Buying Logical Principles with Ontological Coin: The Metaphysical Lessons of Adding epsilon to Intuitionistic Logic

We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one can get an analogue of Diaconescu’s result, but also can disentangle the roles of certain other assumptions that are hidden in mathematical presentations. It is our view that these results have not received the attention they deserve: logicians are unlikely to read a discussion because the results considered are “already well known,” while the results are simultaneously unknown to philosophers who do not specialize in what most philosophers will regard as esoteric logics. This is a problem, since these results have important implications for and promise signif i cant illumination of contem- porary debates in metaphysics. The point of this paper is to make the nature of the results clear in a way accessible to philosophers who do not specialize in logic, and in a way that makes clear their implications for contemporary philo- sophical discussions. To make the latter point, we will focus on Dummettian discussions of realism and anti-realism. Keywords: epsilon, axiom of choice, metaphysics, intuitionistic logic, Dummett, realism, antirealis

Term-forming Operators In First Order Logic

The two main accomplishments of this thesis are that it provides the first adequate semantics for Hilbert\u27s epsilon-operator and that it describes a general semantics for term forming operators (often called variable binding term operators of vbto\u27s ) more flexible than any in the literature.;The epsilon-operator was introduced by David Hilbert in the 1920s as a term forming operator in first order logic. The semantics so far available for epsilon has been designed for classical two-valued logic, and has required that additional extensionality assumptions be made. This thesis provides complete semantics for epsilon in classical extensional, classical non-extensional, Boolean valued, and intuitionistic first order systems. The natural step to generalizing the technique used in the epsilon case to get a general theory of term forming operators which handles the non-extensional and non-classical cases is then taken.;The thesis proceeds as follows. Chapter One gives a historical discussion of term forming operators. A brief, self-contained presentation of the untyped lambda-calculus, which illustrates the inevitable differences between lambda and any possible operator in first order logic, follows. A chapter is devoted to solving the syntactical difficulties involved in introducing a variable binding term forming operator to standard languages for first order logic. The semantics for epsilon, and in the intuitionistic case also for another of Hilbert\u27s creatures, tau, takes up the next several chapters. The discussion includes several new completeness and soundness results, and some new results about the extra strength these operators add to intuitionistic logic, including some new independence results. The final chapter includes an argument to the effect that the results earlier in the thesis show that we need a more general theory of term forming operators than any in the literature, and indicates the shape such a theory should take

Frege On Indexicals: Sense And Context Sensitivity

Indexical expressions--e.g., \u27I\u27, \u27here\u27, \u27yesterday\u27, \u27this\u27, etc.--pose a serious challenge for a Fregean theory of meaning. A Fregean theory holds that the meaning of an expression is its sense, and that this sense determines the reference of the expression independently of context. The most notable feature of indexicals, however, is their sensitivity to context. David Kaplan and John Perry argue that there can be no Fregean solution to this issue. They assume (falsely) that the Fregean sense of a singular term is given by a definite description, and argue that this picture cannot work. Kaplan and Perry advance a theory of indexicals according to which the contribution an indexical makes to a proposition is the referent itself, and the meaning of the indexical is a context-sensitive rule associated with it. However, neither sort of meaning accounts for what a hearer understands. Frege\u27s view on \u27I\u27 involves a \u27special and primitive\u27 mode of presentation of self, so that thoughts involving this mode of presentation are incommunicable. Gareth Evans bases an interpretation on Frege\u27s remarks according to which the notion of sense is understood as a \u27way of thinking\u27 of the reference. Frege\u27s remarks on \u27I\u27, however, violate his own strictures against psychologism. Hence, the view Evans builds on these remarks fails as an interpretation of Frege and is for the same reason unattractive as an account of indexicals.;The proper way to construe Frege\u27s expression \u27mode of presentation\u27 is the way Frege himself did: namely, as a criterion of identity. The appeal of the direct reference theory rests largely on the seeming transparency of indexical reference; but the idea that we have a language-independent grasp of concrete objects is an illusion. Reference requires a criterion of identity. The meaning of a particular utterance of an indexical is a Fregean sense, which is to be understood as a criterion of identity.;Frege\u27s few, tentative remarks on indexicals have been persistently neglected in the secondary literature. The writings of Michael Dummett are an exception in this regard. Nevertheless Dummett has never marshalled a full response to criticism of Frege on indexicals. Drawing on Frege\u27s writings and Dummett\u27s commentary on them, it is shown that Frege\u27s antagonists do not present an attractive alternative theory, and that an account of indexicals consistent with Frege\u27s theory of sense and reference can and must be given

Der Diskurs des Hässlichen bei Friedrich Schlegel

Friedrich Schlegel`s Discourse on the Ugly During the 1950`s debates on the meaning of Romanticism in modern Literature emerged several problems when time came to deal with Friedrich Schlegel`s poetics. Originally focused on the theory and the concept of Ugly, Friedrich Schlegel (1772-1829) - known as one of the main co-founders of the Early Romanticism - has also been regarded as the main responsible for the explosion of the Ugly in the early 20th-century literature. In order to understand to what extent it is legitimate to regard this assertion as philologically accurate, the present study aims at analysing Friedrich Schlegel`s discourse on the Ugly adopting the approaches of historical semantics, of conceptual history, of discourse analysis as well as of narratology and media studies. Unlike the theory and the concept of Romantic, Friedrich Schlegel`s discourse on the Ugly seems to have undergone through a deep-rooted change. It is not only by analysing Friedrich Schlegel`s adoption of new types of media, such as painting descriptions, travel reports and academic lectures, that it becomes possible to identify a thorough reconfiguration of Friedrich Schlegel`s former discourse. One of the crucial roles in determining the shift in his work has also been played by his novel Lucinde (1799) labelled since its first appearance as an aesthetic Monster, but classified also at the same time as one of the most significant Romanticist novels. This research encompasses an overall analysis of this shift in Friedrich Schlegel`s work: starting from one of his most important early essays †ber das Studium der griechischen Poesie (1795/7), crossing through his Charakteristiken (1796-1801) and reaching finally his most problematic writings appeared after 1802. It is according to this shift that from 1802 onwards Friedrich Schlegel`s discourse - regarded at this point as almost inconceivable if separated from its religious, political and aesthetic features - underwent a process of dehistoricization, sacralisation as well as medial dedifferentiation and of denarrativisation leaving an indelible mark on the reception of his work and legacy

ROOTING SUPPOSITION IN WIRELESS SENSOR NETWORKS

An easy method would-be to assign everyone routing path in each one wrapper. The delivery of the manner is quintessence that it’s sense aloft conceivably hefty for cartons with drawn-out routing expressway. Using the routing road separately carton, many measure and symptomatic programs can attend active executive and pact inflation for deployed WSNs self-assured of heaps undervalued sensor nodes. Path puss a different thing of a light-weight hash situation for facts from the deduced expressway. To incur then build up the interpretation facility again the realization readiness, path puss a fast bootstrapping form to overhaul the initially gather of artery. To make the repetitious boosting forceful and valuable, two problems have been addressed. The hash operation requires be featherweight and valuable abundant ago it must be administering on resource-restricted sensor nodes. Using the routing road individually carton, many dimension and indicative procedures can oversee forceful oversight and contract inflation for deployed WSNs self-assured of great ignored sensor nodes. We enforce path and calculate its drama practicing traces from huge-scale WSN deployments too considerable simulations. Results expose that path achieves much outstanding facelift ratios lower different structure settings when reach more condition-of-the-art programs. When equal Path Zip, path exploits high path analogy betwixt legion containers for fast supposition, encompass far beat scalability

Semantics and Proof Theory of the Epsilon Calculus

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing the development of proof-theoretically well-behaved systems are outlined.Comment: arXiv admin note: substantial text overlap with arXiv:1411.362

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Hilbert's epsilon as an Operator of Indefinite Committed Choice

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. 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 choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural language, but may also contribute to philosophy of language. Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of semantics of discourses in natural language.Comment: ii + 73 pages. arXiv admin note: substantial text overlap with arXiv:1104.244

“A suggestive Mix of Divinity and Bestiality”. Friedrich Schlegel’s Concept of the (Un)Human

Im Vergleich zu seinen rüheren Ausätzen versucht Friedrich Schlegel in seinem Roman Lucinde (1799) das, was zuvor als „unendlich Entgegengesetztes“ konzipiert wurde – d. h. die in der Menschheit aundbare Mischung von „Gottheit“ und „Tierheit“ – als „harmonische Zusammensetzung“ darzustellen (KFSA 1: 230). Der vorliegende Beitrag geht der Frage nach, inwiefern sich Friedrich Schlegels narrative ransponierung der „Gottheit“ und der „Tierheit“ als relevant für die Reflexion anthropologischer Konzepte von 1800 bis heute erweist.The mix of “divinity” and “bestiality” as the embodiment of mankind conceived as “innitely opposed” in Friedrich Schlegel’s (1772–1829) earlier essays has eventually been represented as a “harmonious composition” (KFSA 1: 230) in his novel Lucinde (1799). The present paper investigates the extent to which Friedrich Schlegel’s narrative transposition of “divinity” and “bestiality” proves itself as relevant for the reflection upon anthropological concepts around 1800 as well as its continuities