Department of Philosophy

Charles B. Cross

Professor of Philosophy and
Faculty Fellow of the Institute for Artificial Intelligence

Office: Peabody 101A
Phone: (706) 542-2653
e-mail: ccross@uga.edu
mailing address:

Department of Philosophy
Peabody Hall
290 South Jackson Street
University of Georgia
Athens, GA 30602-1627, USA

Office Hours, Fall 2009: Mondays 3:30-4:30pm, Tuesdays 2-3pm, and by appointment.

My office is a Safe Space.

Please note that effective August 24, 2009, the MW lectures are moved to 115 Peabody Hall.

Syllabus.

An introduction to the mathematics of good reasoning.

This course or PHIL 2500H is required for philosophy majors and cognitive science majors, and either course is highly recommended for pre-law students. Indeed, Ken De Leon, a graduate of Boalt Hall and the creator of Top-Law-Schools.com, says, "An undergraduate logic course is like free LSAT prep." PHIL 2500 is an example of the kind of course De Leon is talking about.

Topics include translation of arguments into a symbolic notation and techniques for evaluating symbolized arguments.

No prerequisites.

Required text: Virginia Klenk. Understanding Symbolic Logic, 5th Edition (2008). Prentice-Hall.

An introduction to the formal syntax and semantics of propositional and first-order logic.

Prior knowledge of symbolic logic will be assumed.

For undergraduates, the prerequisite is PHIL 2500 or 2500H.

Course material will come largely from printed handouts, but in addition the following text is required: Merrie Bergmann, James Moor, Jack Nelson. The Logic Book, 5th Edition (2008). McGraw-Hill.

PHIL(LING) 4520/6520 Model Theory, Spring 2010

Meets Tuesdays 9:30am-12:15pm.

A course in the semantic metatheory of classical sentential and predicate logic. The course will be of interest to graduate and advanced undergraduate students in philosophy, artificial intelligence, linguistics, and math education.

We will prove soundness, completeness, and related results for classical sentential logic and predicate logic. We will prove these results for the Fitch-style natural deduction systems of sentential and predicate logic covered in PHIL(LING) 4510/6510.

Time permitting, we may cover an additional advanced topic in philosophical logic.

No text (handouts only).

For both graduates and undergraduates, the prerequisite is PHIL(LING) 4510/6510 or equivalent preparation. If you have not taken PHIL(LING)4510/6510, please check with me and I will be happy to talk with you about whether your background is sufficient.

Research Interests

• Philosophical Logic, with an emphasis on conditionals, logical aspects of epistemology and metaphysics, and logics for artificial intelligence

Work in Progress

• I am interested in how formal theories of nonmonotonic reasoning from artificial intelligence shed light on philosophical issues about induction. I am currently working on two papers that pursue this theme:

  A Pluralistic Theory of Induction: Induction is sometimes viewed as the making of inferences, but it is also common to think of induction as theory choice. There is reason to think that these views of induction are incompatible or at least in tension. I am developing an account of cumulative reasoning---a specific type of inductive reasoning---that resolves this tension.

  Nonmonotonic Inference and the Formalizability of Induction: I examine how systems of nonmonotonic reasoning as conceived in artificial intelligence bear on the achievability of the goal of formalizing inductive reasoning.

• I have been working on two papers about the Principle of the Identity of Indiscernibles (PII) and hope to use this work in the development of a theory of the possible existence of non-actual particulars:

  Causal Independence, the Identity of Indiscernibles, and the Essentiality of Origins: I show that the so-called Continuity Argument against the PII is best reconstructed as having nothing to do with continuity and everything to do with causal independence and counterfactual conditionals, and I show that my analysis of the Continuity Argument sheds light on Kripke’s argument for the essentiality of origins. (The Journal of Philosophy, May 2009.)

  Modal Properties, the Necessity of Identity, and the Identity of Indiscernibles: The aim of this essay is to determine how the introduction of modal properties into the scope of the PII affects the qualitative explicability of numerical difference. I examine Della Rocca’s contention that all purported counter-examples to the PII involve brute facts of non-identity ungrounded in qualitative difference, and I show that the Continuity Argument does not postulate such facts. I conclude that if the PII is understood to quantify over modal as well as non-modal properties, then the qualitative explicability of numerical distinctness does not require the PII.

Selected Publications

Each link provided below allows a paper to be downloaded from the website of the relevant publisher. If you use one of these links and the publisher's website does not recognize your institution's online subscription, it may be necessary for you to access the paper online via a different gateway. If you do not have access to an online subscription, you are welcome to ask me for a hardcopy of the paper.

My Erdös Number is 4.

• C. Cross, "Causal Independence, the Identity of Indiscernibles and the Essentiality of Origins," The Journal of Philosophy 106:277-291, 2009.
• C. Cross, "Conditional Excluded Middle," Erkenntnis 70:173-188, 2009.
• C. Cross, "Nonbelief and the Desire-As-Belief Thesis," Acta Analytica 23:115-124, 2008.
• C. Cross, "Antecedent-Relative Comparative World Similarity," Journal of Philosophical Logic 37:101-120, 2008.
• C. Cross, "Conditional Logic and the Significance of Tooley's Example," Analysis 66:325-335, 2006
• C. Cross, "A Formal Model of Holistic Epistemic Coherence," in Bryson Brown and François Lepage (eds.), Truth and Probability: Essays in Honour of Hugues Leblanc, (London: King’s College Publications, 2005), pp. 111-122.
• C. Cross, "A Correction to 'Nonmonotonic Inconsistency'," Artificial Intelligence 160:191-192, 2004
• C. Cross, "More on the Paradox of the Knower without Epistemic Closure," Mind 113:109-114, 2004
• C. Cross, "Relative Coherence and Cumulative Reasoning," in The Epistemology of Keith Lehrer, Erik Olsson (ed.), (Philosophical Studies Book Series, Kluwer Academic Publishers: Dordrecht, 2003), pp. 109-127
• C. Cross, "Nonmonotonic Inconsistency," Artificial Intelligence 149:161-178, 2003
• C. Cross, "Armstrong and the Problem of Converse Relations," Erkenntnis 56:215-227, 2002
• C. Cross, "Doesn't-Will and Didn't-Did," Australasian Journal of Philosophy 80:101-106, 2002
• C. Cross, "A Theorem Concerning Syntactical Treatments of Nonidealized Belief," Synthese 129:335-341, 2001
• D. Nute and C. Cross, "Conditional Logic," in The Handbook of Philosophical Logic, Second Edition, Volume 4, Dov Gabbay and Franz Guenthner (eds.), (Kluwer: Dordrecht, 2001), pp. 1-98. (Revision of Nute's chapter from the first edition with a new 40+pp section on conditionals and the Ramsey Test written by Cross)
• C. Cross, "The Paradox of the Knower Without Epistemic Closure," Mind 110:319-333, 2001
• C. Cross, "A Characterization of Imaging in Terms of Popper Functions," Philosophy of Science 67:316-338, 2000
• C. Cross, "Coherence and Truth Conducive Justification," Analysis 59:186-193, 1999
• C. Cross, "The Modal Logic of Discrepancy," Journal of Philosophical Logic 26:143-168, 1997
• C. Cross, "Max Black on the Identity of Indiscernibles," Philosophical Quarterly 45:350-360, 1995
• C. Cross, "Probability, Evidence, and the Coherence of the Whole Truth," Synthese 103:153-170, 1995
• C. Cross, "From Worlds to Probabilities: a Probabilistic Semantics for Modal Logic," Journal of Philosophical Logic 22:169-192, 1993
• C. Cross, "Counterfactuals and Event Causation," Australasian Journal of Philosophy 70:307-323, 1992
• C. Cross and R. H. Thomason, "Conditionals and Knowledge-Base Update," in Belief Revision: Cambridge Tracts in Theoretical Computer Science, Volume 29, ed. Peter Gärdenfors, (Cambridge University Press: Cambridge, 1992), pp. 247-275
• C. Cross, "Explanation and the Theory of Questions," Erkenntnis 34:237-260, 1991
• C. Cross, "Temporal Necessity and the Conditional," Studia Logica 49:345-363, 1990
• C. Cross, "Belief Revision, Nonmonotonic Reasoning, and the Ramsey Test," in Knowledge Representation and Defeasible Reasoning, ed. Henry E. Kyburg, Jr., et al, (Kluwer: Boston, 1990), pp. 223-244
• C. Cross and R. H. Thomason, "Update and Conditionals," in Methodologies for Intelligent Systems, ed. Zbigniew Ras and Maria Zemankova, (North-Holland: Amsterdam, 1987), pp. 392-399
• C. Cross, "'Can' and the Logic of Ability," Philosophical Studies 50:53-64, 1986
• C. Cross, "Jonathan Bennett on 'Even If'," Linguistics and Philosophy 8: 353-357, 1985

I regularly teach PHIL 2500 Symbolic Logic, PHIL(LING) 4510/6510 Deductive Systems, PHIL(LING) 4520/6520 Model Theory, and PHIL 8500 Seminar in Problems of Logic. I occasionally teach PHIL 3610 Theory of Knowledge and PHIL(LING) 8300 Seminar in the Philosophy of Language.

I am interested in directing graduate student research in philosophical logic and related areas of metaphysics and epistemology. Possible topics include conditionals, modal logic, quantified modal logic, formal ontology, the metaphysics of modality, essentialism, the essentiality of origins, epistemic logic, belief revision, and logics for artificial intelligence. Prospective graduate students interested in working with me are invited to apply to the Ph.D. Program in Philosophy, the M.A. Program in Philosophy, or the M.S. Program in Artificial Intelligence. Joint enrollment for the M.S. in Artificial Intelligence and the M.A. or Ph.D. in Philosophy is possible and represents a unique opportunity for prospective graduate students interested in logic and its applications.

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