## Logic & Metaphysics Spring 2016 Schedule

**Logic and Metaphysics Workshop**

**Program, Spring 2016**

**Mondays, 4.15-6.15. Room 6421, Graduate Center**

**February 22 ** Mark **Sainsbury**, U Texas, Austin, “Something” (Abstract below)

**February 29** Dave **Ripley**, UConn “Classical Recapture *via* Conflation” (Abstract below)

**March 7** Filippo **Casati**, St Andrews “(Para-)Foundationalism” (Abstract below)

**March 14** Suki **Finn**, York “What’s the problem with adopting a logical rule?” (Abstract below)

**March 21 **Daniel **Hoek**, NYU “Mathematics as a Metaphor” (Abstract below)

**March 28** Charles **Goodman**, SUNY Binghamton “Non-Supervenient Relations, Buddhist Conventionalism, and the Concealed Radicalism of Stage Theory” (Abstract below)

**April 4** Harvey **Lederman**, NYU “Some Recent Work on the Prospects of Naïve Set Theories” (Abstract below)

**April 11** Tommy **Kivatinos**, GC “Grounding, Dependence and the Myth of Ontological Priority” (Abstract below)

**April 18** Matthias** Jenny**, MIT “The ‘If’ of Relative Computability” (Abstract below)

April 26 *No meeting Spring Recess*

**May 2** Federico** Pailos**, Buenos Aires “A Recovery Operator for Non-transitive Theories” (Abstract below)

**May 16** Asya** Passinsky**, NYU “A Response-Dependent Theory of Social Objects” (Abstract below)

The workshop is organized by Graham Priest

Monday **14 May**, 4.15-6.15

Asya **Passinsky**, NYU

**A Response-Dependent Theory of Social Objects**

Room 6421, CUNY Graduate Center

*Abstract*: It appears that under appropriate circumstances, certain people can create “social objects” such as borders, money and states by acts of agreement, decree, declaration and the like. For example, two people on an island can create a border by agreeing that a certain river is to demarcate their respective territories. I develop a theory of social objects that can account for these apparent facts concerning their creation. There are two main ideas. The first is that social objects are a subclass of artifacts, and the creation of artifacts of all kinds involves the intentional conferral of a new property (or properties) onto a pre-existing object (or objects). The second is that what distinguishes social objects from ordinary material artifacts is that one of the conferred properties is a social role, which is response-dependent in a sense that I will flesh out.

Monday **2 May**, 4.15-6.15

Federico **Pailos**, Buenos Aires

**A Recovery Operator for Non-transitive Theories**

Room 6421, CUNY Graduate Center

*Abstract: *I will present a way to expand some non-transitive theories in order to recover cautious versions of Cut. I will show how to do this for ST in a direct way. The resulting logic, STcon (ST with a consistency operator), will be non-trivial, and also sound and complete with respect to a disjunctive three-side sequent system called LSCcon. The way to do the same thing with ST+ (ST with a transparent truth predicate) is not that straightforward. In order to accomplish our goal, we need to change the self-referential procedure, from a Strong to a Weak one. I will show that the resulting theory, ST*, is not only non-trivial, but sound and complete with respect to the proof system LSC*.

Monday** 18 April**, 4.15-6.15

Matthias** Jenny**, MIT

**The ‘If’ of Relative Computability**

Room 6421, CUNY Graduate Center.

*Abstract:*** **I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as

- If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,

which is true, and

- If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,

which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models.

Monday** 11 April**, 4.15-6.15

Tommy **Kivatinos**, Graduate Center

*“*Grounding, Dependence and the Myth of Ontological Priority”

Room 6421, CUNY Graduate Center

*Abstract: *Grounded entities seem to ontologically depend in some way upon the entities that ground them and thus one might think that grounding just is ontological dependence. Alternatively, there might be reasons to think that these relations resemble one another but are fundamentally distinct. I assess two crucial reasons for thinking they are indeed distinct in order to pinpoint what I consider to be plausible and implausible responses to this issue. Further, I seek to address a connected question that arises in this discussion; a question about whether not one needs to posit the phenomenon of ontological priority. Concerning what I argue is a plausible way to distinguish ontological dependence from grounding, I argue as follows: grounding cannot be defined modally and thus it is a “more-than-modal” dependence relation whereas ontological dependence can be defined modally and thus it is a “merely-modal” dependence relation. Concerning what I argue is an implausible way to distinguish these relations, I address the claim that grounding imposes ontological priority upon its relata whereas ontological dependence does not. Against this claim, I argue that upon close inspection it turns out to be implausible that grounding imposes ontological priority. This is because, surprisingly enough, there is no need to even posit the phenomenon of ontological priority in the first place. For the theoretical role for which ontological priority is posited is fulfilled by just the more-than-modal dependence relation itself independently of ontological priority. Thus the discussion not only serves to identify plausible and implausible reasons to distinguish grounding from ontological dependence, but also leads to the (potentially shocking) idea that ontological priority is an un-needed posit.

Monday** 4 April**, 4.15-6.15

Harvey **Lederman**, NYU

**Some Recent Work on the Prospects of Naïve Set Theories**

Room 6421, CUNY Graduate Center. [This is on the 6th floor, but it’s tucked away in a cul-de-sac, so be prepared for a bit of a wander til you find it.]

*Abstract*: In naïve set theory, every property is taken to define a set; the principle which formalizes this idea is called the naïve comprehension schema. Russell famously showed that naïve set theory is inconsistent in classical logic. The axiomatic system of Zermelo-Fraenkel plus Choice fixes the problem by replacing naïve comprehension with a weaker comprehension schema. On a first encounter, the restriction on the comprehension principle can seem *ad hoc*; it’s natural to wonder whether something more closely approximating the the naïve theory can be saved from paradox. In this talk I’ll present the highlights of two recent projects which investigate different ways of building a non-trivial set theory based on the naïve conception of a set. The first weakens the background logic to avoid Russell’s paradox, with the hope that naïve comprehension (together with an axiom of extensionality) will be consistent (this is joint work with Hartry Field and Tore Fjetland Øgaard). The second considers a version of comprehension which is restricted to modalized formulas (this is joint work with Peter Fritz, Tiankai Liu and Dana Scott). The second approach can be motivated by fictionalist theories of mathematics: the modal operator is interpreted as “according to the fiction”; the modalized formulas are thus the ones which describe the mathematical fiction.

Monday** 28 March**, 4.15-6.15

Charles **Goodman**, SUNY Binghampton

**Non-Supervenient Relations, Buddhist Conventionalism, and the Concealed Radicalism of Stage Theory**

Room 6421, CUNY Graduate Center. [This is on the 6th floor, but it’s tucked away in a cul-de-sac, so be prepared for a bit of a wander til you find it.]

*Abstract: *Since stage theory denies that I am identical to anyone in the past or in the future, we might think that this account of persistence would have radically revisionary practical and normative implications. Katherine Hawley attempts to block these implications by positing non-supervenient relations between stages, each of which generates what Parfit would call a ‘deep further fact’ about which person in the past is the same person as me now. The existence of these relations is supported by two impressive arguments from the philosophy of physics. Yet when examined carefully, these arguments do not succeed. Moreover, there is another, quite different view, Buddhist Conventionalism, that can match the flexibility of stage theory and that has no need for non-supervenient relations. The two main versions of this view have potentially revisionary practical implications of their own, but these may be more acceptable than they appear at first glance.

Monday **21 March**, 4.15-6.15

Daniel **Hoek**, NYU

**Mathematics as a Metaphor**

Room 6421, CUNY Graduate Center. [This is on the 6th floor, but it’s tucked away in a cul-de-sac, so be prepared for a bit of a wander til you find it.]

*Abstract*: Scientists and the folk constantly use mathematics in describing the world. How can it be that reference to mathematical entities facilitates the description of concrete reality? The puzzle is especially vexing to the nominalist, who denies that mathematical objects even exist. But even mad-dog Platonists ought to ask themselves from time to time how it can be that investigations of remote and causally inert abstracta can serve a practical purpose.

In an attempt to address the question, Stephen Yablo proposed that our use of mathematics to describe the concrete world around us is just like our use of metaphors to do the same. While that’s an intriguing suggestion, it’s not all that illuminating unless we have an account of how, precisely, the relevant class of metaphors work. In this talk, I try to supply such an account. I’ll outline, in formal terms, a transformation on propositions that, at the same time, explains how relevant information is extracted from the metaphors we wrap them in, and how purely concrete information is extracted from the partly mathematical statements we use to present it. I will also prove a conservativity result, stating (roughly) that derivations involving reference to mathematical objects retain their classical validity after they’ve been transformed in this way into a sequence of propositions about the concrete world.

Monday **14 March**, 4.15-6.15

Suki **Finn**, York

**What’s the problem with adopting a logical rule?**

*Abstract*: There have been many ways to understand what the Tortoise taught us in Carroll’s puzzle, “What the Tortoise Said to Achilles”. Quine famously used the puzzle as a “regress problem” against Carnap to show that the logical rules cannot be true by convention. More recently, Kripke has interpreted the puzzle as an “adoption problem” (coined by Padro) which he uses against Quine to show that the logical rules cannot be empirical. I will argue that Carroll’s puzzle, the regress problem, and the adoption problem, are distinct, and that we learn different lessons from each. The aim of this paper is to map out the debates between Kripke, Quine, and Carnap, in order to show that Kripke’s adoption problem is far further reaching than originally considered. I will show how the problem of adopting a logical rule arises whether we take the rules to be empirical (in Quine’s sense) *or* analytic (in Carnap’s sense), demonstrating that the adoption problem does not discriminate among different interpretations of the status or justification of logical rules. Rather, there is a far more fundamental issue with adopting a logical rule that cannot be resolved by appeal to how we justify our logic. The fundamental issue in the adoption problem is the role that logical rules play in our practice of making inferences. So, the problematic element in adoption is the application, rather than the acceptance or justification, of the logical rules. What we need to do to move forward then is understand what is going on when we make inferences, in a way that doesn’t require a problematic role for rule-following, where the rules are construed as neither analytic in Carnap’s sense or empirical in Quine’s sense. I will briefly gesture at a way to do this at the end of the paper, once the fundamental problem with adopting a logical rule has been extracted from looking at the works of Carroll, Kripke, Padro, Quine, and Carnap.

Monday **7 March** , 4.15-6.15

Filippo **Casati**, St Andrews

**(Para-)Foundationalism**

*Abstract*: In the contemporary literature, the relation between what is grounded and what grounds has been spelled out in many different ways. As Bliss and Priest have shown in ‘*Metaphysical Dependence, East and West’* (forthcoming), given some basic structural properties, it is possible to draw a complete taxonomy, which classifies all the possible accounts of grounding relations in three main categories: **[1]** Foundationalism **[2]** Coherentism and **[3]** Infinitism. Even though these three categories present very different theories of grounding, they have a common feature: they are all consistent theories.

My talk will discuss two new grounding theories (called *para-foundationalism 1* and *para-foundationalism 2*), which do not fit in Bliss and Priest’s taxonomy because they are inconsistent (but non-trivial).

Monday** 29 February**, 4.15-6.15

Dave** Ripley**, UConn

**“Classical Recapture via Conflation”**

*Abstract*: Theories based on nonclassical logics face an explanatory burden: why, if classical logic validates arguments that are really invalid, has it proven so successful in so many applications? A usual way to discharge this burden involves “classical recapture”: showing that all classically-valid arguments have some positive status, even if it is not full validity. For example, perhaps they are enthymematically valid, or valid in a certain restricted range of situations, or valid when certain vocabulary is not involved, or cetera.

One distinctive approach to classical recapture (in the context of a nonclassical theory of truth) has been recently pursued by Edwin Mares and Francesco Paoli. According to them, classical logic is an “ambiguous” logic, one that fails to recognize the distinction between “additive” and “multiplicative” versions of the familiar binary connectives. However, it is not otherwise mistaken. That is, classical logic’s only mistakes stem from its conflating additive and multiplicative connectives.

In this talk, I will consider two ways of making this claim precise. I will argue that Mares and Paoli’s own way of understanding this claim, based on the Grishin-Ono translation of classical into linear logic, does not work, as it requires a number of fine distinctions to be drawn between what is supposedly conflated. I will provide a different formal setting of their claim, one that I take to be truer to their informal remarks, and explore some of the ups and downs of the resulting overall theory.

Monday** 22 February**, 4.15-6.15

Mark **Sainsbury**, University of Texas at Austin

**“Something”**

*Place*: Room 6421, CUNY Graduate Center. [*This is on the 6th floor, but it’s tucked away in a cul-de-sac, so be prepared for a bit of a wander til you find it.*]

*Abstract*: “Something” works in a way quite different from the existential quantifier of first order logic. It does not “range over” a domain, and quantifies into a wide variety of grammatical positions, not just positions fit to be occupied by names. The upshot is that the intuitive truth of “something”-sentences is no guide to ontology. Quite independently of ontological scruples, this undermines attempts to explain intensional idioms by appealing to nonexistent objects as entities over which “something” quantifies.