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The Surveyability Dilemma

Jim Mawby, University of Glasgow (9 Oct 2004)

Second SPPA Seminar Day, University of Glasgow

Mark Addis ('Surveyability and the sorities paradox', Philosophia Mathematica (3), Vol. 3. 1995) has suggested that the epistemological aspects of the notion of surveyability will cause trouble for the strict finitist construal of a foundation for mathematics. Addis maintains that the question as to whether a person can survey a proof at a certain time even if they are not thinking about it at that time presents a dilemma for the strict finitist: if she claims that the question has a determinate answer, Addis asserts that she is committed to an undesirable counterfactual realism. If she responds instead that there is no determinate answer, Addis suggests that the notion of surveyability will be too drastically reduced in application to be of any use.

I consider Addis' counterfactual analysis carefully, and argue that neither horn of the dilemma is particularly sharp; on the one hand I argue that counterfactual realism does not seem obviously undesirable for counterfactuals involving surveyability, and on the other that Addis is guilty of a kind of scope ambiguity.

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