Logical Conventionalism

Warren, Judith J.

doi:10.1093/oso/9780190086152.003.0004

Cited by 5 publications

(18 citation statements)

References 30 publications

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“…Let us take conjunction as our main example. On traditional inferentialist metasemantic theories, possessing the concept of conjunction requires inferring according to the rules of conjunction-introduction and conjunction-elimination, or, at least, inferring according to these rules when “given a chance,” for instance, “when someone or something brings the conclusion to your direct attention, perhaps by querying you on the matter” [55, p. 46] 41 . Our constraints (c)–(h) capture precisely such a view: they entail that an agent who believes a conjunction would assent to its conjuncts if queried about them, and that an agent who believes the conjuncts of a conjunction would eventually (though perhaps not immediately) assent to the conjunction if queried about it.…”

Section: Algorithmic Modelsmentioning

confidence: 99%

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An Algorithmic Impossible-Worlds Model of Belief and Knowledge

Soysal¹

2023

The Review of Symbolic Logic

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In this paper, I develop an algorithmic impossible-worlds model of belief and knowledge that provides a middle ground between models that entail that everyone is logically omniscient and those that are compatible with even the most egregious kinds of logical incompetence. In outline, the model entails that an agent believes (knows) $\phi $ just in case she can easily (and correctly) compute that $\phi $ is true and thus has the capacity to make her actions depend on whether $\phi $ . The model thereby captures the standard view that belief and knowledge ground are constitutively connected to dispositions to act. As I explain, the model improves upon standard algorithmic models developed by Parikh, Halpern, Moses, Vardi, and Duc, among other ways, by integrating them into an impossible-worlds framework. The model also avoids some important disadvantages of recent candidate middle-ground models based on dynamic epistemic logic or step logic, and it can subsume their most important advantages.

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Section: Algorithmic Modelsmentioning

confidence: 99%

“…]), or at least being disposed, when certain normal conditions are in place, to believe if one believes (e.g., Boghossian [9, pp. 493–497], Warren [55, pp. 46f.]).…”

Section: Introductionmentioning

confidence: 99%

An Algorithmic Impossible-Worlds Model of Belief and Knowledge

Soysal¹

2023

The Review of Symbolic Logic

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“…Perhaps only truth by explicit convention is like fictionalism? Modern conventionalists like Jared Warren (2020) rightly insist that any interesting conventionalism involves implicit conventions; these are to be understood as practices of a certain kind, and what's true by convention is what those practices serve to legitimate. But here too I think there is no difference from how fictionalism has been understood: fictionalists always assumed that even arithmetic talk prior to its explicit codification by Dedekind and Peano is best construed as a fiction.…”

Section: Mathematical Conventionalismmentioning

confidence: 99%

“…Conventionalism in mathematics has recently received an impressive book‐length defense in Warren 2020. Few other authors today endorse conventionalism so wholeheartedly, but many seem sympathetic to the Carnapian distinction between questions internal to a framework and questions about the utility of frameworks (Carnap 1950), and ‘framework’ seems like another name for ‘convention’.…”

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confidence: 99%

Conventionalism about mathematics and logic

Field

2022

Nous

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Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti‐objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper then turns to anti‐objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti‐objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property‐theoretic paradoxes.

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“…3. The Carnapian perspective is defended byCarnap (1937Carnap ( , 1939, and more recently byAzzouni (2006);Gabbay (2010);Rayo (2013);Donaldson (2015);Warren (2020);Ruffino, San Mauro, and Venturi (2021);and Soysal (2021) 4. For the former criticism, see, e.g.,(Bjerring & Schwarz 2017, pp.…”

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confidence: 99%

A metalinguistic and computational approach to the problem of mathematical omniscience

Soysal

2022

Philos Phenomenol Research

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In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible‐worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible‐worlds model of knowledge and belief on which these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible‐worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible‐worlds account of mathematical content, knowledge, and inquiry.

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Logical Conventionalism

Cited by 5 publications

References 30 publications

An Algorithmic Impossible-Worlds Model of Belief and Knowledge

An Algorithmic Impossible-Worlds Model of Belief and Knowledge

Conventionalism about mathematics and logic

A metalinguistic and computational approach to the problem of mathematical omniscience

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