Tableaux for Lewis’s V-family (Yale Weiss)

The Logic and Metaphysics Workshop will meet on October 15th from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Yale Weiss (GC).

Title: Tableaux for Lewis’s V-family

Abstract: In his seminal work Counterfactuals, David Lewis presents a family of systems of conditional logic—his V-family—which includes both his preferred logic of counterfactuals (VC/C1) and Stalnaker’s conditional logic (VCS/C2). Graham Priest posed the problem of finding systems of (labeled) tableaux for logics from Lewis’s V-family in his Introduction to Non-Classical Logic (2008, p. 93). In this talk, I present a solution to this problem: sound and complete (labeled) tableaux for Lewis’s V-logics. Errors and shortcomings in recent work on this problem are identified and corrected (especially close attention is given to a recent paper by Negri and Sbardolini, whose approach anticipates my own). While most of the systems I present are analytic, the tableaux I give for Stalnaker’s VCS and its extensions make use of a version of the Cut rule and, consequently, are non-analytic. I conjecture that Cut is eliminable from these tableaux and discuss problems encountered in trying to prove this.

Ontological Reductions of First Order Models (Alfredo Freire)

The Logic and Metaphysics Workshop will meet on October 22nd from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Alfredo Freire (Campinas).

Title: Ontological Reductions of First Order Models

Abstract: Since the discovery of the Loweinheim-Skolem theorem, it has been largely held that there is no purely formal way of fixing a model for any first order theory. Because of this, many have focused on having a relative account of models, establishing the expressive power of one model in its ability to internalize models for other theories. One can, for instance, define a plurality of models for PA from a given model for ZF, and this may be understood as evidence for the ontology of arithmetics being reducible to the ontology of set theory. In this presentation, I argue that a close attention to what it means to reduce an ontology shows that methods of reduction are generally not neutral and make it possible for weaker models to reduce stronger ones. For this, I analyze the known model-theoretical reduction of NBG into ZF proved by Novak, showing that a more demanding method makes it impossible for ZF to internalize NBG. We finish this presentation by showing how this view, together with some technical results, provide a positive account in defense of the multiversalist perspective on set theory.

Inconsistency and the Sorites Paradox (Otávio Bueno)

The Logic and Metaphysics Workshop will meet on October 1st from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Otávio Bueno (Miami).

Title: Inconsistency and the Sorites Paradox

Abstract: The Sorites paradox offers an unsettling situation in which, in light of its premises and the apparent validity of the argument, one may be inclined to take the argument to be sound. But this entails that vague concepts, ubiquitous and indispensable to express salient features of the world, are ultimately inconsistent, or at least the application conditions of these concepts seem to lead one directly into contradiction. In what follows, I argue that this inconsistent understanding of vagueness is difficult to resist, but it is also hard to accept. First, I point out that a number of approaches to vagueness that try to resist this conclusion ultimately fail. But it is also difficult to accept the inconsistency approach. After all, vague concepts do not seem to be inconsistent. Second, even if the inconsistency view turned out to be true, the phenomenology of vague concepts (and such concepts, after all, do not seem to be inconsistent at all) can be accommodated. Contextual factors force one to apply inconsistent concepts consistently by arbitrarily resisting to apply the concepts once a locally determined threshold is met. This yields the impression that vague concepts are consistent. As a result, in light of the apparent non-inconsistent nature of vagueness, on the one hand, and the Sorites argument that supports the opposite view, on the other, it is unclear how to establish whether vague concepts ultimately are inconsistent or not. This explains why the Sorites paradox, despite centuries of reflection, does not go away, and why it is unclear how to settle, in one way or another, a significant aspect of the nature of vagueness.

The Quantified Argument Calculus, with Application to the Barcan Formulas and Necessary Existence (Hanoch Ben-Yami)

The Logic and Metaphysics Workshop will meet on September 24th from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Hanoch Ben-Yami (CEU).

Title: The Quantified Argument Calculus, with Application to the Barcan Formulas and Necessary Existence

Abstract: I present a logic system I recently developed (RSL 2014), the Quantified Argument Calculus or Quarc. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, on any of its versions, and it is no less powerful than the first-order Predicate Calculus. This makes analysing the Barcan formulas and necessary existence by its means particularly interesting. As we shall see, the analogues in Quarc of the Barcan formulas and their converses are straightforwardly invalid. And, since quantification and existence in Quarc come apart, existence isn’t logically necessary. The issues with both the Barcan formulas and necessary existence were an artefact of a specific formal language, the Predicate Calculus, and they are eliminated once it is replaced by a formal language with a claim of providing an improved representation of the logic of Natural Language.

Applying Causal Modeling to Philosophical Issues (Sander Beckers)

The Logic and Metaphysics Workshop will meet on September 17th from 4:15-6:15 in room 4419 of the CUNY Graduate Center for a talk by Sander Beckers (Utrecht).

Title: Applying Causal Modeling to Philosophical Issues

Abstract: Causal modeling was developed within Artificial Intelligence over the last few decades in order to formally capture causal information, which is notably absent from statistics. Aside from the undeniable impact this has had on Artificial Intelligence, where talk of causal networks has become commonplace, the resulting formalisms were also eagerly picked up by philosophers working on causation. In particular, causal modeling has been used rather successfully in constructing formal definitions of actual causation, aka token causation. Given that actual causation occupies a crucial role in many issues in philosophy, causal modeling is a helpful tool to anyone studying those issues, that much is obvious. However, I argue that even in the absence of any definition of causation, causal modeling can still be put to significant use in order to resolve these issues. Concretely, my talk will consist of three parts. First I introduce my own definition of causation using causal models. Second I illustrate how causal models can be used to clarify and possibly settle the debate about Frankfurt-style cases and the Principle of Alternative Possibilities. Third I use causal models to sketch the position of non-reductive physicalism, and show how this allows it to tackle the famous Exclusion Argument.

Fall 2018 Schedule

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 6494 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:

Sep 3. GC CLOSED. NO MEETING

Sep 10. GC CLOSED. NO MEETING

Sep 17. Sander Beckers, Utrecht

Sep 24. Hanoch Ben-Yami, CEU

Oct 1. Otavio Bueno, Miami

Oct 8. GC CLOSED. NO MEETING

Oct 15. Yale Weiss, GC*

Oct 22. Alfredo Freire, Campinas*

Oct 29. Boris Kment, Princeton

Nov 5. Melissa Fusco, Columbia

Nov 12. Amy Seymour, Fordham

Nov 19. Andrew Tedder, UConn

Nov 26. Justin Bledin, Johns Hopkins

Dec 3. Suki Finn, Southampton

Dec 10. Byong Yi, Toronto

(* indicates change to original schedule)

To What Extent is a Group an Individual? (Rohit Parikh)

The Logic and Metaphysics Workshop will meet on May 14th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Rohit Parikh (CUNY).

Title: To What Extent is a Group an Individual?

Abstract: Dennett in his Darwin’s Dangerous Idea (1995) and Kinds of Minds (1996) discusses an evolutionary hierarchy of intellectual progress. He calls the hierarchy the ‘Tower of Generate-and-Test,’ where there are five kinds of creatures.  These range from  ‘Darwinian creatures,’ organisms which are blindly generated and field-tested, to Popperian creatures which can make plans,  to creatures like human beings who use ‘language’ to communicate with others like them. One could ask, “at what level, if any, do groups belong” if indeed we can regard them as individuals or as intentional beings?  Since they do use language, one would think, they are creatures of this last level.  But difficulties arise in thinking of groups as even Popperian. In order for a group to have a real identity, it needs coherence in its “views” and in its actions.  To think of it as a game theoretic opponent (or partner) one needs a certain amount of predictability. Such predictablility is not always absent.  We know quite well how “Russia,” thought of as an agent, will respond in case of a nuclear attack.  But “the Republican party” or “Republicans in Congress” might be less predictable in their response to say the election of Conor Lamb. Two kinds of theoretical issues thus arise. One is epistemic coherence which can exist only if the group possesses mechanisms for intra-group communication.   An army preparing to wage a battle needs scouts to gather information and to transmit it to troops.  A university needs an internal email system. The other is exhibiting coherence of views where issues like the Arrow theorem or the judgment aggregation paradox may arise.  A group where power is more concentrated, at the extreme in one individual, is likely to be more predictable and more consistent in its response.   It applies less to a more diverse group like the Democratic party. So a better question to ask than “do groups exist?” is “to what extent is a given set of individuals (with a name) an individual, and on what issues?”  In other words we suggest an algorithmic and game theoretic alternative to the ontological question.  We will offer some answers while avoiding a surfeit of mathematics.​

The Reduction of Necessity to Essence (Andreas Ditter)

The Logic and Metaphysics Workshop will meet on May 7th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Andreas Ditter (NYU).

Title: The Reduction of Necessity to Essence

Abstract: In ‘Essence and Modality’, Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view ‘Fine’s Thesis’. On its intended interpretation, the view takes for granted a notion of essence that is not analyzable in terms of metaphysical necessity. It can thus be understood as an analysis of metaphysical necessity in terms of an independently understood notion of essence. In this talk, I examine Fine’s Thesis in the context of  Fine’s logic of essence (LE). I consider different ways in which the view might be developed, investigate their philosophical tenability and make precise how the plausibility of the thesis is dependent on general essentialist principles. I argue that Fine’s own development of the view, which rests on the assumption that metaphysical necessity obeys the modal logic S5, is incompatible with an independently plausible essentialist principle. I show that we can still retain S5 for metaphysical necessity by adopting a theory that is slightly weaker than Fine’s. I will conclude, however, that the most promising defense of Fine’s Thesis in the context of LE involves the adoption of a theory in which the logic of metaphysical necessity is exactly S4, not S5.

World-Relative Truth and Pre-Worldly Truth (Sungil Han)

The Logic and Metaphysics Workshop will meet on April 30th from 4:15-6:15 in room 3309 of the CUNY Graduate Center for a talk by Sungil Han (Seoul National University).

Title: World-Relative Truth and Pre-Worldly Truth

Abstract: The problem of contingent existence – the problem of how an actual individual, say Socrates, could have not existed – has been a thorny problem in actualist theorists of modality. To solve the problem, Robert Adams divides world-relative truth into truth-in-a-world and truth-at-a-world and proposes that Socrates’s nonexistence is possible in the sense that his nonexistence is true at some possible world, not in some possible world. Adams’s solution relies on a semantic principle by which to determine what are true at a world, but, as he noted himself, the semantic principle leads to implausible consequences. My aim in this talk is to offer a solution along the line of Adams’s proposal without relying on his semantic principle. The fundamental limitation of Adams’s proposal is that his semantic principle is intended to determine what propositions are true at a world, but he provides no proper account of what it means to say that a proposition is true at a world. I offer an account of the notion of truth-at-a-world: to say that a proposition p is true at a world w is to say that the supposition of p is a precondition for w to perform its representational function qua a world-story in the sense that we need to suppose that p if we are to take w to be a world-story. Then I argue that propositions of identity, nonidentity and essences about all actual individuals are true at any world, which vindicates the view, notably espoused by Kit Fine, that these ‘pre-worldly’ truths are unqualifiedly necessary truths.

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