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Profile: Rafal Urbaniak (University of Ghent, University of Gdansk)
  1. Rafal Urbaniak, Nominalist Neologicism.
    The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...)
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  2. Rafal Urbaniak (2014). Słupecki's Generalized Mereology and Its Flaws. History and Philosophy of Logic 35 (3):289-300.
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  3. Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.
    We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo (...)
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  4. Rafal Urbaniak (2013). Lesniewski's Systems of Logic and Foundations of Mathematics. Springer.
  5. Rafal Urbaniak (2013). Plural Quantifiers: A Modal Interpretation. Synthese:1-22.
    One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...)
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  6. Rafal Urbaniak & Frederik Van De Putte (2013). Induction From a Single Instance: Incomplete Frames. [REVIEW] Foundations of Science 18 (4):641-653.
    In this paper we argue that an existing theory of concepts called dynamic frame theory, although not developed with that purpose in mind, allows for the precise formulation of a number of problems associated with induction from a single instance. A key role is played by the distinction we introduce between complete and incomplete dynamic frames, for incomplete frames seem to be very elegant candidates for the format of the background knowledge used in induction from a single instance. Furthermore, we (...)
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  7. Rafal Urbaniak (2012). Numbers and Propositions Versus Nominalists: Yellow Cards for Salmon & Soames. [REVIEW] Erkenntnis 77 (3):381-397.
    Salmon and Soames argue against nominalism about numbers and sentence types. They employ (respectively) higher-order and first-order logic to model certain natural language inferences and claim that the natural language conclusions carry commitment to abstract objects, partially because their renderings in those formal systems seem to do that. I argue that this strategy fails because the nominalist can accept those natural language consequences, provide them with plausible and non-committing truth conditions and account for the inferences made without committing themselves to (...)
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  8. Rafal Urbaniak (2012). “Platonic” Thought Experiments: How on Earth? Synthese 187 (2):731-752.
    Brown (The laboratory of the mind. Thought experiments in the natural science, 1991a , 1991b ; Contemporary debates in philosophy of science, 2004 ; Thought experiments, 2008 ) argues that thought experiments (TE) in science cannot be arguments and cannot even be represented by arguments. He rest his case on examples of TEs which proceed through a contradiction to reach a positive resolution (Brown calls such TEs “platonic”). This, supposedly, makes it impossible to represent them as arguments for logical reasons: (...)
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  9. Rafal Urbaniak & K. Severi Hämäri (2012). Busting a Myth About Leśniewski and Definitions. History and Philosophy of Logic 33 (2):159 - 189.
    A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Le?niewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Le?niewski's published or unpublished work is known where the standard conditions are discussed. Second, Le?niewski's own logical theories allow for creative definitions. Third, Le?niewski's celebrated ?rules of definition? lay (...)
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  10. Rafal Urbaniak & Agnieszka Rostalska (2011). A Modern Modal Argument for the Soul. In Michael Bruce & Steven Barbone (eds.), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy. Wiley-Blackwell. 93-99.
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  11. Rafal Urbaniak (2010). Capturing Dynamic Conceptual Frames. Logic Journal of the IGPL 18 (3):430-455.
    The main focus of this paper is to develop an adaptive formal apparatus capable of capturing (certain types of) reasoning conducted within the framework of the so-called dynamic conceptual frames. I first explain one of the most recent theories of concepts developed by cognitivists, in which a crucial part is played by the notion of a dynamic frame. Next, I describe how a dynamic frame may be captured by a finite set of first-order formulas and how a formalized adaptive framework (...)
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  12. Rafal Urbaniak (2010). Neologicist nominalism. Studia Logica 96 (2):149-173.
    The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...)
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  13. Agnieszka Rostalska & Rafal Urbaniak (2009). Swinburne's Modal Argument for the Existence of a Soul. Philo 12 (1):73-87.
    This paper evaluates Richard Swinburne’s modal argument for the existence of souls. After a brief presentation of the argument, wedescribe the main known objection to it, which is called the substitution objection (SO for short), and explain Swinburne’s response to that objection. With this as background, we formalize Swinburne’s argument in a quantified propositional modal language, modifying it so that it is logically valid and contains no tacit assumptions, and we explain why we find Swinburne’s response to SO unsatisfactory. Next, (...)
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  14. Rafal Urbaniak (2009). Bogus Singular Terms and Substitution Salva Denotatione. The Reasoner 3.
    This is the third installment of a paper which deals with comparison and evaluation of the standard slingshot argument (for the claim that all true sentences, if they refer, refer to the same object) with the doxastic formulation.
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  15. Rafal Urbaniak (2009). Doxastic Synonymy Vs. Logical Equivalence. The Reasoner 3.
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  16. Rafal Urbaniak (2009). Slingshot Arguments: Two Versions. The Reasoner 3.
    The first installment of a paper comparing the standard slingshot argument with the doxastic version.
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  17. Rafal Urbaniak & Agnieszka Rostalska (2009). Swinburne's Modal Argument for the Existence of the Soul. Philo 12 (1):73-88.
    Richard Swinburne (Swinburne and Shoemaker 1984; Swinburne 1986) argues that human beings currently alive have non{bodily immaterial parts called souls. In his main argument in support of this conclusion (modal argument), roughly speaking, from the assumption that it is logically possible that a human being survives the destruction of their body and a few additional premises, he infers the actual existence of souls. After a brief presentation of the argument we describe the main known objection to it, called the substitution (...)
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  18. Rafal Urbaniak (2008). Lesniewski and Russell's Paradox: Some Problems. History and Philosophy of Logic 29 (2):115-146.
    Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...)
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  19. Rafal Urbaniak (2008). Lesniewski's Systems of Logic and Mereology; History and Re-Evaluation. Dissertation, University of Calgary