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Hilbert's epsilon as an operator of indefinite committed choice

Claus-Peter Wirth
2008 Journal of Applied Logic  
Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator.  ...  After reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite  ...  indefinite and committed choice ( § 2.4).  ... 
doi:10.1016/j.jal.2007.07.009 fatcat:ubqafkw57vffbmra6a3ndq6wpi

A Simplified and Improved Free-Variable Framework for Hilbert's epsilon as an Operator of Indefinite Committed Choice [article]

Claus-Peter Wirth
2017 arXiv   pre-print
We propose a new semantics for Hilbert's epsilon as a choice operator with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice,  ...  Moreover, our semantics for the epsilon supports reductive proof search optimally.  ...  Closely connected to indefinite choice (also called "indeterminism" or "don't care nondeterminism") is the notion of committed choice.  ... 
arXiv:1104.2444v9 fatcat:z4d4xpltd5ggpnriisvu37svfu

The Epsilon-Reconstruction of Theories and Scientific Structuralism

Georg Schiemer, Norbert Gratzl
2015 Erkenntnis: An International Journal of Scientific Philosophy  
The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator.  ...  The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of theoretical terms and a suitable choice semantics for it.  ...  Epsilon terms and their choice semantics The key component in Carnap's logical reconstruction of theories is Hilbert's -operator. 16 This Section will present the logic of this operator as well as its  ... 
doi:10.1007/s10670-015-9747-9 fatcat:mas44o5girbs3knikcbj2obx6a

Choice Functions and the Anaphoric Semantics of Definite NPs

Klaus von Heusinger
2004 Research on Language and Computation  
It is dynamically modified by the context change potential of indefinite and definite NPs.  ...  The salience structure is semantically reconstructed by a global choice function that assigns to each set one (most salient) element.  ...  SYNTAX AND SEMANTICS OF HILBERT'S EPSILON OPERATOR The epsilon operator corresponds to a selection function that assigns to each non-empty set one element of this set. 2 Like the iota operator, the epsilon  ... 
doi:10.1007/s11168-004-0904-6 fatcat:7ftijtu6cffjdcbzuiiibwb5u4

Choice Functions in Semantics

Klaus Heusinger, Ruth Kempson
2004 Research on Language and Computation  
A new operator is added to Jacobson's variable-free semantics of functional readings, which leads to an analysis of theses readings using the general Skolem function interpretation of wide-scope indefinites  ...  It is dynamically modified by the context change potential of indefinite and definite NPs.  ...  The author was also partly supported by the fund for the promotion of research at the Technion, research No. 120-042, and by an NWO grant for visiting the UiL OTS of the Utrecht University in summer 2001  ... 
doi:10.1007/s11168-004-0903-7 fatcat:ye4rpurgcfhebaxlijllutq54a

Mathematical conceptualism [article]

Nik Weaver
2005 arXiv   pre-print
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience.  ...  as formalized in the system ZFC (Zermelo-Fraenkel set theory including the axiom of choice).  ...  of infinitesimals to the epsilon-delta method.  ... 
arXiv:math/0509246v2 fatcat:7thudrd3nre4nlmonlsl6kwazi

A type theoretical framework for natural language semantics: the Montagovian generative lexicon [article]

Christian Retoré
2014 arXiv   pre-print
Among these adaptations of a word's sense to the context, ontological inclusions are handled by an extension of system F with coercive subtyping that is introduced in the present paper.  ...  of a predicate, and the possible adaptation of a word meaning to some contexts.  ...  Existential quantification "some" is faithfully represented by Hilbert's epsilon operator: P ( xP (x)) ≡ ∃x. P (x). As soon as some element enjoys the property P , the term x. P (x) enjoys P as well.  ... 
arXiv:1301.4938v3 fatcat:jrecwr2nqzgl7ir4grui5kfcqy

A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and 2 CV of Gisbert Hasenjaeger [article]

Claus-Peter Wirth
2021 arXiv   pre-print
In May 2017, we identified an incorrectly filed text in Bernays scientific legacy at the archive of the ETH Zurich as a candidate for the beginning of the revoked draft for the 1st edn. or of a revoked  ...  A third of a century later, Bernays preface to the 2nd edn. (1968) of the 1st vol. of Hilbert-Bernays mentions joint work of Hasenjaeger and Bernays on the second edition.  ...  A simplified and improved free-variable framework for Hilbert's epsilon as an operator of indefinite committed choice. IFCoLog J. of Logics and Their Applications, 4:435-526. Received Oct. 23, 2015.  ... 
arXiv:1803.01386v4 fatcat:ai5itqzjnzddpnum2shh5johua

Believing the axioms. I

Penelope Maddy
1988 Journal of Symbolic Logic (JSL)  
to draw logical consequences.The central problem in the philosophy of natural science is when and why the sorts of facts scientists cite as evidence really are evidence.  ...  The next question, naturally, is why we believe the axioms, and here the response will usually be that they are "obvious", or "self-evident", that to deny them is "to contradict oneself" or "to commit  ...  Under the influence of Hilbert's axiomatics, Zermelo hoped to secure his proof by developing a precise list of the assumptions it required, and proposing them (in [1908] ) as an axiomatic foundation for  ... 
doi:10.1017/s0022481200028425 fatcat:k6lbbfkk4vekvbhd7qamczsxcq

Modal Structuralism with Theoretical Terms

Holger Andreas, Georg Schiemer
2021 Erkenntnis: An International Journal of Scientific Philosophy  
AbstractIn this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics.  ...  Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic.  ...  The authors would like to thank two anonymous referees for their helpful comments on an earlier version of the article. Funding Open access funding provided by University of Vienna.  ... 
doi:10.1007/s10670-021-00378-w fatcat:tzpft3oznbg3xnwu75ftxyrwaq

Indiscernibility and Mathematical Structuralism [article]

Teresa Kouri, University Of Calgary, University Of Calgary, Richard Zach
2010
This thesis demonstrates that this problem can be avoided by taking identity as a primitive notion, and by using Hilbert's epsilon calculus as a tool for referring to indistinguishable objects. ii Richard  ...  This project describes a solution to a problem in Stewart Shapiro's ante rem structural ism, a theory in the philosophy of mathematics.  ...  All that is required to solve this problem is some sort of choice function, and Hilbert's epsilon calculus serves well to formalize this.  ... 
doi:10.11575/prism/14329 fatcat:mkzqavkz4bbzzoa3nk7zuknlzu

John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

Joseph F. Grcar
2011 SIAM Review  
Their foresight and the congruence of historical events made their work the first modern paper in numerical analysis.  ...  invented, John von Neumann and Herman Goldstine wrote a paper to illustrate the mathematical analyses that they believed would be needed to use the new machines effectively and to guide the development of  ...  Whereas errors (B), (C) were committed only once, the rounding errors (D) were "continuously injected" each time an arithmetic operation was performed.  ... 
doi:10.1137/080734716 fatcat:6ymfptvzfrg7doc7ajv4iljk24

Leibniz's well-founded fictions and their interpretations [article]

Jacques Bair, Piotr Blaszczyk, Robert Ely, Peter Heinig, Mikhail G. Katz
2018 arXiv   pre-print
Of particular interest is evidence stemming from Leibniz's work Nouveaux Essais sur l'Entendement Humain as well as from his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon.  ...  We analyze a hitherto unnoticed objection of Rolle's concerning the lack of justification for extending axioms and operations in geometry and analysis from the ordinary domain to that of infinitesimal  ...  Acknowledgments We are grateful to John Dawson for providing a copy of Robinson's 23 august 1973 letter to Gödel quoted in Section 3.10; to Roger Ariew for bringing to our attention Leibniz's letter to  ... 
arXiv:1812.00226v1 fatcat:s5fwloxwtbaengfauyew2xlpfe

The meaning of quantifiers and the epsilon calculus : on the logical formalization of dependence relations

Nicola Bonatti, University, My, Francesco Berto
2021
Instead, I will claim that the quantifiers 'for all' and 'there exists' should be interpreted as choice functions − according to the ε-operator of the Epsilon Calculus.  ...  Finally, I will consider as a case study the Set theory formulated in the Epsilon Calculus so as to consider how the choice functions interpretation of quantifiers affects debates concerning impredicative  ...  However, this is just part of the story about the ε-operator: as I have explained above, the ε-operator is an indefinite description operator.  ... 
doi:10.17630/sta/27 fatcat:xra4vxitercrzcr5mw3duvhszi

Symmetry, Almost

Amanda Folsom
2019 Notices of the American Mathematical Society  
Accommodations Participants should make their own arrangements directly with the hotel of their choice. Special discounted rates were negotiated with the hotels listed below.  ...  Invited Addresses Special Sessions If you are volunteering to speak in a Special Session, you should send your abstract as early as possible via the abstract submission form found at http://www.ams.org  ...  Finally, as befitting a mathematical physicist, there is an excellent treatment of unbounded self-adjoint operators as well as operators that have self-adjoint extensions.  ... 
doi:10.1090/noti1775 fatcat:xwrijzvqazg7bdym7un5qq2jjq
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