Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of (...) ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious and explanatorily powerful. Yet, so I suggest, adopting it has important consequences. (...) First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine’s logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell’s logic of analytic containment and to Correia’s system G. (shrink)

Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order (...) to avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground. (shrink)

There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact (...) stated by a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction $$(\phi \wedge \phi )$$ with that stated by its conjunct $$\phi $$. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy. (shrink)

This paper is a contribution to the long-standing debate over the coherence of Charles Sanders Peirce’s overall system of philosophy. It approaches that issue through the lens of a contemporary debate over the notion of metaphysical grounding, or more broadly, the nature of metaphysical explanation, employing the laws of logic as a case study. The central question concerns how we can take seriously what we shall call Peirce’s Rule—that nothing can be admitted to be absolutely inexplicable—without being vulnerable to (...) a vicious regress or equally vicious circularity. I first argue that in Peirce’s early work he offers a quietist conception of grounding that provides a persuasive and ground-breaking answer to this central question. I then raise a familiar concern, that in Peirce’s later work we find hints of a more metaphysical conception of grounding that seems unable to answer that question and is thus inconsistent with his earlier work. The paper ends with a speculative interpretation of Peirce’s approach to metaphysics and its possible role in grounding logical principles. (shrink)

What corresponds to the present-day ‘transcendental-pragmatic’ concept of ultimate grounding in Hegel is his claim to absoluteness of the logic. Hegel’s fundamental intuition is that of a ‘backward going grounding’ obtaining the initially unproved presuppositions, thereby ‘wrapping itself into a circle’ – the project of the self-grounding of logic, understood as the self-explication of logic by logical means. Yet this is not about one of the multiple ‘logics’ which as formal constructs cannot claim absoluteness. It is (...) rather a fundamental logic that only makes logical textures possible at all and so owns transcendental character. The non-contradiction-principle is an example for this. Es- sential is that it is ‘under-cover-effcient’ as soon as meaningful concepts are used. Self-explication of the fundamental logic then means explicating its implicit under-cover validity, in fact by means of the fundamental logic itself. As is shown this is the affair of dialectic which thereby is to be understood as ultimate grounding of the fundamental logic. This is analyzed in detail using the example of the being/non-being-dialectic. As is demonstrated each explication step generates a new implicit issue and therewith a new explication-discrepancy inducing an antinomical structure that anew forwards the explication procedure. So this is entirely determined by itself. Decisive for the ultimate grounding argumentation is that thereby an objectively verifyable procedure is found, which is apparently possible only in a Hegelian framework. In contrast the immediate evidence of a speech act claimed by the transcendental-pragmatic position has only private character, which is grounding-theoretically irrelevant. (shrink)

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces (...) a number of problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure (...) system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

I provide a theory of the metaphysical foundations of identity: an account what grounds facts of the form a=b. In particular, I defend the claim that indiscernibility grounds identity. This is typically rejected because it is viciously circular; plausible assumptions about the logic of ground entail that the fact that a=b partially grounds itself. The theory I defend is immune to this circularity.

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

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 (...) class='Hi'>grounding claims, if true, are zero-grounded in the sense of Fine. (shrink)

In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and (...) show that grounding contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

It is widely thought that grounding is a hyperintensional phenomenon. Unfortunately, the term ‘hyperintensionality’ has been doing double-duty, picking out two distinct phenomena. This paper clears up this conceptual confusion. We call the two resulting notions hyperintensionalityGRND and hyperintensionalityTRAD. While it is clear that grounding is hyperintensionalGRND, the interesting question is whether it is hyperintensionalTRAD. We argue that given well-accepted constraints on the logical form of grounding, to wit, that grounding is irreflexive and asymmetric, (...) class='Hi'>grounding is hyperintensionalTRAD only if one endorses a sentential operator view of grounding. We argue that proponents of the sentential operator view will need to distinguish two importantly different kinds of hyperintensionalityTRAD—weak and strong—and we offer them a way to do so. (shrink)

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that (...) class='Hi'>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. (shrink)

Grounding pluralism is the view that there are multiple kinds of grounding. In this essay, I motivate and defend an explanation-theoretic view of grounding pluralism. Specifically, I argue that there are two kinds of grounding: why-grounding—which tells us why things are the case—and how-grounding—which tells us how things are the case.

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.

Grounding has become all the rage in recent philosophical work and metaphilosophical discussions. While I agree that the concept of ground marks something useful, I am skeptical about the metaphysical weight many imbue it with, and the picture of ‘worldly layering’ that grounding talk inspires. My skepticism centers around the fact that grounding involves necessitation, combined with reasons for thinking matters of necessity are matters of logical or conceptual (semantic, psychological) relations. I sketch an argument for (...) deflationism about ground based on this sort of deflationism about necessity and essence. I also note that in at least some cases, the considerations supporting modal deflationism directly support deflationism about whatever grounding relations may obtain in these cases. (shrink)

Though the study of grounding is still in the early stages, Kit Fine, in ”The Pure Logic of Ground”, has made a seminal attempt at formalization. Formalization of this sort is supposed to bring clarity and precision to our theorizing, as it has to the study of other metaphysically important phenomena, like modality and vagueness. Unfortunately, as I will argue, Fine ties the formal treatment of grounding to the obscure notion of a weak ground. The obscurity of weak (...) ground, together with its centrality in Fine’s system, threatens to undermine the extent to which this formalization offers clarity and precision. In this paper, I show how to overcome this problem. I describe a system, the logic of strict ground (LSG) and demonstrate its adequacy; I specify a translation scheme for interpreting Fine’s weak grounding claims; I show that the interpretation verifies all of the principles of Fine’s system; and I show that derivability in Fine’s system can be exactly characterized in terms of derivability in LSG. I conclude that Fine’s system is reducible to LSG. (shrink)

Hegel's Science of Logic makes the just not low claim to be an absolute, ultimate-grounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of logic (in the sense of Hegel) (...) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge. (shrink)

What is the explanatory role of ‘status-truths’ such as essence-truths, necessity-truths and law-truths? A plausible principle, suggested by various authors, is Ground by Status, according to which status truths ground their prejacents. For instance, if it is essential to a that p, then this grounds the fact that p. But Ground by Status faces a forceful objection: it is inconsistent with widely accepted principles regarding the logic of grounding (Glazier in Philos Stud 174(11):2871–2889, 2017a, Synthese 174(198):1409–1424, 2017b; Kappes in (...) Synthese 199(1–2):2575–2595, 2020, Philos Stud 178(4):1267–1284, 2021). I defend Ground by Status against this objection. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; (...) that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 988-1009, December 2021.

The purpose of this paper is to show how micro-argumentation mechanisms of presumptive reasoning and reasoning from best explanation can be used for explaining some cases of presupposition cancellation. It will be shown how the relationship between presupposition triggers and pragmatic presuppositions can be analyzed in terms of presumptive and non-presumptive polyphonic articulation of an utterance, resulting in different types of commitments for the interlocutors. This approach is grounded on the two interconnected notions of presumptions and commitments. In some complex (...) cases of presupposition “suspension,” the speaker presumes the hearer’s acceptance of and commitment to propositions that cannot be presumed as such, namely that do not belong to the common ground, or that have been explicitly rejected as being commonly shared. This phenomenon triggers a complex type of reasoning that can be represented as an abductive pattern, grounded on hierarchies of presumptions and aimed at providing an interpretation that solves this conflict of presumptions. Several cases of suspension of presupposition will be investigated as resulting from non-presumptive polyphonic articulations, in which different voices responsible for distinct commitments are distinguished. By indirectly reporting an element of discourse, the speaker can refuse to take responsibility for the presupposed proposition, and correct the commitments that may result for him. This polyphonic treatment of utterances shows how and why a presupposition is suspended, and identifies the conflicting presumptions that can be further solved through reasoning from best explanation. This reasoning can result in a different reconstruction of the developed logical form of utterance or of its illocutionary force. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

Grounding is a powerful metaphysical concept; yet there is widespread scepticism about the intelligibility of the notion. In this paper, I propose an account of an entity’s nature or essence, which I then use to provide grounding conditions for that entity. I claim 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, 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. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be beneficial for science as a whole. However, such a change can come at the cost of looking beyond the categories of the disciplines of logic, philosophy and physics. It is through self-inquiry that such a change is possible, along with the realization of the (...) essence of the middle that is otherwise excluded by choice. The logician, who generally holds a reverential attitude towards the physicist, can then actively contribute to the betterment of physics by improving the language through which the physicist expresses his experience. The philosopher, who otherwise chooses to follow the advancement of physics and gets stuck in the trap of sophistication of language, can then be of guidance to the physicist on intellectual grounds by having the physicist’s experience himself. In course of this commentary, I provide a glimpse of how a truthful conversion of verbal statements to physico-mathematical expressions unravels the hitherto unrealized connection between Heisenberg uncertainty relation and Cauchy’s definition of derivative that is used in physics. The commentary can be an essential reading if the reader is willing to look beyond the categories of logic, philosophy and physics by being ‘nobody’. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the (...) Ramseyan indicative conditional. (shrink)

My aim in this paper is to explore how we might understand the relation of Deleuze’s early works to ethics, and to develop the connections between this way of understanding Deleuze and the work of Søren Kierkegaard. I will claim that we can view both figures as arguing that the sense or meaning we take from the world, and the metaphysical structure we ascribe to it, is secondary to an ethical stance we take in the face of a world of (...) becoming. As such, the central preoccupation of both Kierkegaard and Deleuze is how we make sense of an existence which is necessarily temporal. As we shall see, recognizing the importance of temporality involves a move away from the traditional resolution of the problem of sense that operates by making temporality an accidental aspect of a world. In the first half of this paper, I want to explore this claim in relation to Deleuze’s reading of Plato, tying his claim that Plato is essentially developing an ethical rather than metaphysical doctrine with the claim that “the task of modern philosophy has been defined: to overturn [renversement] Platonism” (DR 59). My emphasis in this section is how Deleuze, rather than “overturning” Platonism by simply rejecting the priority it gives to Forms or essences over appearances, the renversement of Deleuze’s reading inverts the relation to show how the search for essence is in fact grounded in an ethical decision, or “selection,” in the world of appearances/simulacra itself. As such, both Plato and Deleuze can be seen as presenting different trajectories for making sense of a world of becoming, either by grounding it in a transcendent, atemporal realm, or by seeing it as an intensive field of processes. In the second half, I will argue that Kierkegaard’s philosophy rests on a claim, similar to the one we find in Deleuze’s work, that we need to develop a logic of sense in response to a world of becoming. I will conclude that Deleuze’s reading of Kierkegaard is limited by a focus on the theological aspects of his thought, and that Kierkegaard provides a sophisticated and complementary taxonomy of the ways in which we try to make sense of our existence in a world of becoming by developing diverse ethical postures. (shrink)

In the present paper we propose a system of propositional logic for reasoning about justification, truthmaking, and the connection between justifiers and truthmakers. The logic of justification and truthmaking is developed according to the fundamental ideas introduced by Artemov. Justifiers and truthmakers are treated in a similar way, exploiting the intuition that justifiers provide epistemic grounds for propositions to be considered true, while truthmakers provide ontological grounds for propositions to be true. This system of logic is then applied both for (...) interpreting the notorious definition of knowledge as justified true belief and for advancing a new solution to Gettier counterexamples to this standard definition. (shrink)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the (...) logical role is merely descriptive. In this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. (shrink)

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata (...) of first order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

Abstract:Skepticism about grounding is the view that ground-theoretic concepts shouldn’t be used in meta­physical theorizing. Possible reasons for adopting this attitude are numerous: perhaps grounding is unintelligible; or perhaps it’s never instantiated; or perhaps it’s just too heterogeneous to be theor­­­­­etically useful. Unfortunately, as currently pursued the debate between grounding enthusiasts and skeptics is insufficiently structured. This paper’s purpose is to impose a measure of conceptual rigor on the debate by offering an opinionated taxonomy of views with (...) a reasonable claim to being “skeptical.” I argue that carving up logical space into pro- and anti-grounding views isn’t especially helpful; rather, we should recognize various degrees of ground-theoretic involvement depending on how inflationary our understanding of the theoretical term ‘ground’ is. (shrink)

Logical realism is a view about the metaphysical status of logic. Common to most if not all the views captured by the label ‘logical realism’ is that logical facts are mind- and language-independent. But that does not tell us anything about the nature of logical facts or about our epistemic access to them. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some (...) of the challenges that these views face. It will be suggested that logical realism is best understood as a metaphysical view about the logical structure of the world, but this raises an important question: does logical realism collapse into standard metaphysical realism? It will be argued that this result can be accommodated, even if it cannot be altogether avoided. (shrink)

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the (...) grounds that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...) the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

The Fregean tradition promotes a conception of logic as being independent from all psychological acts of the knowing subject. Without questioning logic's status as a paradigm of objectivity the present essay rejects this conception, both on logical grounds and in light of the scholastic theory of intentionality. Finding fault with two key doctrines of the analytic movement, the linguistic turn and anti-psychologism, it reinterprets them to exclude only psychological acts that engender subjective interpretive variability. It then describes logic's dependence (...) on non-interpretive psychological acts that ensue as a natural result of objects being apprehended by the intellect. These acts, which Hervaeus Natalis and the scholastic tradition thematize as the imposition of second intentional relations of reason, dictate the logically coherent parameters of logical objectivity. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

The purpose of this paper is to examine the status of logic from a metaphysical point of view – what is logic grounded in and what is its relationship with metaphysics. There are three general lines that we can take. 1) Logic and metaphysics are not continuous, neither discipline has no bearing on the other one. This seems to be a rather popular approach, at least implicitly, as philosophers often skip the question altogether and go about their business, be it (...) logic or metaphysics. However, it is not a particularly plausible view and it is very hard to maintain consistently, as we will see. 2) Logic is prior to metaphysics and has metaphysical implications. The extreme example of this kind of approach is the Dummettian one, according to which metaphysical questions are reducible to the question of which logic to adopt. 3) Metaphysics is prior to logic, and your logic should be compatible with your metaphysics. This approach suggests an answer to the question of what logic is grounded in, namely, metaphysics. Here I will defend the third option. (shrink)

Logic in the Talmud is a ‘thematic compilation’ by Avi Sion. It collects in one volume essays that he has written on this subject in Judaic Logic (1995) and A Fortiori Logic (2013), in which traces of logic in the Talmud (the Mishna and Gemara) are identified and analyzed. While this book does not constitute an exhaustive study of logic in the Talmud, it is a ground-breaking and extensive study. A new essay, The Logic of Analogy, was added in 2022.

The paper proposes a strategy for understanding metaphysical grounding in deflationary terms and, more generally, proposes a form of methodological deflationism with respect to the notions of ground. The idea is to define a deflationary is grounded in-predicate by appeal to the two-place non-causal connective ‘because’ and a deflationary truth predicate. To this end, we discuss the explanatory role of the truth-predicate in non-causal explanations and develop a theory of truth for the language of the ‘because’-connective. We argue that (...) at least from a logical perspective our deflationary notion of ground is up to the task. (shrink)

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

The Russell-Myhill paradox puts pressure on the Russellian structured view of propositions by showing that it conflicts with certain prima facie attractive ontological and logical principles. I describe several versions of RMP and argue that structurists can appeal to natural assumptions about metaphysical grounding to provide independent reasons for rejecting the ontological principles used in these paradoxes. It remains a task for future work to extend this grounding-based approach to all variants of RMP.

The paper compares two theories of the nature of logic: Penelope Maddy's and my own. The two theories share a significant element: they both view logic as grounded not just in the mind (language, concepts, conventions, etc.), but also, and crucially, in the world. But the two theories differ in significant ways as well. Most distinctly, one is an anti-holist, "austere naturalist" theory while the other is a non-naturalist "foundational-holistic" theory. This methodological difference affects their questions, goals, orientations, the scope (...) of their investigations, their logical realism (the way they ground logic in the world), their explanation of the modal force of logic, and their approach to the relation between logic and mathematics. The paper is not polemic. One of its goal is a perspicuous description and analysis of the two theories, explaining their differences as well as commonalities. Another goal is showing that and how (i) a grounding of logic is possible, (ii) logical realism can be arrived at from different perspectives and using different methodologies, and (iii) grounding logic in the world is compatible with a central role for the human mind in logic. (shrink)

This paper offers a modification of Fabrice Correia's and Alexander Skiles' ("Grounding, Essence, and Identity") definition of grounding in terms of generalized identity that extends it to zero-grounding. This definition promises to improve our understanding of zero-grounding by capturing it within the framework of generalized identity and allows an essentialist theory of modality based on Correia's and Skiles' account to resist a recent challenge by Jessica Leech. The latter is achieved by combining the following two ideas: (...) (1) Some necessities are grounded in truths about zero-grounding, and (2) at least some identity truths are zero-grounded. Finally, some advantages of the zero-grounding approach over Correia's and Skiles' recent definition of necessity in terms of generalized identity and logical consequence are argued for. (shrink)

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued (...) that for a logical constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

Early in the Logic of Essence, the second main part of Hegelian Logic, Hegel identifies a logical structure, seeming (Schein), with “the phenomenon of scepticism.” The present paper has two aims: first, to flesh this identification out by describing the argument that leads up to it; and, second, to argue that it is mistaken. I will proceed as follows. Section 1 deciphers the opening statement of the Logic of Essence, “the truth of being is essence,” by specifying the meaning (...) of each of its composing terms. The discussion opens the way for deliberation on the meaning of the notion of seeming, since seeming proves to be what remains of being in the structure of essence. This is done in section 2. It is also shown therein that seeming takes two logical forms, dualistic seeming and monistic seeming. Section 3 argues that Hegel identifies scepticism only with dualistic seeming, and that the scepticism he has in mind is what one may call “subjective scepticism,” namely a scepticism grounded in the subject of cognition. The section concludes that Hegel, judged by his own standards, is mistaken in this identification. Finally, section 4 considers Robert Pippin’s objection to the above conclusion and offers a rejoinder. (shrink)