time to develop. The obvious difficulty with such a methodology, of course, is where to draw the line at all
when so much wriggling is permitted; after all, a degenerating theory could eventually become progressive again if given the opportunity (or even if not). This is where Feyerabend addressed his argument.
Introducing the concept of an epistemological anarchist
, this being a person with an aversion to ideologies and opposing "positively and absolutely" all universal standards (1975, 175), Feyerabend asked how the actions of an epistemological anarchist at the time of Galileo would differ from those of a Lakatosian. It was immediately clear that the former could do as he or she liked, by definition, but what of the Lakatosian? Herein lies the problem: Lakatos' Methodology
enables us to describe
a situation but it does not tell us how
we should act. A Lakatosian could accept Aristotelianism as a progressive research programme and reject Copernicanism as degenerating, but he or she could also do the converse. No restriction is placed on what should
be done; all we have is a new vocabulary to explain ourselves.
in this last case thus consisted in referring again to the "methodology" of epistemological anarchism – or the "anything goes" we began with – and showing that Lakatos' approach could not be distinguished from it. Since "anything goes" is no method at all, rendering everything rational at a stroke, it followed that either we should follow a method that is not a method (which is absurd) or else reject the Methodology of Scientific Research Programmes
The glaring point to notice in each of these arguments is that nowhere is it necessary for us to accept that there is no possible scientific method; that "anything goes"; that we should all become epistemological anarchists; or that Feyerabend was advocating any of these. All these terms and concepts, employed in critiques of Feyerabend then and since, are intended for use inside
the context of a reductio ad absurdum
only. The subtlety of this form of rhetoric (which Galileo himself had mastered) is lost when we interpret it as an attempt to replace one set of rules with another (in the face of Feyerabend's own declaiming the possibility), leaving us with mere caricatures and an understanding of the philosophy of science so much the poorer.
- By Paul Newall (2005)
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(London: Verso, 1975)
Feyerabend, P., Science in a Free Society
(London: New Left Books, 1978)
Kuhn, T.S., The Copernican Revolution
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Lakatos, I., The Methodology of Scientific Research Programmes
(Cambridge: Cambridge University Press, 1978)
Lakatos, I. and Zahar, E., Why did Copernicus' Research Program Supersede Ptolemy's?
, in Westman (ed), The Copernican Achievement
(Berkeley: University of California Press, 1975)
Laudan, L., Beyond Positivism and Relativism
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(Boston: Routledge and Kegan Paul, 1981)
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