- Department of Philosophy,
2210 Speedway,
WAG 316,
Stop C3500
Jon Litland
The University of Texas at Austin, Philosophy, Faculty Member
- I'm an associate professor at the University of Texas at Austin. Before that I was a post.doc at the "Plurals, Predi... moreI'm an associate professor at the University of Texas at Austin. Before that I was a post.doc at the "Plurals, Predicates and Paradox" project directed by prof. Øystein Linnebo at the University of Oslo. My main areas of research are metaphysics and the philosophy of logic.
In metaphysics I'm particularly interested in metaphysical grounding, especially logical issues in connection with grounding. I'm also very interested in the question of combining logics and what light this might throw on metaphysical issues. I'm working on combining logics for vagueness and mathematical modality with logics for metaphysical modality. I'm also interested in the notion of essence and its connection to modality.
In the philosophy of logic my main interest has been proof-theoretic semantics in the style of Dummett-Prawitz. I'm also very interested in the notion of indefinite extensibility.edit
Many authors have proposed that grounding is closely related to metaphysical laws. However, we argue that no existing theory of metaphysical laws is sufficiently general. In this paper we develop a general theory of grounding laws,... more
Many authors have proposed that grounding is closely related to metaphysical laws. However, we argue that no existing theory of metaphysical laws is sufficiently general. In this paper we develop a general theory of grounding laws, proposing that they are generative relations between pluralities of propositions and propositions. We develop the account in an essentialist language; this allows us to state precisely the sense in which grounding might be reduced to laws. We then put the theory to use in showing how moral laws can play a role in grounding particular moral facts, in defending monism about ground, and in showing in what sense there is no gap between the grounds and the grounded. Finally, we make a novel proposal about what grounds facts about ground.
Research Interests:
This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic... more
This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations.
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This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical... more
This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground.
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This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical... more
This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground.
Research Interests:
I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero-grounded. First, the Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying... more
I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero-grounded. First, the Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this framework to give a definition of identity, and show how the central features of the identity relation can be deduced from this definition.
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Wilhelm has recently shown that widely accepted principles about immediate ground are inconsistent with some principles of propositional identity. This note responds to this inconsistency by developing two ground-theoretic accounts of... more
Wilhelm has recently shown that widely accepted principles about immediate ground are inconsistent with some principles of propositional identity. This note responds to this inconsistency by developing two ground-theoretic accounts of propositional individuation. On one account some of the grounding principles are incorrect; on the other account, the principles of propositional individuation are incorrect.
Research Interests: Philosophy and Analysis
Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of... more
Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper-drawing on graph-theoretic and topological ideas-I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that there is no unique method of decycling. An important upshot is that the notion of asymmetric ground may be indeterminate. Grounding is therefore not so much like covering all the bases as like having a leg to stand on Stephen Yablo [16]
Research Interests:
Grounding is bicollective if it is possible for some truths δ0, δ1, … to be grounded in the some truths γ0, γ1, …. without its being the case that each δi is grounded in some subcollection of γ0, γ1, …. This paper shows how to do... more
Grounding is bicollective if it is possible for some truths δ0, δ1, … to be grounded in the some truths γ0, γ1, …. without its being the case that each δi is grounded in some subcollection of γ0, γ1, …. This paper shows how to do develop a (hyper)graphtheoretic account of bicollective ground, taking the notion of immediate ground as basic. I also indicate how bicollective ground helps with formulating mathematical structuralism.
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This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ... more
This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.
Research Interests:
[Extract] How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality... more
[Extract] How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model‐theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.1 We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists
Research Interests:
A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a... more
A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground (plg) can be extended to the many-many case, giving rise to the Pure Logic of Many-Many Ground (plmmg). In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete.
Research Interests:
Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it's necessary that if the grounds and the grounded both obtain, then the grounds ground the grounded. The negative part of... more
Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it's necessary that if the grounds and the grounded both obtain, then the grounds ground the grounded. The negative part of this essay exploits empirical and provably nonparadoxical self-reference to prove conclusively that even immediate full grounding isn't an internal relation in this sense. The positive, second part of this essay uses the notion of a “completely satisfactory explanation” to shed light on the logic of ground in the presence of self-reference. This allows us to develop a satisfactory logic of ground and recover a sense in which grounding is still an internal relation.
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How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This... more
How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework. We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists.
Research Interests:
This paper develops a novel theory of abstraction-what we call collective abstraction. The theory solves a notorious problem for non-eliminative structuralism. The non-eliminative structuralist holds that in addition to various isomorphic... more
This paper develops a novel theory of abstraction-what we call collective abstraction. The theory solves a notorious problem for non-eliminative structuralism. The non-eliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for non-rigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations.
Research Interests:
If Γ’s being the case grounds φ’s being the case, what grounds that Γ’s being the case grounds φ’s being the case? This is the Problem of Iterated Ground. Dasgupta (2014b), Bennett (2011), and deRosset (2013) have grappled with this... more
If Γ’s being the case grounds φ’s being the case, what grounds that Γ’s being the case grounds φ’s being the case? This is the Problem of Iterated Ground. Dasgupta (2014b), Bennett (2011), and deRosset (2013) have grappled with this problem from the point of view of metaphysics. But iterated ground is a problem not just for metaphysicians: the existing logics of ground have had nothing to say about such iterated grounding claims. In this paper I propose a novel account of iterated ground and develop a logic of iterated ground. The account—what I will call the Zero-Grounding Account (ZGA for short)—is based on three mutually supporting ideas: (i) taking non-factive ground as a primitive notion of ground; (ii) tying nonfactive ground to explanatory arguments; and (iii) holding that true non-factive grounding claims are zero-grounded (in Fine’s sense). A notion of ground is factive if the truth of “Γ grounds φ” entails that each γ∈ Γ as well as φ is true; the notion is non-factive othe...
Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon (forthcoming) and Rabin and Rabern... more
Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon (forthcoming) and Rabin and Rabern (2015).
Research Interests:
Wilhelm has recently shown that widely accepted principles about immediate ground are inconsistent with some principles of propositional identity. This note responds to this incon- sistency by developing two ground-theoretic accounts of... more
Wilhelm has recently shown that widely accepted principles about immediate ground are inconsistent with some principles of propositional identity. This note responds to this incon- sistency by developing two ground-theoretic accounts of propositional individuation. On one account some of the grounding principles are incorrect; on the other account, the principles of propositional individuation are incorrect.
This paper develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “φ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground... more
This paper develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “φ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth φ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion φ. By developing a deductive system that distinguishes between explanatory and non-explanatory arguments we can give introduction rules for operators for factive and non-factive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.
Research Interests:
Could φ's partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this... more
Could φ's partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this never happens. I show that this inconsistency turns on different principles than the puzzles of ground already discussed in the literature, and I propose a way of resolving the inconsistency.
Research Interests:
Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of... more
Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper-drawing on graph-theoretic and topological ideas-I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that there is no unique method of decycling. An important upshot is that the notion of asymmetric ground may be indeterminate. Grounding is therefore not so much like covering all the bases as like having a leg to stand on Stephen Yablo [16]
Research Interests:
Grounding is bicollective if it is possible for some truths δ,δ,... to be grounded in the some truths γ,γ,... without its being the case that each δi is grounded in some subcollection of γ,γ,.... In this paper I show how to do... more
Grounding is bicollective if it is possible for some truths δ,δ,... to be grounded in the some truths γ,γ,... without its being the case that each δi is grounded in some subcollection of γ,γ,.... In this paper I show how to do develop a hypergraph-theoretic account of bicollective ground, taking the notion of immediate ground as basic. I also indicate how bicollective ground helps with formulating mathematical structuralism.
Fine (2012) is a pluralist about grounding. He holds that there are three fundamentally distinct notions of grounding: metaphysical, normative, and natural. Berker (2017) argues for monism on the grounds that the pluralist cannot account... more
Fine (2012) is a pluralist about grounding. He holds that there are three fundamentally distinct notions of grounding: metaphysical, normative, and natural. Berker (2017) argues for monism on the grounds that the pluralist cannot account for certain principles describing how the distinct notions of grounding interact. This paper defends pluralism. By building on work by Fine (2010) and Litland (2015) I show how the pluralist can systematically account for Berker's interaction principles.
Could φ's partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this... more
Could φ's partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this never happens. I show that this inconsistency turns on different principles than the puzzles of ground already discussed in the literature, and I propose a way of resolving the inconsistency.
Research Interests:
How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This... more
How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework. We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists.
Research Interests:
A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a... more
A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta (2014). In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground (PLG) can be extended to the many-many case, giving rise to the Pure Logic of Many-Many Ground (PLMMG). In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of PLG; this allows us to simplify Fine’s completeness proof for PLG. Second, I formalize PLMMG using an infinitary sequent calculus and prove that this formalization is sound and complete.
Research Interests:
The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory... more
The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: non-factive grounding claims, if true, are zero-grounded in the sense of Fine.
Research Interests:
Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon (forthcoming) and Rabin and Rabern... more
Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon (forthcoming) and Rabin and Rabern (2015).
Research Interests:
Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it’s necessary that if the grounds and the grounded both obtain then the grounds ground the grounded. In the negative part of... more
Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it’s necessary that if the grounds and the grounded both obtain then the grounds ground the grounded. In the negative part of the paper I exploit empirical and provably non- paradoxical self-reference to prove conclusively that even immediate full grounding isn’t an internal relation in this sense. In the positive second part of the paper I use the notion of a “completely satisfactory explanation” to shed light on the logic of ground in the presence of self-reference. This allows me to develop a satisfactory logic of ground and recover a sense in which grounding is still an internal relation.
Research Interests:
I discuss three recent counterexamples to the transitivity of grounding due to Jonathan Schaffer. I argue that the counterexamples don’t work and draw some conclusions about the relationship between grounding and explanation.
Research Interests:
This paper develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with iterated grounding-claims: claims of the form “φ grounds that (ψ grounds θ)”. The core idea is that some truths Γ ground a truth φ... more
This paper develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with iterated grounding-claims: claims of the form “φ grounds that (ψ grounds θ)”. The core idea is that some truths Γ ground a truth φ when there is a distinctively explanatory argument from premisses Γ to conclusion φ. By developing a deductive system that distinguishes between explanatory and non-explanatory arguments we can give introduction rules for grounding operators for factive and non-factive, strict and weak full ground. Elimination rules are then found by using a proof-theoretic inversion principle.
Research Interests:
Dummett () considers two proof-theoretic justifications of logic. One takes the introduction rules for granted and tries to justify the elimination rules. This gives rise to verificationist meaning-theories. The other takes the... more
Dummett () considers two proof-theoretic justifications
of logic. One takes the introduction rules for granted and tries to justify
the elimination rules. This gives rise to verificationist meaning-theories.
The other takes the elimination rules for granted and tries to justify the
introduction rules. This gives rise to pragmatist meaning-theories. In part
, I give a streamlined presentation of verificationist meaning-theories
for the intuitionistic logical constants and prove that if we start with
intuitionistic introduction rules we can justify exactly the intuitionistic
elimination rule. This settles a conjecture of Prawitz’s (, ). I then
rigorously develop a pragmatist meaning-theory for the intuitionistic log-
ical constants. I prove that if we start with the intuitionistic elimination
rules the strongest introduction rules that are validated are the intuition-
istic introduction rules. In part I consider verificationist and pragmatist
meaning-theories based on arbitrary introduction and elimination rules
and prove that, in a precise sense, intuitionistic logic is the strongest logic
which can be validated by either a verificationist or pragmatist meaning-
theory. I end by discussing the notion of stability and make precise and
prove a conjecture of Dummett’s about stability and total harmony.
of logic. One takes the introduction rules for granted and tries to justify
the elimination rules. This gives rise to verificationist meaning-theories.
The other takes the elimination rules for granted and tries to justify the
introduction rules. This gives rise to pragmatist meaning-theories. In part
, I give a streamlined presentation of verificationist meaning-theories
for the intuitionistic logical constants and prove that if we start with
intuitionistic introduction rules we can justify exactly the intuitionistic
elimination rule. This settles a conjecture of Prawitz’s (, ). I then
rigorously develop a pragmatist meaning-theory for the intuitionistic log-
ical constants. I prove that if we start with the intuitionistic elimination
rules the strongest introduction rules that are validated are the intuition-
istic introduction rules. In part I consider verificationist and pragmatist
meaning-theories based on arbitrary introduction and elimination rules
and prove that, in a precise sense, intuitionistic logic is the strongest logic
which can be validated by either a verificationist or pragmatist meaning-
theory. I end by discussing the notion of stability and make precise and
prove a conjecture of Dummett’s about stability and total harmony.
Research Interests:
The presently existing logics of ground have not had anything to say about iterated grounding claims, that is, claims of the form: “A grounds that (B grounds C)”. I develop a pure logic of iterated ground providing a systematic account... more
The presently existing logics of ground have not had anything to say about iterated grounding claims, that is, claims of the form: “A grounds that (B grounds C)”. I develop a pure logic of iterated ground providing a systematic account of such iterated grounding claims. The logic is developed as a Prawitz style natural deduction system; the grounding operators are provided with both introduction and elimination rules, and normalization can be proved. The resulting logic is a conservative extension of Kit Fine's Pure Logic of Ground.
I develop two logics (pplg and pnlg) of grounding which can deal with iterated grounding claims. The logics are developed in naturaldeduction form and the grounding operators are equipped with bothintroduction and elimination rules. I... more
I develop two logics (pplg and pnlg) of grounding which can
deal with iterated grounding claims. The logics are developed in naturaldeduction form and the grounding operators are equipped with bothintroduction and elimination rules. I prove normalization results for pplg and pnlg and determine their relationship to Fine’s Pure Logic of Ground.
deal with iterated grounding claims. The logics are developed in naturaldeduction form and the grounding operators are equipped with bothintroduction and elimination rules. I prove normalization results for pplg and pnlg and determine their relationship to Fine’s Pure Logic of Ground.