The Role of Truth-Values in Indirect Meanings

2018 ◽  
pp. 185-206
Author(s):  
Basil Lourié ◽  
Olga Mitrenina
Keyword(s):  
Truth Values

scholarly journals SUSZKO’S PROBLEM: MIXED CONSEQUENCE AND COMPOSITIONALITY

2019 ◽  
Vol 12 (4) ◽  
pp. 736-767 ◽  
Author(s):  
EMMANUEL CHEMLA ◽  
PAUL ÉGRÉ
Keyword(s):  
Structural Properties ◽  
Semantic Interpretation ◽  
Structural Constraints ◽  
General Representation ◽  
Representation Theorems ◽  
Consequence Relation ◽  
Truth Values ◽  
General Meaning ◽  
Semantic Properties

AbstractSuszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of so-called mixed consequence, allowing the notion of a designated value to vary between the premises and the conclusions of an argument. In this article we give a more systematic perspective on Suszko’s problem and on mixed consequence. First, we prove general representation theorems relating structural properties of a consequence relation to their semantic interpretation, uncovering the semantic counterpart of substitution-invariance, and establishing that (intersective) mixed consequence is fundamentally the semantic counterpart of the structural property of monotonicity. We use those theorems to derive maximum-rank results proved recently in a different setting by French and Ripley, as well as by Blasio, Marcos, and Wansing, for logics with various structural properties (reflexivity, transitivity, none, or both). We strengthen these results into exact rank results for nonpermeable logics (roughly, those which distinguish the role of premises and conclusions). We discuss the underlying notion of rank, and the associated reduction proposed independently by Scott and Suszko. As emphasized by Suszko, that reduction fails to preserve compositionality in general, meaning that the resulting semantics is no longer truth-functional. We propose a modification of that notion of reduction, allowing us to prove that over compact logics with what we call regular connectives, rank results are maintained even if we request the preservation of truth-functionality and additional semantic properties.

ON MODELS FOR CROSS-WORLD PREDICATION

2021 ◽  
pp. 310-315
Author(s):  
Константин Геннадьевич Фролов
Keyword(s):  
Modal Epistemology ◽  
Truth Conditions ◽  
Truth Values ◽  
Mental Modeling

Я выдвигаю два методологических возражения против концепции кросс-мировой предикации, которую предлагает Е. Борисов: (1) Данный подход не учитывает того обстоятельства, что истинностный статус утверждений модального дискурса, как правило, интересует нас не в теоретико-модельном смысле, а в смысле истинности simpliciter. При этом данный подход не оставляет нам никакой возможности говорить о модальной эпистемологии и содержательном обосновании модальных утверждений. (2) Данный подход не учитывает роли воображения и ментального моделирования в том, что Е. Борисовым называется «интуитивным пониманием» рассматриваемых им утверждений. Учёт воображения и ментального моделирования, в свою очередь, переводит содержание подавляющего числа рассматриваемых Евгением примеров в разряд эпистемической модальности говорящего. При этом корректный переход от субъективной эпистемической модальности говорящего к любым типам объективных модальностей в рамках подхода Евгения попросту не может быть осуществлён, поскольку такой переход предполагает наличие внятной концепции модальной эпистемологии, чего Евгений нам не предлагает. Истинность любых рассматриваемых им примеров - это истинность на моделях говорящих, то есть на фреймах, в рамках которых говорящие полагают некоторые миры достижимыми из актуального. I raise two objections to E. Borisov’s methodology for building the theory of cross-world predication: (1) This approach does not take into account the fact that usually we are interested in truth values of modal claims not in the model-theoretical sense, but in the sense of truth simpliciter. However, this approach does not leave us any opportunity to talk about modal truths simpliciter, modal epistemology and substantive truth conditions for modal claims. (2) This approach does not take into account the role of imagination and mental modeling in what E. Borisov calls the ‘intuitive meaning’ of the analysed claims. However, taking into account imagination and mental modeling shows that the vast majority of the cases under consideration deal with epistemic and not alethic modality. In the absence of any modal epistemology we cannot simply postulate the validity of modal truths. Such postulation would be puzzling and unexplainable. And without such postulation of factuality, all the modalities we consider turn out epistemic.

scholarly journals Truth in Mathematics

2018 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Mathematical Truth ◽  
Mathematical Objects ◽  
Truth Values ◽  
Objective Truth ◽  
The Third ◽  
Philosophical Account ◽  
Classical Conception ◽  
Concept Of Truth

This chapter discusses four questions concerning the nature and role of the concept of truth in mathematics. First, the question as to whether the concept of truth is needed in a philosophical account of mathematics is answered affirmatively: a formalist approach to the language of mathematics is inadequate. Next, following Frege, a classical conception of mathematical truth is defended, involving the existence of mathematical objects. The third question concerns the relation between the existence of mathematical objects and the objectivity of mathematical truth. A traditional platonist seeks to explain the latter in terms of the former, while Frege reverses this order of explanation. Finally, the question regarding the extent to which mathematical statements have objective truth-values is discussed.

scholarly journals FREGE’S ĮNAŠAS Į REIKŠMĖS SAMPRATĄ

Problemos ◽  
1970 ◽  
Vol 68 ◽  
pp. 82-91
Author(s):  
Mindaugas Japertas
Keyword(s):  
Semantic Features ◽  
Declarative Sentence ◽  
Truth Values ◽  
Theory Of Meaning ◽  
Proper Name ◽  
Sense And Reference ◽  
Language Meaning

Straipsnyje dėstoma, komentuojama ir interpretuojama Gottlobo Frege’s reikšmės teorija, kurios pagrindą sudaro reikalavimas kiekvieno kalbos ženklo semantikoje skirti prasmės (Sinn) ir referencijos (Bedeutung) lygmenis. Atskleidþiamos loginės lingvistinės priežastys, nulėmusios Frege’s sprendimą laikytis diferencinės reikšmės sampratos, taip pat remiantis „prasmės“ ir „referencijos“ terminologiniu instrumentarijumi parodoma, kuo skiriasi, o kita vertus, kuo panašūs Frege’s įtvirtinti požiūriai į tikrinio vardo ir į teigiamojo (asertorinio) sakinio reikšmes. Vadovaujantis prielaida, kad žodžio ar posakio reikšmės sudedamąja dalimi gali būti tik tie veiksniai, kurie yra būtini kompetentingam kalbos supratimui, Frege’s išskirti semantiniai aspektai straipsnyje įvertinami ir šiuo atžvilgiu. Daroma išvada, kad tikrasis semantinis terminas yra „prasmė“, o referencijos lygmens esybės (objektai, teisingumo vertės) nėra nekeliančios abejonių reikšmės sudedamosios dalys, todėl referencijos aspekto statusas Frege’s tipo reikšmės teorijoje tampa neaiškus.Reikšminiai žodžiai: Frege, kalba, reikšmė, prasmė, referencija FREGE’S CONTRIBUTION TO THE NOTION OF MEANINGMindaugas Japertas SummaryThe article aims at exposition, commenting and interpreting Frege’s theory of meaning, based on the requirement to distinguish, in the meaning of a sign, the level of sense (Sinn) and the correlative level of reference (Bedeutung). The author directs attention to some logico-linguistic reasons which seem to have urged Frege to advocate the differential conception of meaning. In accordance with Frege’s decision to use the theoretical notions of sense and reference, the relevant semantic features of a proper name as well as of a declarative sentence are explored. Since only something which constitutes what someone who understands the word or expression implicitly grasps can be counted as a possible ingredient in meaning, the claim is made that entities on the level of reference (objects, truth-values) are not undeniable ingredients of meaning. Sense therefore is left in the role of a genuine semantic concept.Keywords: Frege, language, meaning, sense, reference.

scholarly journals A local deterministic model of quantum spin measurement

1995 ◽  
Vol 451 (1943) ◽  
pp. 585-608 ◽  
Keyword(s):  
State Vector ◽  
Quantum Physics ◽  
Deterministic Model ◽  
Quantum Spin ◽  
The State ◽  
Spin States ◽  
Truth Values ◽  
Conventional View ◽  
State Vector Reduction

The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrized model, ' Q ' for the state vector evolution of spin-1/2 particles during measurement is developed. Q draws on recent work on ‘riddled basins’ in dynamical systems theory, and is local, determin­istic, nonlinear and time asymmetric. Moreover, the evolution of the state vector to one of two chaotic attractors (taken to represent observed spin states) is effectively uncomputable. Motivation for considering this model arises from speculations about the (time asymmetric and uncomputable) nature of quantum gravity, and the (nonlinear) role of gravity in quantum state vector reduction. Although the evolution of Q s state vector cannot be determined by a numerical algorithm, the probability that initial states in some given region of phase space will evolve to one of these attractors, is itself computable. These probabilities can be made to correspond to observed quantum spin probabilities. In an ensemble sense, the evolution of the state vector to an attractor can be described by a diffusive random walk process, suggesting that deterministic dynamics may underlie recent attempts to model state vector evolution by stochastic equations. Bell’s theorem and a version of the Bell-Kochen-Specker quantum entanglement paradox, as illustrated by Penrose’s ‘magic dodecahedra’, are discussed using Q as a model of quantum spin measurement. It is shown that in both cases, proving an inconsistency with locality demands the existence of definite truth values to certain counterfactual propositions. In Q these deterministic propositions are uncomputable, and no non-algorithmic mathematical solution is either known or suspected. Adapt­ing the mathematical formalist approach, the non-existence of definite truth values to such counterfactual propositions is posited. No inconsistency with experiment is found. As a result, it is claimed that Q is not constrained by Bell’s inequality, locality and determinism notwithstanding.

scholarly journals Peran Pendidik Kristen terhadap Dampak New Morality dari Era Digital

2021 ◽  
Vol 2 (1) ◽  
pp. 49-59
Author(s):  
Wandri Lumbantoruan
Keyword(s):  
Qualitative Research ◽  
Significant Role ◽  
Research Method ◽  
Negative Impact ◽  
Qualitative Research Method ◽  
Truth Values ◽  
Digital Era ◽  
Christian Educators

One of the important indicators that Christian educators must do is to build the character of students well. The negative impact that has emerged in this digital era demands that Christian educators have a more real and significant role, not just teaching in the classroom. This article aims to show the role of Christian educators in building the character of students in the digital era that has an impact on this New Morality. This article uses a qualitative research method by examining the role of Christian religious teachers in building student character in a digital era that is threatened with moral decline. The results of the study confirmed that Christian educators played a role in building students' self-concepts in accordance with Bible truth values so that students could distinguish between good and bad.AbstrakSalah satu indikator penting yang harus dilakukan oleh pendidik Kristen adalah membangun karakter siswa dengan baik. Dampak negatif yang muncul di era digital ini menuntut pendidik Kristen memiliki peran yang lebih nyata dan signifikan, bukan sekadar mengajar dalam kelas saja. Artikel ini bertujuan untuk menunjukkan peran pendidik Kristen dalam membangun karakter Siswa di era digital yang memiliki dampak pada New Morality ini. Artikel ini menggunakan metode penelitian kualitatif dengan melakukan kajian terhadap peran guru Agama Kristen dalam membangun karakter siswa di era digital yang terancam kemerostan moral. Hasil kajian menegaskan bahwa pendidik Krisren berperan untuk membangun konsep diri siswa sesuai dengan nilai-nilai kebenaran Alkitab, agar siswa dapat membedakan mana yang baik dan buruk.

scholarly journals Ordered combinatory algebras and realizability

2015 ◽  
Vol 27 (3) ◽  
pp. 428-458 ◽  
Author(s):  
WALTER FERRER SANTOS ◽  
JONAS FREY ◽  
MAURICIO GUILLERMO ◽  
OCTAVIO MALHERBE ◽  
ALEXANDRE MIQUEL
Keyword(s):  
Higher Order ◽  
Dual Role ◽  
Order Logic ◽  
Higher Order Logic ◽  
Truth Values ◽  
Precise Sense ◽  
Order Language ◽  
The Difference

We propose the new concept ofKrivine ordered combinatory algebra($\mathcal{^KOCA}$) as foundation for the categorical study of Krivine's classical realizability, as initiated by Streicher (2013).We show that$\mathcal{^KOCA}$'s are equivalent to Streicher'sabstract Krivine structuresfor the purpose of modeling higher-order logic, in the precise sense that they give rise to the same class oftriposes. The difference between the two representations is that the elements of a$\mathcal{^KOCA}$play both the role of truth values and realizers, whereas truth values aresetsof realizers in$\mathcal{AKS}$s.To conclude, we give a direct presentation of the realizability interpretation of a higher order language in a$\mathcal{^KOCA}$, which showcases the dual role that is played by the elements of the$\mathcal{^KOCA}$.

Opposites attract: the role of predicate dimensionality in preschool children's processing of negations

2003 ◽  
Vol 30 (2) ◽  
pp. 419-440 ◽  
Author(s):  
BRADLEY J. MORRIS
Keyword(s):  
Preschool Children ◽  
Truth Values

Three experiments investigated the role of oppositional predicate dimensionality in four- and five-year-old children's processing of negation. In Experiment 1 children (37 four-year-olds, mean age 4;8, and 20 five-year-olds, mean age 5;9) were asked to produce opposites for common terms (e.g. ‘big’). In Experiment 2 children (27 four-year-olds, mean age 4;8; 23 five-year-olds, mean age 5;9) were asked to make pictures corresponding to statements phrased as negations (e.g. The arrow is NOT pointing up). In Experiment 3, children were asked to evaluate a series of pictures made by ‘another child’ using materials and procedures similar to those used in Experiment 2. Preschool children made use of predicate dimensionality when producing negations but could accurately evaluate truth-values regardless of content. Children often recalled negated items as affirmations (usually corresponding to antipodal opposites), which suggests that children's use of predicate dimensionality contributes to non-classical processing.

scholarly journals The Logic of Self-Organized Criticality

Studia Humana ◽  
2015 ◽  
Vol 4 (3) ◽  
pp. 37-40
Author(s):  
Kamil I. Bakhtiyarov
Keyword(s):  
Genetic Code ◽  
Classical Logic ◽  
Truth Values ◽  
Self Organized ◽  
Self Organized Criticality

Abstract A consideration of non-classical logic in terms of classical one allows us to show a role of designated truth values. In this way we show that our version of non-classical many-valued logic can be based on the structure of genetic code.

Role of dactinomycin in the improved survival of children with Wilms' tumor

JAMA ◽  
1966 ◽  
Vol 195 (12) ◽  
pp. 1005-1009 ◽  
Author(s):  
D. J. Fernbach
Keyword(s):  
Wilms Tumor
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