Letter | Published:

The Commutative Law of Addition, and Infinity

Naturevolume 81page69 (1909) | Download Citation



NEITHER Dr. Hilbert nor the reviewer make any suggestion that the commutative law of addition is best proved as a deduction from the laws of multiplication. But the laws of multiplication are so often treated as deductions from those of addition that it is interesting to have a case of the converse procedure. The fact that both these operations and their laws have been treated independently and in a strictly logical manner by Dedekind, Peano, and others is, of course, perfectly well known to all who have paid any attention to this part of mathematics. Whether Dedekind's critics have really avoided metaphysical arguments without at the same time making metaphysical assumptions is a question on which a difference of opinion is permissible.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. Search for G. B. M. in:

About this article

Publication history

Issue Date




By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.