Logical Philosophy of Science

SUMMARY: At the dawn of the 20th century, philosophical thought was transformed by the discovery of the "new logic", i.e. mathematical or symbolic logic. Equipped with the tools of this new logic, philosophers hoped to be able to make progress on general questions about metaphysics and epistemology, and on more specific questions about how scientific theories give us knowledge about the world. 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 classical first-order predicate logic. You should know what it is, but we will learn the meta-theoretical results along the way. I do not plan to talk about (1) modal logic, or (2) 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 predicate logic, namely multi-sorted logic and second-order logic.

Besides the readings for the individual sessions, we will be guided by 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

Note: The readings in parentheses are more tangential, and may not be discussed in the seminar.

1. Introduction and overview

2. Axiomatic Theories
   Frege Hilbert controversy [SEP article]
   Schlick, selections from General Theory of Knowledge [pdf]
   Carnap, "Eigentliche und Uneigentliche Begriffe" [pdf]

3. Wissenschaftslogik
   Carnap, "Die Aufgabe der Wissenschaftslogik" [pdf]
   Carnap, selections from Logical Syntax of Language [pdf] and [pdf]
   Friedman, "Carnap's Wissenschaftslogik" [pdf]
   (Carnap, Philosophy and Logical Syntax [pdf])

4. The "Received View of Theories"; The Problem of Theoretical Terms
   Mormann, "The structure of scientific theories in logical empiricism" [pdf]
   (Andreas, "Another solution to the problem of theoretical terms" [pdf])

5. The Semantic Turn
   Tarski, "The concept of truth in formalized languages"
   Model theory handout

6. Craig's Theorem on Axiomatizability
   Putnam, "Craig's theorem" [pdf]
   Hempel, "The theoretician's dilemma" [pdf]
   (Ketland [pdf])

7. Ramsey sentences
   Lewis, "How to define theoretical terms" [pdf]
   Friedman, "Carnap on theoretical terms: structure without metaphysics" [pdf]
   (Menzies & Price, "Is semantics in the plan?" [pdf])

8. Implicit Definition
   Quine, "Implicit definition sustained" [pdf]
   Winnie, "The implicit definition of theoretical terms" [pdf]
   (Hale and Wright, "Implicit definition and the apriori" [pdf])

9. The Lowenheim-Skolem Theorem; Putnam's Model-Theoretic Argument
   Putnam, "Realism and reason" [pdf]
   (Putnam, "Models and reality" [pdf] gives a more technically nuanced version of the argument)
   (responses by Bays, Lewis, Douven, van Fraassen, and others)

10. Craig's Interpolation Theorem; Beth's Theorem
    Hellman, "Physicalism: ontology, determination, and reduction" [pdf]
    Tennant, "Beth's theorem and reductionism" [pdf]
    (Humberstone, "Note on supervenience and definability" [pdf])
    (Encyclopedia of philosophy article on Beth's theorem [pdf])

11. Criticisms of the "Received View" of Theories
    Suppe, "Understanding scientific theories: an assessment of developments, 1969-1998" [pdf]
    van Fraassen, selections from The Scientific Image [pdf]
    (van Fraassen, "The semantic view of scientific theories" [pdf])

12. Criticisms of the Criticisms of the "Received View"
    Halvorson, "What scientific theories could not be" [pdf]
    Glymour, "Theoretical equivalence and the semantic view of theories" [pdf]
    (Pearce and van Benthem, "A mathematical characterization of interpretation between theories")

13. Equivalent Theories; Interpretations between Theories
    Glymour, "Theoretical realism and theoretical equivalence"
    de Bouvere, "Synonymous theories"
    Kanger, "Equivalent theories"

14. Quine: logic, regimentation, and ontology
    Hylton, selections from Quine

15. Overflow
    Winnie, "Invariants and objectivity"
    Turney, "Embeddability, syntax, and semantics in accounts of scientific theories"
    Hempel, "The standard conception of scientific theories"