FOM: Lakatos references

[Solomon Feferman]

The references provided by Moshe Machover and Reuben Hersh in response to
Jeffery Zucker's question are useful to me too.  To fill out Reuben's
reference to my own paper on Lakatos, it is "The logic of mathematical
discovery vs. the logical structure of mathematics", in PSA 1978 (1981),
309-327, published by the Philosophy of Science Association.  This may not
have made it into many libraries, but it will be reprinted in my
collection of essays "In the Light of Logic" slated to be published by
Oxford Press in 1998.  It is a critique of Lakatos, which concludes with
the following: "Lakatos' fireworks briefly illuminate limited portions of
mathematics conceived as an active growing intellectual endeavor which is
subject to confusion, uncertainty and error.  In contrast, logic gives us
a coherent picture of mathematics but which at first sight appears ideal
and static and which is irrelevant to everyday experience.  Hoewever,it
alone throws light on which is distinctive about mathematics, its concepts
and methods.  Polya's heuristic provides one bridge from theory to
practice.  I believe that Lakatos' successes should inspire us to seek a
more realistic theory of mathematics.  But his failures and limitations
should make us aware that much more from logic will have to be recognized
as basic and incorporated into such a theory.  It would be best to reserve
the name 'the logic of mathematical discovery' [Lakatos] for that which is
yet to come."

For those sympathetic to Lakatos (or even if not) I recommend reading
Hersh's *What is Mathematics, Really?*. For pedagogy, I recommend reading
Polya's works.  

Sol Feferman