**SUMMARY: **At the beginning of the 20th century,
philosophical thought was transformed by the discovery of the
"new logic", i.e. mathematical or symbolic logic. With
this *novum organum*, philosophers hoped to slice through
thorny problems in metaphysics and epistemology, and to model
philosophy after the exact sciences. We will look at how
mathematical logic has been used as an instrument in philosophical
argument; and we will consider ways that we might refine the
instrument, and use it to best effect.

The backbone of this seminar will be first-order predicate logic. We presuppose that participants in the seminar have a basic knowledge of symbolic logic.

We do *not* plan to talk about modal logic, inductive logic,
or probability theory, simply because the scope must be restricted in
some way, and each of those topics is too big for us to cover. But we
will talk about some modifications of first-order logic, in
particular, many-sorted logic, second-order logic, and infinintary
logic. One of the questions that I'll discuss is whether first-order
logic is in some sense privileged.

Readings, problem sets, etc. can be found at sites.google.com/a/princeton.edu/phi520/

If you want to get a sense of the perspective of the seminar, you might want to look at the following overview articles:

- Douven and Horsten. "Formal methods in the philosophy of science."
- Leitgeb. "Logic in general philosophy of science: old things and new things." [PDF]
- van Benthem. "The logical study of science." [PDF]
- van Fraassen. "Logic and the philosophy of science." [PDF]

**SCHEDULE**

- Background to logical syntax
- Logical syntax
- review of predicate calculus
- signatures and theories
- metalogical proof techniques
- explicit definition and definitional extension
- common definitional extension
- translations between theories
- theoretical equivalence

- Early logical positivism (Carnap’s syntax program, received view of theories)
- Hempel, "The theoretician’s dilemma"
- Putnam, "Craig's theorem"
- Carnap, "Foundations of logic and mathematics"
- Background to logical semantics
- fear of semantics
- set theory
- Tarski

- Logical semantics
- compactness theorem
- completeness theorem
- embeddings of structures
- Lowenheim-Skolem theorem
- topology and
*n*-types

- Later logical positivism
- external questions
- Carnap, "Empricism, semantics, and ontology"
- Quine, "Two dogmas of empiricism"
- Carnap, selections from
*The logical syntax of language* - Carnap, "Meaning postulates"
- the flat view of theories

- Second order logic
- Quine, "The scope of logic"
- Boolos, "On second order logic"

- Infinitary logic
- Beth’s theorem and reductionism
- Nagel, selections from
*The structure of science* - implicit definition and supervenience
- Hellman and Thompson, "Physicalism: ontology, determination and reduction"
- Tennant, "Beth’s theorem and reductionism"
- Humberstone, "Note on supervenience and definability"

- Nagel, selections from
- Putnam's paradox
- Putnam, "Realism and reason"
- Lewis, "Putnam’s paradox"
- van Fraassen, "Putnam’s paradox: metaphysical realism revamped and evaded"
- Ramsey sentences
- Lewis, "How to define theoretical terms"
- Canberra Plan
- structural realism
- The Newman objection to Ramsey sentence structuralism

- Many sorted logic
- Quine's conjecture
- Arguments against the received view of theories
- van Fraassen, selections from
*The Scientific Image*

- van Fraassen, selections from
- Equivalent theories
- Glymour, "Theoretical realism and theoretical equivalence"
- Sklar, "Saving the noumena"
- Quine, "On empirically equivalent systems of the world"
- Morita equivalence
- Quantifier variance