Two proof-systems P and P* are said to be complementary when one proves exactly the non-theorems of the other. Complementary systems come as a particular kind of refutation calculi whose patterns of inference always work by inferring unprovable conclusions form unprovable premises. In the first part of my talk, I will focus on LK*, the sequent system complementing Gentzen’s system LK for classical logic. I will show, then, how to enrich LK* with two admissible (unary) cut rules, which allow for a simple and efficient cut-elimination algorithm. In particular, two facts will be highlighted: 1) for any given provable sequent, complementary cut-elimination always returns one of its simplest proofs, and 2) provable LK* sequents turn out to be “deductively polarized” by the empty sequent. In the second part, I will observe how an alternative complementary sequent system can be obtained by slightly modifying the Gentzen-Schütte system G3. I will finally show how this move could pave the way for a novel approach to multi-valuedness and proof-theoretic semantics for classical logic.
Russell proved over a century ago that a naive conception of structured propositions is inconsistent. Hodes (2015), Dorr (2016), and Goodman (2017) have recently reformulated Russell’s argument in the language of higher-order logic, and concluded from it that distinctions in reality cannot always reflect all the syntactic structure of the language in which we draw those distinctions. But they also float the idea that such distinctions might nevertheless have sentence-like structure, so long as this structure fails to neatly correspond to the syntactic structure of the sentences we use to draw those distinction. Perhaps, that is, the popular metaphor of facts being like sentences written in God’s “book of the world” is tenable after all. In this talk I’ll give a way of making this metaphor precise, and prove a new limitative result showing that, given natural assumptions, it too is inconsistent.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
Two ways of giving an epistemic justification of basic logical principles will be introduced, intuition-based accounts and concept or meaning constitution-based accounts. We will briefly consider different versions of these views and argue that they face parallel dilemmas. While ‘robust’ accounts are subject to what I call the ‘adoption problem,’ ‘weak’ accounts fail to ground our basic inferential dispositions. Either way, intuitions and meaning-constituting rules turn out to be irrelevant. A more general moral for the epistemology of logic and its priorities will be drawn from the discussion.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
Abstract: I provide a truth-maker semantics for the conditional and consider the application to imperative and deontic conditionals.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
In my talk I argue for the thesis CT: contradiction is the norm of truth, and ask about its relevance for contemporary philosophical logic. I first present three positions in the history of philosophy that have advocated some versions of CT, namely Plato’s idea of the “dialectical gymnastics” in the Parmenides (Plato, Parmenides 136 B-E), Aristotle’s notion of dialectics in the Topics (Aristotle, Topics I, 2-3) and Metaphysics (Aristotle, Met III 1, 995 a 24-29), and Hegel’s contradictio est regula veri (Hegel Werke 2, 533), then derive from them some answers to the questions:
What is meant by “contradiction” in CT?
What is meant by “truth” in CT?
What is meant by “norm” in CT?
I will show that to examine the meaning of CT in historical perspective is useful to understand the seeds of genuine glut theories.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
In this talk I will do three things. First: I will present the central results from Barrio, Pailos and Szmuc’s recent paper “A hierarchy of classical and paraconsistent logics” (forthcoming in the JPL) along with some generalizations derived by observing certain symmetries; second, I will discuss the relation between the strict tolerant logics and classical logic, K3 and LP; third, I will try to convey the exact state of uncertainty about the philosophical significance of the foregoing I find myself in on the day.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
Structural causal models lend themselves to an analysis of counterfactuals – a structural semantics of counterfactuals. The basic idea is that a causal model allows for the clear and precise evaluation of any counterfactual encoded by it. Many argue that a structural semantics is superior to a more traditional similarity semantics, in part due to the latter’s independence from any notion of similarity(Galles & Pearl, 1998; Gallow, 2016; Hiddleston, 2005; Hitchcock, 2018; Pearl, 2000; Starr, 2019). I argue, though, that this is too quick. A similarity semantics employs the notion of similarity to answer what Priest (2018) calls the importation problem– the question of what information is to be held fixed in a counterfactual evaluation. I argue that where similarity semantics relies on an unarticulated notion of similarity, a structural semantics relies on an unarticulated notion of aptness. The superiority of structural semantics depends on its ability to deliver on a principled guide to determining which model(s) is apt. In this talk I go some way towards providing this guide.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7314 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:
Feb 4. Melvin Fitting, CUNY
Feb 11. Benjamin Neeser, Geneva
Feb 18. GC CLOSED. NO MEETING
Feb 25. Achille Varzi, Columbia
Mar 4. Eric Bayruns Garcia, CUNY
Mar 11. Jeremy Goodman, USC
Mar 18. Romina Padro, CUNY
Mar 25. Kit Fine, NYU
Apr 1. Elena Ficara, Paderborn
Apr 8. Chris Scambler, NYU
Apr 15. Jenn McDonald, CUNY
Apr 22. GC CLOSED. NO MEETING
Apr 29. Tommy Kivatinos, CUNY
May 6. Daniel Durante, Natal
May 13. Martina Botti, Columbia
May 20. Vincent Peluce, CUNY
14.30 – 15.30: Kit Fine: A Truthmaker Semantics for Conditional Imperatives
15.30 – 15.45: Coffee Break
15.45 – 16.45: Friederike Moltmann: Underspecification of Attitudes and Truthmaker
Semantics
16.45-17.00: Coffee Break
17.00 – 18.00: Federico Faroldi: Truthmaker Semantics for Justification Logics – Open
Problems (joint work with Tudor Protopopescu)
18.00-18.15: Coffee Break
18.15 – 19.15: Cian Dorr: Truthmaking in the Object Language
K. Fine: A Truthmaker Semantics for Conditional Imperatives
I provide a truth-maker semantics for conditional imperatives and indicate how it might be extended to other conditional constructions.
F. Moltmann: Underspecification of Attitudes and Truthmaker Semantics
It has been argued that the satisfaction conditions of a desire can be underspecified by the complement clause. This provides support for the view according to which the complement clause gives a partial content of the reported desire, where partial content is formulated in terms of truthmaker theory. In this talk, I will discuss the extent of such underspecification and whether it truly supports a truthmaker-based approach to the content of attitudes.
Optional preparatory reading here.
F. Faroldi: Truthmaker Semantics for Justification Logics – Open Problems
Justification logics are a family of logic where "implicit" modal operators are substituted by explicit terms to get formulas of the form t : A, where t could be evidence, a reason, etc. why A is known, believed, obligatory, etc., thus resulting in an “objectual” approach to modalities. In this talk we explore how to give a truthmaker semantics for justification logics, we provide some philosophical reasons to do so, and note some technical open problems.
Cian Dorr: Truthmaking in the Object Language
I consider a simple language with Boolean connectives, sentential variables and quantifiers binding them, and a connective for propositional identity (‘for it to be the case that … is for it to be the case that …’). Using familiar techniques, the possible-worlds model theory for such a language can be ‘internalised’ to derive a theory stated in the language itself, based on the definition of ‘world-proposition’ as ‘maximal consistent proposition’, and this theory can be shown to follow from the theory that propositions form a complete atomic Boolean algebra. In this paper, I will consider to what extent something similar can be done for Fine’s truthmaker semantics. This will involve looking for a way of picking out a class of special propositions to serve as surrogates for the states, and a binary relation among propositions to serve as a surrogate for the verification relation, and using these definitions to rewrite the metalinguistic definition of a model as theory in the object-language. I will make a start at considering to what extent the axioms of this theory can be derived from an independently natural weakening of the theory that propositions form a complete atomic Boolean algebra.