Results for 'apriority operator'

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  1. Two-Dimensional Semantics and the Nesting Problem.David J. Chalmers & Brian Rabern - 2014 - Analysis 74 (2):210-224.
    Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional (...)
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  2. What is the Correct Logic of Necessity, Actuality and Apriority?Peter Fritz - 2014 - Review of Symbolic Logic 7 (3):385-414.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines (...)
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  3.  67
    Linking Necessity to Apriority.Tristan Haze - forthcoming - Acta Analytica:1-7.
    There is an important and fairly straightforward link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. Casullo (2003) discusses one such proposal, argues - following Anderson (1993) - that it fails, and suggests an alternative. In this paper, I argue that Casullo’s alternative also fails, before making a suggestion for which I can find no counterexamples and which, notably, handles (...)
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  4. Operator Arguments Revisited.Juhani Yli-Vakkuri, John Hawthorne & Peter Fritz - manuscript
    Certain passages in Kaplan’s ‘Demonstratives’ are often read as constituting an argument for the conclusion that the presence of a non-vacuous sentential operator associated with a certain parameter of sentential truth in a language requires the assertoric contents-cum-compositional semantic values of sentences in that language to vary in truth value with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have assertoric contents that have different truth values (...)
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  5. Safety, Content, Apriority, Self-Knowledge.David Manley - 2007 - Journal of Philosophy 104 (8):403-423.
    This essay motivates a revised version of the epistemic condition of safety and then employs the revision to (i) challenge traditional conceptions of apriority, (ii) refute ‘strong privileged access’, and (iii) resolve a well-known puzzle about externalism and self-knowledge.
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  6.  12
    The Complexity of the Dependence Operator.P. D. Welch - 2015 - Journal of Philosophical Logic 44 (3):337-340.
    We show that Leitgeb’s dependence operator of Leitgeb is a \-operator and that this is best possible.
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  7. Putnam's Account of Apriority and Scientific Change: Its Historical and Contemporary Interest.Jonathan Y. Tsou - 2010 - Synthese 176 (3):429-445.
    In the 1960s and 1970s, Hilary Putnam articulated a notion of relativized apriority that was motivated to address the problem of scientific change. This paper examines Putnam’s account in its historical context and in relation to contemporary views. I begin by locating Putnam’s analysis in the historical context of Quine’s rejection of apriority, presenting Putnam as a sympathetic commentator on Quine. Subsequently, I explicate Putnam’s positive account of apriority, focusing on his analysis of the history of physics (...)
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  8. Eternalism and Propositional Multitasking: In Defence of the Operator Argument.Clas Weber - 2012 - Synthese 189 (1):199-219.
    It is a widely held view in philosophy that propositions perform a plethora of different theoretical roles. Amongst other things, they are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, and the referents of that-clauses. This assumption is often combined with the claim that propositions have their truth-values eternally. In this paper I aim to show that these two assumptions are incompatible: propositions cannot both fulfill the mentioned roles and (...)
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  9. Counterpart Theory and the Actuality Operator.Ulrich Meyer - 2013 - Mind 122 (485):27-42.
    Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.
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  10. Expereincer Phrases, Predicates of Personal Taste and Relativism: On Cappelen and Hawthorne's Critique of the Operator Argument.Dan Zeman - 2013 - Croatian Journal of Philosophy (39):375-398.
    In the debate between relativism and contextualism about various expressions, the Operator Argument, initially proposed by Kaplan , has been taken to support relativism. However, one widespread reaction against the argument has taken the form of arguing against one assumption made by Kaplan: namely, that certain natural language expressions are best treated as sentential operators. Focusing on the only extant version of the Operator Argument proposed in connection to predicates of personal taste such as “tasty” and experiencer phrases (...)
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  11.  21
    Natural Deduction for Diagonal Operators.Fabio Lampert - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics. CSHPM 2016. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Cham: Birkhäuser. pp. 39-51.
    We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility (...)
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  12. Experimental Philosophy and Apriority.Jonathan Jenkins Ichikawa - 2014 - In Al Casullo & Josh Thurow (eds.), The A Priori in Philosophy. Oxford: Oxford University Press. pp. 45-66.
    One of the more visible recent developments in philosophical methodology is the experimental philosophy movement. On its surface, the experimentalist challenge looks like a dramatic threat to the apriority of philosophy; ‘experimentalist’ is nearly antonymic with ‘aprioristic’. This appearance, I suggest, is misleading; the experimentalist critique is entirely unrelated to questions about the apriority of philosophical investigation. There are many reasons to resist the skeptical conclusions of negative experimental philosophers; but even if they are granted—even if the experimentalists (...)
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  13.  77
    Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-Reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics. [REVIEW]Diego L. Rapoport - 2011 - Foundations of Physics 41 (1):33-76.
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...)
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  14.  19
    Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - Mathematical Logic Quarterly 45 (2):207-218.
    In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.
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  15.  2
    Weak-Operator Continuity and the Existence of Adjoints.Douglas Bridges & Luminita Dediu - 1999 - Mathematical Logic Quarterly 45 (2):203-206.
    It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A.
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  16.  14
    Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras.Jan Paseka & Zdenka Riečanová - 2011 - Foundations of Physics 41 (10):1634-1647.
    We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.
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  17.  7
    An Uncertainty Relation for the Orbital Angular Momentum Operator.H. Fakhri & M. Sayyah-Fard - 2016 - Foundations of Physics 46 (8):1062-1073.
    A common reducible representation space of the Lie algebras su and su is equipped with two different types of scalar products. The representation bases are labeled by the azimuthal and magnetic quantum numbers. The generators of su are the x-, y- and z-components of the orbital angular momentum operator. The representation of each of these Lie algebras is unitary with respect to only one of the scalar products. To each positive magnetic quantum number a family of the su-Barut–Girardello coherent (...)
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  18.  4
    Categorical Abstract Algebraic Logic: The Diagram and the Reduction Operator Lemmas.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (2):147-161.
    The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 (...)
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  19.  2
    Categorical Abstract Algebraic Logic: The Categorical Suszko Operator.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (6):616-635.
    Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non-protoalgebraic logics, paralleling the well-known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so-called, protoalgebraic π-institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko (...)
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  20. Forms of Luminosity: Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2017 - Gutenberg.
    This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; (...)
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  21.  15
    The Issue of “Closure” in Jagers Op Akkerhuis's Operator Theory.Nico van Straalen - 2011 - Foundations of Science 16 (4):319-321.
    Attempts to define life should focus on the transition from molecules to cells and the “closure” aspects of this event. Rather than classifying existing objects into living and non-living entities I believe the challenge is to understand how the transition from non-life to life can take place, that is, the how the closure in Jagers op Akkerhuis’s hierarchical classification of operators, comes about.
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  22.  2
    Apriority, Necessity and the Subordinate Role of Empirical Warrant in Mathematical Knowledge.Mark McEvoy - forthcoming - Theoria.
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  23.  2
    Isolation and the Jump Operator.G. Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.
    We show the existence of a high d. c. e. degree d and a low2 c.e. degree a such that d is isolated by a.
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  24.  19
    Simplement, as a Metalinguistic Operator.T. Nyan - 1999 - Argumentation 13 (3):275-295.
    This paper aims to provide a description of a metalinguistic use of simplement, one which occurs primarily in ce n'est pas que P simplement Q constructions. The two main points that will be raised concern the nature and function of the negation preceding P, and the meaning of simplement, which, following Anscombre and Ducrot, I will construe in procedural terms.
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  25.  12
    Modal Dynamics for Positive Operator Measures.Jay Gambetta & H. M. Wiseman - 2004 - Foundations of Physics 34 (3):419-448.
  26.  7
    Sampled-Data Tracking: Sampling of the Operator's Output.Corwin A. Bennett - 1956 - Journal of Experimental Psychology 51 (6):429.
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  27.  6
    Logic TK: Algebraic Notions From Tarski's Consequence Operator.Hércules A. Feitosa, Mauri C. Do Nascimento & Maria Claudia C. Grácio - 2010 - Principia: An International Journal of Epistemology 14 (1):47-70.
    Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.
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  28.  4
    One- and Two-Operator Versions of a Two-Phase Model Applied to the Performances of Vs and Cs in Human Eyelid Conditioning.William F. Prokasy & Karol L. Kumpfer - 1969 - Journal of Experimental Psychology 80 (2p1):231.
  29. The Standard Model's Form Derived From Operator Logic, Superluminal Transformations and Gl(16).Stephen Blaha - 2010 - Pingree-Hill.
  30. Necessity and Apriority.Gordon Prescott Barnes - 2007 - Philosophical Studies 132 (3):495-523.
    The classical view of the relationship between necessity and apriority, defended by Leibniz and Kant, is that all necessary truths are known a priori. The classical view is now almost universally rejected, ever since Saul Kripke and Hilary Putnam discovered that there are necessary truths that are known only a posteriori. However, in recent years a new debate has emerged over the epistemology of these necessary a posteriori truths. According to one view – call it the neo-classical view – (...)
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  31. Kant and the Apriority of Space.Daniel Warren - 1998 - Philosophical Review 107 (2):179-224.
    In interpretations of the "Transcendental Aesthetic" section of the first Critique, there is a widespread tendency to present Kant as establishing that the representation of space is a condition for individuating or distinguishing objects, and to claim that it is on this basis that Kant establishes the apriority of this representation. The aim of this paper is to criticize this way of interpreting the "Aesthetic," and to defend an alternative interpretation. On this alternative, questions about the formation of the (...)
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  32.  22
    Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator.Burghard Herrmann - 1997 - Studia Logica 58 (2):305-323.
    In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz (...). Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)
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  33.  8
    Systems of Explicit Mathematics with Non-Constructive Μ-Operator. Part II.Solomon Feferman & Gerhard Jäger - 1996 - Annals of Pure and Applied Logic 79 (1):37-52.
    This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0).
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  34.  9
    Systems of Explicit Mathematics with Non-Constructive Μ-Operator. Part I.Solomon Feferman & Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 65 (3):243-263.
    Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus (...)
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  35. Apriority.Sinan Dogramaci - 2012 - In Gillian Russell Delia Graff Fara (ed.), The Routledge Companion to Philosophy of Language. Routledge.
    After briefly expositing some fundamental issues in current debates about apriority, I go on to critically examine meaning-based explanations of how we acquire apriori justification.
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  36.  54
    Expanding Quasi-MV Algebras by a Quantum Operator.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2007 - Studia Logica 87 (1):99-128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
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  37.  28
    The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181 - 231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory (...)
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  38. Paraconsistent Belief Revision Based on a Formal Consistency Operator.Rafael R. Testa, Marcelo E. Coniglio & Márcio M. Ribeiro - 2015 - CLE E-Prints 15 (8):01-11.
    In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion (...)
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  39.  84
    The Operator Theory of Instantiation.Peter Forrest - 2006 - Australasian Journal of Philosophy 84 (2):213 – 228.
    Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This (...)
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  40.  84
    Remarks on Gregory's “Actually” Operator.Patrick Blackburn & Maarten Marx - 2002 - Journal of Philosophical Logic 31 (3):281-288.
    In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" operator with the work of Arthur Prior now known (...)
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  41.  37
    First-Order Modal Logic with an 'Actually' Operator.Yannis Stephanou - 2005 - Notre Dame Journal of Formal Logic 46 (4):381-405.
    In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas (...)
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  42.  3
    The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1):181-231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory (...)
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  43.  1
    The Jump Operator on the Ω-Enumeration Degrees.Hristo Ganchev & Ivan N. Soskov - 2009 - Annals of Pure and Applied Logic 160 (3):289-301.
    The jump operator on the ω-enumeration degrees was introduced in [I.N. Soskov, The ω-enumeration degrees, J. Logic Computat. 17 1193–1214]. In the present paper we prove a jump inversion theorem which allows us to show that the enumeration degrees are first order definable in the structure of the ω-enumeration degrees augmented by the jump operator. Further on we show that the groups of the automorphisms of and of the enumeration degrees are isomorphic. In the second part of the (...)
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  44.  22
    On Operator N and Wittgenstein’s Logical Philosophy.James R. Connelly - 2017 - Journal for the History of Analytical Philosophy 5 (4).
    In this paper, I provide a new reading of Wittgenstein’s N operator, and of its significance within his early logical philosophy. I thereby aim to resolve a longstanding scholarly controversy concerning the expressive completeness of N. Within the debate between Fogelin and Geach in particular, an apparent dilemma emerged to the effect that we must either concede Fogelin’s claim that N is expressively incomplete, or reject certain fundamental tenets within Wittgenstein’s logical philosophy. Despite their various points of disagreement, however, (...)
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  45.  64
    Formalizing Common Sense: An Operator-Based Approach to the Tibbles–Tib Problem.Ingvar Johansson - 2008 - Synthese 163 (2):217-225.
    The paper argues, that a direct formalization of the way common sense thinks about the numerical identity of enduring entities, requires that traditional predicate logic is developed. If everyday language mirrors the world, then persons, organisms, organs, cells, and ordinary material things can lose some parts but nonetheless remain numerically exactly the same entity. In order to formalize this view, two new logical operators are introduced; and they bring with them some non-standard syntax. One of the operators is called ‘the (...)
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  46.  50
    Propositional Apriority and the Nesting Problem.Jens Kipper - 2017 - Philosophical Studies 174 (5):1091-1104.
    According to the modal account of propositional apriority, a proposition is a priori if it is possible to know it with a priori justification. Assuming that modal truths are necessarily true and that there are contingent a priori truths, this account has the undesirable consequence that a proposition can be a priori in a world in which it is false. Epistemic two-dimensionalism faces the same problem, since on its standard interpretation, it also entails that a priori propositions are necessarily (...)
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  47.  22
    Explaining the Actuality Operator Away.John Mackay - 2017 - Philosophical Quarterly 67 (269):709-21.
    I argue that ‘actually’ does not have a reading according to which it is synonymous with the actuality operator of modal logic, and propose an alternative account of ‘actually’. The cases that have been thought to show that ‘actually’ is synonymous with the actuality operator are modal and counterfactual sentences in which an embedded clause's evaluation is held fixed at the world of the context. In these cases, though, this embedded clause's evaluation is not due to the presence (...)
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  48.  10
    Hilbert Spaces Expanded with a Unitary Operator.Camilo Argoty & Alexander Berenstein - 2009 - Mathematical Logic Quarterly 55 (1):37-50.
    We study Hilbert spaces expanded with a unitary operator with a countable spectrum. We show that the theory of such a structure is ω -stable and admits quantifier elimination.
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  49.  28
    Tractarian First-Order Logic: Identity and the N-Operator.Brian Rogers & Kaif Wehmeier - 2012 - Review of Symbolic Logic 5 (4):538-573.
    In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikkas, (...)
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    Systems of Explicit Mathematics with Non-Constructive Μ-Operator and Join.Thomas Glaß & Thomas Strahm - 1996 - Annals of Pure and Applied Logic 82 (2):193-219.
    The aim of this article is to give the proof-theoretic analysis of various subsystems of Feferman's theory T1 for explicit mathematics which contain the non-constructive μ-operator and join. We make use of standard proof-theoretic techniques such as cut-elimination of appropriate semiformal systems and asymmetrical interpretations in standard structures for explicit mathematics.
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