**Meeting 14: December 9**

Simon and Larkin

- characterization of the project
- role of diagrammatic representations
- pulley example
- geometry example

Giaqiunto, Chapter 12

- examples
- diagrammatic vs. symbolic

Summary and recap

- framing the project
- central questions
- what we've seen
- conclusions

**Meeting 13: November 30**

Wickelgren

- comparison with Schoenfeld; focus on problems rather than cognition
- comparison with Polya: emphasis on AI, algorithms
- overview of the book
- problem "similarity"

Avigad, Dean, and Mumma on Euclidean geometry

**Meeting 12: November 16**

Schoenfeld

- heuristics, and specificity
- examples of "special cases"
- examples of "setting subgoals"
- forms of control
- expert vs. novice behavior
- belief

**Meeting 11: November 9**

Polya

- notions of "plausible inference"
- supports: instances, extreme cases
- case study: a limit inequality
- proof that motivates the discovery

Schoenfeld

- resources, heuristics, control, belief
- discussion of resources

**Meeting 10: November 2**

Polya

- preface to
*How to Solve It* - Polya's list
- rectangular prism example
- preface to
*Induction and analogy* - generalization, specialization, and analogy (and the Pythagorean theorem)
- Euler and the Basel problem

**Meeting 9: October 26**

Method and proof

- three proofs of the sum of squares theorem
- constraints on a model of proof to support the evaluations

Arana on purity

- logical vs. semantical purity
- case studies: casus irreducibilus, Desargue's theorem, induction, Gödel's theorem

Polya

- Normative aspects, rationality
- Models of the mind

**Meeting 8: October 19**

Becky Morris' presentation of "Character and object," and discussion.

**Meeting 7: October 12**

Discussion of Chapters 4 and 5 of Sandbord's thesis:

- various proofs of Pick's theorem
- two (among possibly more) axes of explanation: reduction of arbitrariness, and directness (in this case, geometric interpretation)

Concern: how to ground the analysis and make it more precise?

Method and proof:

- interactive theorem proving
- the corresponding view of proof

**Meeting 6: October 5**

Tappendenden

- concepts, explanation, natural kinds, and essences
- case studies: the Legendre symbol, and the definition of "prime"

Mancosu on explanation

Steiner

- Examples: summing 1 to n, irrationality of sqrt(2), Pythagorean theorem
- Steiner's analysis
- critique

**Meeting 5: September 28**

Comparing the understandings of "concept" in Kant, Jackendoff, Rittle-Johnson et al., Frege, Wilson, Husserl, Tappenden

Back to Wilson

- "Imaginary points" revisited
- Ideals in number theory

Husserl

- Historical background
- Husserl's project (from the preface)
- The difference between "primary" and "psychical" relations
- A concept map: the pen, the key, the watch, something, one, collective combination, multiplicity, cardinal number

**Meeting 4: September 21**

Rittle-Johnson et al.

- conceptual knowledge vs. procedural knowledge
- problem representations
- testing procedures
- discussion of the model

Wilson on Frege's mathematical background

- Relative logicism
- "Imaginary points"

**Meeting 3: September 14**

Back to "senses" or "meanings." Some dichotomies:

- internal / private / subjective vs. external / public / objective
- descriptive / behavioral vs. normative / theoretical (propositional attitudes)
- cognitive significance / how we grasp things vs. informational significance / how the world is
- appropriateness / "methodology" / "pragmatics" vs. justification, correctness, truth
- knowing how or why vs. knowing that

Jackendoff

- I-semantics vs. E-semantics
- Sketch of the theory: categories, attributes, constructors

Frege

- Sense and reference, means of representation
- The telescope analogy

**Meeting 2: September 7**

Kant

- Understanding vs. sensibility (concepts vs. intuitions)
- Cognition of mathematical objects, example from Euclid
- Schemata
- Quanta, quantitatum, and time
- Kant's concerns, more general concerns

**Meeting 1: August 31**

Overview of seminar goals (roughly as described on the main page)

Discussion of some of the general difficulties in making sense of "concepts"

- "meanings," between syntax and reference
- do we really need a theory of concepts?

Background for reading Kant

- The project of the
*Critique* - Transcendental idealism
- Some attractive features of Kant's views