The Basic Laws of Arithmetic

Frege, Gottlob

doi:10.1525/9780520312364

Cited by 224 publications

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“…Throughout I use Γ to refer to a set of propositions, and ϕ and ψ to refer to individual propositions (or whatever one takes the relata of the logical consequence relation to be).2 One alternative proposal is that logic is normative for public practices such as assertion and debate-seeDogramaci (2015) andDutilh-Novaes (2015).3 Historical traditionalists include Aristotle (cf.,Smith 1995, p. 27),Kant (1787), andFrege (1893). Contemporary proponents includeBeall and Restall (2006), Field (2009), MacFarlane (2004),Milne (2009),Priest (1979), Steinberger (2019a, b, c), and Streumer (2007.…”

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confidence: 99%

Another way logic might be normative

Evershed

2021

Synthese

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Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form $$\varGamma \models \varphi $$ Γ ⊧ φ —to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form $$\varGamma \not \models \psi $$ Γ ⊭ ψ to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic.

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confidence: 99%

Another way logic might be normative

Evershed

2021

Synthese

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“…O psicologismo, a tese de que os fazedores de verdade das leis lógicas sejam fatos sobre entidades mentais, é considerado "morto e enterrado", por assim dizer, desde Frege (1964;1979). Não pretendo ressuscitar o psicologismo aqui, até porque a evidência empírica disponível mostra que o psicologismo estava, sim, errado, como veremos.…”

Section: Convertendo Metafísica Em Questões Tratáveis Empiricamenteunclassified

Filosofia da Lógica Empiricamente Informada: uma ilustração via metafísica da lógica

Santos

2020

Perspec. Filos.

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Dados da psicologia são relevantes na abordagem de alguns problemas em filosofia da lógica mesmo que não se assuma, de antemão, uma posição psico-logista. Para ilustrar um método de abordar problemas na filosofia da lógica que faz largo uso de dados da psicologia, neste artigo considero a questão sobre a metafísica da lógica—qual o objeto de estudo da lógica?—à luz de resultados da psicologia do pensamento e da psicologia do desenvolvimento. Estes resultados nos permitem concluir que sistemas lógicos não são meramente descritivos de aspectos gerais da linguagem natural, do mundo ou da racionalidade humana. Os dados são consistentes com a hipótese de que sis-temas lógicos dedutivos sejam conjuntos de regras de caráter primordialmente não-descritivo, criadas mediante reflexão ativa de filósofos, matemáticos e lógicos, visando garantir inferências dedutivas em certos contextos.

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“…But let's not rush to make too much of this: the fact that we can make mistakes in arguing for the cogency of a formal system on the basis of our sup-10 The first volume of Basic Laws was published in 1893, the second in 1903. For a partial translation, see Frege (1964).…”

Section: A Very Brief Aside: Presburger Arithmeticmentioning

confidence: 99%

An Introduction to Gödel's Theorems

Smith¹

2001

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we go along, when needed? Similarly we will also need to call upon some ideas from the general theory of computation -for example, we will make use of both the notion of a 'primitive recursive function' and the more general notion of a 'recursive function'. Again, do we explain these together? Or do we give the explanations many chapters apart, when the respective notions first get used? I've mostly adopted the second policy, introducing new ideas as and when needed. This has its costs, but I think that there is a major compensating benefit, namely that the way the book is organized makes it clearer just what depends on what. It also reflects something of the historical order in which ideas emerged.Many thanks are due to generations of students and to

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The Basic Laws of Arithmetic

Cited by 224 publications

References 0 publications

Another way logic might be normative

Another way logic might be normative

Filosofia da Lógica Empiricamente Informada: uma ilustração via metafísica da lógica

An Introduction to Gödel's Theorems

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