Phil 795L –
Seminar: Neo-Logicism
Fall 2007. Thursdays 4:00-6:30pm in Herter 204? (Or
Bartlett 374?)
Prof. Kevin Klement (Please call me “Kevin”.)
CLICK HERE for the same information in .PDF format (better for printing)
Course description:
An in-depth examination of the recent attempts to revive the position
in the philosophy of mathematics known as logicism: the theory that
arithmetical truths are a species of logical or analytical truth, or
that pure mathematics (or arithmetic at least) reduces to logic in one
form or another. Requirements:
weekly reading assignments, presentation and term paper. Prerequisites:
Graduate student with strong background in formal logic, or consent of
instructor
Contact info:
My office is 353 Bartlett Hall. My office phone is 545-5784. My office
hours are Tuesdays 2:30pm-3:30pm, Thursdays 11am-12pm and by
appointment. I'm often in my office many other times. Feel free to drop
by any time. You may also e-mail me at klement@philos.umass.edu
or call me at home at 665-9559. Our course web page is http://courses.umass.edu/phil795l/
Texts:
Short readings will be made available for photocopy in the metal
cabinet on the 3rd floor of Bartlett, or will be distributed by e-mail,
or are available online. Owning a copy of Frege’s Foundations
of Arithmetic or the portions thereof in The Frege Reader might be
worthwhile, however.
Course requirements:
Your final grade will be based on the following requirements, (1)
in-class participation (15%), (2) one class presentation (15%), (3)
weekly assignments (25%), and (4) a final term paper (45%).
Weekly Assignments: You are expected to carefully read the selected
texts for each session before the seminar meeting and come prepared to
discuss them. To help facilitate this, each week you are expected to
write a 1-3 page essay in which you (1) summarize the reading, and (2)
identify any criticisms or points of discussion (including points in
need of clarification) involving the reading. These essays are due at
the start of class on the day on which we will be discussing the
relevant readings. You will be graded on 1-5 scale, with 1 representing
a barely acceptable essay, 2 representing a deeply problematic essay,
that misrepresents the views of the philosopher or philosophers in
question or commits other abuses of philosophical method, 3
representing an essay that is slightly lacking in some area, but
generally acceptable, 4 representing a good essay that performs the
desired tasks as expected, and 5 representing an essay with substantial
and original insight. (You should never expect to receive anything
above 4. A student receiving a 4 on every assignment should still
expect a good grade for this portion. I will only award a 5 to an essay
that surpasses my expectations.) In determining your grade, I will take
into account only your 10 highest scores of 12 possible essays. This
means you may either drop your two lowest scores, or simply not write
two essays (or combine the two options). You need not prepare an
assignment for the week you will be presenting.
Presentation: Early in the semester, each student will choose (or be
assigned) one week in which he or she is expected to give a
presentation on the readings for that week (approx. 20 minutes), to be
given at the beginning of the seminar meeting, and should also be
prepared to lead the discussion for that class period. The presentation
should (1) summarize the main points of the readings, though at his or
her discretion the presenter may focus on certain issues he or she
finds most interesting, (2) identify any questions or concerns the
presenter has with understanding or interpreting the material, which he
or she would like to discuss in class, (3) critically discuss one or
more philosophical issues raised in the readings, as a starting point
for seminar discussion.
Term Paper: Each student is prepared to write a 15-25 page term paper
that aims to contribute something original to the discussion of any of
the texts or logical/philosophical issues discussed in the course. The
paper should constitute critical and original discussion of the
philosophical issues concerning logicism and/or neo-logicism. The
amount of outside research done for the paper is left to your
discretion, but a careful search of the relevant secondary material is
strongly recommended. It is due either at the end of finals week
(December 22nd), or by the first day of Spring Semester (if you take an
incomplete).
READING SCHEDULE
(tentative and likely to change)
Sept. 6 — Course Introduction
Sept. 13 — Frege, The Foundations of Arithmetic,
Introduction, §§1-4, 45-69, 87-91, 104-09. [This can
all also be found in The Frege Reader.]
Sept. 20 — Zalta, “Frege's Logic, Theorem, and
Foundations for Arithmetic” in The Stanford Encyclopedia of
Philosophy. (http://plato.stanford.edu/entries/frege-logic/)
Sept. 27 — Russell, “The Regressive Method of
Discovering the Premises of Mathematics,” Essays in Analysis
pp. 272-83; “Mathematical Logic As Based on the Theory of
Types,” in Logic and Knowledge, pp. 59-102.
Oct. 4 — Hodes, “Logicism and the Ontological
Commitments of Arithmetic,” Journal of Philosophy 81 (1984),
pp. 123-49.
Oct. 11 — Wright, “Number Theory and
Logic,” chap. 4 of Frege’s Conception of Numbers As
Objects.
Oct. 18 — Boolos, “Saving Frege From
Contradiction,” in Logic, Logic and Logic, pp. 171-82
[originally published in Proceedings of the Aristotelian Society 1987];
“Is Hume’s Principle Analytic?” in Logic,
Logic and Logic, pp. 301-14. [Originally published in Heck, ed. Logic,
Language and Thought, OUP 1997.]
Oct. 25 — Heck, “On the Consistency of Second-Order
Contextual Definitions,” Noûs 26 (1992), pp. 491-4;
Dummett, “Neo-Fregeans: In Bad Company?” in The
Philosophy of Mathematics Today, ed. M. Schirn, OUP, 1998, pp. 368-88;
Wright, “Reply to Dummett”, ibid., pp. 389-406.
Nov. 1 — Wright, “Is Hume’s Principle
Analytic?” in The Reason’s Proper Study, pp.
307-334; [First published in Notre Dame Journal of Formal Logic 40
(1999), pp. 6-30.] ; Hale and Wright, “Implicit Definition
and the A Priori,” RPS, pp. 117-151. [First published in New
Essays on the A Priori, ed. Boghossian and Peacocke, 2000.]
Nov. 8 —Shapiro, “Prolegomenon to Any Future
Neo-Logicist Set Theory: Abstraction and Indefinite
Extensibility”, British Journal for the Philosophy of Science
54 (2003), pp. 59-91; Burgess, Fixing Frege (Princeton UP 2005), sec.
3.7 “Second-Order Logic Reconsidered,” pp. 201-214.
Nov. 15 — Rayo, “Logicism Reconsidered,”
in Oxford Handbook of the Philosophy of Mathematics and Logic, ed.
Shapiro, 2005, pp. 203-35; Linsky and Zalta, “What Is
Neo-Logicism?” Bulletin of Symbolic Logic 13 (2006), pp.
60-99 .
Nov. 22. — Thanksgiving. No class.
Nov. 29 — OPEN (TBA)
Dec. 6. — OPEN (TBA)
Dec. 13. — OPEN (TBA)
Possible “Open” Topics:
- More historical stuff
- Field/Wright/others debate on mathematical realism more generally
- Work (especially Hale’s) on neo-logicist real number theory
- Completely distinct forms of (neo?-)logicism: e.g., Bostock,
Cocchiarella, etc.
- Lots more on Hume’s law, abstraction, including Hale and
Wright’s recent “To Bury Caesar”
- Further work on New V, and other revisions of Frege’s
system, including predicative ones (Wehmeier, etc.)
- Relationship of set theory and logic
- More on the topic: “What is Logic?”