The Department of Logic & Philosophy of Sciences Colloquium Series presents
"Embedding the Classical in the Intuitionistic Continuum"
with Joan Moschovakis, Professor Emerita, Mathematics, Occidental College, Los Angeles / UCLA
Friday, April 4, 2014
Social Science Tower, Room 777 (LPS Conference Room)
The points of the linear continuum can be represented in various ways by infinitely proceeding sequences of natural numbers, or "choice sequences" in Brouwer's terminology. Call the class of all choice sequences "the intuitionistic continuum." Every function on the whole intuitionistic continuum is continuous; this requires intuitionistic logic for properties of all choice sequences. Brouwer called "lawlike" those sequences all of whose choices are predetermined. With intuitionistic logic, just the lawlike sequences may represent Bishop's constructive continuum. Kreisel called "lawless" those sequences all of whose properties depend only on finite initial segments. Other kinds of choice sequences exist; for example, the merge of a lawlike with a lawless sequence is neither lawlike nor lawless, but something in between. Intuitionistic arithmetic results from classical arithmetic by weakening the logic; in this sense, intuitionistic arithmetic is a part of classical arithmetic. In contrast, the classical continuum can be viewed as the result of strengthening the logic on the lawlike part of the intuitionistic continuum. By varying the logic, a consistent unified theory of the continuum emerges.
Talk is jointly sponsored by the Department of Logic & Philosophy of Science and Center for the Advancement of Logic, its Philosophy, History, and Applications.
For further information, please contact Patty Jones, firstname.lastname@example.org or 949-824-1520.