printer friendly pagePHIL 349: Evidence and Evolution (PHIL 249)
The logic behind the science. The concept of evidence and how it is used in science with regards to testing claims in evolutionary biology and using tools from probability theory, Bayesian, likelihoodist, and frequentist ideas. Questions about evidence that arise in connection with evolutionary theory. Creationism and intelligent design. Questions that arise in connection with testing hypotheses about adaptation and natural selection and hypotheses about phylogenetic relationships.
PHIL 350A: Model Theory
Back-and-forth arguments with applications to completeness, quantifier-elimination and omega-categoricity. Elementary extensions and the monster model. Preservation theorems. Interpolation and definability theorems. Imaginaries. Prerequisite: Phil151A or consent of the instructor.
PHIL 350B: Model Theory B (MATH 290B)
Decidable theories. Model-theoretic background. Dense linear orders, arithmetic of addition, real closed and algebraically closed fields, o-minimal theories.
| Repeatable
for credit
PHIL 351B: Proof Mining
Uses of proof theory in analysis and number theory. Proof mining: extraction of bounds from non-effective proofs. May be repeated for credit. Prerequisite: 151,152 or equivalents, and a calculus course.
| Repeatable
for credit
PHIL 352A: Set Theory (MATH 292A)
The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and set-theoretical problems. Prerequisites: PHIL151 and
MATH 161, or equivalents.
PHIL 353A: Proof Theory (MATH 293A)
Gentzen's natural deduction and sequential calculi for first-order propositional and predicate logics. Normalization and cut-elimination procedures. Relationships with computational lambda calculi and automated deduction. Prerequisites: 151, 152, and 161, or equivalents.
PHIL 353B: Proof Theory B
Consistency ordinal as a measure of the strength of a mathematical theory. The open problem of describing the ordinal of mathematical analysis (second order arithmetic). Present state of the problem and approaches to a solution. Prerequisites:
Phil 151,152 or equivalents
| Repeatable
2 times
(up to 6 units total)
PHIL 353C: Functional Interpretations
Finite-type arithmetic. Gödel's functional interpretation and Kreisel's modified realizability. Systems based on classical logic. Spector's extension by bar-recursive functionals. Kohlenbach's monotone interpretation and the bounded functional interpretation. The elimination of weak Kônig's lemma. Uniform boundedness. A look at Tao's hard/soft analysis distinction.
PHIL 355: Logic and Social Choice
Topics in the intersection of social choice theory and formal logic. Voting paradoxes, impossibility theorems and strategic manipulation, logical modeling of voting procedures, preference versus judgment aggregation, role of language in social choice, and metatheory of social choice. May be repeated for credit. Prerequisite: 151 or consent of instructor.
| Repeatable
for credit
PHIL 356: Applications of Modal Logic
Applications of modal logic to knowledge and belief, and actions and norms. Models of belief revision to develop a dynamic doxastic logic. A workable modeling of events and actions to build a dynamic deontic logic on that foundation. (Staff)
Filter Results: