What is predicativity? While the term suggests that there is a single idea involved, what the history will show is that there are a number of ideas of predicativity which may lead to different logical analyses, and I shall uncover these only gradually. A central question will then be what, if anything, unifies them. Though early discussions are often muddy on the concepts and their employment, in a number of important respects they set the stage for the further developments, and (...) so I shall give them special attention. NB. Ahistorically, modern logical and set-theoretical notation will be used throughout, as long as it does not conflict with original intentions. (shrink)

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

Semantic pathology is most widely recognized in the liar paradox, where an apparent inconsistency arises in ‘‘liar sentences’’ and their ilk. But the phenomenon of semantic pathology also manifests a sibling symptom—an apparent indeterminacy—which, while not largely discussed (save for the occasional nod to ‘‘truthteller sentences’’), is just as pervasive as, and exactly parallels, the symptom of inconsistency. Moreover, certain ‘‘dual symptom’’ cases, which we call naysayers, exhibit both inconsistency and indeterminacy and also manifest a higher-order indeterminacy between them. In (...) this paper, we explore and lay out the full, broader extent of semantic pathology. We then turn to the best-known attempts to diagnose and treat the phenomenon: consistentist approaches, proposed by Alfred Tarski and Saul Kripke, and an inconsistentist approach, originally presented by Graham Priest and dubbed ‘‘dialetheism’’. We explain the basic elements of each view and argue that each fails to provide an adequate way of dealing with the full extent of semantic pathology. We conclude that a new kind of approach is required and briefly sketch the pretense-based view that we favor. (shrink)

Ttler=‘Ttler is true’ says of itself that it is true. It is a truth-teller. I argue that we have equally telling arguments (i) to the effect that all truth-tellers must have the same truth-value (ii) and the effect that truth-tellers differ in truth-value. This is what I call the Truth-Tellers paradox. This paradox stems from the fact that the truth-value of a truth-teller like Ttler should be determined by the fact that it says of itself that it is true (which (...) entails (i)) but that it cannot be determined by that fact (as witnessed by (ii)). The Truth-Tellers paradox resem- bles the classical semantic paradoxes like the Liar. In both cases, a form of self-reference allows us to derive a contradiction from oth- erwise plausible semantic and logical principles. Furthermore the Truth-Tellers paradox can be formulated without using sentences which are in an intuitive sense ungrounded, it thus severs the link, almost universally taken for granted, between the semantic para- doxes and ungroundedness. Finally, some classical solutions to the Liar do not generalize to the Truth-Tellers paradox. (shrink)