Is reliabilism compatible with mathematical knowledge?

Philosophical Forum

Volumn 35, Issue 4, 2004, Pages 423-437

  Mcevoy, Mark ^a  

^a NONE

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EID: 60949478219     PISSN: 0031806X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0031-806X.2004.00183.x     Document Type: Article

References (13)

1. Paul Benacerraf, "Mathematical Truth," Philosophy of Mathematics, 2nd ed., ed. Paul Benacerraf and Hilary Putnam (Cambridge: Cambridge UP, 1983) 403-420
2. The reliabilist, instead of explaining our basic mathematical knowledge via appeal to intuition, might opt to account for mathematical knowledge by embracing a Quinean holism, and denying that there is any basic mathematical knowledge. On such a view, all mathematical knowledge is justified via its application to empirical science, thus, ultimately, by inference from observable empirical phenomena (for the canonical statement of this view, see Quine, "Two Dogmas of Empiricism" In W. V. Quine, From a Logical Point of View, 2nd ed. (Cambridge, MA: Harvard UP, 1961) 42-46
3. This view has some very counterintuitive consequences, however. It treats mathematical truths as contingent; it is committed to the claim that even very simple mathematical truths are highly theoretical; it leaves the justification of mathematical statements awaiting their application by physical scientists; and it regards unapplied mathematics as "mathematical recreation without ontological rights" (W. V. O. Quine, "Reply to Parsons," The Philosophy of W.V. Quine, ed. L. Hahn and P. Schilpp (LaSalle, Illinois: Open Court, 1986) 400. For these reasons, I think the reliabilist would do better to proceed on the assumption that there are non-inferential mathematical truths, and that belief in such truths is justified via the process of intuition
4. Albert Casullo, "Causality, Reliabilism, and Mathematical Knowledge," Philosophy and Phenomenological Research (September 1992): 557-84
5. RJ is, with one important exception, a paraphrase of Casullo's conditions on a minimally plausible version of reliabilism. His own wording ("Causality, Reliabilism, and Mathematical Knowledge" 572-7) involves a certain amount of jargon, which is unnecessary for present purposes. More importantly, Casullo makes no mention of the possibility of a belief being justified by virtue of the reliability of the process that sustains, rather than produces, the belief. This is a serious oversight: a belief in a mathematical truth could initially be produced in a subject through some unreliable process (such as believing all sentences of English that are exactly eleven syllables long), but could then be sustained by the subject coming to understand a sound proof of the truth in question. Casullo's formulation of reliabilism would count such a belief as unjustified; I explicitly include a reference to sustaining processes to allow such beliefs to count, properly, as justified
6. See, for example, the enormously influential counterexamples in Lawrence BonJour, The Structure of Empirical Knowledge (Cambridge, MA: Harvard UP, 1985) 34-57
7. Casullo, "Causality, Reliabilism, and Mathematical Knowledge" 579
8. Jerrold Katz, Realistic Rationalism (Cambridge, MA: Bradford MIT, 1998), Chapter 2
9. Lawrence Bon Jour, In Defense of Pure Reason (Cambridge: Cambridge UP, 1998) 98-129
10. BonJour, In Defense of Pure Reason 109
11. For more on how platonism and fallibilism can be combined, see James Robert Brown, Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures (New York: Rouledge, 1999)
12. Casullo, "Causality, Reliabilism, and Mathematical Knowledge" 582
13. W. H. Hart, "Review of Mark Steiner's Mathematical Knowledge" Journal of Philosophy 74 (1977): 125