Mark Jago

Grounding is a powerful metaphysical concept; yet there is widespread scepticism about the intelligibility of the notion. This paper proposes an account of an entity’s _nature_ or _essence_, which is then used to provide _grounding conditions_ for that entity. It is claimed that an understanding of an entity’s nature, together with an account of how logically complex entities are grounded, provides all we need to understand how that entity is grounded. This approach not only allows us to say what grounds what, but it also sheds light on the formal features of the grounding relation. It provides a principled argument for the orthodox view that grounding is irreflexive, asymmetrical, and transitive, but it allows that it may not be well-founded. The resulting approach gives us a powerful framework for understanding nature, grounding, and the relationship between them.

Bob and Ulf say logic should make explicit / The kinds of inference we take as licit. / They give a formalism that’s classically complete, / But in which an extra premise may defeat / An inference that seems a reasonable fact. / Thus reason’s made explicit but is it exact? / For reason in the sense of Brandom and Hlobil, / May explode like a logical Chernobyl. / This is the point on which I’d like to push back, / And keep the game of giving reasons exact. / So with the help of fancy formal antics, / I’ll give nonmonotonic truthmaker semantics.

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources.

Truthmaker semantics is a recent development in formal and philosophical semantics, with similar motivation and scope to possible worlds semantics. The technical background is rather different, however, and results in a more fine-grained hyperintensional notion of content, allowing us to distinguish between classically equivalent propositions. After briefly introducing the main ideas, this entry will describe the technical apparatus of state spaces and the central notions of content and partial content. It will then outline applications of truthmaker semantics in language, logic, and other areas of philosophy.

Stephen Yablo has argued that ascriptions of belief and knowledge are sensitive to _subject matter_ and that theorising in such terms may help resolve philosophical questions about the semantics of such ascriptions. _Truthmaker semantics_ offers a way of theorising about subject matters. My main aim in this paper is to investigate what a semantics for knowledge or belief ascriptions might look like within truthmaker semantics. I then discuss what the resulting account might have to say about the problem of logical omniscience, the nature of concepts, and rational belief.

Fine (J. Philos. Logic 46(6):625–674, 2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend the notion of disjunctive parthood in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable-determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (J. Philos. Logic 3(4):347–372, 1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom.

Essentialists understand modal properties in terms of the essences of things. Given this view, it is natural to think that our knowledge of modality ultimately derives from our knowledge of the essences of things. Is that view plausible? Do we genuinely have knowledge of the essences of things, in a form substantial enough to ground our modal knowledge? The more we pack into the notion of essence to allow it to underpin modal properties, the harder it is to claim genuine knowledge. I will argue that realists about essence of a certain kind can have the best of both worlds. They can co-opt a conventionalist explanation of our knowledge of essence, but against the background of a fully realist notion of essence.

There are many ways for truths to be true. How should we understand that idea? One is that there are different kinds of truth: the _ways_ are different truth-like properties. Another understanding is that a truth can be made true in different ways, by different kinds of entities. The former understanding supports alethic pluralism. But the latter can be understood as a kind of monism: truth is the existential property of having some truthmaker or other. On this view, the differences reside in how a truth is made true, but not in its being true. I’ll discuss how these two understandings differ and what the potential advantages of the latter idea might be.

An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results.

I know that I could have been where you are right now and that you could have been where I am right now, but that neither of us could have been turnips or natural numbers. This knowledge of metaphysical modality stands in need of explanation. I will offer an account based on our knowledge of the natures, or essencess, of things. I will argue that essences need not be viewed as metaphysically bizarre entities; that we can conceptualise and refer to essences; and that we can gain knowledge of them. We can know about which properties are, and which properties are not, essential to a given entity. This knowledge of essence offers a route to knowledge of the ways those entities must be or could be.

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it.Essential bundle theoryattempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the objection. To avoid the problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories.

Impossible Worlds focuses on an exciting new theory in philosophy, with applications in metaphysics, logic, and the theory of meaning. Its central topic is: how do we meaningfully talk and reason about situations which, unbeknownst to us, are impossible? This issue emerges as a central problem in contemporary philosophical accounts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition. The book is written bytwo of the leading philosophers in the area and contains original research of relevance to professional philosophers and logicians working in metaphysics, philosophy of language, formal logic, and adjacentareas.

Fine (2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend the notion of disjunctive parthood in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable- determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom.

John White (2016) defends the UK private school system from the accusation that it allows an unfair form of ‘queue jumping’ in university admissions. He offers two responses to this accusation, one based on considerations of harm, and one based on meritocratic distribution of university places. We will argue that neither response succeeds: the queue-jumping argument remains a powerful case against the private school system in the UK. We begin by briefly outlining the queue-jumping argument (§1), before evaluating White’s no-harm (§2) and meritocracy (§3) arguments.

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge.

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics.