Natural deduction and arbitrary objects

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43180/1/10992_2004_Article_BF00542649.pd

Indefinites, Skolem functions and arbitrary objects

Peer reviewe

How Universal Generalization Works According to Natural Reason

Universal Generalization, if it is not the most poorly understood inference rule in natural deduction, then it is the least well explained or justified. The inference rule is, prima facie, quite ambitious: on the basis of a fact established of one thing, I may infer that the fact holds of every thing in the class to which the one belongs—a class which may contain indefinitely many things. How can such an inference be made with any confidence as to its validity or ability to preserve truth from premise to conclusion? My goal in this paper is to explain how Universal Generalization works in a way that makes sense of its ability to preserve truth. In doing so, I shall review common accounts of Universal Generalization and explain why they are inadequate or are explanatorily unsatisfying. Happily, my account makes no ontological or epistemological presumptions and therefore should be compatible with whichever ontological or epistemological schemes the reader prefers

The solo numero paradox

[No abstract available