HT 2018

This term we are meeting for only four of the eight weeks, as announced in the weekly digest. The papers include the following:

  1. Uzquiano, G. (2015) ‘A Neglected Resolution of Russell’s Paradox of Propositions’, in The Review of Symbolic Logic 8: 328-344. (Presented by Alex Roberts)
  2. Correia, F. and Skiles, A. (2017), ‘Grounding, Essence, And Identity’. Philos Phenomenol Res. doi:10.1111/phpr.12468 (Presented by Ben Brast-McKie)
  3. TBA
  4. TBA

Recent Papers

We will start off the year with a mix of recent papers in metaphysics, language, and epistemology. Here is the list of papers we will be reading each week:

  1. Dasgupta – Metaphysical Rationalism
    • Abstract: The Principle of Sufficient Reason states that everything has an explanation. But different notions of explanation yield different versions of this principle. Here a version is formulated in terms of the notion of a “grounding” explanation. Its consequences are then explored, with particular emphasis on the fact that it implies necessitarianism, the view that every truth is necessarily true. Finally, the principle is defended from a number of objections, including objections to necessitarianism. The result is a defense of a “rationalist” metaphysics, one that constitutes an alternative to the contemporary dogmas that some aspects of the world are “metaphysically brute” and that the world could in so many ways have been different.
  2. Dixon – What Is the Well-Foundedness of Grounding?
    • Abstract: A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. In what follows, I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call ‘full foundations’, best captures the relevant claim. My argument is by the process of elimination. For each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out.
  3. Arthur Prior – A Family of Paradoxes
  4. Rayo – Essence Without Fundamentality
    • Abstract: I argue for a conception of essence that does not rely on distinctions of metaphysical fundamentality.
  5. Salow & Goodman – Taking a chance on KK
    • Abstract: Dorr et al. (Philos Stud 170:277–287, 2014) present a case that poses a challenge for a number of plausible principles about knowledge and objective chance. Implicit in their discussion is an interesting new argument against KK, the principle that anyone who knows p is in a position to know that they know p. We bring out this argument, and investigate possible responses for defenders of KK, establishing new connections between KK and various knowledge-chance principles.
  6. Necessities and Necessary Truths
    • Abstract: In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as ‘There are necessary a posteriori propositions’ or ‘All laws of physics are necessary’ in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate ‘is necessary’ can then be replaced by ‘is necessarily true’. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators.
  7. Mandelkern et al – Agentive Modals
    • Abstract: We propose a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches − the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis − we present a new account that builds on both the existential and conditional analyses. On our account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action (in a sense we make precise) which is such that, if John tries to do it, he swims across the river. We argue that the act conditional analysis avoids the problems faced by existing accounts of agentive modality, and show how it can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of non-hypothetical guarantee.
  8. Alex Paseau – What is the point in complete rigour?
    • Abstract: Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous (‘atomized’) by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds that none of them fits the bill. In particular, atomized arguments do not ground the correctness of their unatomized counterparts; they are typically not credence-preserving; and they need not reveal the source of inferential disagreement. The moral this suggests is that complete rigour is not even a defeasible epistemic ideal.
  9. Jeff Russell – Temporary Safety Hazards
    • The Epistemic Objection says that certain theories of time (like the “growing block” and “moving spotlight”) imply that it is impossible to know which time is absolutely present. Standard presentations of the Epistemic Objection are elliptical—and some of the most natural premises one might fill in to complete the argument end up leading to radical skepticism. But there is a way of filling in the details which avoids this problem, using epistemic safety. The new version has two interesting upshots. First, while Ross Cameron alleges that the Epistemic Objection applies to presentism as much as to theories like the growing block, the safety version does not overgeneralize this way. Second, the Epistemic Objection does generalizin a different, overlooked way. The safety objection is a serious problem for widely held combination of views: “propositional temporalism” (objects of belief change truth-value) together with “metaphysical eternalism” (the world does not objectively privilege any particular time).


Metasemantics — TT2017

BLOCK 1: What fixes reference?

Week 1

Lewis (1974) — Radical Interpretation


As Lewis formulates it, the challenge of radical interpretation is the challenge of specifying how the totality of facts about a subject qua physical system determine that subject’s beliefs, desires, and meanings. Lewis proposes six constraints for any proposed solution to the problem of radical interpretation; included among these constraints are the principles of charity (i.e., a subject should be represented as believing and desiring what he or she ought to believe and desire), rationalization (i.e., subjects should be represented as rational agents), and truthfulness (i.e., subjects should be interpreted as operating within a convention of truthfulness). Invoking these constraints, Lewis then considers several methods (one of which he advocates) for solving the problem of radical interpretation. Notably, the Davidsonian method is found to be inadequate because it flouts the principles of truthfulness and rationalization.

Week 2

Magidor & Kearns (2012) – Semantic Sovereignty


The question we are concerned with in this paper is this: do semantic facts supervene on use facts? According to the thesis we label Semantic Supervenience (SSUP), semantic facts do supervene on use facts. According to the thesis we label Semantic Sovereignty (SSOV), semantic facts do not supervene on use facts. Semantic Supervenience is widely (indeed almost universally) assumed to be correct. Of course, many philosophers accept the thesis only if ‘use facts’ is given a sufficiently broad interpretation: perhaps one that includes facts about the behaviour of the linguistic community as a whole, or about the background physical environment, or about the relative naturalness of properties. But the commonly accepted assumption is that on some such sufficiently wide interpretation, Semantic Supervenience is correct. […] In this paper we argue that (even given a wide interpretation of ‘use facts’) Semantic Supervenience should be rejected in favour of Semantic Sovereignty: semantic properties really do go that deep.

Week 3

Williams (2007) – Eligibility and Inscrutability

(Background Reading: Lewis (1984): Putnam’s Paradox.)


Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory.

Week 4

Williamson (2007) – Knowledge Maximization (Philosophy of Philosophy, Ch.8)

Hawthorne (2007) – Craziness and Metasemantics.


Consider a crazy interpretation of our utterances that has the virtue of being charitable—most of our utterances come out true1—but the vice of being crazy. What makes such an interpretation incorrect? David Lewis (and various philosophers since) have pinned their hopes on an eligibility constraint: interpretations that assign more natural properties to predicates are, other things being equal, better. On this picture, our words have fairly determinate meanings (contra Quine [1960] and “Kripkenstein” [Kripke 1982])—and, at a pretty good fi rst pass, it is the twin constraints of charity and eligibility that explain why this is so.2 In his admirable “Eligibility and Inscrutability” (in this issue), J. Robert G. Williams makes trouble for this package. In section 1 I describe some cases that reinforce Williams’s misgivings. In section 2 I note a general problem that affl icts the Lewisian vision. In section 3 I offer a few constructive suggestions concerning how the “crazy interpretation” problem should be approached. Finally, in section 4 I try to shed some light on the role of the interpreter in metasemantics.

BLOCK 2: Semantic Plasticity

Week 5

Hawthorne (2006): Epistemicism and Semantic Plasticity


I shall endeavour to make vivid a kind of puzzle that arises when Timothy Williamson’s epistemicist machinery2 is applied to borderline cases of (i) personhood and (ii) semantic properties. My aim will be to raise some concerns about his development of the epistemicist view, and then to explore an alternative way of thinking about epistemicism. What follows is very much a progress report on unfinished business, but I hope there is enough progress to warrant the report.

Week 6

Magidor & Kearns (2008): Epistemicism about Vaguness and Metasemantic Safety.


In this paper, we challenge Williamson’s safety based explanation for why we cannot know the cut-off points associated with vague expressions. We will assume throughout (most of) the paper that Williamson is correct in saying that vague expressions have sharp cut-off points, but we argue that Williamson’s explanation for why we do not and cannot know these cut-off points is unsatisfactory.

Week 7
Hawthorne & Dorr (2014): Semantic Plasticity and Speech Reports


Most meanings we express belong to large families of variant meanings, among which it would be implausible to suppose that some are much more apt for being expressed than others. This abundance of candidate meanings creates pressure to think that the proposition attributing any particular meaning to an expression is modally plastic: its truth depends very sensitively on the exact microphysical state of the world. However, such plasticity seems to threaten ordinary counterfactuals whose consequents contain speech reports, since it is hard to see how we could reasonably be confident in a counterfactual whose consequent can be true only if a certain very finely tuned microphysical configuration obtains. This essay develops the foregoing puzzle and explores several possible solutions.

BLOCK 3: Models

Week 8

Stephen Yablo (MS): Models and Reality.


The title comes from a well-known paper of Putnam’s (Putnam [1980]). The content is very different. Putnam uses model theory1 to cast doubt on our ability to engage semantically with an objective world. The role of mathematics for him is to prove this pessimistic conclusion. I on the other hand am wondering how models can help us to engage semantically with the objective world. Mathematics functions for me as an analogy. Numbers among their many other accomplishments boost the language’s expressive power; they give us access to recondite physical facts. Models, among their many other accomplishments, do the same thing; they give us access to recondite physical facts. This anyway is the analogy I will try to develop in this paper.

Higher Order Metaphysics – HT 2017

6.00 Thursdays at The Ertegun House

The aim of this reading group is to familiarise participants with the technical apparatus of higher-order logic, and discuss recent philosophical research which applies higher-order logic to issues in metaphysics and philosophical logic. Some of the issues we will discuss include: the ‘primitivist’ interpretation of higher-order logic, absolute generality, the individuation of propositions, properties and relations, Frege’s Puzzle, truth, and modality. No familiarity with the issues will be presupposed: the articles to be discussed in the first two weeks are accessible introductions to the core technical material, and later articles accessibly introduce further resources when required.

[Week 1] Background: Gallin’s Type Theory & The Interpretation of Higher-Order Logic

Timothy Williamson – Modal Logic as Metaphysics, Chapter 5: From First-Order to Higher-Order Modal Logic

Abstract: First-order logic permits quantification into name position. Second-order logic permits quantification into predicate or sentence position too. Higher-order logic takes the generalization even further. The growth of higher-order modal logic is traced, starting with Lewis and Langford’s quantification into sentence position in propositional modal logic, and on to the higher-order modal logics of Barcan Marcus, Carnap, Montague, Gallin, and others. Higher-order modal logic is proposed as a suitably general setting in which to assess fundamental issues in modal metaphysics. However, there are difficulties in interpreting higher-order quantification, since it lacks adequate paraphrases in natural language. Although Boolos’s paraphrase of quantification into monadic predicate position in terms of plural quantification works well in non- modal settings, for many purposes it is unsuitable in modal settings since plurals are modally rigid. Nevertheless, we can hope to reach a suitable understanding of irreducibly higher-order quantification by the direct method, without paraphrase.

[Week 2] Type Theory & Absolute Generality

Agustin Rayo – Beyond Plurals (in Rayo & Uzquiano Absolute Generality)

Abstract: I have two main objectives. The first is to get a better understanding of what is at issue between friends and foes of higher-order quantification, and of what it would mean to extend a Boolos-style treatment of second-order quantification to third- and higher-order quantification. The second objective is to argue that in the presence of absolutely general quantification, proper semantic theorizing is essentially unstable: it is impossible to provide a suitably general semantics for a given language in a language of the same logical type. I claim that this leads to a trilemma: one must choose between giving up absolutely general quantification, settling for the view that adequate semantic theorizing about certain languages is essentially beyond our reach, and countenancing an open-ended hierarchy of languages of ever ascending logical type. I conclude by suggesting that the hierarchy may be the least unattractive of the options on the table.

[Week 3] Type Theory & Set Theory

Øystein Linnebo & Agustin Rayo – Hierarchies Ontological and Ideological (in Mind (2012) 121: 269 – 308)

Abstract: Godel claimed that Zermelo-Fraenkel set theory is ‘what becomes of the theory of types if certain superfluous restrictions are removed’. The aim of this paper is to develop a clearer understanding of Godel’s remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.

[Week 4] Absolute Generality

James Studd – Quantifiers (Ch. 2)

[Please get in touch if you would like a copy of the draft we will be reading.]


[Week 5] Type Confusions

Ofra Magidor – The Last Dogma of Type Confusions (in Proceedings of the Aristotelian Society 109 (1pt1): 1-29 (2009))

Abstract: In this paper I discuss a certain kind of ‘type confusion’ which involves use of expressions of the wrong grammatical category, as in the string ‘runs eats’. It is (nearly) universally accepted that such strings are meaningless. My purpose in this paper is to question this widespread assumption (or as I call it, ‘the last dogma’). I discuss a range of putative reasons for accepting the last dogma: in §II, semantic and metaphysical reasons; in §III, logical reasons; and in §IV, syntactic reasons. I argue that none of these reasons is conclusive, and that consequently we should be willing to question this last dogma of type confusions.

[Week 6] Frege’s Puzzle

Andrew Bacon & Jeffrey Sanford Russell – The Logic of Opacity (manuscript)

Abstract: We explore the view that Frege’s puzzle is a source of straightforward counterexamples to Leibniz’s law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show that these logics are not degenerate.

[Week 7] How Fine-Grained is Reality?

Jeremy Goodman – Reality is Not Structured (forthcoming in Analysis)

Abstract: The identity predicate can be defined using second-order quantification: a 1⁄4 b 1⁄4 df 8FðFa $ FbÞ. Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ’ 1⁄4 df 8XðX’ $ X Þ, where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality?

I will argue that reality is not structured in anything like the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented.

[Week 8] Higher-Order Logic & Modality

Andrew Bacon – The Broadest Necessity (manuscript)

Abstract: In this paper we explore the logic of broad necessity. Definitions of what it means for one modality to be broader than another are formulated, and we prove, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. We show, moreover, that it is possible to give a reductive analysis of this necessity in extensional language (using truth functional connectives and quantifiers). This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. We formulate this conjecture precisely in higher-order logic, and examine concrete cases in which it fails. We end by investigating the logic of broad necessity. It is shown that consistently with higher-order logic, the logic of broad necessity can be anywhere between S4 and Ver; we give some reasons to think that it is strictly weaker than S5.


[Week 9] Propositional Quantification & Truth


MT 2016

We will begin term by reading four papers in the philosophy of language, beginning with Brett Sherman’s Open Questions and Epistemic Necessity. The second four weeks of term will be devoted to the metaphysics of essence. The papers under consideration include:

  1. Open Questions and Epistemic Necessity (Sherman)
  2. Necessary Connections in Context (Kaiserman)
  3. Relative-Sameness and Counterpart Theory (Graff Fara)
  4. On The Dynamics of Conversation (Rothschild & Yalcin)
  5. Generic Essence, Objectual Essence, and Modality (Correia)
  6. Unified Foundations for Essence and Ground  (Fine)
  7. To Be F Is To Be G (Dorr)
  8. To Be F Is To Be G (Dorr)

HT 2016 — Recent Papers

We will continue HT 2016 by reading recent papers in MLE. We will meet in the Ertegun House on Wednesdays from 4-5:30pm. The weekly readings (subject to revision) that have been so far selected are as follows:

  1. (Skipped First Week)
  2. Modal Science (Williamson)
  3. Quantifying In From A Fregean Perspective (Yalcin)
  4. Ideology, Generics and Common Ground (Haslanger)
  5. Evidence and its Limits (Littlejohn)
  6. Credal Dilemmas (Moss)

MT 2015 — Block 1: State Semantics

We will begin MT 2015 by reading four of Kit Fine’s recent papers on truthmaker semantics during the first four weeks of Michaelmas 2015. The weekly readings corresponding to the first four weeks of MT 2015 are as follows:

  1. Survey of Truthmaker Semantics (Fine)
  2. Counterfactuals Without Possible Worlds (Fine)
  3. Truth-Maker Semantics for Intuitionistic Logic (Fine)
  4. Angellic Content (Fine) [Handout]

Meetings will be held this term at 6.00pm every Thursday in the Ertegun, 37a St Giles’.