Descriptions

This article investigates David Lewis's influential account of the implicit definition of theoretical terms, especially his curious, often overlooked use of non-classical logic. It is explained why Lewis opted for the positive free logic of descriptions FD2, which implausibly renders all identities between empty terms true. And it is argued that Lewis's account is best implemented in the weaker free logic of descriptions MFD, with classical second-order logic as an alternative. The philosophical core of Lewis's account is also clarified and (...) motivated, including the controversial view that true term-introducing theories are uniquely realized. (shrink)

This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas additional to those familiar from standard intuitionist and classical logic. When $\invertediota$ is added it must be ensured that reduction procedures involving replacements of parameters by terms do not introduce new maximal formulas of higher degree than the ones removed. The problem is solved by a rule (...) that permits restricting these terms in the rules for $\forall$, $\exists$ and $\invertediota$ to parameters or constants. A restricted subformula property for deductions in systems without $\invertediota$ is considered. It is improved upon by an alternative formalisation of free logic building on an idea of Ja\'skowski's. In the classical system the rules for $\invertediota$ require treatment known from normalisation for classical logic with $\lor$ or $\exists$. The philosophical significance of the results is also indicated. (shrink)

Recenzja: Saul Kripke, Kłopoty filozoficzne, Warszawa: Wydawnictwo Naukowe PWN, 2023. Review of the Polish-language edition of Saul Kripke's Philosophical Troubles, vol. 1.

This paper explores the hypothesis that proper names serve as anchors identifying the individuals in the possible or real world. This hypothesis is tested on Old Icelandic narratives. A prominent feature of Old Icelandic sagas is that the narrative matter is not quite new. A Saga is reliable iff it refers to the events relevant for its audience and accepted as true by the whole community. I argue that proper names must be regarded as references to the background knowledge of (...) the medieval audience. I follow two contemporary Sagas based on the fresh events and show that proper names in a Saga mind were arranged in form of a database, each type of a personal designation having its charachteristic text-building profile. The form of the name and its frequency in the Saga are linked with the rank of the character. The high number of people mentioned in the Sagas is explained by the fact that the Sagas aimed at describing the real world, where the names of the individuals and the events they were involved cross-identified each other. Every character had its rigid identifiers. The total amount of propria is always higher than the number of active figures. I classify the Saga characters into five ranks and discuss their information-structural profiles. (shrink)

In this paper, I outline a novel approach to the semantics of natural language pronouns. On this account, which I call 'demonstrativism', pronouns are semantically equivalent to demonstratives. I begin by presenting some contrasts that provide support for demonstrativism. Then I try to explain these contrasts by developing a particular demonstrativist proposal. I build on the "hidden argument" theory of demonstratives. On this theory, demonstratives are semantically similar to definite descriptions, with one important difference: demonstratives take two arguments, rather than (...) one. Using these ideas, I propose that pronouns also take two (covert) arguments, and that the second argument needs to be sufficiently salient to members of the conversation in order for the use of a pronoun to be felicitous. As for the first argument, I maintain that its content is constrained by the process of noun-phrase deletion. Taken together, I argue that these constraints provide us with a satisfying account of the uses to which pronouns are put. (shrink)

The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like The square root of 4, rigidly designate their referents, so too are necessary truths rigidly true, and so too does cat rigidly have only animals in its extension. (...) After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms. (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be (...) sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

François Recanati; IV*—Contextual Dependence and Definite Descriptions, Proceedings of the Aristotelian Society, Volume 87, Issue 1, 1 June 1987, Pages 57–74, h.

Slingshot arguments aim to show that an allegedly non-extensional sentential connective—such as “necessarily ” or “the statement that Φ corresponds to the fact that ”—is, to the contrary, an extensional sentential connective. Stephen Neale : 761-825, 1995, 2001) argues that a reformulation of Gödel’s slingshot puts pressure on us to adopt a particular view of definite descriptions. I formulate a revised version of the slingshot argument—one that relies on Kaplan’s notion of “dthat.” I aim to show that if Neale’s version (...) of the slingshot argument is successful, then there is another slingshot available, parallel in structure to Neale’s, but independent of definite descriptions. So either there is a version of the slingshot that succeeds independent of any particular theory of descriptions or else Neale’s slingshot was never threatening to begin with. (shrink)

This paper defends 'plural reference', the view that definite plurals refer to several individuals at once, and it explores how the view can account for a range of phenomena that have been discussed in the linguistic literature.

In a recent paper Horsten embarked on a journey along the limits of the domain of the unknowable. Rather than knowability simpliciter, he considered a priori knowability, and by the latter he meant absolute provability, i.e. provability that is not relativized to a formal system. He presented an argument for the conclusion that it is not absolutely provable that there is a natural number of which it is true but absolutely unprovable that it has a certain property. The argument depends (...) on a description principle. I will argue that the latter principle implies the knowability of all arithmetical truths. Therefore, Horsten's argument is either sound but its conclusion is trivial, or his argument is unsound. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

A detailed interpretation is provided of the ‘Gray's Elegy’ passage in Russell's ‘On Denoting’. The passage is suffciently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the thesis that definite descriptions are singular terms is untenable. The thesis demands a distinction be drawn between content and designation, but the attempt to form a proposition directly about the content (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated (...) instead of the content expressed. In light of this collapse, argues Russell, the thesis that definite descriptions are singular terms must accept that all propositions about a description's content represent it by means of a higher-level descriptive content, so that knowledge of a description's content is always ‘by description’, not ‘by acquaintance’. This, according to Russell, renders our cognitive grip on definite descriptions inexplicable. Separate responses on behalf of Fregeans and Millians are offered. (shrink)

Definite descriptions are expressions of the form `the F'. The present entry begins by explaining Russell's theory of definite descriptions, according to which `The F is G' means `There is exactly one F and it is G'. It then discusses the alternative theories of Frege and Carnap, two influential criticisms by Strawson and Donnellan, and some formalisations of theories of definite descriptions building on Hintikka's and Lambert's work in free logic.

This note (it is not a full-fledged academic paper) introduces a novel approach to classic thought experiments in consciousness studies through the incorporation of non-referential terms—symbols that present experiences directly rather than referring to them. By analyzing the Hard Problem, Knowledge Argument, Philosophical Zombies, and Spectrum Inversion thought experiments using both referential terms (like "blackness") and non-referential terms (like █), the paper reveals that many apparent philosophical puzzles arise from conflating referential descriptions with direct presentational experiences. The analysis shows that (...) attempting to formulate these thought experiments using non-referential terms often requires instantiating the very experiences in question, creating self-referential paradoxes that solve or dissolve the original problems. (shrink)

Humility is a paradoxical virtue. This should come as no great surprise. It doesn’t take much explanation for one to realize that if someone is boasting about how humble he is, then he probably is not humble. In fact, as we shall see, the paradoxical nature of humility has a long history, going back to at least Thomas Aquinas in the thirteenth century. While it may not be a novel claim that there exists an apparent paradox of humility, I will (...) argue that there is more than one humility paradox, perhaps as many as five: the epistemic paradox, the paradox of self-attribution, the inculcation paradox, the agentic paradox, and the axiological paradox. All these paradoxes are distinct, yet seemingly intertwined. Upon examining them each in turn, we will be left with a Gordian knot of humility paradoxes. (shrink)

In order to understand a sentence, one must know the relevant semantic rules. Those rules are not learned in a vacuum; they are given to one through one's senses. As a result, knowledge of semantic rules sometimes comes bundled with semantically irrelevant, but cognitively non-innocuous, knowledge of the circumstances in which those rules were learned. Thus, one must work through non-semantic information in order to know what is literally meant by a given sentence-token. A consequence is that one's knowledge of (...) what is literally meant by a given sentence-token is sometimes embedded in non-semantic knowledge, resulting in a cleavage between what that sentence-token literally means and what the auditor in question takes it to mean. Such deviations obviously have nothing to do with the principles put forth by Grice, since those principles only concern sentence-tokens that have already been understood---since, to put it another way, those principles only concern post-semantic implicature. The just-described deviations are appropriately described as being due to "pre-semantic implicature." Given the phenomenon of pre-semantic implicature, it is easily shown that Russell's Theory of Descriptions, if taken as a theory of literal meaning, is false. In the present volume, these rather elementary principles are entirely ignored, and all of the articles in it are sterile repetitions of the points made by Russell and Strawson. The blinkered approach to language embodied in this volume must be reconsidered in light of psychological principles relating to language-acquisition and language-use. Unfortunately, analytic philosophers shy away from such topics, as is made clear by the papers in this grim volume. (shrink)

Kripke (1977) views Donnellan's (1966) misdescription cases as cases where semantic reference and speaker's reference come apart. Such cases, however, are also cases where semantic reference conflicts with a distinct species of reference I call "public reference", i.e. the object that the cues publicly available at the time of utterance indicate is the speaker's referent of the utterance. This raises the question: do the misdescription cases trade on the distinction between semantic reference and speaker's reference, or the distinction between semantic (...) reference and public reference? I argue that Kripke's own construal in terms of semantic reference and speaker's reference is at best incomplete, and probably wrong. I also explain the general importance of the notion of 'public reference'. (shrink)

DOIhttps://doi.org/10.25247/P1982-999X.2019.v19n1.p103-134• Esta obra está licenciada sob uma licençaCreative Commons Atribuição 4.0 InternacionalISSN 1982-999x|Pragmatic ambiguity and Kripke’s dialogue against DonnellanAmbiguidade Pragmática e o diálogo de Kripke contra DonnellanCarlo Penco (Universidade de Genova, Itália)AbstractIn this paper I discuss Donnellan’s claim of the pragmatic ambiguity of the distinction between referential and attributive uses of definite des-criptions. The literature on the topic is huge and full of alternative analysis. I will restrict myself to a very classical topos: the challenge posed by Kripke to Donnellan’s (...) distinction with the case of a dialogue on an attempt to update a misdescription. I claim that to treat the problem of the referential use of definite descriptions we need not only to take into account the context of utterance, but also the cognitive context with its epistemic restrictions and the possible different contexts of reception of the same utterance. I try to show different aspects of what can be called “pragmatic ambiguity”, which seem not correctly considered by Kripke, and connect them to the basic tenets of Grice Cooperative principle. (shrink)

People often speak loosely, uttering sentences that are plainly false on their most strict interpretation. In understanding such speakers, we face a problem of underdetermination: there is often no unique interpretation that captures what they meant. Focusing on the case of incomplete definite descriptions, this paper suggests that speakers often mean bundles of propositions. When a speaker means a bundle, their audience can know what they mean by deriving any one of its members. Rather than posing a problem for the (...) interpretation of loose talk, the underdetermination of a uniquely correct interpretation allows for various ways in which the audience can grasp the speaker’s meaning. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

Keith Donnellan wrote his paper on definite descriptions in 1966 at Cornell University, an environment where nearly everybody was discussing Wittgenstein’s ideas of meaning as use. However, his idea of different uses of definite descriptions became one of the fundamental tenets against descriptivism, which was considered one of the main legacies of the Frege–Russell– Wittgenstein view; and I wonder whether a more Wittgensteinian interpretation of Donnellan’s work is possible.

Las descripciones definidas pueden ser interpretadas de acuerdo con las dos lecturas propuestas por Donnellan. El presente trabajo presenta una interpretación contextualista de la lectura referencial de estas expresiones.

Some contemporary semantic views defend an asymmetry thesis concerning defi-nite descriptions and indexicals. Semantically, indexicals are devices of singular refer-ence; they contribute objects to the contents of the speech acts made with utterances including them. Definite descriptions, on the other hand, are generalized quantifiers, behaving roughly the way Russell envisaged in “On Denoting”. The asymmetry thesis depends on the existence of a sufficiently clear-cut distinction between semantics and pragmatics, because indexicals and descriptions are often used in ways that apparently contradict (...) the asymmetry thesis; the semantics/pragmatics distinction is invoked to see behind the appearances. The paper critically examines arguments by Schiffer against the asymmetry thesis, based on referential uses of incomplete descriptions. (shrink)

In this paper I revisit the main arguments for a predicate analysis of descriptions in order to determine whether they do in fact undermine Russell's theory. I argue that while the arguments without doubt provide powerful evidence against Russell's original theory, it is far from clear that they tell against a quantificational account of descriptions.

According to James McCawley (1981) and Richard Larson and Gabriel Segal (1995), the following sentence is three-ways ambiguous: -/- Harry wants to be the mayor of Kenai. -/- According to them also, the three-way ambiguity cannot be accommodated on the Russellian view that definite descriptions are quantified noun phrases. In order to capture the three-way ambiguity of the sentence, these authors propose that definite descriptions must be ambiguous: sometimes they are predicate expressions; sometimes they are Russellian quantified noun phrases. After (...) explaining why the McCawley-Larson-Segal solution contains an obvious flaw, I discuss how an effort to correct the flaw brings to light certain puzzles about the individuation of desires, about quantifying in, and about the disambiguation of desire ascriptions. (shrink)

In this paper I revisit the main arguments for a predicate analysis of descriptions in order to determine whether they do in fact undermine Russell's theory. I argue that while the arguments without doubt provide powerful evidence against Russell's original theory, it is far from clear that they tell against a quantificational account of descriptions.

Determiner phrases embedded under a propositional attitude verb have traditionally been taken to denote answers to implicit questions. For example, 'the capital of Vermont' as it occurs in 'John knows the capital of Vermont' has been thought to denote the proposition which answers the implicit question 'what is the capital of Vermont?' Thus, where 'know' is treated as a propositional attitude verb rather than an acquaintance verb, 'John knows the capital of Vermont' is true iff John knows that Montpelier is (...) the capital of Vermont. The traditional view lost its popularity long ago, because it was thought to rest on the controversial assumption that determiner phases embedded under a propositional attitude verb function semantically in the same way as the corresponding wh-clauses. Here we defend the traditional assumption against objections. We then argue that wh-clauses are not to be given a uniform treatment as indirect questions. When occurring under a propositional attitude verb, wh-clauses are better treated as having a predicate-type semantic value. We conclude by considering some possible objections to the predicate view. (shrink)

The paper revisits Sharvy's theory of plural definite descriptions. An alternative account of plural definite descriptions building on the ideas of plural quantification and non-distributive plural predication is developed. Finally, the alternative is extrapolated to account for generic uses of definite descriptions.

Although Strawson’s main aim in “On Referring” was to argue that definite descriptions can be used referentially – that is, “to mention or refer to some individual person or single object . . . , in the course of doing what we should normally describe as making a statement about that person [or] object” (1950, p. 320) – he denied that definite descriptions are always used referentially. The description in ‘Napoleon was the greatest French soldier’ is not used referentially, says (...) Strawson, since it is used not to mention an individual, but only “to say something about an individual already mentioned” (p. 320). This is an example of what we may call a predicative use of a definite description, though such uses might be better illustrated by considering the false sentence.. (shrink)

In “Descriptions as Predicates” (Fara 2001) I argued that definite and indefinite descriptions should be given a uniform semantic treatment as predicates rather than as quantifier phrases. The aim of the current paper is to clarify and elaborate one of the arguments for the descriptions-aspredicates view, one that concerns the interaction of descriptions with adverbs of quantification.

This paper shows that the closed quartic variational framework introduced in The Universal Equation generates, without any external physical structure, a novel spectral line in the hydrogen atom. The result follows exclusively from the full functional, its static and dynamic equations, and the global decision rule; no potentials, operators, perturbative schemes, or adjustable constants are used. The analysis reveals that the hydrogen ground configuration necessarily possesses a core–shell geometry whose torsional sector gives rise to a unique, strictly positive, spectrally isolated (...) eigenfrequency. -/- This frequency is not derivable from Coulomb-based quantum mechanics, does not scale with the Rydberg hierarchy, and cannot be incorporated into any Schrödinger-type description. Its existence therefore constitutes a direct case of spectral irreducibility: a physical observable determined solely by the intrinsic algebra of the functional, rather than by empirical input or theoretical assumptions. -/- The prediction is structurally rigid, parameter-free, and falsifiable. More broadly, the result illustrates how the quartic framework yields physical quantities—spectra, temporal scales, and structural invariants—purely from internal variational consistency, offering a radically different foundation for atomic physics and for the ontology of physical laws. (shrink)

intersection; exists predicate; mixed example; what it’s like; multiplication; simulation; prop. calc.; existence; Kant; equivalence classes; qualia screens; 3rd-person theories; territory; noumena; 0th-order terms; diagonal arguments; models; semiotics; CQ properties; example; CQ doubles vocab.; AI problems.

Contemporary paradigms in artificial intelligence, cognitive science, and philosophy often equate intelligence with efficient compression-be it via statistical learning, formal abstraction, or narrative simplification. This paper challenges that assumption by identifying and formalizing a foundational paradox: the pursuit of maximal simplicity can annihilate meaning. We define this tension as the Non Grata Problem-the systemic exclusion of semantically rich but compression-resistant thoughts and tokens. Through a synthesis of information theory, predictive processing, game theory, and phenomenology, we introduce a new framework for (...) understanding cognition as a dynamic Nash equilibrium between multiple cognitive agents, each optimizing different compression strategies. We propose the Semantic Incompleteness Theorem, showing that no compressed formal system can fully capture the expressivity of natural language. Further, we demonstrate the Compression-Tail Paradox, revealing how aggressively compressed probabilistic models produce blind spots for high-impact outliers-so-called Black Swans. To integrate these insights, we construct the notion of a Transcendent Probability Space, a formal model for state-space overflow and the epistemology of surprise. By tracing these mathematical, philosophical, and aesthetic arguments through diverse domains-from haiku and hyperrealism to semantic dementia and LLMs-we argue for an ecology of understanding that honors the ineffable, irreducible, and richly entangled nature of human meaning. Compression, while essential, must be decentered from its absolutist role; the razor must not sever the roots of cognition. -/- . (shrink)

For nearly a century, information theory and logic have defined truth as a static product of syntactic consistency or statistical regularity. This paradigm—anchored by Shannon’s entropy, Gödel’s incompleteness, and formal logic—has generated powerful tools, but it cannot resolve the epistemological breakdowns observed in modern AI, symbolic systems, and formal mathematics. This paper introduces a post-symbolic, coherence-based model of truth: Recursive Compression via Structured Resonance. We define the Coherence Threshold—the minimum structural alignment necessary for a proposition or inference to phase-lock with (...) reality—as the foundation of epistemic stability. Truth is reframed not as symbolic closure, but as recursive coherence across compression layers (C_n, chirality χ, and phase θ). Under this model, both Gödel’s incompleteness and Shannon’s entropy are reinterpreted as failures of recursive resonance rather than limits of knowledge. We prove that all meaningful inference must meet a coherence threshold defined by deterministic recursion across chiral-phase fields. This paper completes the epistemological scaffolding of the CODES framework and formally declares the end of probabilistic or symbolic truth approximation. From mathematics to AI to cognition, truth is no longer a predicate—it is a resonance invariant. (shrink)

A Calculus of Qualia (CQ) was proposed (on PhilPapers). The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader's mind and is non-referential, *it does not even refer to itself*. The meaning and behavior of these terms is radically different. In this paper in this series of papers, we discuss Godel Incompleteness and the incompleteness or (...) not of CQ. (shrink)

In order to understand a sentence, one must know the relevant semantic rules. Those rules are not learned in a vacuum; they are given to one through one's senses. As a result, knowledge of semantic rules sometimes comes bundled with semantically irrelevant, but cognitively non-innocuous, knowledge of the circumstances in which those rules were learned. Thus, one must work through non-semantic information in order to know what is literally meant by a given sentence-token. A consequence is that one's knowledge of (...) what is literally meant by a given sentence-token is sometimes embedded in non-semantic knowledge, resulting in a cleavage between what that sentence-token literally means and what the auditor in question takes it to mean. Such deviations obviously have nothing to do with the principles put forth by Grice, since those principles only concern sentence-tokens that have already been understood---since, to put it another way, those principles only concern post-semantic implicature. The just-described deviations are appropriately described as being due to "pre-semantic implicature." Given the phenomenon of pre-semantic implicature, it is easily shown that Russell's Theory of Descriptions, if taken as a theory of literal meaning, is false. In the present volume, these rather elementary principles are entirely ignored, and all of the articles in it are sterile repetitions of the points made by Russell and Strawson. The blinkered approach to language embodied in this volume must be reconsidered in light of psychological principles relating to language-acquisition and language-use. Unfortunately, analytic philosophers shy away from such topics, as is made clear by the papers in this grim volume. (shrink)

나는 컴퓨터로 계산과 우주의 한계에 대한 많은 최근의 토론을 읽었습니다, polymath 물리학자 및 결정 이론가 데이비드 울퍼트의 놀라운 작품에 대한 몇 가지 의견을 찾을 수 있기를 바라고 있지만 하나의 인용을 발견하지 않은 그래서 나는이 매우 간단한 요약을 제시. Wolpert는 계산을 수행하는 장치와 는 별개이며 물리학법칙과는 무관하므로 컴퓨터, 물리학 및 인간의 행동에 적용되므로 추론(계산)에 대한 제한에 대해 놀라운 불가능또는 불완전성 정리(1992년에서 2008년 참조 arxiv dot org)를 입증했습니다. 그들은 캔터의 대각선화, 거짓말쟁이 역설 및 세계관을 사용하여 튜링 머신 이론의 궁극적 인 정리가 될 (...) 수있는 것을 제공하고, 겉보기에 불가능, 불완전성, 계산의 한계, 그리고 컴퓨터로서의 우주, 가능한 모든 우주와 모든 존재 또는 메커니즘에서, 생성, 비 양자 기계적 불확실성 및 증거. 차이틴, 솔로모노프, 코몰가로프, 비트겐슈타인의 고전 적 작품과 어떤 프로그램 (따라서 어떤 장치)이 소유보다 더 큰 복잡성시퀀스 (또는 장치)를 생성 할 수 없다는 개념에 명백한 연결이 있습니다. 이 작품의 몸은 물리적 우주보다 더 복잡한 어떤 실체가 있을 수 없고 비트겐슈타인의 관점에서 볼 때 '더 복잡한'은 의미가 없다고 말할 수 있습니다(즉, 진리를 제작자나 시험하는 조건은 없습니다). 심지어 '신'(즉, 무한한 시간과 에너지를 가진 '장치')은 주어진 '숫자'가 '무작위'인지 여부를 결정할 수없으며, 주어진 '수식', '정리' 또는 '문장' 또는 '장치'(이 모든 것이 복잡한 언어 게임)가 특정 '시스템'의 일부임을 보여줄 수 있는 특정 방법을 찾을 수 없습니다. 현대 의 두 systems보기에서인간의 행동에 대한 포괄적 인 최신 프레임 워크를 원하는 사람들은 내 책을 참조 할 수 있습니다'철학의 논리적 구조, 심리학, 민d와 루드비히 비트겐슈타인과 존 Searle의언어' 2nd ed (2019). 내 글의 더 많은 관심있는 사람들은 '이야기 원숭이를 볼 수 있습니다-철학, 심리학, 과학, 종교와 운명 행성에 정치 - 기사 및 리뷰 2006-2019 2nd 에드 (2019) 및 21st 세기 4번째 에드 (2019) 및 기타. (shrink)

Em "Godel's Way", três cientistas eminentes discutem questões como a undecidability, incompletude, aleatoriedade, computabilidade e paraconsistência. Eu abordar estas questões do ponto de vista Wittgensteinian que existem duas questões básicas que têm soluções completamente diferentes. Há as questões científicas ou empíricas, que são fatos sobre o mundo que precisam ser investigados observacionalmente e questões filosóficas sobre como a linguagem pode ser usada inteligìvelmente (que incluem certas questões em matemática e lógica), que precisam ser decidido por olhar uma como nós realmente (...) usar palavras em contextos específicos. Quando nós começ claros sobre que jogo da língua nós estamos jogando, estes tópicos são vistos para ser perguntas científicas e matemáticas ordinárias como qualquer outro. As idéias de Wittgenstein raramente foram igualadas e nunca ultrapassaram e são tão pertinentes hoje como eram 80 anos atrás, quando ele ditou os livros azul e marrom. Apesar de suas falhas-realmente uma série de notas em vez de um livro acabado-esta é uma fonte única do trabalho destes três estudiosos famosos que têm trabalhado nas bordas sangrantes da física, matemática e filosofia por mais de meio século. Da costa e Doria são citados por Wolpert (veja abaixo ou meus artigos sobre Wolpert e minha revisão de Yanofsky ' s "os limites exteriores da razão") desde que escreveu sobre a computação universal, e entre suas muitas realizações, da costa é um pioneiro em a paraconsistência. Aqueles que desejam um quadro até à data detalhado para o comportamento humano da opinião moderna dos dois sistemas consultar meu livros Falando Macacos 3ª Ed (2019), A Estrutura Lógica da Filosofia, Psicologia, Mente e Linguagem em Ludwig Wittgenstein e John Searle 2a Ed (2019), Suicídio Pela Democracia,4aEd(2019), Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política e Economia Artigos e Análises 2006-2019 (2019), Ilusões Utópicas Suicidas no 21St século 5a Ed (2019), A Estrutura Lógica do Comportamento Humano (2019), e A Estrutura Lógica da Consciência (2019) y outras. (shrink)

It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than as (...) a motley of pieces assembled by the random processes of natural selection. “Gödel shows us an unclarity in the concept of ‘mathematics’, which is indicated by the fact that mathematics is taken to be a system” and we can say (contra nearly everyone) that is all that Gödel and Chaitin show. Wittgenstein commented many times that ‘truth’ in math means axioms or the theorems derived from axioms, and ‘false’ means that one made a mistake in using the definitions, and this is utterly different from empirical matters where one applies a test. Wittgenstein often noted that to be acceptable as mathematics in the usual sense, it must be useable in other proofs and it must have real world applications, but neither is the case with Godel’s Incompleteness. Since it cannot be proved in a consistent system (here Peano Arithmetic but a much wider arena for Chaitin), it cannot be used in proofs and, unlike all the ‘rest’ of PA it cannot be used in the real world either. As Rodych notes “…Wittgenstein holds that a formal calculus is only a mathematical calculus (i.e., a mathematical language-game) if it has an extra- systemic application in a system of contingent propositions (e.g., in ordinary counting and measuring or in physics) …” Another way to say this is that one needs a warrant to apply our normal use of words like ‘proof’, ‘proposition’, ‘true’, ‘incomplete’, ‘number’, and ‘mathematics’ to a result in the tangle of games created with ‘numbers’ and ‘plus’ and ‘minus’ signs etc., and with -/- ‘Incompleteness’ this warrant is lacking. Rodych sums it up admirably. “On Wittgenstein’s account, there is no such thing as an incomplete mathematical calculus because ‘in mathematics, everything is algorithm [and syntax] and nothing is meaning [semantics]…” -/- I make some brief remarks which note the similarities of these ‘mathematical’ issues to economics, physics, game theory, and decision theory. -/- Those wishing further comments on philosophy and science from a Wittgensteinian two systems of thought viewpoint may consult my other writings -- Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 4th ed (2019), The Logical Structure of Human Behavior (2019), The Logical Structure of Consciousness (2019, Understanding the Connections between Science, Philosophy, Psychology, Religion, Politics, and Economics and Suicidal Utopian Delusions in the 21st Century 5th ed (2019), Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal-Sharrock and Yanofsky (2019), and The Logical Structure of Philosophy, Psychology, Sociology, Anthropology, Religion, Politics, Economics, Literature and History (2019). (shrink)

People often speak loosely, uttering sentences that are plainly false on their most strict interpretation. In understanding such speakers, we face a problem of underdetermination: there is often no unique interpretation that captures what they meant. Focusing on the case of incomplete definite descriptions, this paper suggests that speakers often mean bundles of propositions. When a speaker means a bundle, their audience can know what they mean by deriving any one of its members. Rather than posing a problem for the (...) interpretation of loose talk, the underdetermination of a uniquely correct interpretation allows for various ways in which the audience can grasp the speaker’s meaning. (shrink)

Der Topos von der Unerschöpflichkeit des Gegenstands wird mit der Phänomenologie assoziiert. Den ihm verwandten Topos von der Unaussprechlichkeit des Individuellen haben Goethe und die deutschen Romantiker in die Welt getragen. Der Diktion der analytischen Philosophie sind die Ausdrücke „unerschöpflich“ und „unaussprechlich“ fremd. Dieser Umstand sollte analytische Philosophen nicht davon abhalten, sich den sprachphilosophischen und ontologischen Problemen zuzuwenden, die sich hinter den besagten Formeln verbergen. Husserls Wort für Unerschöpflichkeit ist „Fülle“. Die „Fülle des Gegenstandes“ erläutert Husserl als den „Inbegriff der (...) ihn konstituierenden Bestimmtheiten“, seine „individualisierenden Bestimmtheiten“ eingeschlossen. Ich werde in diesem Aufsatz von deskriptiver Unerschöpflichkeit sprechen, die ich auf eine ontische Eigenart der konkreten Einzeldinge zurückführe. Den Begriff der deskriptiven Unerschöpflichkeit werde ich zunächst anhand des Problems entwickeln, die Eigenschaften eines Einzeldings zu zählen. Aristoteles, Leibniz und Kant beantworten die Frage, wie viele Eigenschaften ein Einzelding hat, gleichlautend: es sind potentiell unendlich viele (1.). Die ontologische Kategorie, für die dies gilt, ist die der konkreten, raumzeitlichen Einzeldinge (2.). Unter (3.) wird der Befund der deskriptiven Unerschöpflichkeit näher erläutert und ausdifferenziert. Unter (4.) wird ein sprachphilosophisch motivierter Einwand gegen die Unerschöpflichkeitsthese diskutiert und zurückgewiesen: der Einwand aus der endlichen Zahl der Prädikate. Dann werde ich die Begriffe Leerstelle, Auflösung und ontische Dichte einführen, um meinen Befund zu sichern und zu präzisieren (5.). Unter dem Stichwort „Unerschöpflich oder bloß faktisch unerschöpft?“ diskutiere ich die Frage, worin das prinzipielle Hindernis für das Unternehmen liegen soll, ein Einzelding erschöpfend zu beschreiben (6.). Anschließend kontrastiere ich die Unerschöpflichkeitsthese mit der pathetischen Formel von der „Unaussprechlichkeit des Individuellen“, um zu verdeutlichen, was mit ersterer nicht gemeint ist (7.). Diese Diskussion führt zu ontologischen Überlegungen über Individualität, Einzigkeit und haecceitas (8.). Schließlich bringe ich den Gedanken ins Spiel, daß wir in der natürlichen Sprache beliebig feine semantische Unterscheidungen treffen können, der auf den ersten Blick in einer gewissen Spannung zur These der deskriptiven Unerschöpflichkeit steht. Diese Spannung werde ich unter (9.) und (10.) zu mildern suchen und dabei meinen Begriff der ontischen Dichte zu Goodmans Begriff der semantischen Dichte in Beziehung setzen. (shrink)

In 'The Reference Book' (2012), Hawthorne and Manley observe the following contrast between (1) and (2): -/- (1) In every race John won. (2) In every race, the colt won. -/- The name 'John' in (1) must intuitively refer to the same single individual for each race. However, the description 'the colt' in (2) has a co-varying reading, i.e. a reading where for each race it refers to a different colt. This observation is a prima facie problem for proponents of (...) so-called The-Predicativism which is the view that the name in (1) is really a covert definite description, viz. 'the John'. If the The-Predicativism is correct, (1) and (2) are therefore syntactically equivalent, but this makes it mysterious why only (2) would have a co-varying reading. In a recent paper, Fara (2015) argues that there is a simple and elegant way for proponents of The-Predicativism to explain this contrast. This explanation relies on discerning some subtle syntactic differences between (1) and (2) which in turn are based on assumptions about nominal restrictions a la Stanley and Szabó (2000). In this short paper, I demonstrate that Fara's proposed explanation has a variety of serious shortcomings and hence that the contrast between (1) and (2) remains a significant problem for Predicativism. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...) array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)