Abstract: This paper provides a solution to the liar paradox, in the sense of an answer to those who believe that the liar is both true and not true, based on the premise that language is conventional. According to David Lewis's theory of conventions, for a sentence to have truth conditions is for the language community in question to have a convention regarding the circumstances in which the sentence is appropriately assertible (in a certain sense). The power to institute language conventions does not come with the power to make a state of affairs both obtain and not obtain, and therefore the liar is not both conventionally appropriately assertible and not conventionally appropriately assertible. Whether it is one or the other is an empirical question that depends on contingent details about our conventions. I draw on Thomas Nagel's ideas about a view from nowhere to explain why our language psychology can make it seem that the liar ought to be true if and only if it is not.
Keywords: Liar Paradox, Conventions, View From Nowhere, Theories of Truth, Dialetheism
Abstract: 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.
Keywords: Liar Paradox, Gap Theory, Glut Theory, Communication
Abstract: According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by lawless choice sequences, i.e., sequences created by repeated random choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of free choice sequences, it is the purpose of this paper to argue against Brouwer's claim.
Keywords: Intuitionism, Potential infinity, Choice sequences, The continuum, Platonism
Abstract: The main conclusion is this conditional: If the principle of reflection is a valid constraint on rational credences, then so is the principle of countable additivity. The argument for it is a slight variation on two arguments that are already in the literature, but with crucial differences that makes it much stronger. The conditional can be used for either a modus ponens or a modus tollens; some reasons for thinking that the former is most reasonable is given. Finally, a version of the main conclusion with "countable additivity" replaced by "perfect additivity" is considered.
Keywords: Countable Additivity, Uniform Probability Distributions, Reflection, Perfect Additivity