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  1. Bolzano versus Kant: mathematics as a scientia universalis.Paola Cantù - 2011 - Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...)
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  • Explanation in Metaphysics?Johannes Persson - 2011 - Metaphysica 12 (2):165-181.
    Arguments from explanation, i.e. arguments in which the explanatory value of a hypothesis or premise is appealed to, are common in science, and explanatory considerations are becoming more popular in metaphysics. The paper begins by arguing that explanatory arguments in science—even when these are metaphysical explanations— may fail to be explanatory in metaphysics; there is a distinction to be drawn between metaphysical explanation and explanation in metaphysics. This makes it potentially problematic to deploy arguments from explanation in, for instance, metaphysics (...)
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  • Scientific Explanation as a Guide to Ground.Markel Kortabarria & Joaquim Giannotti - 2024 - Synthese 203 (3):1-27.
    Ground is all the rage in contemporary metaphysics. But what is its nature? Some metaphysicians defend what we could call, following Skiles and Trogdon (2021), the inheritance view: it is because constitutive forms of metaphysical explanation are such-and-such that we should believe that ground is so-and-so. However, many putative instances of inheritance are not primarily motivated by scientific considerations. This limitation is harmless if one thinks that ground and science are best kept apart. Contrary to this view, we believe that (...)
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  • Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity.Francesca Poggiolesi - 2024 - Philosophia Mathematica 32 (2):145-176.
    This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having (...)
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  • From thin objects to thin concepts?Massimiliano Carrara, Ciro De Florio & Francesca Poggiolesi - 2023 - Theoria 89 (3):256-265.
    In this short paper we consider Linnebo's thin/thick dichotomy: first, we show that it does not overlap with the very common one between abstract/concrete objects; second, on the basis of some difficulties with the distinction, we propose, as a possible way out, to move from thin/thick objects to thin/thick concepts.
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  • Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically impure (...)
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  • Judgement and the Epistemic Foundation of Logic.Maria van der Schaar (ed.) - 2012 - Dordrecht, Netherland: Springer.
    This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...)
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  • Kant’s Ideal of Systematicity in Historical Context.Hein van den Berg - 2021 - Kantian Review 26 (2):261-286.
    This article explains Kant’s claim that sciences must take, at least as their ideal, the form of a ‘system’. I argue that Kant’s notion of systematicity can be understood against the background of de Jong & Betti’s Classical Model of Science (2010) and the writings of Georg Friedrich Meier and Johann Heinrich Lambert. According to my interpretation, Meier, Lambert, and Kant accepted an axiomatic idea of science, articulated by the Classical Model, which elucidates their conceptions of systematicity. I show that (...)
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  • Grounding principles for (relevant) implication.Francesca Poggiolesi - 2020 - Synthese 198 (8):7351-7376.
    Most of the logics of grounding that have so far been proposed contain grounding axioms, or grounding rules, for the connectives of conjunction, disjunction and negation, but little attention has been dedicated to the implication connective. The present paper aims at repairing this situation by proposing adequate grounding principles for relevant implication. Because of the interaction between negation and implication, new grounding principles concerning negation will also arise.
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  • Bolzano and Kim on grounding and unification.Stefan Roski - 2019 - Synthese 196 (7):2971-2999.
    It is sometimes mentioned that Bernard Bolzano’s work on grounding anticipates many insights of the current debate on metaphysical grounding. The present paper discusses a certain part of Bolzano’s theory of grounding that has thus far not been discussed in the literature. This part does not so much anticipate what are nowadays common assumptions about grounding, but rather goes beyond them. Central to the discussion will be a thesis of Bolzano’s by which he tries to establish a connection between grounding (...)
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  • The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof. as a Case Study.Iris Loeb & Stefan Roski - 2014 - Philosophia Scientiae 18 (1):113-129.
    In the 18th and 19th centuries two transitions took place in the development of mathematical analysis: a shift from the geometric approach to the formula-centered approach, followed by a shift from the formula-centered approach to the concept-centered approach. We identify, on the basis of Bolzano's Purely Analytic Proof [Bolzano 1817], the ways in which Bolzano's approach can be said to be concept-centered. Moreover, we conclude that Bolzano's attitude towards the geometric approach on the one hand and the formula-centered approach on (...)
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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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  • (1 other version)Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof.Francesca Poggiolesi & Francesco Genco - 2023 - Erkenntnis 88 (4):1481-1507.
    This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...)
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  • In defence of explanatory realism.Stefan Roski - 2021 - Synthese 199 (5-6):14121-14141.
    Explanatory realism is the view that explanations work by providing information about relations of productive determination such as causation or grounding. The view has gained considerable popularity in the last decades, especially in the context of metaphysical debates about non-causal explanation. What makes the view particularly attractive is that it fits nicely with the idea that not all explanations are causal whilst avoiding an implausible pluralism about explanation. Another attractive feature of the view is that it allows explanation to be (...)
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  • THE TRANSCENDENTAL METAPHYSIC OF G.F. STOUT: HIS DEFENCE AND ELABORATION OF TROPE THEORY.Fraser Macbride - 2014 - In A. Reboul (ed.), Mind, Value and Metaphysics: Papers Dedicated to Kevin Mulligan. Springer. pp. 141-58.
    G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...)
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  • Bolzano and the Analytical Tradition.Sandra Lapointe - 2014 - Philosophy Compass 9 (2):96-111.
    In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...)
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  • Bradley’s Regress.Anna-Sofia Maurin - 2012 - Philosophy Compass 7 (11):794-807.
    Ever since F. H. Bradley first formulated his famous regress argument philosophers have been hard at work trying to refute it. The argument fails, it has been suggested, either because its conclusion just does not follow from its premises, or it fails because one or more of its premises should be given up. In this paper, the Bradleyan argument, as well as some of the many and varied reactions it has received, is scrutinized.
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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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  • (1 other version)Why metaphysicians do not explain.Ingar Brinck, Göran Hermerén, Johannes Persson & Nils-Eric Sahlin - unknown
    The paper discusses the concept of explanation in metaphysics. Different types of explanation are identified and explored. Scientific explanation is compared with metaphysical explanation. The comparison illustrates the difficulties with applying the concept of explanation in metaphysics.
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  • Formal explanations as logical derivations.Francesco A. Genco - 2021 - Journal of Applied Non-Classical Logics 31 (3-4):279-342.
    According to a longstanding philosophical tradition dating back to Aristotle, certain proofs do not only certify the truth of their conclusion but also explain it. Lately, much effort is being devo...
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  • Early Bolzano on ground-consequence proofs.Stefania Centrone - 2016 - Bulletin of Symbolic Logic 22 (2):215-237.
    In his earlyContributions to a Better-Grounded Presentation of Mathematics Bernard Bolzano tries to characterizerigorous proofs.Rigorousis,prima facie, any proof that indicates the grounds for its conclusion. Bolzano lists a number of methodological constraints all rigorous proofs should comply with, and tests them systematically against a specific collection of elementary inference schemata that, according to him, are evidently of ground-consequence-kind. This paper intends to give a detailed and critical account of the fragmentary logic of theContributions, and to point out as well some (...)
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  • (1 other version)Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof.Francesca Poggiolesi & Francesco Genco - 2021 - Erkenntnis:1-27.
    This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...)
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  • Bolzano on conceptual and intuitive truth: the point and purpose of the distinction.Mark Textor - 2013 - Canadian Journal of Philosophy 43 (1):13-36.
    Bolzano incorporated Kant's distinction between intuitions and concepts into the doctrine of propositions by distinguishing between conceptual (Begriffssätze an sich) and intuitive propositions (Anschauungssätze an sich). An intuitive proposition contains at least one objective intuition, that is, a simple idea that represents exactly one object; a conceptual proposition contains no objective intuition. After Bolzano, philosophers dispensed with the distinction between conceptual and intuitive propositions. So why did Bolzano attach philosophical importance to it? I will argue that, ultimately, the value of (...)
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  • Exemplification as Explanation.Anna-Sofia Maurin - 2013 - Axiomathes 23 (2):401-417.
    In this paper I critically investigate an unorthodox attempt to metaphysically explain in virtue of what there are states of affairs. This is a suggestion according to which states of affairs exist thanks to, rather than, as is the common view, in spite of, the infinite regress their metaphysical explanation seems to engender. I argue that, no matter in which form it is defended, or in which theoretical framework it is set, this suggestion cannot provide us with the explanation we (...)
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