*JC Beall*

- Published in print:
- 2005
- Published Online:
- October 2011
- ISBN:
- 9780199288403
- eISBN:
- 9780191700491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199288403.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Logical pluralism is a pluralism about logical consequence. Crudely put, a pluralist maintains that there is more than one relation of logical consequence. By way of illustrating the kind of claim ...
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Logical pluralism is a pluralism about logical consequence. Crudely put, a pluralist maintains that there is more than one relation of logical consequence. By way of illustrating the kind of claim involved in logical pluralism, a few analogies are considered in this chapter. According to the Generalised Tarski Thesis (GTT), an argument is valid if and only if, in every case in which the premises are true, so is the conclusion. Logical pluralism is the claim that at least two different instances of GTT provide admissible precisifications of logical consequence. Unlike the restricted Tarski Thesis, which admits only one instance of case (Tarski's models), the pluralist endorses at least two instances, giving rise to two different accounts of deductive logical consequence (for the same language), two different senses of ‘follows from’. There are at least two ways to not be a logical pluralist: reject the GTT or endorse exactly one instance.Less

Logical pluralism is a pluralism about logical consequence. Crudely put, a pluralist maintains that there is more than one relation of logical consequence. By way of illustrating the kind of claim involved in logical pluralism, a few analogies are considered in this chapter. According to the Generalised Tarski Thesis (GTT), an argument is valid if and only if, in every case in which the premises are true, so is the conclusion. Logical pluralism is the claim that at least two different instances of GTT provide admissible precisifications of logical consequence. Unlike the restricted Tarski Thesis, which admits only one instance of case (Tarski's models), the pluralist endorses at least two instances, giving rise to two different accounts of deductive logical consequence (for the same language), two different senses of ‘follows from’. There are at least two ways to not be a logical pluralist: reject the GTT or endorse exactly one instance.

*JC Beall*

- Published in print:
- 2005
- Published Online:
- October 2011
- ISBN:
- 9780199288403
- eISBN:
- 9780191700491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199288403.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Intuitionistic logic, also known as constructive logic, is a particular account of logical consequence, at variance with both classical and relevant logical consequence. One way to introduce ...
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Intuitionistic logic, also known as constructive logic, is a particular account of logical consequence, at variance with both classical and relevant logical consequence. One way to introduce intuitionistic logic is by means of constructions. This chapter gives an account of constructive validity by first indicating what it is to construct a statement, and then instantiating Generalised Tarski Thesis (GTT) cases with constructions: an argument is constructively valid if and only if a construction for the premises provides a construction for the conclusion. Before turning to constructions, the relationship between intuitionistic logic and intuitionism is discussed. Intuitionism maintains that constructive reasoning is required by the nature of mathematical entities themselves. The entities in question are constructions of the reasoner in intuition, and such entities have only the properties bestowed upon them by their construction.Less

Intuitionistic logic, also known as constructive logic, is a particular account of logical consequence, at variance with both classical and relevant logical consequence. One way to introduce intuitionistic logic is by means of constructions. This chapter gives an account of constructive validity by first indicating what it is to construct a statement, and then instantiating Generalised Tarski Thesis (GTT) cases with constructions: an argument is constructively valid if and only if a construction for the premises provides a construction for the conclusion. Before turning to constructions, the relationship between intuitionistic logic and intuitionism is discussed. Intuitionism maintains that constructive reasoning is required by the nature of mathematical entities themselves. The entities in question are constructions of the reasoner in intuition, and such entities have only the properties bestowed upon them by their construction.

*JC Beall*

- Published in print:
- 2005
- Published Online:
- October 2011
- ISBN:
- 9780199288403
- eISBN:
- 9780191700491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199288403.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Logical pluralism addresses the following conditions. First, the settled core of consequence is given in the Generalised Tarski Thesis (GTT). Second, an instance of GTT is obtained by a specification ...
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Logical pluralism addresses the following conditions. First, the settled core of consequence is given in the Generalised Tarski Thesis (GTT). Second, an instance of GTT is obtained by a specification of the cases in GTT, and a specification of the relation is true in a case. Such a specification can be seen as a way of spelling out truth conditions. Third, an instance of GTT is admissible if it satisfies the settled role of consequence, and if its judgements about consequence are necessary, normative, and formal. Fourth, a logic is given by an admissible instance of GTT. Lastly, there are at least two different admissible instances of GTT. Logic is a matter of preservation of truth in all cases, which lies at the heart of logical consequence, the settled core of follows from. This chapter considers two well-known specifications of cases x : possible worlds and models for classical predicate logic. It notes the extent to which the canvassed accounts of consequence are admissible: the extent to which their respective judgements are necessary, normative, and formal.Less

Logical pluralism addresses the following conditions. First, the settled core of consequence is given in the Generalised Tarski Thesis (GTT). Second, an instance of GTT is obtained by a specification of the cases in GTT, and a specification of the relation is true in a case. Such a specification can be seen as a way of spelling out truth conditions. Third, an instance of GTT is admissible if it satisfies the settled role of consequence, and if its judgements about consequence are necessary, normative, and formal. Fourth, a logic is given by an admissible instance of GTT. Lastly, there are at least two different admissible instances of GTT. Logic is a matter of preservation of truth in all cases, which lies at the heart of logical consequence, the settled core of *follows from*. This chapter considers two well-known specifications of cases_{ x }: possible worlds and models for classical predicate logic. It notes the extent to which the canvassed accounts of consequence are admissible: the extent to which their respective judgements are necessary, normative, and formal.

*JC Beall*

- Published in print:
- 2005
- Published Online:
- October 2011
- ISBN:
- 9780199288403
- eISBN:
- 9780191700491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199288403.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The Generalised Tarski Thesis (GTT) yields classical consequence when its cases are taken to be possible worlds, where possible worlds are complete and consistent with respect to negation. That ...
More

The Generalised Tarski Thesis (GTT) yields classical consequence when its cases are taken to be possible worlds, where possible worlds are complete and consistent with respect to negation. That (classical) precisification of ‘follows from’ is familiar and useful, however, it is not the only sense of ‘follows from’ apparent in English. Another strongly apparent sense of ‘follows from’ takes ‘from’ seriously. There is a sense of ‘follows from’ that is more restrictive than the classical sense; it demands that premises be ‘relevant’ to conclusions. That sense of ‘follows from’ is more restrictive than the classical one: it imposes constraints that go beyond truth-preservation over possible worlds. The constraints, in effect, concern the behaviour of negation. What is required is not only truth-preservation over possible worlds, but truth-preservation over cases that go beyond the constraints of worlds, beyond the constraints of completeness and consistency. The task is to specify such cases, thereby cashing out relevant consequence.Less

The Generalised Tarski Thesis (GTT) yields classical consequence when its cases are taken to be possible worlds, where possible worlds are complete and consistent with respect to negation. That (classical) precisification of ‘follows from’ is familiar and useful, however, it is not the only sense of ‘follows from’ apparent in English. Another strongly apparent sense of ‘follows from’ takes ‘from’ seriously. There is a sense of ‘follows from’ that is more restrictive than the classical sense; it demands that premises be ‘relevant’ to conclusions. That sense of ‘follows from’ is more restrictive than the classical one: it imposes constraints that go beyond truth-preservation over possible worlds. The constraints, in effect, concern the behaviour of negation. What is required is not only truth-preservation over possible worlds, but truth-preservation over cases that go beyond the constraints of worlds, beyond the constraints of completeness and consistency. The task is to specify such cases, thereby cashing out relevant consequence.