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Frege's theorem and foundations for arithmetic

In Peter Adamson (ed.), Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy (2012)

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  1. Logic in mathematics and computer science.Richard Zach - forthcoming - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...)
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  • Expert-oriented abilities vs. novice-oriented abilities: An alternative account of epistemic authority.Michel Croce - 2018 - Episteme 15 (4):476-498.
    According to a recent account of epistemic authority proposed by Linda Zagzebski (2012), it is rational for laypersons to believe on authority when they conscientiously judge that the authority is more likely to form true beliefs and avoid false ones than they are in some domain. Christoph Jäger (2016) has recently raised several objections to her view. By contrast, I argue that both theories fail to adequately capture what epistemic authority is, and I offer an alternative account grounded in the (...)
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  • Techno-phenomenology: Martin Heidegger and Bruno Latour on how phenomena come to presence.Arianne Conty - 2013 - South African Journal of Philosophy 32 (4):311-326.
    This article will set out to elucidate the ways in which the philosophies of technology of Martin Heidegger and Bruno Latour seek to explain how the phenomenal world of nature, objects and tools come to presence as events through their interrelations with each other and with us. Both thinkers seek to overcome a subject/object divide that they both understand as characterising modernity in order to reveal a greater interdependence between nature and culture, human and machine. Not only do they both (...)
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  • On the concept of a spirit.Andrew M. Bailey - 2017 - Religious Studies 53 (4):449-457.
    Substance dualism is on the move. Though the view remains unfashionable, a growing and diverse group of philosophers endorse it on impressive empirical, religious, and purely metaphysical grounds. In this note, I develop and evaluate one conceptual argument for substance dualism. According to that argument, we may derive a conclusion about our nature from the mere fact that we have the concept of a spirit. The argument is intriguing and fruitful; but I shall contend that it is, nonetheless, unsound.
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  • Quasi-truth and defective knowledge in science: a critical examination.Jonas R. Becker Arenhart & Décio Krause - 2023 - Manuscrito 46 (2):122-155.
    Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the formalism available does not deliver all that is promised. We examine the standard account of quasi-truth in the literature, advanced by da Costa and collaborators in many places, and argue that it (...)
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  • Reasons and Causes in Psychiatry: Ideas from Donald Davidson’s Work.Elisabetta Lalumera - 2018 - In Annalisa Coliva, Paolo Leonardi & Sebastiano Moruzzi (eds.), Eva Picardi on Language, Analysis and History. Londra, Regno Unito: Palgrave. pp. 281-296.
    Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.
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  • What did Frege take Russell to have proved?John Woods - 2019 - Synthese 198 (4):3949-3977.
    In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...)
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  • There Is No Knowledge From Falsehood.Ian Schnee - 2015 - Episteme 12 (1):53-74.
    A growing number of authors defend putative examples of knowledge from falsehood (KFF), inferential knowledge based in a critical or essential way on false premises, and they argue that KFF has important implications for many areas of epistemology (whether evidence can be false, the Gettier debate, defeasibility theories of knowledge, etc.). I argue, however, that there is no KFF, because in any supposed example either the falsehood does not contribute to the knowledge or the subject lacks knowledge. In particular, I (...)
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  • Panmetaphoricism.Daniel Howard-Snyder - 2017 - Religious Studies 53:25-49.
    Panmetaphoricism is the view that our speech about God can only be metaphorical. In this essay, I do not assess the reasons that have been given for the view. Rather, I assess the view itself. My aim is to develop the most plausible version of panmetaphoricism in order to gain a clear view of the God it offers for our consideration.
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  • Los números y el contar en Berkeley y Hume.Mauricio Algalan - 2015 - Dissertation, Universidad Panamericana Sede México
    Se puede considerar que Berkeley y Hume son antecedentes filosóficos del Formalismo Matemático. Ambos sostienen una visión instrumentalista y no-realista de las matemáticas. En la conferencia se explora las diferencias y similitudes de ambos autores, así como el porque se les puede considerar ser antecesores del Formalismo.
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