New Virtual Issue from the BJPS on the work of Colin Howson

Colin Howson was a stalwart of the British Society for the Philosophy of Science. As well as serving as its President from 2003 to 2005, he also acted as Assistant Editor for the BJPS, first under Imre Lakatos and then under the co-editorship of John Watkins and John Worrall. He also published extensively within the pages of the journal, and so it is fitting that our new virtual issue is devoted to this work. Peter Urbach and John Worrall introduce Colin’s collected BJPS papers, and we reproduce that introduction below. The full issue can be found over on our main site.

Colin Howson: A Life in Evidence

Peter Urbach & John Worrall

Our friend and former colleague, Colin Howson, died on 5 January 2020, aged 74. Details of his life and distinguished academic career and a complete publications list can be found here. Colin published extensively. Aside from his logic textbook, Logic with Trees, he authored three influential books: Scientific Reasoning: The Bayesian Approach (with Peter Urbach), Hume’s Problem, and Objecting to God. He also published more than ninety articles in leading journals, almost all of them concerned with clarifying the foundations and applications of probability theory. He continued to work on these issues until the end of his life. Indeed, just a few days before he died, he submitted an article entitled ‘Beyond Finite Additivity’ to Philosophy of Science; this has now been accepted for publication.  That article deals with the Dutch Book argument for the axiom of countable additivity for subjective probability functions. Most of his articles that were published in the British Journal for the Philosophy of Science are here reproduced in his memory. Many constitute central contributions to their fields and all remain valuable and instructive. The articles are grouped into four parts.

The first consists of some early articles, which reveal important elements of the development of Colin’s views about probability. Colin emerged as a subjective Bayesian gradually. In his second BJPS publication, ‘Must the Logical Probability of Laws Be Zero?’ ([1973]), he showed that Popper’s purported demonstration that law-like statements must have zero logical probability begged the question, concluding that logic does not in fact prescribe zero probability to such statements. This conclusion opened the possibility of a probabilistic inductive alternative. But starting with his review article ‘The End of the Road for Inductive Logic?’ ([1975a]), Colin was sharply critical of Carnap’s attempt to place such induction on a purely objective basis (Carnap and Jeffrey [1970]), a basis which depended on normative, rationality postulates that Colin argued were unfounded and arbitrary. Later study led him to conclude that ‘all attempts to show that factual evidence determines a uniquely warranted degree of belief in any uncertain proposition have come to nothing’ ([1995], p. 26). But following von Mises ([1939], [1964]), Colin defended the idea of objective physical probabilities, based on hypothetical, limiting relative frequencies of events, which could be combined with personalist Bayesian assessments of those probabilities.

The other two articles reproduced in this section are critical, though always respectful, book reviews. In his first publication in the BJPS, ‘The Plain Man’s Guide to Probability’ ([1972]), Colin argued against J. R. Lucas’s claim, made in his The Concept of Probability ([1970]), that attention to the vagaries of ordinary language affords the key to understanding probability.  In his ‘The Prehistory of Chance’ ([1978]), Colin wrestled with the interesting (if sometimes obscure) views expressed by Ian Hacking in his The Emergence of Probability ([1975]) about the sense in which the notion of probability can be said to have ‘emerged’ historically.

The second part consists of contributions to the foundations of probability theory, culminating in an important article on the justification of the principle of countable additivity—a dominant concern of the latter part of Colin’s career. A good place to start is his excellent survey article ‘Theories of Probability’ ([1995]). The other articles have a more specific focus. In his ‘The Rule of Succession, Inductive Logic, and Probability Logic’ ([1975b]), Colin argued that ‘the charge of inconsistency [often] brought against the Rule of Succession [as articulated by Laplace and Venn] is unsuccessful—indeed that […] charge is based on a simple fallacy’. His ‘Bayesian Conditionalization and Probability Kinematics’ ([1994]), written with Allan Franklin, focuses on issues concerning uncertain evidence and argues that these present no insuperable problem: ‘Bayesian conditionalization suffices to deal with most if not all of the methodologically important cases of adjusting beliefs, even where uncertain evidence is involved’. Colin’s ‘Logic and Probability’ ([1997a]) defended Ramsey’s ([1964]) view that the axioms of subjective probability theory are in effect logical axioms and argued that this view has powerful heuristic value, particularly in clarifying the role of conditionalization in the Bayesian theory. His ([1997b]), in the process of defending the account given of Bayesian principles in (Howson and Urbach [1989]) against criticisms raised by Chihara ([1994]), argues persuasively against the claim that the Bayesian account of scientific reasoning presupposes logical omniscience. Finally, Colin’s ‘De Finetti, Countable Additivity, Consistency, and Coherence’ ([2008]) presents an insightful explanation of why de Finetti ([1964]) rejected countable additivity as a constraint on probabilistic coherence.

The third part contains articles that defend the Bayesian account based on subjective probabilities against claims that it is at odds with some aspects of scientific reasoning, principally that it succumbs to the so-called problem of old evidence: if evidence e was known at the time theory T was proposed, then e was presumably part of ‘background knowledge’ at that time and hence p(e) = 1, from which it straightforwardly follows that e cannot increase T’s probability, and hence cannot confirm it on the Bayesian account; and yet there are many cases of old evidence that clearly did confirm scientific theories. Colin took on this problem in his ‘Bayesianism and Support by Novel Facts’ ([1984]), and in his ‘Some Recent Objections to the Bayesian Theory of Support’ ([1985]) (this latter article also addressed the claim that the lack of constraint on the values of prior probabilities is a problem for the Bayesian account). And he took it up again in his ‘The “Old Evidence” Problem’ ([1991]).

The fourth and final part comprises two articles, which respond to two attempts to show that the whole idea of a probabilistic approach to induction is fatally flawed—one by Miller ([1966]) and the other by Popper and Miller (Miller and Popper [1983]). Colin’s article ‘Miller’s So-Called Paradox of Information’ ([1979]; written with Graham Oddie) demonstrated that the alleged paradox in fact involves a fallacy, analogous to fallacies that result from failing to distinguish bound and open occurrences of variables in deductive logic. Finally, Colin’s article ‘A Bayesian Analysis of Excess Content and the Localisation of Support’ ([1985]; written with Allan Franklin) responds to Popper and Miller’s ‘Proof of the Impossibility of Inductive Probability’. It accepts the claim made by Michael Redhead ([1985]) and others that this ‘proof’ rests on an indefensible characterization of the notion of a theory’s ‘excess content’ relative to one of its empirical consequences and proceeds to develop a more satisfactory characterization of that notion which, moreover, is immune to the Miller–Popper objection.

Colin continued to work and publish on these topics after he retired from the LSE in 2008, during his subsequent tenure at the University of Toronto, and also after he retired from there in 2014. A representative list of the articles he published in journals other than the BJPS, which indicates the breadth of his contributions, is appended below.

Peter Urbach
London School of Economics
pm44urbach@gmail.com

and

John Worrall
London School of Economics
J.Worrall@lse.ac.uk

References

Carnap, R. and Jeffrey, R. C. [1970]: Studies in Inductive Logic and Probability, Berkeley, CA: University of California Press.

Chihara, C. [1994]: ‘The Howson–Urbach Proofs of Bayesian Principles’, in E. Eells and B. Skyrms (eds), Probability and Conditionals, Cambridge: Cambridge University Press, pp. 161–79.

de Finetti, B. [1964]: ‘Foresight, Its Logical Laws, Its Subjective Sources’, in H. Kyburg and H. Smokler (eds), Studies in Subjective Probability, New York: Wiley, pp. 93–159.

Hacking, I. [1975]: The Emergence of Probability: A Philosophical Study of Early Ideas About Probability Induction and Statistical Inference, Cambridge: Cambridge University Press.

Howson, C. [1972]: ‘The Plain Man’s Guide to Probability’, British Journal for the Philosophy of Science, 23, pp. 157–70.

Howson, C. [1973]: ‘Must the Logical Probability of Laws Be Zero?’, British Journal for the Philosophy of Science, 24, pp. 153–63.

Howson, C. [1975a]: ‘The End of the Road for Inductive Logic?’, British Journal for the Philosophy of Science, 26, pp. 143–9.

Howson, C. [1975b]: ‘The Rule of Succession, Inductive Logic, and Probability Logic’, British Journal for the Philosophy of Science, 26, pp. 187–98.

Howson, C. [1978]: ‘The Prehistory of Chance’, British Journal for the Philosophy of Science, 29, pp. 274–80.

Howson, C. [1984]: ‘Bayesianism and Support by Novel Facts’, British Journal for the Philosophy of Science, 35, pp. 245–51.

Howson, C. [1985]: ‘Some Recent Objections to the Bayesian Theory of Support’, British Journal for the Philosophy of Science, 36, pp. 305–9.

Howson, C. [1991]: ‘The “Old Evidence” Problem’, British Journal for the Philosophy of Science, 42, pp. 547–55.

Howson, C. [1995]: ‘Theories of Probability’, British Journal for the Philosophy of Science, 46, pp. 1–32.

Howson, C. [1997a]: ‘On Chihara’s “The Howson–Urbach Proofs of Bayesian Principles”’, British Journal for the Philosophy of Science, 48, pp. 83–90.

Howson, C. [1997b]: ‘Logic and Probability’, British Journal for the Philosophy of Science, 48, pp. 517–31.

Howson, C. [2008]: ‘De Finetti, Countable Additivity, Consistency, and Coherence’, British Journal for the Philosophy of Science, 59, pp. 1– 23.

Howson, C. and Franklin, A. [1985]: ‘A Bayesian Analysis of Excess Content and the Localisation of Support’, British Journal for the Philosophy of Science, 36, pp. 425–31.

Howson, C. and Franklin, A. [1994]: ‘Bayesian Conditionalization and Probability Kinematics’, British Journal for the Philosophy of Science, 45, pp. 451–66.

Howson, C. and Oddie, G. [1979]: ‘Miller’s So-Called Paradox of Information’, British Journal for the Philosophy of Science, 30, pp. 253–61.

A selection of other work by Colin Howson (a complete list is available here)

Howson, C. [1977]: ‘Why Once May Be Enough’, Australasian Journal of Philosophy, 55, pp. 142–7.

Howson, C. [1988]: ‘On the Consistency of Jeffreys’s Simplicity Postulate, and Its Role in Bayesian Inference’, Philosophical Quarterly, 38, pp. 68–83.

Howson, C. [1992]: ‘Mathematics in Philosophy’, in J. Echeverria, A. Ibarra and T. Mormann (eds), The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations, Berlin: Walter de Gruyter, pp. 192–201.

Howson, C. [1996]: ‘Bayesian Rules of Updating’, Erkenntnis, 45, pp. 195–208.

Howson, C. [2003]: ‘Probability and Logic’, Journal of Applied Logic, 1, pp. 151–65.

Howson, C. [2005]: ‘Ramsey’s Big Idea’, in M. J. Frapolli (ed.), F. P. Ramsey: Critical Reassessments, London: Continuum Press, pp. 139–61.

Howson, C. [2005]: ‘Some Formal Analogies between Logic and Probability: The Good, the Bad, and the Ugly’, We Will Show Them: Essays in Honour of Dov Gabbay, London: College Publications.

Howson, C. [2007]: ‘Logic with Numbers’, Synthese, 156, pp. 491–512.

Howson, C. [2008]: ‘Degrees of Belief as Subjective Probabilities’, in F. Huber and C. Schmidt-Petri (eds), Degrees of Belief: An Anthology, Dordrecht: Springer, pp. 97–119.

Howson, C. [2009]: ‘Sorites Is No Threat to Modus Ponens: Reply to Kochan’, International Studies in the Philosophy of Science, 23, pp. 209–13.

Howson, C. [2014]: ‘Finite Additivity, Another Lottery Paradox, and Conditionalisation’, Synthese, 191, pp. 989–1012.

Howson, C. [2014]: ‘A Continuum-Valued Logic of Degrees of Probability’, Erkenntnis, 79, pp. 1001–13.

Howson, C. [2015]: ‘David Hume’s No-Miracles Argument Begets a Valid No-Miracles Argument’, Studies in History and Philosophy of Science, 54, pp. 41–5.

Howson, C. [2015]: ‘Does Information Inform Confirmation?’, Synthese, 193, pp. 2307–21.

Howson, C. [2016]: ‘Repelling a Prussian Charge with the Solution to a Paradox of Dubins’, Synthese, 195, pp. 225–33.

Howson, C. [2018]: ‘The Curious Case of Frank Ramsey’s Proof of the Multiplication Theorem of Probability’, Analysis, 78, pp. 431–9.

Howson, C. [forthcoming]: ‘Timothy Williamson’s Coin-Flipping Argument: Refuted before It Was Published?’, Erkenntnis, available at .

Howson, C. and Urbach, P. [1991]: ‘Bayesian Reasoning in Science’, Nature, 350, pp. 371–4.