[FOM] alleged Hilbert quote

[Jeffrey Ketland]

Vladik Kreinovich:

> While Hilbert probably never said that math is a meaningless game with
> symbols,
> ths spirit of this phrase is somewhat similar to a famous actual citation
> from
> Hilbert's Intro to his Foundations of Geometry:
>
> "One must be able to say at all times -- instead of points, straight
> lines, and
> planes -- tables, beer mugs, and chairs."

Actually, this quote comes from a conversation with Otto Blumenthal at a 
Berlin train
station. It certainly doesn't appear in Hilbert's Foundations of Geometry.

The Introduction to The Foundations of Geometry is quite short, and says the 
following:

    Introduction
    Geometry, like arithmetic, requires only a few and
    simple principles for its logical development. These
    principles are called the axioms of geometry. The
    establishment of the axioms of geometry and the
    investigation of their relationships is a problem which
    has been treated in many excellent works of the
    mathematical literature since the time of Euclid. This
    problem is equivalent to the logical analysis of our
    perception of space.
    This present investigation is a new attempt to establish
    for geometry a complete, and as simple as possible,
    set of axioms and so deduce from them the most
    important geometric theorems in such a way that the
    meaning of the various groups of axioms, as well as
    the significance of the conclusions that can be drawn
    from the individual axioms, come to light.
    (D. Hilbert, 1899, Foundations of Geometry,
    Open Court, 1997. Translated by Leo Unger.
    "Introduction", p. 2.)

Regards --- Jeff
~~~~~~~~~~~~~~~~~~~~
Jeffrey Ketland
Department of Philosophy
University of Edinburgh
George Square
Edinburgh EH8 9JX
United Kingdom
jeffrey.ketland at ed.ac.uk
~~~~~~~~~~~~~~~~~~~~