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  1. Grounding: Toward a Theory of the I n-Virtue-Of Relation.Paul Audi - 2012 - Journal of Philosophy 109 (12):685-711.
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  • Explanatory Asymmetries: Laws of Nature Rehabilitated.Lina Jansson - 2015 - Journal of Philosophy 112 (11):577-599.
    The problem of explanatory non-symmetries provides the strongest reason to abandon the view that laws can figure in explanations without causal underpinnings. I argue that this problem can be overcome. The solution that I propose starts from noticing the importance of conditions of application when laws do explanatory work, and I go on to develop a notion of nomological dependence that can tackle the non-symmetry problem. The strategy is to show how a strong notion of counterfactual dependence as guaranteed by (...)
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  • A Certain Kind of Trinity: Dependence, Substance, Explanation.Benjamin Sebastian Schnieder - 2006 - Philosophical Studies 129 (2):393-419.
    The main contribution of this paper is a novel account of ontological dependence. While dependence is often explained in terms of modality and existence, there are relations of dependence that slip through the mesh of such an account. Starting from an idea proposed by Jonathan Lowe, the article develops an account of ontological dependence based on a notion of explanation; on its basis, certain relations of dependence can be established that cannot be accounted by the modal-existential account. Dependence is only (...)
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  • (1 other version)The Coarse-Grainedness of Grounding.Kathrin Koslicki - 2015 - Oxford Studies in Metaphysics 9:306-344.
    After many years of enduring the drought and famine of Quinean ontology and Carnapian meta-ontology, the notion of ground, with its distinctively philosophical flavor, finally promises to give metaphysicians something they can believe in again and around which they can rally: their very own metaphysical explanatory connection which apparently cannot be reduced to, or analyzed in terms of, other familiar idioms such as identity, modality, parthood, supervenience, realization, causation or counterfactual dependence. Often, phenomena such as the following are cited as (...)
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  • The Deductive-Nomological Account of Metaphysical Explanation.Tobias Wilsch - 2016 - Australasian Journal of Philosophy 94 (1):1-23.
    The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I argue (...)
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  • Ground.Michael J. Raven - 2015 - Philosophy Compass 10 (5):322-333.
    This essay focuses on a recently prominent notion of ground which is distinctive for how it links metaphysics to explanation. Ground is supposed to serve both as the common factor in diverse in virtue of questions as well as the structuring relation in the project of explaining how some phenomena are “built” from more fundamental phenomena. My aim is to provide an opinionated synopsis of this notion of ground without engaging with others. Ground, so understood, generally resists illumination by appeal (...)
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  • La Logique Ou L'Art de Penser (1709).Antoine Arnauld & Pierre Nicole - 2009 - Vrin.
    This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
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  • Grounding in the image of causation.Jonathan Schaffer - 2016 - Philosophical Studies 173 (1):49-100.
    Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.
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  • The Structure of Scientific Theories.Rasmus Grønfeldt Winther - 2015 - Stanford Encyclopedia of Philosophy.
    Scientific inquiry has led to immense explanatory and technological successes, partly as a result of the pervasiveness of scientific theories. Relativity theory, evolutionary theory, and plate tectonics were, and continue to be, wildly successful families of theories within physics, biology, and geology. Other powerful theory clusters inhabit comparatively recent disciplines such as cognitive science, climate science, molecular biology, microeconomics, and Geographic Information Science (GIS). Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating predictions. Moving from their (...)
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  • Explanation in metaphysics and Bolzano’s theory of ground and consequence.Arianna Betti - 2010 - Logique Et Analyse 211:281-316.
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  • Grounding: an opinionated introduction.Fabrice Correia & Benjamin Schnieder - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical grounding: understanding the structure of reality. Cambridge: Cambridge University Press. pp. 1-36.
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  • Bolzano’s concept of grounding against the background of normal proofs.Antje Rumberg - 2013 - Review of Symbolic Logic 6 (3):424-459.
    In this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano’s (...)
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  • A logic for 'because'.Benjamin Schnieder - 2011 - Review of Symbolic Logic 4 (3):445-465.
    In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truth-functional connectives.
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  • Logical grounds.Fabrice Correia - 2014 - Review of Symbolic Logic 7 (1):31-59.
    I identify a notion of logical grounding, clarify it, and show how it can be used (i) to characterise various consequence relations, and (ii) to give a precise syntactic account of the notion of “groundedness” at work in the literature on the paradoxes of truth.
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  • Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical grounding: understanding the structure of reality. Cambridge: Cambridge University Press. pp. 37--80.
    A number of philosophers have recently become receptive to the idea that, in addition to scientific or causal explanation, there may be a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some constitutive form of determination. I myself have long been sympathetic to this idea of constitutive determination or ‘ontological ground’; and it is the aim of the present paper to help put the idea on a firmer (...)
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  • (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Constructing the World.David Chalmers (ed.) - 2012 - Oxford: Oxford University Press.
    Inspired by Rudolf Carnap's Der Logische Aufbau Der Welt, David J. Chalmers argues that the world can be constructed from a few basic elements. He develops a scrutability thesis saying that all truths about the world can be derived from basic truths and ideal reasoning. This thesis leads to many philosophical consequences: a broadly Fregean approach to meaning, an internalist approach to the contents of thought, and a reply to W. V. Quine's arguments against the analytic and the a priori. (...)
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  • Defending the Axioms: On the Philosophical Foundations of Set Theory.Penelope Maddy - 2011 - Oxford, England: Oxford University Press.
    Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...)
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  • In Defence of Ground.Michael J. Raven - 2012 - Australasian Journal of Philosophy 90 (4):687 - 701.
    I defend (metaphysical) ground against recent, unanswered objections aiming to dismiss it from serious philosophical inquiry. Interest in ground stems from its role in the venerable metaphysical project of identifying which facts hold in virtue of others. Recent work on ground focuses on regimenting it. But many reject ground itself, seeing regimentation as yet another misguided attempt to regiment a bad idea (like phlogiston or astrology). I defend ground directly against objections that it is confused, incoherent, or fruitless. This vindicates (...)
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  • Bolzano's Theory of Ground and Consequence.Armin Tatzel - 2002 - Notre Dame Journal of Formal Logic 43 (1):1-25.
    The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of grounding (...)
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  • (1 other version)The basic laws of arithmetic.Gottlob Frege - 1893 - Berkeley,: University of California Press. Edited by Montgomery Furth.
    ... as 'logicism') that the content expressed by true propositions of arithmetic and analysis is not something of an irreducibly mathematical character, ...
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  • Ambitious, yet modest, metaphysics.Thomas Hofweber - 2009 - In Ryan Wasserman, David Manley & David Chalmers (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford, England: Oxford University Press. pp. 260--289.
    There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the greatest threat to metaphysics (...)
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  • Depth: An Account of Scientific Explanation.Michael Strevens - 2008 - Cambridge: Harvard University Press.
    Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Making things happen: a theory of causal explanation.James F. Woodward - 2003 - New York: Oxford University Press.
    Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.
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  • (1 other version)Basic proof theory.A. S. Troelstra - 2000 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much (...)
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  • The classical model of science: A millennia-old model of scientific rationality.Willem R. de Jong & Arianna Betti - 2010 - Synthese 174 (2):185-203.
    Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...)
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  • Counterfactual theories of causation.Peter Menzies - 2008 - Stanford Encyclopedia of Philosophy.
    The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form “If A had not occurred, C would not have occurred”. While counterfactual analyses have been given of type-causal concepts, most counterfactual analyses have focused on singular causal or token-causal claims of the form “event c caused event e”. Analyses of token-causation have become popular in the last thirty years, especially since the development in the (...)
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  • Mathematical explanation: Problems and prospects.Paolo Mancosu - 2001 - Topoi 20 (1):97-117.
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  • Scientific explanation.James Woodward - 1979 - British Journal for the Philosophy of Science 30 (1):41-67.
    Issues concerning scientific explanation have been a focus of philosophical attention from Pre- Socratic times through the modern period. However, recent discussion really begins with the development of the Deductive-Nomological (DN) model. This model has had many advocates (including Popper 1935, 1959, Braithwaite 1953, Gardiner, 1959, Nagel 1961) but unquestionably the most detailed and influential statement is due to Carl Hempel (Hempel 1942, 1965, and Hempel & Oppenheim 1948). These papers and the reaction to them have structured subsequent discussion concerning (...)
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  • Explanatory unification.Philip Kitcher - 1981 - Philosophy of Science 48 (4):507-531.
    The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting the (...)
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  • The function of general laws in history.Carl Gustav Hempel - 1942 - Journal of Philosophy 39 (2):35-48.
    The classic logical positivist account of historical explanation, putting forward what is variously called the "regularity interpretation" (#Gardiner, The Nature of Historical Explanation), the "covering law model" (#Dray, Laws and Explanation in History), or the "deductive model" (Michael #Scriven, "Truisms as Grounds for Historical Explanations"). See also #Danto, Narration and Knowledge, for further criticisms of the model. Hempel formalizes historical explanation as involving (a) statements of determining (initial and boundary) conditions for the event to be explained, and (b) statements of (...)
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  • Phenomenal Structuralism.David J. Chalmers - 2012 - In David Chalmers (ed.), Constructing the World. Oxford: Oxford University Press. pp. 412-422.
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  • Metaphysical and Conceptual Grounding.Robert Smithson - 2020 - Erkenntnis 85 (6):1501-1525.
    In this paper, I clarify the relation between two types of grounding: metaphysical and conceptual. Metaphysical grounding relates entities at more and less fundamental ontological levels. Conceptual grounding relates semantically primitive sentences and semantically derivative sentences. It is important to distinguish these relations given that both types of grounding can underwrite non-causal “in-virtue-of” claims. In this paper, I argue that conceptual and metaphysical grounding are exclusive: if a given in-virtue-of claim involves conceptual grounding, then it does not involve metaphysical grounding. (...)
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  • Untersuchungen über das logische Schließen. II.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 39:405–431.
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  • Disjunction and the Logic of Grounding.Giovanni Merlo - 2020 - Erkenntnis 87 (2):567-587.
    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 (...)
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  • Fundamental Truths and the Principle of Sufficient Reason in Bolzano's Theory of Grounding.Stefan Roski & Benjamins Schnieder - 2019 - Journal of the History of Philosophy 57 (4):675-706.
    reality is a complex affair. It comprises a huge variety of different elements. Importantly, though, reality is not a mere aggregate of its elements but rather a structured whole or system whose building blocks are not all on the same level. Instead, they form hierarchical networks ordered by relations of priority. In such networks, derivative aspects of reality obtain in virtue of their grounds, that is, in virtue of more fundamental aspects of reality that are prior to them.This picture of (...)
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  • Fundamentality.Tuomas E. Tahko - 2023 - Stanford Encyclopedia of Philosophy.
    The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical notions.
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  • Identity criteria: an epistemic path to conceptual grounding.Massimiliano Carrara & Ciro De Florio - 2020 - Synthese 197 (7):3151-3169.
    Are identity criteria grounding principles? A prima facie answer to this question is positive. Specifically, two-level identity criteria can be taken as principles related to issues of identity among objects of a given kind compared with objects of a more basic kind. Moreover, they are grounding metaphysical principles of some objects with regard to others. In the first part of the paper we criticise this prima facie natural reading of identity criteria. This result does not mean that identity criteria could (...)
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  • Grounding and metaphysical explanation: it’s complicated.Anna-Sofia Maurin - 2019 - Philosophical Studies 176 (6):1573-1594.
    Grounding theorists insist that grounding and explanation are intimately related. This claim could be understood as saying either that grounding ‘inherits’ its properties from explanation or it could be interpreted as saying that grounding plays an important—possibly an indispensable—role in metaphysical explanation. Or both. I argue that saying that grounding ‘inherits’ its properties from explanation can only be justified if grounding is explanatory by nature, but that this view is untenable. We ought therefore to be ‘separatists’ and view grounding and (...)
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  • The Classical Model of Science: a millennia-old model of scientific rationality.Willem Jong & Arianna Betti - 2010 - Synthese 174 (2):185-203.
    Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science. In this paper we will do two things. First of all, we will propose a (...)
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  • Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos.Günter Buhl - 1961 - Köln: Kölner Universitäts-Verlag.
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  • Explanatory Asymmetries, Ground, and Ontological Dependence.Lina Jansson - 2017 - Erkenntnis 82 (1):17-44.
    The notions of ground and ontological dependence have made a prominent resurgence in much of contemporary metaphysics. However, objections have been raised. On the one hand, objections have been raised to the need for distinctively metaphysical notions of ground and ontological dependence. On the other, objections have been raised to the usefulness of adding ground and ontological dependence to the existing store of other metaphysical notions. Even the logical properties of ground and ontological dependence are under debate. In this article, (...)
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  • On defining the notion of complete and immediate formal grounding.Francesca Poggiolesi - 2016 - Synthese 193 (10).
    The aim of this paper is to provide a definition of the the notion of complete and immediate formal grounding through the concepts of derivability and complexity. It will be shown that this definition yields a subtle and precise analysis of the concept of grounding in several paradigmatic cases.
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  • On the Mathematical Method and Correspondence with Exner.Bernard Bolzano (ed.) - 2004 - Rodopi.
    The Prague Philosopher Bernard Bolzano (1781-1848) has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy. Praised by Husserl as "one of (...)
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  • Logique et mathématique chez Bernard Bolzano.Jan Sebestik - 1992 - Paris: J. Vrin.
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  • Uniform proof-theoretic semantics for logical constants.Peter Schroeder-Heister - 1991 - Journal of Symbolic Logic 56:1142.
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  • Bolzano and Cournot on mathematical explanation / Bolzano et Cournot à propos de l'explication mathématique.Paolo Mancosu - 1999 - Revue d'Histoire des Sciences 52 (3):429-456.
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  • Bolzano e le dimostrazioni matematiche.Francesco Paoli - 1991 - Rivista di Filosofia 82 (2):221-242.
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  • Fregean hierarchies and mathematical explanation.Michael Detlefsen - 1988 - International Studies in the Philosophy of Science 3 (1):97 – 116.
    There is a long line of thinkers in the philosophy of mathematics who have sought to base an account of proof on what might be called a 'metaphysical ordering' of the truths of mathematics. Use the term 'metaphysical' to describe these orderings is intended to call attention to the fact that they are regarded as objective and not subjective and that they are conceived primarily as orderings of truths and only secondarily as orderings of beliefs. -/- I describe and consider (...)
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