Working papers in the philosophy of logic
These are papers that are progress (at various stages). If a draft is not posted, feel free to write for a copy.
Inconsistency - Pragmatic, Semantic, Logical, and Metaphysical
commissioned for a forthcoming collection of papers on the semantics/pragmatics divide.
Inconsistency comes in different flavors. Even though `Joe is a father and a credit card account’, `grass is green and it isn’t’, and `Bob is a bigamous bachelor’ are all inconsistent, the type of inconsistency seems quite different. There is nevertheless a pervasive tendency to run these different types of inconsistency together. There is some reason to do so—they can be treated as species of the same general phenomenon—but the reasons for doing so and the details of how to distinguish them are rarely discussed. In my view, the four types listed in the title arise from different ways of contravening the functional role of thought and talk. In particular, the distinctions between them correspond to different types of guarantee that a speaker or believer would incur contravention of functional role.
Characterizing Invariance
Draft
I address a response from (Sagi 2015) to Willian Hanson and Timothy McCarthy's arguments against the invariance critierion for logicality. I argue that we can distinguish "invariance of content" from "invariance of character" and, by doing so, resuscitate a version of Hanson and McCarthy's argument as targeted against content-invariance being sufficient for logicality. I go on to show that invariance of content and character entail general and real world necessity under plausible assumptions.
Redundancy and the Stoic Themata
A historical paper offering an account of the rules of proof (or themata) of the Stoic logicians. I argue that the correct understanding of the Stoics' rejection of redundant arguments suggests that their logic is antimonotonic. I then show how to reconstruct an antimonotonic fragment of their proof system. Copy available on request.
Modest Inferentialism for Classical Logic
Draft
Modest Inferentialism, the view that inferential role fixes the meaning of (at least logical) expressions, against a background grasp of meaning, has had a bit of a checkered history. In this piece, I show discuss problems with this view and criteria for a successful version of it. I show how the best extant version of modest inferentialism, due to James Garson, has trouble with these criteria and discuss what is needed to overcome these problems. To solve them, I develop an interpretation of the formal model-theoretic conditions which Garson-style modest inferentialism generates for the classical rules for the connectives which, in turn, motivates a principled restriction on admissible models. This interpretation satisfies the intuitive criteria for a successful modest-inferentialist account of the meaning of the logical connectives; it is a strong con- tender, I reckon, for an internally satisfying account of the meaning of the logical connectives—and one which does not extend to intu- itionistic logic. This last point furnishes a not entirely disreputable argument against intuitionistic logic
These are papers that are progress (at various stages). If a draft is not posted, feel free to write for a copy.
Inconsistency - Pragmatic, Semantic, Logical, and Metaphysical
commissioned for a forthcoming collection of papers on the semantics/pragmatics divide.
Inconsistency comes in different flavors. Even though `Joe is a father and a credit card account’, `grass is green and it isn’t’, and `Bob is a bigamous bachelor’ are all inconsistent, the type of inconsistency seems quite different. There is nevertheless a pervasive tendency to run these different types of inconsistency together. There is some reason to do so—they can be treated as species of the same general phenomenon—but the reasons for doing so and the details of how to distinguish them are rarely discussed. In my view, the four types listed in the title arise from different ways of contravening the functional role of thought and talk. In particular, the distinctions between them correspond to different types of guarantee that a speaker or believer would incur contravention of functional role.
Characterizing Invariance
Draft
I address a response from (Sagi 2015) to Willian Hanson and Timothy McCarthy's arguments against the invariance critierion for logicality. I argue that we can distinguish "invariance of content" from "invariance of character" and, by doing so, resuscitate a version of Hanson and McCarthy's argument as targeted against content-invariance being sufficient for logicality. I go on to show that invariance of content and character entail general and real world necessity under plausible assumptions.
Redundancy and the Stoic Themata
A historical paper offering an account of the rules of proof (or themata) of the Stoic logicians. I argue that the correct understanding of the Stoics' rejection of redundant arguments suggests that their logic is antimonotonic. I then show how to reconstruct an antimonotonic fragment of their proof system. Copy available on request.
Modest Inferentialism for Classical Logic
Draft
Modest Inferentialism, the view that inferential role fixes the meaning of (at least logical) expressions, against a background grasp of meaning, has had a bit of a checkered history. In this piece, I show discuss problems with this view and criteria for a successful version of it. I show how the best extant version of modest inferentialism, due to James Garson, has trouble with these criteria and discuss what is needed to overcome these problems. To solve them, I develop an interpretation of the formal model-theoretic conditions which Garson-style modest inferentialism generates for the classical rules for the connectives which, in turn, motivates a principled restriction on admissible models. This interpretation satisfies the intuitive criteria for a successful modest-inferentialist account of the meaning of the logical connectives; it is a strong con- tender, I reckon, for an internally satisfying account of the meaning of the logical connectives—and one which does not extend to intu- itionistic logic. This last point furnishes a not entirely disreputable argument against intuitionistic logic
Working papers in Metaethics, Metaphysics, and the Philosophy of Language
On Vacuous Grounding: The Case Study of Ethical Autonomy
I introduce and motivate the notion of vacuous grounding. The occurrence of a fact q in a set of grounds for some fact p is vacuous when any fact could have done the work q does in grounding p. This notion turn out to be useful in cashing out metaphysical intuitions about what grounds what. I start my investigation with a lengthy case study: how to formulate the autonomy of the ethical. This is the view that we cannot ''get'' an ethical fact from a natural fact. Following recent work by Barry Maguire, we can make sense of this by saying that no ethical fact is fully grounded in natural facts and that any fact partially grounded by ethical facts is ethical. I show that this is false---natural facts can be partially grounded in ethical facts---but that natural facts cannot be non-vacuously grounded in ethical facts. We can better characterize the autonomy of the ethical from the natural in terms of vacuous grounding and resolve several other difficulties, such as characterizing Ronald Dworkin's view of the law; distinguishing between basic and non-basic values, and resolving a paradox of grounding due to Kit Fine and Stephen Kramer.
Footing the Cost (of Normative Subjectivism) . Draft
I attempt to articulate general criticisms of the view that normative claims are contingent and show that plausible subjectivist views can easily avoid violating the intuitions driving these criticisms without abandoning the intuitive virtues of their view. Much of the paper is dedicated to explaining the different senses in which normativity might be contingent.
Emptying a Paradox of Ground Draft
I show that applying a distinction between vacuous and non-vacuous grounds (which I describe in detail in "On Vacuous Grounding: The Case Study of Ethical Autonomy") allows us to give a principled solution to Kit Fine and Stephen Kramer's paradox of (reflexive) ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer's paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account.
Epistemic Teleology is the view that epistemic normativity is explained by facts about value, broadly construed. It comes in two familiar versions which differ about whether the normative status of any given epistemic state is explained directly in
terms of the epistemic value of that state, or, alternatively, directly in terms of its practical value. Both versions face compelling counterexamples. We here develop an indirect alternative. We distinguish two normative properties: fittingness and criticism-worthiness. Fittingness is a property of epistemic attitudes such as beliefs or credences, or sets thereof. The mark of a genuine normative standard, however, is criticism-worthiness for failure to meet the standard. We argue that this view enjoys many of the advantages of familiar versions of epistemic teleology, without suffering from their shortcomings.
On Vacuous Grounding: The Case Study of Ethical Autonomy
I introduce and motivate the notion of vacuous grounding. The occurrence of a fact q in a set of grounds for some fact p is vacuous when any fact could have done the work q does in grounding p. This notion turn out to be useful in cashing out metaphysical intuitions about what grounds what. I start my investigation with a lengthy case study: how to formulate the autonomy of the ethical. This is the view that we cannot ''get'' an ethical fact from a natural fact. Following recent work by Barry Maguire, we can make sense of this by saying that no ethical fact is fully grounded in natural facts and that any fact partially grounded by ethical facts is ethical. I show that this is false---natural facts can be partially grounded in ethical facts---but that natural facts cannot be non-vacuously grounded in ethical facts. We can better characterize the autonomy of the ethical from the natural in terms of vacuous grounding and resolve several other difficulties, such as characterizing Ronald Dworkin's view of the law; distinguishing between basic and non-basic values, and resolving a paradox of grounding due to Kit Fine and Stephen Kramer.
Footing the Cost (of Normative Subjectivism) . Draft
I attempt to articulate general criticisms of the view that normative claims are contingent and show that plausible subjectivist views can easily avoid violating the intuitions driving these criticisms without abandoning the intuitive virtues of their view. Much of the paper is dedicated to explaining the different senses in which normativity might be contingent.
Emptying a Paradox of Ground Draft
I show that applying a distinction between vacuous and non-vacuous grounds (which I describe in detail in "On Vacuous Grounding: The Case Study of Ethical Autonomy") allows us to give a principled solution to Kit Fine and Stephen Kramer's paradox of (reflexive) ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer's paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account.
Epistemic Teleology is the view that epistemic normativity is explained by facts about value, broadly construed. It comes in two familiar versions which differ about whether the normative status of any given epistemic state is explained directly in
terms of the epistemic value of that state, or, alternatively, directly in terms of its practical value. Both versions face compelling counterexamples. We here develop an indirect alternative. We distinguish two normative properties: fittingness and criticism-worthiness. Fittingness is a property of epistemic attitudes such as beliefs or credences, or sets thereof. The mark of a genuine normative standard, however, is criticism-worthiness for failure to meet the standard. We argue that this view enjoys many of the advantages of familiar versions of epistemic teleology, without suffering from their shortcomings.
Work no longer intended for publication
Reply to Skorupski (superceded by a very nice paper of Sebastian Koehler's in JESP)
On behalf of Mark Schroeder's expressivist account set out in his Being For, I point out that John Skorupski's objections in "The Frege--Geach objection to expressivism: still unanswered" are misplaced. Skorupski confuses what Schroeder needs - a mapping from normative language to mental states - with a mapping from mental states to normative language, a mapping that no expressivist or semantic account could or should give. This arises, I think, from Skorupski's conflation of the intuitive notion of being for in the sense of being pro with the stipulated notion of being for that Schroeder works with.
Reply to Skorupski (superceded by a very nice paper of Sebastian Koehler's in JESP)
On behalf of Mark Schroeder's expressivist account set out in his Being For, I point out that John Skorupski's objections in "The Frege--Geach objection to expressivism: still unanswered" are misplaced. Skorupski confuses what Schroeder needs - a mapping from normative language to mental states - with a mapping from mental states to normative language, a mapping that no expressivist or semantic account could or should give. This arises, I think, from Skorupski's conflation of the intuitive notion of being for in the sense of being pro with the stipulated notion of being for that Schroeder works with.
