By J.E. (third edition by Max Peters) Thompson
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Extra resources for Arithmetic for the Practical Man
Different examples had different purposes. I cited Hodes splendid observation that the relation-number principle (the relation-number belonging to R is identical with that belonging to S if and only if R and S are isomorphic relations) leads to the Burali-Forti paradox in order to point out that Basic Law V was not an isolated case and that HP might well be expected to be powerful if consistent (as it is). I gave the example of parities in order to show that one couldn’t say that a contextual definition is OK if only it is consistent.
68–81. The quotation, together with other extremely interesting observations, appears on p. 80. 3 Roy T. ), The Arché Papers on the Mathematics of Abstraction, 3–15. c 2007 Springer. 4 The Arché Papers on the Mathematics of Abstraction how the deduction of the Peano postulates from HP could be carried out and in formulating the conjecture, subsequently verified, that HP is consistent. 3 The first issue I want to take up is whether a derivation of arithmetic from HP vindicates logicism. My view is: no logic, no logicism.
Moreover the formula defining this condition doesn’t contain #. So if one wants merely to sum up this state of affairs by saying that HP explains the concept of cardinal number, I would not object. However, it is hard to avoid the impression that more is meant, that Wright holds that to call a statement an explanation of a concept is to assign it an epistemological status importantly similar to the one it was once thought analytic judgments, including definitions, enjoy. It is to this further suggestion that I wish to demur.
Arithmetic for the Practical Man by J.E. (third edition by Max Peters) Thompson