Can a good scientific theory be logically inconsistent with itself? If you think not you’d be in good company: Karl Popper, the famous philosopher of science, believed that consistency was the sine qua non of a good scientific theory. It seems obvious why. If a theory is internally inconsistent, after all, then anything follows from it. If anything follows from it then it wouldn’t matter what experimental results we get, the theory would not be falsified. To Popper an unfalsifiable theory cannot even be counted as science, never mind bad science.
It is Classical Logic that tells us that anything follows from a contradiction. This is the (in)famous ex contradictione quodlibet or logical explosion. If a theory contains the proposition A and the proposition not-A, then it doesn’t exclude any proposition at all. Imagine if someone told you that Marianne is wearing jeans, and moments later told you that it is not the case that Marianne is wearing jeans. Such a person has not, in his utterances, excluded any possibility has he? You have no idea at all what Marianne is wearing. Nothing at all she might be wearing falsifies the conjunction of these two propositions.
It would seem, though, that logical consistency as a constraint on a good scientific theory, is often flouted. There are, in the literature, many cases of scientific theories that have been inconsistent. And these are not any old theories either – they include Bohr’s Theory of the Atom, Classical Electrodynamics, Newtonian Cosmology, and the early calculus.
This cries out for explanation. But how should it be explained? It would seem that there are only two possible explanations:
- we are wrong to think these theories are internally inconsistent;
- we are wrong to insist classical logic is a constraint on scientific theorising.
During the weekend school on 9/10 January we had representatives of both explanations.
Peter Vickers, of Durham University and author of the book on which the weekend was based, believes that most of the canonical examples of inconsistency in science are not examples of inconsistency at all. In fact he can find only two inconsistencies, one is the contradiction between Bohr’s postulates and Paul Ehrenfest’s adiabatic principle (see chapter 4, section 3.3. pages 58-71). The other can be seen only on a particular reading of the main theses of Newtonian Cosmology (see chapter 5).
Neither of these inconsistencies, furthermore, is a worrying inconsistency, says Vickers. Neither is a doxastic inconsistency – a case of scientists believing a contradiction, both are pragmatic inconsistencies, similar to using approximations, idealisations or abstractions. There is no threat, therefore, to Classical Logic from any scientific theory that is both internally inconsistent and a good scientific theory.
Our other speakers, though, Christian Straaser and Dunja Seselja of The Institute for Philosophy II at Ruhr University Bochum, Germany disagree. They believe that pragmatic inconsistencies are every bit as important to our reasoning as doxastic inconsistencies. The inconsistencies identified by Vickers, therefore, are a threat to Classical Logic: as internal contradictions are not always and everywhere treated by scientists as a threat to their theorizing, the logic implicitly used by scientists cannot be classical logic.
Both Strasser and Seselja believe that the inconsistencies found in science motivate the introduction of some Paraconsistent Logic; a logic that permits contradiction without its leading to logical explosion. Such logics – and there are many – can accommodate inconsistencies. According to those who embrace such logics much scientific reasoning, especially in the early stages of a theory, can only be described in terms of some paraconsistent logic.
So do you think that scientific theorising accommodates inconsistencies? Or do you think that any appearance of inconsistency must be either misleading, or taken as a black mark – a sign that the theory is false?
If you find the topic of this weekend school fascinating (as most participants at the weekend school did) you can, by joining the OUDCE Philosophical Society, listen to the podcasts of the lectures. Alternatively you can read the books and papers on the reading list:
Seselja, D., and C. Strasser (2014): ‘Concerning Peter Vickers’s Recent Treatment of Paraconsistencitis’, International Studies in the Philosophy of Science 28, Issue 3, pp.325-340.
Vickers, P. (2013a): Understanding Inconsistent Science. Oxford: OUP.
Recommended additional reading
Harman, G. (1986): Change in View, Cambridge, MA: MIT Press. **Especially Chapter 1**
Saatsi, J. and Vickers, P. (2011): ‘Miraculous Success? Inconsistency and Untruth in Kirchhoff’s Diffraction Theory’, British Journal for the Philosophy of Science 62, no.1, pp.29-46.
Vickers, P. (2013b): ‘A Confrontation of Convergent Realism’, Philosophy of Science 80(2), 189-211.
Weingartner, P. (1993): ‘Can there be Reasons for Putting Limitations on Classical Logic?’, in P. Humphreys (ed.) Patrick Suppes: Scientific Philosopher, Vol.3, Kluwer, pp.89-124.
 Vickers is adamant that the concept of ‘theory’ carries no weight in his argument. In fact he relies on ‘theory eliminativism’ throughout his book, thinking of an inconsistency as holding between propositions, rather than between, or within theories. This, he argues, avoids all the confusions and vaguenesses of ‘theory’ talk.