A computational interpretation of conceptivism

Ferguson, Thomas Macaulay

doi:10.1080/11663081.2014.980116

Cited by 36 publications

(58 citation statements)

References 29 publications

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“…Counterexample for (17)- (19): These schemas are invalid due to fragmentation. W.l.o.g., let F = {i, j } and consider the model…”

Section: Proof Of Theorem 2: Invaliditiesmentioning

confidence: 99%

“…j ) ⊆ |q|, respectively). For (18) and (19), consider M 2 with μ(P , Q) = P ∩ Q for all P , Q ∈ I @ . Then, (18) is invalid since…”

Section: Proof Of Theorem 2: Invaliditiesmentioning

confidence: 99%

“…Compare the clause for 'analytic implication' in the conceptivist logic literature (see[19,22]) and the clause for knowledge ascriptions in the awareness logic literature (see[17]). The version of awareness logic closest to our framework is the one in terms of 'awareness generated by primitive propositions' (see[55], p. 81), where an agent is aware of a formula ϕ just in case it is aware of all of its atomic constituents, taken together.…”

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confidence: 99%

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The Fundamental Problem of Logical Omniscience

2019

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We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: (i) an intension, taking care of truth conditions; and (ii) a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: (1) the topicsensitivity of content; (2) the fragmentation of knowledge states; (3) the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections.

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“…Counterexample for (17)- (19): These schemas are invalid due to fragmentation. W.l.o.g., let F = {i, j } and consider the model…”

Section: Proof Of Theorem 2: Invaliditiesmentioning

confidence: 99%

“…j ) ⊆ |q|, respectively). For (18) and (19), consider M 2 with μ(P , Q) = P ∩ Q for all P , Q ∈ I @ . Then, (18) is invalid since…”

Section: Proof Of Theorem 2: Invaliditiesmentioning

confidence: 99%

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confidence: 99%

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The Fundamental Problem of Logical Omniscience

2019

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“…Here, we will be concerned with logics L (with a binary connective → in their language) that satisfy what Ferguson [13] calls the proscriptive principle for theorems (PP → ): letting V ar (χ) be the set of propositional variables in χ for any formula χ , PP → requires that if L ϕ → ψ, then V ar (ψ) ⊆ V ar (ϕ). PP → can be motivated in various ways [12], for instance as a relevance constraint-indeed, a tighter one than the customary variable-sharing requirement of relevance logics.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Analysis of Demodalised Analytic Implication

2019

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The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn (and independently investigated by R.D. Epstein) as a variation on a timehonoured logical system by C.I. Lewis' student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is "analytically contained" in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic (PWK). This fact sheds further light on the relationship between containment logics and logics of nonsense.

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“…I'm not so happy with that terminology anymore: it has topic-preservation expressed as 'content containment', and this reminds one of some Kantian analyticity, which is misleading in this context. The terminology of contents was influenced by the fact that the semantics bears similarities with some 'logics of content containment' inspired by the work ofParry (1933) (Angell 1977;Fine 1986;Urquhart 1973), of which(Ferguson 2014) is an excellent survey and interpretation.…”

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confidence: 99%

Taming the runabout imagination ticket

Berto

2018

Synthese

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The 'puzzle of imaginative use' (Kind and Kung in Knowledge through imagination, Oxford University Press, Oxford, 2016) asks: given that imagination is arbitrary escape from reality, how can it have any epistemic value? In particular, imagination seems to be logically anarchic, like a runabout inference ticket: one who imagines A may also imagine whatever B pops to one's mind by free mental association. This paper argues that at least a certain kind of imaginative exercisereality-oriented mental simulation-is not logically anarchic. Showing this is part of the task of solving the puzzle. Six plausible features of imagination, so understood, are listed. Then a formal semantics is provided, whose patterns of logical validity and invalidity model the six features.

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A computational interpretation of conceptivism

Cited by 36 publications

References 29 publications

The Fundamental Problem of Logical Omniscience

The Fundamental Problem of Logical Omniscience

Algebraic Analysis of Demodalised Analytic Implication

Taming the runabout imagination ticket

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