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Volume 66 (2021): Issue 4 (December 2021)

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Volume 66 (2021): Issue 1 (December 2021)

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Volume 64 (2020): Issue 1 (December 2020)

Volume 63 (2020): Issue 1 (September 2020)

Volume 62 (2020): Issue 1 (June 2020)

Volume 61 (2020): Issue 1 (March 2020)

Volume 60 (2019): Issue 1 (December 2019)

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Volume 58 (2019): Issue 1 (June 2019)

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Volume 56 (2018): Issue 1 (December 2018)

Volume 55 (2018): Issue 1 (September 2018)

Volume 54 (2018): Issue 1 (June 2018)

Volume 53 (2018): Issue 1 (March 2018)

Volume 52 (2017): Issue 1 (December 2017)

Volume 51 (2017): Issue 1 (September 2017)

Volume 50 (2017): Issue 1 (June 2017)

Volume 49 (2017): Issue 1 (March 2017)

Volume 48 (2016): Issue 1 (December 2016)

Volume 47 (2016): Issue 1 (December 2016)

Volume 46 (2016): Issue 1 (September 2016)

Volume 45 (2016): Issue 1 (June 2016)

Volume 44 (2016): Issue 1 (March 2016)

Volume 43 (2015): Issue 1 (December 2015)

Volume 42 (2015): Issue 1 (September 2015)

Volume 41 (2015): Issue 1 (June 2015)

Volume 40 (2015): Issue 1 (March 2015)

Volume 39 (2014): Issue 1 (December 2014)

Volume 38 (2014): Issue 1 (September 2014)

Volume 37 (2014): Issue 1 (June 2014)
Mechanisms and Methods of Decision Making / Ed. by Ewa Roszkowska

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Volume 34 (2013): Issue 1 (October 2013)

Volume 33 (2013): Issue 1 (August 2013)

Volume 32 (2013): Issue 1 (May 2013)

Journal Details
Format
Journal
eISSN
2199-6059
ISSN
0860-150X
First Published
08 Aug 2013
Publication timeframe
4 times per year
Languages
English

Search

Volume 54 (2018): Issue 1 (June 2018)

Journal Details
Format
Journal
eISSN
2199-6059
ISSN
0860-150X
First Published
08 Aug 2013
Publication timeframe
4 times per year
Languages
English

Search

12 Articles
Open Access

Introduction with remarks on the history of negation

Published Online: 16 Nov 2018
Page range: 7 - 13

Abstract

Abstract

In the introduction to the volume on negation, first the source ways of understanding it from antiquity to modern times are presented, as well as the basic points of contention connected with it. Subsequently, the works contained in this volume are briefly presented in the order in which they appeared.

Open Access

Negation and presupposition, truth and falsity

Published Online: 16 Nov 2018
Page range: 15 - 46

Abstract

Abstract

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a complete list, nor to analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable.

Keywords

  • negation of propositions
  • presupposition
  • wide-scope vs. narrow-scope negation
  • topic-focus articulation
  • truth-value gaps
  • requisites and prerequisites
  • Transparent Intensional Logic
  • if-then-else-fail function
Open Access

Contentual approach to negation1

Published Online: 16 Nov 2018
Page range: 47 - 60

Abstract

Abstract

Interpretations of logics with only truth-functional connectives create a number of problems regarding the understanding of interpreted sentences. A particular problem is caused by the understanding of a sentence that is the negation of another. What is the meaning of sentence ¬p, for a particular sentence p? Even when we know what the semantic correlate of the sentence p is, we still do not know how to understand the semantic correlate of the sentence ¬p. The standard algebraic approach does not explain much. The problem is still open, because it is still unclear how to understand the element of algebra −v(p). The propositional logic with the connective of the content implication, as it is a non-Fregean logic, proposes a simple solution to this problem. The key to understanding the content of the sentence ¬p is to understand the content of the sentence p. Because, the content of the natural language sentence usually has a partial understanding, so it can be understood differently. Therefore, the negation ¬p is here understood adequately to the current and partial understanding of the sentence p. It seems that the proposed approach is consistent with our daily thinking.

Keywords

  • content implication
  • sentential identity non-Fregean logic
  • Suszko
  • negation
Open Access

I believe that he didn’t do it and I don’t believe that he did it. The influence of context on the semantic-communicative relations between sentence negation and performative negation

Published Online: 16 Nov 2018
Page range: 61 - 76

Abstract

Abstract

The subject matter of the paper is an analysis of the semantic relations between sentence negation, performative negation, and declarations in reference to utterances which speech acts theory gives the label of representatives. Apart from linguistic-semantic analyses, empirical studies have been conducted on the manner in which sentence negation and performative negation are processed. The results of Study I demonstrate that the semantic relation between sentence negation and performative negation changes depend on the type of comment (positive vs. negative), and contextual factors (type of expectations towards events being commented on). As it turned out, when the situational context suggests a negative comment by the sender, participants offer similar interpretations of utterances with sentence negation and performative negation. In Study II the participants assessed the likelihood of the occurrence of the facts spoken of by a sender who uses sentence negation or performative negation. In a context suggesting positive utterances by the sender, a clear difference emerged between sentence negation and performative negation. This difference was not present in respect of negative expectations. The results achieved confirm the assumptions of the model of conversational inference regarding the influence of context on interpretation of a message. The recorded results indicate the semantic relations between declarations, sentence negation, and performative negation, which change depending on the affective significance of the message and contextual factors.

Keywords

  • speech acts
  • performative negation
  • sentence negation
  • verbal politeness
  • representatives
Open Access

Logical analysis of empirical expressions. What is wrong with empiricism

Published Online: 16 Nov 2018
Page range: 77 - 88

Abstract

Abstract

The following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity.

Keywords

  • abstract
  • concrete
  • empirical
  • sense
  • denotation
  • reference
Open Access

Logical rules and the determinacy of meaning

Published Online: 16 Nov 2018
Page range: 89 - 98

Abstract

Abstract

The use of conventional logical connectives either in logic, in mathematics, or in both cannot determine the meanings of those connectives. This is because every model of full conventional set theory can be extended conservatively to a model of intuitionistic set plus class theory, a model in which the meanings of the connectives are decidedly intuitionistic and nonconventional. The reasoning for this conclusion is acceptable to both intuitionistic and classical mathematicians. En route, I take a detour to prove that, given strictly intuitionistic principles, classical negation cannot exist.

Keywords

  • negation
  • truth value
  • intuitionistic set theory
  • use theory of meaning
Open Access

Comments on the acceptance and rejection of sentences in theology

Published Online: 16 Nov 2018
Page range: 99 - 113

Abstract

Abstract

This work is interdisciplinary as it lies at the crossroads of three disciplines: philosophy, theology, and logic. The article attempts to discuss the way in which sentences (judgements) are accepted and rejected within theology. First, the role of the argument of authority in theology is discussed. Subsequently, the most important types of theorems with certain degrees of theological certainty were identified. Finally, censorship was presented as a means of rejecting theorems in theology. Finally, censorship was indicated as a model for philosophical-logical research on denial.

Keywords

  • notae theologice
  • certainty
  • rejection
  • argument ex auctoritate
  • censures
Open Access

Negating as turning upside down

Published Online: 16 Nov 2018
Page range: 115 - 129

Abstract

Abstract

In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns upside down the structure almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs.

Keywords

  • negation
  • opposition
  • adjointness
  • duality
  • category theory
  • negative states of affairs
Open Access

Negation and infinity

Published Online: 16 Nov 2018
Page range: 131 - 148

Abstract

Abstract

Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic issues will be considered.

Keywords

  • negation
  • infinity
Open Access

The logical challenge of negative theology

Published Online: 16 Nov 2018
Page range: 149 - 174

Abstract

Abstract

In this paper I present four interpretations of so-called negative theology and provide a number of attempts to model this theory within a formal system. Unfortunately, all of them fail in some manner. Most of them are simply inconsistent, some contradict the usual religious praxis and discourse, and some do not correspond to the key theses of negative theology. I believe that this paper shows how challenging this theory is from a logical perspective.

Keywords

  • logic
  • negative theology
  • apophatic theology
  • negation
  • self-reference
  • paradoxes
Open Access

Something, nothing and Leibniz’s question. negation in logic and metaphysics

Published Online: 16 Nov 2018
Page range: 175 - 190

Abstract

Abstract

This paper discusses the concept of nothing (nothingness) from the point of logic and ontology (metaphysics). It is argued that the category of nothing as a denial of being is subjected to various interpretations. In particular, this thesis concerns the concept of negation as used in metaphysics. Since the Leibniz question ‘Why is there something rather than nothing?’ and the principle of sufficient reason is frequently connected with the status of nothing, their analysis is important for the problem in question. Appendix contains a short critical analysis of Heidegger’s famous statement Das Nichts nichtet.

Keywords

  • nothingness
  • creatio ex nihilo)
  • non-being
  • Principle of Sufficient Reason
  • Leibniz
  • Heidegger
  • Das Nichts nichtet
  • negation
Open Access

A contra-linguistic study of negation in Korean and English

Published Online: 16 Nov 2018
Page range: 191 - 207

Abstract

Abstract

Negation is frequently found in every language, and many logicians or linguists have been carrying out research on it. Their investigations are, however, mostly confined to the languages of Europe. Although some of them pay attention to non-European languages, we can hardly find research on negation in Korean. In this paper, we carry out contra-linguistic analysis of four aspects of negation in Korean and English. First, we compare the expressions of negative elements in Korean and English sentences. Second, we contrast the types of negation in Korean with those of English. Third, we draw a distinction between Korean and English in what decides the scope of negation. Finally, we contrast the answers to questions which contain negative elements.

Keywords

  • contra-linguistics
  • English
  • Korean
  • negation
  • yes-no question
12 Articles
Open Access

Introduction with remarks on the history of negation

Published Online: 16 Nov 2018
Page range: 7 - 13

Abstract

Abstract

In the introduction to the volume on negation, first the source ways of understanding it from antiquity to modern times are presented, as well as the basic points of contention connected with it. Subsequently, the works contained in this volume are briefly presented in the order in which they appeared.

Open Access

Negation and presupposition, truth and falsity

Published Online: 16 Nov 2018
Page range: 15 - 46

Abstract

Abstract

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a complete list, nor to analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable.

Keywords

  • negation of propositions
  • presupposition
  • wide-scope vs. narrow-scope negation
  • topic-focus articulation
  • truth-value gaps
  • requisites and prerequisites
  • Transparent Intensional Logic
  • if-then-else-fail function
Open Access

Contentual approach to negation1

Published Online: 16 Nov 2018
Page range: 47 - 60

Abstract

Abstract

Interpretations of logics with only truth-functional connectives create a number of problems regarding the understanding of interpreted sentences. A particular problem is caused by the understanding of a sentence that is the negation of another. What is the meaning of sentence ¬p, for a particular sentence p? Even when we know what the semantic correlate of the sentence p is, we still do not know how to understand the semantic correlate of the sentence ¬p. The standard algebraic approach does not explain much. The problem is still open, because it is still unclear how to understand the element of algebra −v(p). The propositional logic with the connective of the content implication, as it is a non-Fregean logic, proposes a simple solution to this problem. The key to understanding the content of the sentence ¬p is to understand the content of the sentence p. Because, the content of the natural language sentence usually has a partial understanding, so it can be understood differently. Therefore, the negation ¬p is here understood adequately to the current and partial understanding of the sentence p. It seems that the proposed approach is consistent with our daily thinking.

Keywords

  • content implication
  • sentential identity non-Fregean logic
  • Suszko
  • negation
Open Access

I believe that he didn’t do it and I don’t believe that he did it. The influence of context on the semantic-communicative relations between sentence negation and performative negation

Published Online: 16 Nov 2018
Page range: 61 - 76

Abstract

Abstract

The subject matter of the paper is an analysis of the semantic relations between sentence negation, performative negation, and declarations in reference to utterances which speech acts theory gives the label of representatives. Apart from linguistic-semantic analyses, empirical studies have been conducted on the manner in which sentence negation and performative negation are processed. The results of Study I demonstrate that the semantic relation between sentence negation and performative negation changes depend on the type of comment (positive vs. negative), and contextual factors (type of expectations towards events being commented on). As it turned out, when the situational context suggests a negative comment by the sender, participants offer similar interpretations of utterances with sentence negation and performative negation. In Study II the participants assessed the likelihood of the occurrence of the facts spoken of by a sender who uses sentence negation or performative negation. In a context suggesting positive utterances by the sender, a clear difference emerged between sentence negation and performative negation. This difference was not present in respect of negative expectations. The results achieved confirm the assumptions of the model of conversational inference regarding the influence of context on interpretation of a message. The recorded results indicate the semantic relations between declarations, sentence negation, and performative negation, which change depending on the affective significance of the message and contextual factors.

Keywords

  • speech acts
  • performative negation
  • sentence negation
  • verbal politeness
  • representatives
Open Access

Logical analysis of empirical expressions. What is wrong with empiricism

Published Online: 16 Nov 2018
Page range: 77 - 88

Abstract

Abstract

The following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity.

Keywords

  • abstract
  • concrete
  • empirical
  • sense
  • denotation
  • reference
Open Access

Logical rules and the determinacy of meaning

Published Online: 16 Nov 2018
Page range: 89 - 98

Abstract

Abstract

The use of conventional logical connectives either in logic, in mathematics, or in both cannot determine the meanings of those connectives. This is because every model of full conventional set theory can be extended conservatively to a model of intuitionistic set plus class theory, a model in which the meanings of the connectives are decidedly intuitionistic and nonconventional. The reasoning for this conclusion is acceptable to both intuitionistic and classical mathematicians. En route, I take a detour to prove that, given strictly intuitionistic principles, classical negation cannot exist.

Keywords

  • negation
  • truth value
  • intuitionistic set theory
  • use theory of meaning
Open Access

Comments on the acceptance and rejection of sentences in theology

Published Online: 16 Nov 2018
Page range: 99 - 113

Abstract

Abstract

This work is interdisciplinary as it lies at the crossroads of three disciplines: philosophy, theology, and logic. The article attempts to discuss the way in which sentences (judgements) are accepted and rejected within theology. First, the role of the argument of authority in theology is discussed. Subsequently, the most important types of theorems with certain degrees of theological certainty were identified. Finally, censorship was presented as a means of rejecting theorems in theology. Finally, censorship was indicated as a model for philosophical-logical research on denial.

Keywords

  • notae theologice
  • certainty
  • rejection
  • argument ex auctoritate
  • censures
Open Access

Negating as turning upside down

Published Online: 16 Nov 2018
Page range: 115 - 129

Abstract

Abstract

In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns upside down the structure almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs.

Keywords

  • negation
  • opposition
  • adjointness
  • duality
  • category theory
  • negative states of affairs
Open Access

Negation and infinity

Published Online: 16 Nov 2018
Page range: 131 - 148

Abstract

Abstract

Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic issues will be considered.

Keywords

  • negation
  • infinity
Open Access

The logical challenge of negative theology

Published Online: 16 Nov 2018
Page range: 149 - 174

Abstract

Abstract

In this paper I present four interpretations of so-called negative theology and provide a number of attempts to model this theory within a formal system. Unfortunately, all of them fail in some manner. Most of them are simply inconsistent, some contradict the usual religious praxis and discourse, and some do not correspond to the key theses of negative theology. I believe that this paper shows how challenging this theory is from a logical perspective.

Keywords

  • logic
  • negative theology
  • apophatic theology
  • negation
  • self-reference
  • paradoxes
Open Access

Something, nothing and Leibniz’s question. negation in logic and metaphysics

Published Online: 16 Nov 2018
Page range: 175 - 190

Abstract

Abstract

This paper discusses the concept of nothing (nothingness) from the point of logic and ontology (metaphysics). It is argued that the category of nothing as a denial of being is subjected to various interpretations. In particular, this thesis concerns the concept of negation as used in metaphysics. Since the Leibniz question ‘Why is there something rather than nothing?’ and the principle of sufficient reason is frequently connected with the status of nothing, their analysis is important for the problem in question. Appendix contains a short critical analysis of Heidegger’s famous statement Das Nichts nichtet.

Keywords

  • nothingness
  • creatio ex nihilo)
  • non-being
  • Principle of Sufficient Reason
  • Leibniz
  • Heidegger
  • Das Nichts nichtet
  • negation
Open Access

A contra-linguistic study of negation in Korean and English

Published Online: 16 Nov 2018
Page range: 191 - 207

Abstract

Abstract

Negation is frequently found in every language, and many logicians or linguists have been carrying out research on it. Their investigations are, however, mostly confined to the languages of Europe. Although some of them pay attention to non-European languages, we can hardly find research on negation in Korean. In this paper, we carry out contra-linguistic analysis of four aspects of negation in Korean and English. First, we compare the expressions of negative elements in Korean and English sentences. Second, we contrast the types of negation in Korean with those of English. Third, we draw a distinction between Korean and English in what decides the scope of negation. Finally, we contrast the answers to questions which contain negative elements.

Keywords

  • contra-linguistics
  • English
  • Korean
  • negation
  • yes-no question

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