Free of Detachment: Logic, Rationality, and Gluts

Beall, Jc

doi:10.1111/nous.12029

Cited by 81 publications

(45 citation statements)

References 32 publications

(42 reference statements)

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“…According to this view, logics constrain a reasoner by providing rational choices, while for example evidence weighing determines that choice (Knorpp 1997;Beall 2013). …”

Section: Notesmentioning

confidence: 97%

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Concerning Peter Vickers's Recent Treatment of ‘Paraconsistencitis’

Šešelja¹,

Straßer²

2014

International Studies in the Philosophy of Science

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“…According to this view, logics constrain a reasoner by providing rational choices, while for example evidence weighing determines that choice (Knorpp 1997;Beall 2013). …”

Section: Notesmentioning

confidence: 97%

“…, A n and B are in question' (Field 2009, 260). Beall (2013) phrases the commitment in terms of a constraint according to which one is not to reject consequences: 'If XrA, then it's irrational to accept X and reject A' (Beall 2013, 4). Meheus (2002) offers a finer-grained analysis distinguishing between sensible and acceptable consequences.…”

Section: Notesmentioning

confidence: 99%

Concerning Peter Vickers's Recent Treatment of ‘Paraconsistencitis’

Šešelja¹,

Straßer²

2014

International Studies in the Philosophy of Science

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“…Whether we are concerned with presenting a full theory via one of its subtheories, or with connecting explicit claims to commitments thereby taken up, we use consequence to tie a smaller body of information Γ to a larger one C (Γ), its closure, in the following way: a claim A is in C (Γ) iff it is entailed by Γ; that is, iff Γ ⊢ A . This use has been recently emphasized in Beall (, notation tweaked): “Give to logic your theory Γ, and then sit back: logic ‘freely’ or ‘automatically’ expands your theory to C (Γ), which contains all of Γ's (singleton) consequences.”…”

Section: Closurementioning

confidence: 99%

“…These systems form one family of substructural logical systems: systems that do not impose the full budget of what are called structural rules , or in which there are counterexamples to the structural metainferences associated with these rules. My main goal here is to consider the connection between consequence and closure , a connection recently emphasized in (Beall ), and point to a seeming difficulty faced by many familiar noncontractive consequence relations in upholding this connection. The trouble I will point out in what follows applies to approaches explored and defended in Barker (), Beall and Murzi (), Grišin (), Mares and Paoli (), Petersen (), Restall (), and Zardini ().…”

mentioning

confidence: 99%

Contraction and closure

Ripley

2015

Thought: A Journal of Philosophy

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“…With the notable exception of Beall (2013), the failure of such a basic and intuitive rule as Modus Ponens in lp led many paraconsistent-minded philosophers (e.g. Priest 2006, chap.…”

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confidence: 99%

Disquotation and Infinite Conjunctions

Picollo

Schindler

2017

Erkenn

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One of the main logical functions of the truth predicate is to enable us to express so-called 'infinite conjunctions'. Several authors claim that the truth predicate can serve this function only if it is fully disquotational (transparent), which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a truth predicate and argue that they fail to support the necessity of transparency for that purpose. Second, we show that, with the aid of some regimentation, many expressive functions of the truth predicate can actually be performed using truth principles that are consistent in classical logic. Finally, we suggest a reconceptualisation of deflationism, according to which the principles that govern the use of the truth predicate in natural language are largely irrelevant for the question of what formal theory of truth we should adopt. Many philosophers think that the paradoxes pose a special problem for deflationists; we will argue, on the contrary, that deflationists are in a much better position to deal with the paradoxes than their opponents. The ProblemMany philosophers maintain that the truth predicate can serve certain expressive roles of a quasi-logical nature, the most salient of which is to enable us to express so-called 'infinite conjunctions'. These are sentences of the form All Ps are true.where P is a predicate of the language that applies to infinitely many sentences. 1They are considered to express the infinitely many Ps at once or, as is often said, their infinite conjunction, without turning to infinitary or higher-order resources (cf. Quine 1970;Leeds 1978;Putnam 1978; Horwich 1998;Field 2007).(The phrase 'expressing infinite conjunctions' is taken from the literature-e.g. Putnam 1978; Gupta 1993-and of course in need of clarification. For the moment, the reader should take it as a technical term.) We call this function of the truth predicate the 'infinite-conjunction' function.As Quine (1970, chap. 1) points out, the universal quantifier serves a similar purpose. If the infinitely many sentences we want to express differ in one or several individual terms-e.g. ''0 is divisible by 2'', ''2 is divisible by 2'', ''4 is divisible by 2'', etc.-and the class of objects these terms denote is definable in the language by a suitable predicate (e.g. ''is an even number''), we can express the infinitely many sentences at once just generalising over those terms using this predicate-e.g. uttering ''All even numbers are divisible by 2''. However, if the infinitely many sentences we want to express don't differ just in one or more individual terms, this strategy is no longer available. In that case, the truth predicate, interacting with the universal quantifier, might do the job, as long as the sentences at issue share a property definable in the language. For instance, we can assert al...

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Free of Detachment: Logic, Rationality, and Gluts

Cited by 81 publications

References 32 publications

Concerning Peter Vickers's Recent Treatment of ‘Paraconsistencitis’

Concerning Peter Vickers's Recent Treatment of ‘Paraconsistencitis’

Contraction and closure

Disquotation and Infinite Conjunctions

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