Casper Storm Hansen

Lasersohn has argued that the use of Russell's analysis of the definite determiner in Montague Grammar, which is responsible for giving the correct prediction in the case of the Temperature Paradox, is also responsible for giving the wrong prediction in the case of the Gupta Syllogism. In this paper I argue against Lasersohn, and show that the problem of the Gupta Syllogism can be solved by making a minor addition to Intensional Montague Grammar. This solution is one that Lasersohn discusses but rejects. I will show that his critique of it is ill-founded.

Two reverse supertasks—one new and one invented by Pérez Laraudogoitia —are discussed. Contra Kerkvliet and Pérez Laraudogoitia, it is argued that these supertasks cannot be used to conduct fair infinite lotteries, i.e., lotteries on the set of natural numbers with a uniform probability distribution. The new supertask involves an infinity of gods who collectively select a natural number by each removing one ball from a collection of initially infinitely many balls in a reverse omega-sequence of actions.

Radical glut and gap theorists deny—in opposite ways—that the liar sentence has exactly one of the two values true and not true. I describe a scenario where a signalman finds himself in a situation analogous to the liar paradox: if he lights a fire at a certain time, that is analogous to the liar being true, and if he does not, that is analogous to the liar not being true. It is obvious that he must make exactly one of those states of affairs come about. It is argued that there are no relevant differences between the liar and the signalman’s dilemma, implying that the glut and gap theorists are wrong about the former. A further point is that whether or not the liar is true/the signalman lights the fire, language/the signalman is misleading relative to the conditions under which the liar/the fire “ought” to be true/lit.

This paper offers a unification and systematization of the grounding approaches to truth, denotation, classes and abstraction. Its main innovation is a method for “kleenifying” bivalent semantics so as to ensure that the trivalent semantics used for various linguistic elements are perfectly analogous to the semantics used by Kripke, rather than relying on intuition to achieve similarity. The focus is on generalizing strong Kleene semantics, but one section is devoted to supervaluation, and the unification method also extends to weak Kleene semantics.