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Bahram Assadian
University of Leeds
  1.  72
    Abstractionism and Mathematical Singular Reference.Bahram Assadian - 2019 - Philosophia Mathematica 27 (2):177-198.
    ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by (...)
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  2. The semantic plights of the ante-rem structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):1-20.
    A version of the permutation argument in the philosophy of mathematics leads to the thesis that mathematical terms, contrary to appearances, are not genuine singular terms referring to individual objects; they are purely schematic or variables. By postulating ‘ante-rem structures’, the ante-rem structuralist aims to defuse the permutation argument and retain the referentiality of mathematical terms. This paper presents two semantic problems for the ante- rem view: (1) ante-rem structures are themselves subject to the permutation argument; (2) the ante-rem structuralist (...)
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  3.  16
    The insubstantiality of mathematical objects as positions in structures.Bahram Assadian - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 20.
    The realist versions of mathematical structuralism are often characterized by what I call ‘the insubstantiality thesis’, according to which mathematical objects, being positions in structures, have no non-structural properties: they are purely structural objects. The thesis has been criticized for being inconsistent or descriptively inadequate. In this paper, by implementing the resources of a real-definitional account of essence in the context of Fregean abstraction principles, I offer a version of structuralism – essentialist structuralism – which validates a weaker version of (...)
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  4. Are the Natural Numbers Fundamentally Ordinals?Bahram Assadian & Stefan Buijsman - 2018 - Philosophy and Phenomenological Research 99 (3):564-580.
    There are two ways of thinking about the natural numbers: as ordinal numbers or as cardinal numbers. It is, moreover, well-known that the cardinal numbers can be defined in terms of the ordinal numbers. Some philosophies of mathematics have taken this as a reason to hold the ordinal numbers as (metaphysically) fundamental. By discussing structuralism and neo-logicism we argue that one can empirically distinguish between accounts that endorse this fundamentality claim and those that do not. In particular, we argue that (...)
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  5. Indeterminacy and Failure of Grounding.Bahram Assadian & Jonathan Nassim - 2019 - Theoria (4):1.
    Cases of grounding failure present a puzzle for fundamental metaphysics. Typically, solutions are thought to lie either in adding ontology such as haecceities or in re‐describing the cases by means of the ideology of metaphysical indeterminacy. The controversial status of haecceities has led some to favour metaphysical indeterminacy as the way to solve the puzzle. We consider two further treatments of grounding failure each of which, we argue, is a more plausible alternative. As such, the initial dichotomy is a false (...)
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  6.  78
    In defence of utterly indiscernible entities.Bahram Assadian - 2019 - Philosophical Studies 176 (10):2551-2561.
    Are there entities which are just distinct, with no discerning property or relation? Although the existence of such utterly indiscernible entities is ensured by mathematical and scientific practice, their legitimacy faces important philosophical challenges. I will discuss the most fundamental objections that have been levelled against utter indiscernibles, argue for the inadequacy of the extant arguments to allay perplexity about them, and put forward a novel defence of these entities against those objections.
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  7.  10
    Mathematical structuralism and bundle theory.Bahram Assadian - forthcoming - Ratio.
    According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging picture is (...)
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  8.  23
    Abstraction and semantic presuppositions.Bahram Assadian - 2023 - Analysis 15 (3):419-428.
    According to the neo-Fregean abstractionism, numerical expressions of the form ‘the number of Fs’, introduced by Hume’s Principle, should be read as purportedly referential singular terms. I will explore the prospects of a version of abstractionism in which such expressions have presuppositional content, as in Strawson’s account. I will argue that the thesis that ‘the number of Fs’ semantically presupposes the existence of a number is inconsistent with the required ‘modest’ stipulative character of the truth of Hume’s Principle: since Hume’s (...)
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  9. Introduction to Knowledge, Number and Reality. Encounters with the Work of Keith Hossack.Nils Kürbis, Jonathan Nassim & Bahram Assadian - 2022 - In Nils Kürbis, Bahram Assadian & Jonathan Nassim (eds.), Knowledge, Number and Reality: Encounters with the Work of Keith Hossack. London: Bloomsbury. pp. 1-30.
    The Introduction to "Knowledge, Number and Reality. Encounters with the Work of Keith Hossack" provides an overview over Hossack's work and the contributions to the volume.
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  10.  15
    Performative reference.Bahram Assadian & Giorgio Sbardolini - 2023 - Synthese 202 (2):1-18.
    Reference may be fixed by stipulation through a speech act, just like bets and marriages. An utterance of _Let n refer to an/the F_ is a speech act by means of which, if successful, a speaker institutes a practice of referring, and a hearer coordinates by choosing a referent from the domain of discourse. We articulate a metasemantics for this view. On our view, the interlocutors can select a referent randomly, if necessary, motivated by the incentive to coordinate on the (...)
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  11.  19
    Linnebo on reference by abstraction.Bahram Assadian - 2023 - Analytic Philosophy 2.
    According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling (...)
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  12.  38
    Mathematical structures, universals, and singular terms.Bahram Assadian - 2022 - In B. Assadian N. Kürbis (ed.), Knowledge, Number, and Reality; Encounters with the Work of Keith Hossack. pp. 203-216.
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  13.  21
    Correction to: The semantic plights of the ante-rem structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):3237-3237.
    In the original publication of the article, footnote 17 was incorrectly published. The corrected footnote is given below.
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  14.  11
    Deflationary Reference and Referential Indeterminacy.Bahram Assadian - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 365-377.
    Indeterminacy of reference appears to be incompatible with the deflationist conceptions of reference: in deflationismDeflationism, the singular term ‘a’ refers to a, if it exists, and to nothing else, whereas if the term is referentially indeterminate, it has a variety of equally permissible reference-candidates: referential indeterminacyReferential indeterminacy and deflationismDeflationism cannot both be maintained. In this paper, I discuss the incompatibility thesis, critically examine the arguments leading to it, and thereby point towards ways in which the deflationist can explain referential indeterminacyReferential (...)
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  15.  83
    Knowledge, Number and Reality: Encounters with the Work of Keith Hossack.Nils Kürbis, Bahram Assadian & Jonathan Nassim (eds.) - 2022 - London: Bloomsbury.
    Throughout his career, Keith Hossack has made outstanding contributions to the theory of knowledge, metaphysics and the philosophy of mathematics. -/- This collection of previously unpublished papers begins with a focus on Hossack's conception of the nature of knowledge, his metaphysics of facts and his account of the relations between knowledge, agents and facts. Attention moves to Hossack's philosophy of mind and the nature of consciousness, before turning to the notion of necessity and its interaction with a priori knowledge. Hossack's (...)
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  16.  52
    Abstractionism: Essays in Philosophy of MathematicsBy Philip A. Ebert and Marcus Rossberg. [REVIEW]Bahram Assadian - 2018 - Analysis 78 (1):188-191.
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  17.  71
    The Metaphysics of Relations. [REVIEW]Bahram Assadian - 2017 - Philosophical Quarterly 67 (269):871-874.
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