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  1. Was Wittgenstein a radical conventionalist?Ásgeir Berg - 2024 - Synthese 203 (2):1-31.
    This paper defends a reading of Wittgenstein’s philosophy of mathematics in the Lectures on the Foundation of Mathematics as a radical conventionalist one, whereby our agreement about the particular case is constitutive of our mathematical practice and ‘the logical necessity of any statement is a direct expression of a convention’ (Dummett 1959, p. 329). -/- On this view, mathematical truths are conceptual truths and our practices determine directly for each mathematical proposition individually whether it is true or false. Mathematical truths (...)
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  • Conceptual Engineering Should be Empirical.Ethan Landes - manuscript
    Conceptual engineering is a philosophical method that aims to design and spread conceptual and linguistic devices to cause meaningful changes in the world. So far, however, conceptual engineers have struggled to successfully spread the conceptual and linguistic entities they have designed to their target communities. This paper argues that conceptual engineering is far more likely to succeed if it incorporates empirical data and empirical methods. Because the causal factors influencing successful propagation of linguistic or conceptual devices are as complicated and (...)
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  • Conceptual Engineering Between Representational Skepticism and Complacency: Is There a Third Way?Delia Belleri - 2023 - Topoi 42 (4):1051-1062.
    Conceptual engineering has been linked by Herman Cappelen to a position called “representational skepticism”, described as one’s refusal to uncritically take over the conceptual representations one is handed. This position is contrasted with an uncritical attitude, called “representational complacency”. Arguably, neither position, or a hybrid of the two, is rationally sustainable. This paper therefore proposes an alternative option, called “critical concept conservatism”, stating that having a concept makes it rational (in a suitable sense of “rational”) for one to retain it, (...)
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  • Conceptual Engineering or Revisionary Conceptual Analysis? The Case of Russell's Metaphilosophy Based on Principia Mathematica's Logic.Landon Elkind - 2021 - Dialogue 60 (3):447-474.
    Conceptual engineers have made hay over the differences of their metaphilosophy from those of conceptual analysts. In this article, I argue that the differences are not as great as conceptual engineers have, perhaps rhetorically, made them seem. That is, conceptual analysts asking ‘What is X?’ questions can do much the same work that conceptual engineers can do with ‘What is X for?’ questions, at least if conceptual analysts self-understand their activity as a revisionary enterprise. I show this with a study (...)
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  • What the heck is Logic? Logics-as-formalizations, a nihilistic approach.Aadil Kurji - 2020 - Dissertation,
    Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...)
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  • (2 other versions)Broad‐spectrum conceptual engineering.Manuel Gustavo Https://Orcidorg Isaac - 2021 - Ratio 34 (4):286-302.
    Ratio, Volume 34, Issue 4, Page 286-302, December 2021.
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  • What Should Conceptual Engineering Be All About?Isaac Manuel Gustavo - 2021 - Philosophia: A Global Journal of Philosophy 49 (5):2041-2051.
    Conceptual engineering is commonly characterized as the method for assessing and improving our representational devices. Little has been said, however, on how best to construe these representational devices—in other words, on what conceptual engineering should be all about. This paper tackles this problem with a basic strategy: First, by presenting a taxonomy of the different possible subject matters for conceptual engineering; then, by comparatively assessing them and selecting the most conducive one with a view to making conceptual engineering an actionable (...)
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  • (1 other version)Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  • How To Conceptually Engineer Conceptual Engineering?Manuel Gustavo Https://Orcidorg Isaac - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy:1-24.
    Conceptual engineering means to provide a method to assess and improve our concepts working as cognitive devices. But conceptual engineering still lacks an account of what concepts are (as cognitive devices) and of what engineering is (in the case of cognition). And without such prior understanding of its subject matter, or so it is claimed here, conceptual engineering is bound to remain useless, merely operating as a piecemeal approach, with no overall grip on its target domain. The purpose of this (...)
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  • Philosophical Investigations into AI Alignment: A Wittgensteinian Framework.José Antonio Pérez-Escobar & Deniz Sarikaya - 2024 - Philosophy and Technology 37 (3):1-25.
    We argue that the later Wittgenstein’s philosophy of language and mathematics, substantially focused on rule-following, is relevant to understand and improve on the Artificial Intelligence (AI) alignment problem: his discussions on the categories that influence alignment between humans can inform about the categories that should be controlled to improve on the alignment problem when creating large data sets to be used by supervised and unsupervised learning algorithms, as well as when introducing hard coded guardrails for AI models. We cast these (...)
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  • (1 other version)Disagreement about logic.Ole Thomassen Hjortland - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):660-682.
    ABSTRACT What do we disagree about when we disagree about logic? On the face of it, classical and nonclassical logicians disagree about the laws of logic and the nature of logical properties. Yet, sometimes the parties are accused of talking past each other. The worry is that if the parties to the dispute do not mean the same thing with ‘if’, ‘or’, and ‘not’, they fail to have genuine disagreement about the laws in question. After the work of Quine, this (...)
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  • Indeterminacy, coincidence, and “Sourcing Newness” in mathematical research.James V. Martin - 2022 - Synthese 200 (1):1-23.
    Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical (...)
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  • Structural Relativity and Informal Rigour.Neil Barton - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics. Springer. pp. 133-174.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...)
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  • Two Types of Refutation in Philosophical Argumentation.Catarina Dutilh Novaes - 2022 - Argumentation 36 (4):493-510.
    In this paper, I highlight the significance of practices of _refutation_ in philosophical inquiry, that is, practices of showing that a claim, person or theory is wrong. I present and contrast two prominent approaches to philosophical refutation: refutation in ancient Greek dialectic (_elenchus_), in its Socratic variant as described in Plato’s dialogues, and as described in Aristotle’s logical texts; and the practice of providing counterexamples to putative definitions familiar from twentieth century analytic philosophy, focusing on the so-called Gettier problem. Moreover, (...)
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  • Mathematical consensus: a research program.Roy Wagner - 2022 - Axiomathes 32 (3):1185-1204.
    One of the distinguishing features of mathematics is the exceptional level of consensus among mathematicians. However, an analysis of what mathematicians agree on, how they achieve this agreement, and the relevant historical conditions is lacking. This paper is a programmatic intervention providing a preliminary analysis and outlining a research program in this direction.First, I review the process of ‘negotiation’ that yields agreement about the validity of proofs. This process most often does generate consensus, however, it may give rise to another (...)
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  • Open texture, rigor, and proof.Benjamin Zayton - 2022 - Synthese 200 (4):1-20.
    Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues that mitigate the (...)
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  • Frameworks, models, and case studies: a new methodology for studying conceptual change in science and philosophy.Matteo De Benedetto - 2022 - Dissertation, Ludwig Maximilians Universität, München
    This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...)
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  • Mathematical SETIbacks: Open Texture in Mathematics as a New Challenge for Messaging Extra-Terrestrial Intelligence.Jennifer Whyte - forthcoming - International Studies in the Philosophy of Science:1-19.
    Beyond the obvious technical difficulties, human attempts to communicate with hypothetical Extra-Terrestrial Intelligences also present a number of philosophical puzzles. After all, an alien intelligence is likely the closest thing to a Wittgensteinian lion humanity could ever encounter. In this paper I advance a new challenge for the feasibility of communication with extra-terrestrials. The problem I raise is a practical problem that falls out of the history and philosophy of mathematics and the implementation of METI projects—specifically, the semiprime self-decryption schema (...)
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  • (2 other versions)Broad-spectrum conceptual engineering.Manuel Gustavo Https://Orcidorg Isaac - 2021 - Ratio 34 (4):286-302.
    Conceptual engineering is the method for assessing and improving our representational devices. On its ‘broad‐spectrum’ version, it is expected to be appropriately applicable to any of our representation‐involving cognitive activities, with major consequences for our whole cognitive life. This paper is about the theoretical foundations of conceptual engineering thus characterised. With a view to ensuring the actionability of conceptual engineering as a broad‐spectrum method, it addresses the issue of how best to construe the subject matter of conceptual engineering and successively (...)
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  • Cognitive Structuralism: Explaining the Regularity of the Natural Numbers Progression.Paula Quinon - 2022 - Review of Philosophy and Psychology 13 (1):127-149.
    According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...)
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  • When clarity and consistency conflicts with empirical adequacy: conceptual engineering, anthropology, and Evans-Pritchard’s ethnography.C. M. Djordjevic - 2020 - Synthese 198 (10):9611-9637.
    In recent analytic philosophy, there is a growing interest in the project of conceptual engineering. This paper examines two ways this project might be applied to scientific research, specifically anthropological research. It argues that both of them are harmful to this research. Specifically, it argues that a reliance on the axiological standards of analytic philosophy conflicts with the goal of empirical adequacy. Section one proffers two forms that the engineering project might take when applied to the science. Section two proffers (...)
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  • Ontological disputes and the phenomenon of metalinguistic negotiation: Charting the territory.Delia Belleri - 2020 - Philosophy Compass 15 (7):e12684.
    Paradigmatic cases of ontological disputes are taken to concern whether or not certain objects exist. Some theorists, however, prefer to view ontologists as really debating about what we should mean with the term “exist” (or other cognate terms). This implies interpreting ontological disputes as metalinguistic negotiations, in keeping with a recent trend to interpret other philosophical disputes along these lines (Plunkett and Sundell. Philosopher's Imprint; 2013;13:1–37). A number of issues arise from such proposal. The first is what counts as evidence (...)
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  • Against a global conception of mathematical hinges.Jordi Fairhurst, José Antonio Pérez-Escobar & Deniz Sarikaya - forthcoming - Philosophical Quarterly.
    Epistemologists have developed a diverse group of theories, known as hinge epistemology, about our epistemic practices that resort to and expand on Wittgenstein's concept of ‘hinges’ in On Certainty. Within hinge epistemology there is a debate over the epistemic status of hinges. Some hold that hinges are non-epistemic (neither known, justified, nor warranted), while others contend that they are epistemic. Philosophers on both sides of the debate have often connected this discussion to Wittgenstein's later views on mathematics. Others have directly (...)
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  • Justified Epistemic Exclusions in Mathematics.Colin Jakob Rittberg - 2023 - Philosophia Mathematica 31 (3):330-359.
    Who gets to contribute to knowledge production of an epistemic community? Scholarship has focussed on unjustified forms of exclusion. Here I study justified forms of exclusion by investigating the phenomenon of so-called ‘cranks’ in mathematics. I argue that workload-management concerns justify the exclusion of these outsiders from mathematical knowledge-making practices. My discussion reveals three insights. There are reasons other than incorrect mathematical argument that justify exclusions from mathematical practices. There are instances in which mathematicians are justified in rejecting even correct (...)
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