🚀 go-pugleaf

The fourth annual series of Alfred Tarski lectures will be 
presented this year by Donald A. Martin, Professor of 
Mathematics and Philosophy at UCLA.  He will give two public 
lectures on the topic 

			LARGE CARDINALS, DETERMINACY
				
				And The Role Of 

    		NON-DEMONSTRATIVE EVIDENCE IN MATHEMATICS
    
The times and places are

  Part I:   March 16 (Monday), 4:15 p.m. in Room 60, Evans Hall
  Part II:  March 17 (Tuesday), 5 p.m. in Room 105, North Gate Hall

All members of the mathematics and philosophy communities in 
Berkeley are urged to attend these talks.  Professor Martin 
has supplied the following abstract for his talks.

			ABSTRACT

The standard route to mathematical knowledge is through proof.  But
the basic principles, usually codified as axioms of set theory, are
assumed without proof.  How are they known to be true?  By convention?
By being self-evident?  In some other way?  Precisely because the 
standard axioms are so standard, it is hard to approach the question 
of why they are accepted.

Independence theorems, such as those of Godel and Cohen, show that
many mathematical problems, especially ones about set theory itself, are
not resolvable on the basis of the standard axioms.  The natural route
toward resolving such problems is via new axioms.  An examination of
arguments for adopting particular candidates for new axioms may shed
light on the question posed above.

Among the candidates for new axioms are large cardinal axioms and
determinacy axioms.  These have been very successful in solving problems 
not solvable with the standard axioms alone.  Even though these two
kinds of axiom candidates seem unrelated, the main determinacy axioms
have been shown to be essentially equivalent with large cardinal axioms.  
Moreover a variety of evidence has been put forward in favor of the two
sorts of axioms.

The major portion of the two talks will be an exposition of the concepts
of and the mathematical results about large cardinals and determinacy.
Interleaved with this exposition will be an account of some proposed
evidence for large cardinal and determinacy axioms, a mostly favorable 
evaluation of it, and an attempt to use this example to support the 
broader conclusion that the status of mathematical knowledge is 
fundamentally like that of knowledge in empirical sciences.