Properties and Propositions

Trueman, Robert

doi:10.1017/9781108886123

Cited by 8 publications

(5 citation statements)

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“…See (Klev 2018, Klev 2017) for a philosophical discussion. 22 See, for instance, (Jones 2016, Klev 2018, Trueman 2020. See also (Klev 2018), for a higher-order solution of the "concept horse paradox" that makes use of type predication, rather than functions, to express predicates such as "is a concept".…”

Section: An Examplementioning

confidence: 99%

Constructive Type Theory, An Appetizer

Crosilla

2024

Higher-Order Metaphysics

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Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A further aim is to argue that a comparison between a plurality of theories is beneficial to the philosophical analysis. We may, for example, discover helpful features of one theory that we may want to import into another context, thus enriching our repertoire of formal tools. Or, through comparison with a less well-known theory, we may gain a better understanding of the characteristics of the theories we are familiar with. As argued in this chapter, CTT has much to offer in all of these respects.

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Section: An Examplementioning

confidence: 99%

Constructive Type Theory, An Appetizer

Crosilla

2024

Higher-Order Metaphysics

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“…One way to be a noncumulativist is to follow Frege's (1891) semantic insights, as developed by Trueman (2020) and by Button and Trueman (2022); there may be other ways. If Fregeanism or any other form of noncumulativism is true, (1) does not make sense and there is no need for extra-order modal relations.…”

Section: Extra-ordermentioning

confidence: 99%

“…In the end, Trueman argues, the official, philosophically strict thought that we (and Frege) mean to express with sentences like (6) has more to do with the impossibility of building a Fregean thought by combining the senses of phrases in the form of '( ) is an object' with senses of phrases in the form of '( ) is a property' and the sense of the existential quantifier. (For the exact definition of this view, and Trueman's case for it, see Trueman, 2020).…”

Section: Extra-ordermentioning

confidence: 99%

Against relationalism about modality

Romero

2023

Philos Stud

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On a highly influential way to think of modality, that I call 'relationalism', the modality of a state is explained by its being composed of properties, and these properties being related by a higher-order and primitively modal relation. Examples of relationalism are the Dretske-Tooley-Armstrong account of natural necessity, many dispositional essentialist views, and Wang's incompatibility primitivism. I argue that relationalism faces four difficulties: that the selection between modal relations is arbitrary, that the modal relation cannot belong to any logical order, that to explain how the modal relation can relate properties of different adicities additional ideological complexity has to be introduced, and that not all modal constraints are relational. From the discussion, I will extract desiderata for a successor theory of modality.

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“…Recently, there have been various attempts to improve on the above characterisation of the broadly Fregean conception of concepts, e.g. Williamson (2013), Jones (2018), Trueman (2021). For instance, according to primitivists about type 12 A further alternative is to interpret the higher-order variables plurally.…”

Section: Type Theory and Ranges Of Significancementioning

confidence: 99%

Unrestricted quantification and ranges of significance

Schindler

2022

Philos Stud

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Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is assumed. However, the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. This alternative emerges very naturally by reflecting on the features on which the type-theoretic solution of the problem of unrestricted quantification relies. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way. The ideas developed in this paper make crucial use of Russell’s notion of range of significance.

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Properties and Propositions

Cited by 8 publications

References 0 publications

Constructive Type Theory, An Appetizer

Constructive Type Theory, An Appetizer

Against relationalism about modality

Unrestricted quantification and ranges of significance

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