•  603
    Stable Harmony
    In Peliš Michal (ed.), Logica Yearbook 2007, . 2008.
    In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
  •  535
    What is wrong with classical negation?
    Grazer Philosophische Studien 92 (1): 51-86. 2015.
    The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory …Read more
  •  466
    Some Comments on Ian Rumfitt’s Bilateralism
    Journal of Philosophical Logic 45 (6): 623-644. 2016.
    Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ : 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I…Read more
  •  462
    Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality
    Journal of Philosophical Logic 44 (6): 713-727. 2015.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects …Read more
  •  411
    How Fundamental is the Fundamental Assumption?
    Teorema: International Journal of Philosophy 2 (2): 5-19. 2012.
    The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ project of…Read more
  •  405
    Review of Bob Hale's Necessary Beings (review)
    Disputatio (40): 92-100. 2015.
    Review of Bob Hale's "Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them". Oxford: Oxford University Press 2013, ISBN 9780199669578.
  •  266
    Molnar on Truthmakers for Negative Truths
    Metaphysica 19 (2): 251-257. 2018.
    Molnar argues that the problem of truthmakers for negative truths arises because we tend to accept four metaphysical principles that entail that all negative truths have positive truthmakers. This conclusion, however, already follows from only three of Molnar´s metaphysical principles. One purpose of this note is to set the record straight. I provide an alternative reading of two of Molnar´s principles on which they are all needed to derive the desired conclusion. Furthermore, according to Molna…Read more
  •  201
    An Argument for Minimal Logic
    Dialectica 73 (1-2): 31-63. 2019.
    The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A rule based account of the …Read more
  •  190
    Bilateralist Detours: From Intuitionist to Classical Logic and Back
    Logique Et Analyse 60 (239): 301-316. 2017.
    There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no…Read more
  •  182
    Is Incompatibilism Compatible with Fregeanism?
    European Journal of Analytic Philosophy 14 (2): 27-46. 2018.
    This paper considers whether incompatibilism, the view that negation is to be explained in terms of a primitive notion of incompatibility, and Fregeanism, the view that arithmetical truths are analytic according to Frege’s definition of that term in §3 of Foundations of Arithmetic, can both be upheld simultaneously. Both views are attractive on their own right, in particular for a certain empiricist mind-set. They promise to account for two philosophical puzzling phenomena: the problem of negati…Read more
  •  126
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
  •  124
    This short paper has two loosely connected parts. In the first part, I discuss the difference between classical and intuitionist logic in relation to different the role of hypotheses play in each logic. Harmony is normally understood as a relation between two ways of manipulating formulas in systems of natural deduction: their introduction and elimination. I argue, however, that there is at least a third way of manipulating formulas, namely the discharge of assumption, and that the difference be…Read more
  •  91
    The paper begins with a conceptual discussion of Michael Dummett's proof-theoretic justification of deduction or proof-theoretic semantics, which is based on what we might call Gentzen's thesis: 'the introductions constitute, so to speak, the "definitions" of the symbols concerned, and the eliminations are in the end only consequences thereof, which could be expressed thus: In the elimination of a symbol, the formula in question, whose outer symbol it concerns, may only "be used as that which it…Read more
  •  62
    What is interpretation? A dilemma for Davidson
    Conceptus: Zeitschrift Fur Philosophie 40 (98): 54-66. 2014.
    The core idea of Davidson’s philosophy of language is that a theory of truth constructed as an empirical theory by a radical interpreter is a theory of meaning. I discuss an ambiguity that arises from Davidson's notion of interpretation: it can either be understood as the hypothetical process of constructing a theory of truth for a language or as a process that actually happens when speakers communicate. I argue that each disambiguation is problematic and does not result in a theory of meaning.
  •  59
    Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
    Bulletin of the Section of Logic 48 (4): 299-317. 2019.
    Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (Kürbis …Read more
  •  57
    Sketch of a Proof-Theoretic Semantics for Necessity
    In Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.), Advances in Modal Logic 13. Booklet of Short Papers, . pp. 37-43. 2020.
    This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.
  •  51
    Definite Descriptions in Intuitionist Positive Free Logic
    Logic and Logical Philosophy 30 1. 2020.
    This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descr…Read more
  •  43
    Proof and Falsity: A Logical Investigation
    Cambridge University Press. 2019.
    This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Kürbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech a…Read more
  •  29
    Normalisation for Bilateral Classical Logic with some Philosophical Remarks
    Journal of Applied Logics 2 (8): 531-556. 2021.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent sys…Read more
  •  15
    The Importance of Being Erroneous
    Australasian Philosophical Review 2 (3): 155-166. 2021.
    This is a commentary on MM McCabe's "First Chop your logos... Socrates and the sophists on language, logic, and development". In her paper MM analyses Plato's Euthydemos, in which Plato tackles the problem of falsity in a way that takes into account the speaker and complements the Sophist's discussion of what is said. The dialogue looks as if it is merely a demonstration of the silly consequences of eristic combat. And so it is. But a main point of MM's paper is that there is serious philosophy …Read more
  •  13
    The Importance of Being Erroneous
    Australasian Philosophical Review 3 (2): 155-166. 2019.
    ABSTRACT In this commentary, I draw parallels between the sophists’ and the Socratic account of meaning that McCabe reconstructs from the Euthydemus and views on logic and language found in the works of classical authors of analytic philosophy. I argue that the ingredients of the sophist’s account of truth, which McCabe describes as ‘chopped logos’, correspond to widely held philosophical theses concerning meaning. It shares three of its four ingredients with the direct reference theory of the m…Read more
  •  4
    Kurbis_Necessary beings, by Bob Hale.