1. W&O: §§ 48 - 52 Pete Mandik Chairman, Department of Philosophy Coordinator, Cognitive Science Laboratory William Paterson University, New Jersey USA

2. 2 Ch VII: Ontic Decision What exists? How do we decide?

3. 3 §48. Nominalism and realism Do abstract objects exist? Nominalist says “No” Realist aka Platonist says “Yes”

4. 4 Are concreta preferable due to proximity to our senses? If so, wouldn’t sense data then be preferable to physical objects? The preference for physical objects is based on their utility in theory. But theoretical utility also favors abstracta like numbers.

5. 5 §49 False predilections. Ontic commitment Against those who think that two senses of ‘exist’ or ‘there are’ apply to concreta and abstracta:

6. 6 “[T]here remain two difficulties, a little one and a big one. The little one is that the philosopher who would repudiate abstract objects seems to be left saying that there are such after all, in the sense of ‘there are’ appropriate to them. The big one is that the distinction between there being one sense of ‘there are’ for concrete objects and another for abstract ones, and there being just one sense of ‘there are’ for both, makes no sense.” pp. 241-242 Mandik: What sense of “there are” is intended when one says “There are two senses of ‘there are’…”?

7. 7 “In our canonical notation of quantification, then, we find resoration of law and order. Insofar as we adhere to this notation, the objects we are to be understood to admit are precisely the objects which we reckon to the universe of values over which the bound variables of quantification are to be considered to range. Such is simply the intended sense of the quantifiers ‘(x)’ and ‘(x)’…The quantifiers are encapsulations of these specially selected, unequivocally referential idioms of ordinary language. To parapharse a sentence into the canonical notation of quantification is, first and formost, to make its ontic content explicit, quantification being a device for talking in general of objects.” p. 242

8. 8 §50. Entia non grata Miles and facts are more like sakes than physical objects. “Thus instead of ‘length of Manhattan = 11 miles’ we would now say ‘length-in-miles of Manhattan = 11’ …This leaves us recognizing numbers as objects.” p. 245

9. 9 Against facts as concreta “The sentences ‘Fifth Avenue is six miles long’ and ‘Fifth avenue is a hundred feet wide’, if we suppose them true, presumably state different facts; yet the only concrete or at any rate physical object involved is Fifth Avenue…In ordinary usage ‘fact’ often occurs where we could without loss say ‘true sentence’… p. 247

10. 10 §51. Limit myths Infinitessimals were useful in differential calculus but gave rise to absurdities. Weierstrass showed how to dissolve the absurdities with reconstructions that took only proper numbers as the variables. A similar treatment may be given for ideal objects in general: mass points, frictionless surfaces, etc.

11. 11 §52. Geometrical objects Should we count among the objects that exist, geometrical objects as separate from both numbers and physical objects? If we admit of physical objects and numbers already, then the objects of geometry may be reduced along the lines of analytic geometry by reference to a coordinate system.

12. 12 Study question: How are numbers more like physical objects than sakes?

13. 13 THE END