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’.

The MLE blog returns!

Yep, that’s right: this blog is now back in business, in order to provide an online accompaniment to the MLE seminar series, now being run by Natalia Hickman and Neil Dewar. Although we can’t promise reports on the seminars in the manner of Al, we will post announcements of upcoming sessions and links to (Weblearn-held) copies of the reading.

We only have one more session this term: that will be on Wednesday of 8th week (4th December), from 4:30pm-6:00pm in the Colin Matthew Room; the paper will be “The Last Dogma of Type Confusions” by Ofra Magidor (presenter to be announced shortly). Other than that, the sessions from this term have been as follows:

Session 1 (Wednesday 23rd October)

Jonathan Schaffer, “Spacetime the One Substance” (presenter: Neil Dewar)

Session 2 (Wednesday 6th November)

Paul Hovda, “What is Classical Mereology?” (presenter: Josh Parsons)

Session 3 (Wednesday 20th November)

Daniel Greco, “Iteration and Fragmentation” (presenter: Natalia Hickman)

The future of this blog…

… is uncertain. Next term we’re passing on the running of the MLE seminar to James Studd and Andrew Bacon – it’ll be up to them if they want to continue blogging here about our discussions. It’s been fun – thanks everyone/anyone for reading!


Week 8 – Bennett on metametaphysics

In my and Natalja’s final session convening MLE we discussed Karen Bennett’s ‘Composition, colocation, and meta-ontology’, available here. The handout is here.

In this paper, Bennett distinguishes three different versions of the ‘dismissive’ attitude towards metaphysical questions, and asks whether any of them are appropriate in the case of the debates over composition and colocation. She (rightly, we thought) argues that we shouldn’t automatically put all metaphysical debates in the same category – dismissivism might be appropriate for some debates, but inappropriate for others.

The three kinds of dismissivism discussed are ‘anti-realism’, which claims that there is no fact of the matter about the answer to some metaphysical question; ‘semanticism’, which claims that some metaphysical question is ‘merely verbal’, and that the answer to it is analytic in our language (whichever language that is); and ‘epistemicism’, which claims that while a metaphysical question does have a non-analytic answer, we are not currently in a position to judge either way on it. Bennett goes on to argue that, for the debates she considers, semanticism is implausible and epistemicism is a live option. But because she doesn’t say much about anti-realism, the positive arguments for epistemicism seem pretty weak. (I wasn’t really convinced by the negative argument against semanticism either – it boils down to the claim that we can’t define things into existence, which will be denied by anyone with neo-Fregean sympathies.)

The argument for the disjunctive conclusion that either anti-realism or epistemicism is true about the debates considered goes via the claim that these debates are ‘difference-minimizing’. I wasn’t entirely sure what this was meant to mean – does whether a debate is difference-minimizing depend on the intrinsic properties of the issue being debated, or on the participants in the debate, or both? For the argument to lead to any substantive conclusions, I think it must be that the issue is intrinsically such that rational philosophers debating it will tend to difference-minimize – but Bennett on various occasion mentions philosophers (Burke, Rea, Cameron, Parsons) who don’t difference-minimize. Couldn’t this form the basis for a counter-argument? I suppose Bennett has to rely on the claim that these philosophers are just badly mistaken and have misjudged the intrinsic properties of the issue the debate is about. Either way, I thought the notion of ‘difference-minimizing’ was too vague and weak to have a strong metametaphysical conclusion founded on it.

Part of the argument that these debates are intrinsically difference-minimizing seems to be that structurally symmetrical problems arise for both sides of the debates. This feature of the dialectic, if genuine, does seem to be of real metametaphysical interest – someone who wanted to defend a form of structuralism about metaphysics might argue that the different sides agree on the structure of the correct view, which is all there really is to a view, so that they’re not really disagreeing at all (I take it this would amount to a form of anti-realism.) But it’s not clear how this feature gives us much motivation for epistemicism – if the debate really is symmetrical in nature, then the claim that there is an unknowable fact of the matter about which side is right seems dubious. Such a fact of the matter would be ‘metaphysically arbitrary’.

In any case, I wasn’t convinced that the debates are totally symmetric. Bennett argues by induction from 4 cases where a ‘twin’ argument can be given against one of the arguments used by one side, but that’s a pretty weak inductive base. Moreover, one of the examples looks flawed. Bennett argues that the ‘causal exclusion’ or ‘overdetermination’ argument used by the nihilist against the believer in composite objects has a twin argument which works against the nihilist – where a believer would say that a ball broke the window, even though the simples arranged ballwise were causally sufficient for the breaking, the nihilist must accept many pluralities of simples, all of which are causally sufficient to break the window. It doesn’t matter exactly which plurality we settle on. But this doesn’t look like a twin for the causal exclusion problem, it looks like a twin for the problem of the many.

Consider the following case – two simples travelling together jointly break a window. Neither of the simples by itself would have been sufficient for the breaking. The believer, who says that the pair which the simples composed was the object which broke the window, seems vulnerable to the causal exclusion argument; the simples were jointly sufficient, so why postulate the ball as a cause? (I’m assuming the simples aren’t many-one identical to the ball.) But the nihilist seems vulnerable to no analogous argument. There’s only one plurality of simples sufficient for the breaking – both of them. Thus, no causal overdetermination. And the reason there’s no argument against the nihilist here is just that, as I’ve set the case up, the problem of the many can’t get a grip. Hence my suggestion that while the nihilist does face an analogue of the problem of the many, he faces no analogue of the causal exclusion argument.