Philosophical Applications of Modal Logic
Wednesday June 13:
- 09:30-11:00 Jessica Leech (KCL), Relative Necessity Extended
- 11:15-12:45 Sven Rosenkranz (Barcelona), Towards a logic for being in a position to know
- 13:30-15:00 Brian Rabern (Edinburgh), A proper solution to the nesting problem for two-dimensionalism
- 15:15-16:45 Susanne Bobzien (Oxford), TBA
Thursday June 14:
- 09:30-11:00 Peter Fritz (Oslo), Possible Worlds in Higher-Order Logic
- 11:15-12:45 Wesley Holliday (Berkeley), TBA
- 13:30-15:00 Øystein Linnebo (Oslo), Predicativism and potential infinity (joint work with Stewart Shapiro)
- 15:15-16:45 Stephan Leuenberger (Glasgow), Fragmentation and introspection in epistemic logic (joint work with Martin Smith)
Jessica Leech (KCL), Relative Necessity Extended
One can fruitfully define various kinds of alethic necessity as relative, that is, as the logical consequences of a particular set of true propositions. For example, one might take the natural necessities to be what is logically necessary relative to the laws of nature. One merit of such an approach is that we can explain the commonality between different necessities; they are all relativizations of one and the same fundamental necessity. One might then ask: what about non-alethic (and epistemic) necessities? There is a sense in which epistemic, doxastic, legal, deontic, and other necessities are also necessities. But the relativist approach, in taking these to be the logical consequences of, say, known propositions, believed propositions, the laws of morality, etc., runs in to serious and familiar problems (that arise from the logic). In my talk, I assess various options for solving these problems, with a view to exploring whether a larger-scale unification of necessity – alethic and non-alethic – is possible (or desirable) for the relativist.
Sven Rosenkranz (Barcelona), Towards a logic for being in a position to know
My concern is with an epistemic logic governing the notion of being in a position to know. Such a logic is of independent interest. My own interest stems more specifically from my work on justification. According to the view I’ve defended elsewhere, p is propositionally justified iff one is in no position to know that one is in no position to know p. More recently, I have argued that p is doxastically justified iff one is in no position to know that one doesn’t know p – where a belief is justified iff it is held under circumstances under which p is doxastically justified in this sense. I will not here argue for these claims. Instead, I wish to explore the features that the underlying epistemic logic and semantics ought to have. After introducing principles of knowledge, and of being in a position to know, that should be acceptable to almost everyone, I suggest two non-standard principles governing these notions and provide a rationale for them. After highlighting a number of interesting theorems, I then proceed to argue that, just like knowledge-operators, operators for being in a position to know behave non-normally and create hyperintensional contexts, with well-known consequences for formal semantics. I make some suggestions of what shape a suitable semantic treatment should take, and dwell on some unresolved issues to which this treatment gives rise, and whose proper resolution bears on the larger project of characterising justification in the ways proposed.
Peter Fritz (Oslo), Possible Worlds in Higher-Order Logic
Let intensionalism be the view that necessarily equivalent propositions are identical. Assuming intensionalism, there is a promising account of possible worlds according to which they are special propositions, namely those which are possible although maximally strong. For such propositions to behave as worlds are widely expected to behave, it is necessary that each possible proposition can be strengthened to a maximally strong one; call this claim "atomicity". Using higher-order logic as a framework in which to regiment our talk of propositions, properties and relations, this talk will explain why atomicity does not follow straightforwardly from intensionalism, but also show that it follows with plausible additional assumptions once the framework is expanded to include higher-order analogues of plural quantifiers. These considerations will presuppose necessitism, the claim that it is necessary what there is. The talk will conclude by sketching some of the ways in which the situation becomes much more complicated when necessitism is rejected.
Øystein Linnebo (Oslo), Predicativism and potential infinity (joint work with Stewart Shapiro)
We develop some predicativist approaches within the modal framework for potentiality that was developed in Linnebo (2010) and Linnebo and Shapiro (2018). The result is illuminating, as it puts predicativism into a more general framework and helps to sharpen some of the key theses.
Stephan Leuenberger (Glasgow), Fragmentation and introspection in epistemic logic (joint work with Martin Smith)
All standard epistemic and doxastic logics legitimate something akin to the principle of closure. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. In this paper we describe a family of weak logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these – which we term plurality semantics – is relatively unfamilar and unexplored. What makes this framework significant is that it can be interpreted in a very natural way in light of one motivation for rejecting closure: that epistemic agents may be fragmented. Fragmentation is one way of falling short of an epistemic or doxastic ideal. Another one, which has taken central stage in traditional epistemic and doxastic logic, is lack of introspection. The paper then investigates the relationship between these two dimensions of non-ideality.