[FOM] Logic moving from philosophy to mathematics

Chris Gray cpgray at library.uwaterloo.ca
Thu Feb 3 10:18:05 EST 2005

In a certain narrow sense your observation is true of "academic"
mathematics and philosophy.  There was a definite shift in what professors
of philosophy and mathematics taught as logic in the wake of the logicist

(I'd recommend the book "Men of Ideas: Some Creators of Contemporary
Philosophy" by Bryan Magee, based on a series of TV interview Magee did.
In that there are some personal reminiscences by and about philosophers
who had a major impact on what got taught in universities.)

It's good to remember that logic, mathematics, and philosophy have always
been closely intertwined from Thales, Pythagoras, Plato, Euclid, and
Aristotle on.  Much of what followed on from the achievement of Euclid was
investigation of questions of logic.  (A good source here is "Foundations
and Fundamental Concepts of Mathematics" by Howard Eves.)

In fact, I'd be willing to argue that logic and philosophy as fundamental
disciplines don't really have a coherent internal history.  Logic and
philosophy move forward when certain fundamental problems (paradigmatic
problems) are felt to arise in other areas of thought.  In the middle
ages, for instance, it was largely issues of theology that drove the
development of logic and philosophy.

Husserl's work on phenomenology was a response to some of the same issues
in mathematics as Frege's work on logic.  These two men knew and responded
to each other's early work even though we might think of the schools of
philosophy that followed on from them as diametrically opposed.

The history of the development of logic, mathematics, and philosophy in
this complex period (late 19th/early 20th centuries) is only beginning to
be studied in books such as José Ferreirós Domínguez's "The Labyrinth of
Thought : a history of set theory and its role in modern mathematics".
There is a need for much detailed research and a reassessing of the
standard historical accounts written by the inheritors of logicism.


"The brain is a wonderful organ. It starts working the moment you get up
in the morning and does not stop until you get into the office." -Robert

On Tue, 1 Feb 2005, Daniel Crosby wrote:

> Apologies in advance if this is not the appropriate forum, but I think
> it is a question of interest to FOM.
> It seems to me that "logic" as a subject moved from being the interest
> of some philosophers -- in the early 19th century, and maybe later --
> to the interest of some mathematicians, by the early 20th century, and
> maybe earlier. Philosophers still study logic, of course, but they now
> study mathematical logic. Everyone that I've talked to about this
> agrees that this has happened, but I have not been able to find a
> secondary source analyzing this important shift.
> Can someone point me to such a source? Or correct my characterization
> of (or the existence of) this change?
> Dan Crosby
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> FOM at cs.nyu.edu
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