Carnap and Beth on the Limits of Tolerance

Marschall, Benjamin

doi:10.1017/can.2021.16

Cited by 4 publications

(2 citation statements)

References 42 publications

(14 reference statements)

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“…30 For a very interesting and elaborate discussion on the ability of human beings to perform infinite inferences see (Warren, 2021). For a criticism, see (Marschall, 2021). Marschall assumes, however, that we do not have dispositions for following infinite rules and, thus, he concludes that only languages with recursive rules are permissible.…”

Section: The ω-Rule Againmentioning

confidence: 99%

Inferential Quantification and the ω-Rule

Brîncuş

2024

Synthese Library

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Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions "all" and "there is" leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning.

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Section: The ω-Rule Againmentioning

confidence: 99%

Inferential Quantification and the ω-Rule

Brîncuş

2024

Synthese Library

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“…Ebbs has previously stressed that the adoption of Carnapian languages for practical use is a crucial element of Beth's argument (1997, sections 60‐61). The connection between these two ideas has recently been drawn by Marschall (2021). It is easiest to appreciate the potential problem for Language I, in which Carnap characterises the analytic sentences by means of the infinitary

\omega

‐rule.…”

Section: Beth's Argument From Non‐standard Modelsmentioning

confidence: 99%

Carnap's philosophy of mathematics

Marschall

2022

Philosophy Compass

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For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture.It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made.

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Carnap and the a priori

Marschall

2023

European J of Philosophy

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What are Carnap's views on the epistemology of mathematics? Did he believe in a priori justification, and if so, what is his account of it? One might think that such questions are misguided, since in the 1930s Carnap came to reject traditional epistemology as a confused mixture of logic and psychology. But things are not that simple. Drawing on recent work by Richardson and Uebel, I will show that Carnap's mature metaphilosophy leaves room for two distinct notions of a priori justification: one propositional, the other doxastic. The latter is especially interesting since it comes closest to a traditional understanding of a priority. On the other hand, Carnap has little to say about doxastic justification in his writings. This lacuna can be filled by drawing on an unpublished exchange with Irving M. Copi. In it, so I will show, Carnap endorses the view that agents can come to know all mathematical truths a priori. This fact, so I will further argue, can be used to adjudicate a dispute between Ricketts and Friedman about the nature and viability of Carnap's philosophy of mathematics—specifically his reliance on infinitary methods.

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Carnap and Beth on the Limits of Tolerance

Cited by 4 publications

References 42 publications

Inferential Quantification and the ω-Rule

Inferential Quantification and the ω-Rule

Carnap's philosophy of mathematics

Carnap and the a priori

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