Projects in Previous Years

2nd Semester 2019/20: Logics of Sense and Reference


Reinhard Muskens

If you are interested in this project, please contact  by email.

Registration until 31 May 2020


Leibniz’s Law (LL) tells us that if two expressions have the same meaning, one can be substituted for the other in a third expression without changing its truth-value. The principle clearly is fundamental to formal reasoning, but, as many have noticed, does not seem to hold in natural language. Consider the following sentences.

a) Fred knows that if the front door is locked, the back door isn’t.

b) Fred knows that if the back door is locked, the front door isn’t.

Suppose Fred has been informed that if the front door is locked, the back door is open. Then a) has become true. Has b) become true? Not as long as Fred has not made the necessary deductive step, and so a) may be true while b) is false. Conclusion (LL): the embedded sentences do not mean the same thing. But how can this be? Most logical formalisations of the two embedded sentences assign to them the same semantic values (change the example if your preferred logic does not validate contraposition). On the other hand, giving up LL is not an attractive option as it entails giving up a lot of impeccable reasoning.

Frege 1892, as we all know, considered a similar substitutivity problem and proposed the solution that expressions have two kinds of meaning, sense and reference, and that for substitution in certain contexts identity of sense is required. But how can the sense/reference distinction be modelled logically? In this course we will look at several possibilities. We will consider at least

  1. Logics with impossible possible worlds (Hintikka 1975 and subsequent literature),

  2. Structured meanings (Carnap 1947, Lewis 1972, Cresswell 1985),

  3. Senses as primitive entities (Thomason 1980, Muskens 2005, 2007),

  4. Senses as algorithms (Moschovakis 1994, 2006), and

  5. Zalta’s Typed Object Theory (Zalta 1983, 1988, forthcoming).

Since solutions should be applicable to natural language semantics, higher-order logics will often be in focus.


The first two weeks will be organised around a series of lectures. During the third week students each prepare a presentation and a hand-out supporting it. The presentations will be held in week 4.


Basic familiarity with higher-order logics and the simply typed lambda calculus.


Pass/Fail on the basis of class participation, the hand-out, and the presentation.

[1] R. Carnap. Meaning and Necessity. Chicago UP, Chicago, 1947.
[2] M. J. Cresswell. Structured Meanings. MIT Press, Cambridge, MA, 1985.
[3] G. Frege. Über Sinn und Bedeutung. In G. Patzig, editor, Funktion, Begriff, Bedeutung. Fünf Logische Studien. Vanden Hoeck, Göttingen, 1892.
[4] J. Hintikka. Impossible Possible Worlds Vindicated. Journal of Philosophical Logic, 4:475--484, 1975.
[5] D. Lewis. General Semantics. In D. Davidson and G. Harman, editors, Semantics of Natural Language, pages 169--218. Reidel, Dordrecht, 1972.
[6] Y. Moschovakis. Sense and Denotation as Algorithm and Value. In Logic Colloquium '90 (Helsinki 1990), volume 2 of Lecture Notes in Logic, pages 210--249. Springer, Berlin, 1994.
[7] Y. Moschovakis. A Logical Calculus of Meaning and Synonymy. Linguistics and Philosophy, 29:27--89, 2006.
[8] Reinhard Muskens. Sense and the Computation of Reference. Linguistics & Philosophy, 28(4):473--504, 2005.
[9] Reinhard Muskens. Intensional Models for the Theory of Types. The Journal of Symbolic Logic, 72(1):98--118, 2007.
[10] R. Thomason. A Model Theory for Propositional Attitudes. Linguistics and Philosophy, 4:47--70, 1980.
[11] Edward N. Zalta. Abstract Objects: An Introduction to Axiomatic Metaphysics. D. Reidel, 1983.
[12] Edward N. Zalta. Intensional Logic and the Metaphysics of Intentionality. MIT Press, 1988.
[13] Edward N. Zalta. Typed Object Theory. In José L. Falguera and Concha Martínez-Vidal, editors, Abstract Objects: For and Against. Springer, forthcoming.

The course will be offered online.