We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)
Andrew Bacon, John Hawthorne, and Gabriel Uzquiano have recently argued that free logics—logics that reject or restrict Universal Instantiation—are ultimately not promising approaches to resolving a family of intensional paradoxes due to Arthur Prior. These logics encompass ramified and contextualist approaches to paradoxes, and broadly speaking, there are two kinds of criticism they face. First, they fail to address every version of the Priorean paradoxes. Second, the theoretical considerations behind the logics make absolutely general statements about all propositions, properties of (...) propositions, etc., but because this sort of intensional quantification is always restricted in the logics, they cannot even express those considerations. I present a novel sort of free logic, which rejects the standard Universal Instantiation but validates a restricted form of the rule, and which addresses both kinds of criticism by allowing some propositions to be unrestricted in their quantification. (shrink)
In , Frank Ramsey separates paradoxes into two groups, now taken to be the logical and the semantical. But he also revises the logical system developed in Whitehead and Russellthe intensional paradoxess interest in these problems seriously, then the intensional paradoxes deserve more widespread attention than they have historically received.
Jörg Hansen, John Horty, and Xavier Parent and Leendert van der Torre have all recently described some sort of nonmonotonic logic to model reasons and their interactions. Horty’s framework is broader in scope than the other two, encompassing both reasoning about the relative strengths of reasons and reasoning about which reasons to consider in the first place. Hansen discusses a plethora of approaches and examples, including Horty’s, arguing that his preferred system best captures our intuitions. And Parent and van der (...) Torre present a family of systems of input/output logic, which are in some ways the most flexible. In this paper, I aim to combine these features. Without attempting to answer the question of which intuitions are the best to capture, I first argue that there are good reasons to explore systems that behave more like Hansen’s than Horty’s. I then show that Parent and van der Torre’s framework of input/output logic can exactly duplicate Hansen’s system but is flexible enough to produce other results as well. Finally, I extend their framework to include the additional kinds of reasoning Horty discusses, showing that the resulting theory can handle a wider range of cases than Horty’s. (shrink)
A number of authors have taken a family of paradoxes, whose members trace back to theorems due either in whole or in part to Richard Montague, to pose a serious, possibly fatal challenge to theories of fine-grained, hyperintensional content. These paradoxes all assume that we can represent attitudes such as knowledge and belief with sentential predicates, and this assumption is at the heart of the purported challenge: the thought is that we must reject such predicates to avoid the paradoxes, and (...) that hyperintensionality precludes such a rejection. In this paper I examine in more detail both parts of this thought. I first argue that while there are relatively few satisfactory alternatives to rejecting sentential attitude predicates, we cannot conclusively rule them all out—there are, at least, bullets that proponents of hyperintensionality can bite. I then argue that while most forms of hyperintensional content do in fact guarantee the existence of sentential attitude predicates, one relatively underexplored sort of content, due to Max Cresswell, does not. I thus conclude that while these Montagovian paradoxes present a serious challenge to nearly every popular theory of hyperintensionality, they do not on their own require that we retreat all the way to a familiar, coarse-grained, possible-worlds account of propositions. (shrink)
Propositions are more than the bearers of truth and the meanings of sentences: they are also the objects of an array of attitudes including belief, desire, hope, and fear. This variety of roles leads to a variety of paradoxes, most of which have been sorely neglected. Arguing that existing work on these paradoxes is either too heavy-handed or too specific in its focus to be fully satisfactory, I develop a basic intensional logic and pursue and compare three strategies for addressing (...) the paradoxes, one employing truth-value gaps, one restricting propositional quantification, and one restricting our ability to have attitudes like belief and desire. This results in four distinct resolutions of the paradoxes, all but one of which are novel and all of which receive novel and general implementations. While resolving the paradoxes is of course the ultimate goal, I do not here argue that any one of the resolutions is superior. These paradoxes have been so little studied that my primary goal is only to identify the most fundamental costs and benefits of the various approaches one can take to addressing them. Each resolution I develop has significant drawbacks, which I argue highlight tensions between the different roles propositions play. Past researchers have skirted these tensions, and the issues raised by these paradoxes more generally, by focusing on non-propositional paradoxes, such as the most familiar forms of the Liar paradox. At the least, then, I hope this dissertation establishes that the propositional paradoxes deserve attention not only because of their consequences for intensional logic, but also because of their consequences for our understanding of content, truth, quantification, and a host of mental attitudes. (shrink)
Propositions are central to at least most theorizing about the connection between our mental lives and the world: we use them in our theories of an array of attitudes including belief, desire, hope, fear, knowledge, and understanding. Unfortunately, when we press on these theories, we encounter a relatively neglected family of paradoxes first studied by Arthur Prior. I argue that these paradoxes present a fatal problem for most familiar resolutions of paradoxes. In particular, I argue that truth-value gap, contextualist, situation (...) theoretic, revision theoretic, ramified, and dialetheist approaches to the paradoxes must deny us the conceptual resources that they themselves make use of, on pain of contradiction. I then detail the costs of the extant strategies that avoid this issue: Hartry Field’s paracomplete approach; Andrew Bacon’s classical treatment of indeterminacy; a generalization of ideas from Prior, Nicholas J.J. Smith, and Hartley Slater; and free logics as recently explored by Bacon, John Hawthorne, and Gabriel Uzquiano. I argue that none of these is perfect, and that each restricts the theories we can endorse in a variety of areas of philosophy. I spell these restrictions out, showing, I hope, that the further investigation of these paradoxes must be a part of future research on propositional attitudes. (shrink)