<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Negating as turning upside down

Studies in Logic, Grammar and Rhetoric

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Negating as turning upside down"}

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...

Negating as turning upside down

Published Online: Nov 16, 2018

Page range: 115 - 129

DOI: https://doi.org/10.2478/slgr-2018-0020

Keywords
negation, opposition, adjointness, duality, category theory, negative states of affairs

© 2018 Bartłomiej Skowron, Wiesław Kubiś, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Negating as turning upside down

Published Online: Nov 16, 2018

Page range: 115 - 129

DOI: https://doi.org/10.2478/slgr-2018-0020

Keywordsnegation, opposition, adjointness, duality, category theory, negative states of affairs

© 2018 Bartłomiej Skowron, Wiesław Kubiś, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
negation, opposition, adjointness, duality, category theory, negative states of affairs