The development of non-classical logics undermines the justification for logical monism.
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While some philosophical literature suggests that non-classical logics challenge logical monism by questioning the uniqueness of a single system, other work argues that every logic remains unique.
Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism | Journal of Philosophical Logic | Springer Nature Link Skip to main content Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism Open access Published: 06 September 2021 Volume 51 , pages 27–55 ( 2022 ) Cite this article You have full access to this open access article Download PDF Save article View saved research Journal of Philosophical Logic Aims and scope Submit manuscript Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism Download PDF Abstract In order to prove the validity of logical rules, one has to assume these rules in the metalogic.
However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5).
Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.
Article PDF Download to read the full article text Similar content being viewed by others Why classical logic is privileged: justification of logics based on translatability Article Open access 01 November 2021 A Hierarchy of Classical and Paraconsistent Logics Article 08 April 2019 Anti-exceptionalism and methodological pluralism in logic Article Open access 04 May 2022 Explore related subjects Discover the latest articles, books and news in related subjects, suggested using machine learning. Algebraic Logic Formal Logic General Logic Linear Logic Logic Philosophical Logic Algebraic Logic and Non-Classical Systems References Ashcroft, M. (2010).
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https://doi.org/10.1007/s10992-021-09608-6 Download citation Received : 03 October 2020 Accepted : 31 May 2021 Published : 06 September 2021 Version of record : 06 September 2021 Issue date : February 2022 DOI : https://doi.org/10.1007/s10992-021-09608-6 Share this article Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Keywords Translations of non-classical into classical logics Meaning-preserving translations Representational optimality, logical pluralism Advertisement
What is the proper way to transfinitely extend the usual hierarchy of finite metainferential levels? McAllister (Journal of Philosophical Logic, 51, 1345–1365, 2022; Belief Revision About Logic, PhD Thesis, University of Auckland, 2024) has proven that classical logic and numerous other logics are non-unique in classical set theory. On the basis of these results, she argues for a range of philosophical consequences, including problems for logical monism, classical set theory, and the identification of logics. This paper demonstrates that McAllister’s key results are merely artifacts of the level labels which she adds to the transfinite hierarchy. It is proven that, in the absence of labels, every logic is unique in classical set theory. Moreover, I argue that if labels are not innocent additions, but instead influence the results in substantial ways, then they must be left out of the hierarchy. Therefore, in the final analysis, every logic is unique. The various problems which McAllister extracts from non-uniqueness accordingly dissolve.
language to a single sorted one. 5 Non-Classical Logics and Plurcdism The papers by Bell and … lection address other issues surrounding non-classical logics. Introduction 15 5.1 Expressive Power … sorts and commitment to classical or non-classical logics. The connection between the metaphysi¬
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rather of its pretension to ultimate validity and see logic as one logical tool among others—or perhaps, considering the multitude of formal logics, one
Pragmatism is a philosophical tradition that views language and thought as tools for prediction, problem solving, and action, rather than describing, representing, or mirroring reality. Pragmatists contend that most philosophical topics—such as the nature of knowledge, language, concepts, meaning, belief, and science—are best viewed in terms of their practical uses and successes.
Pragmatism began
Pragm…
Pragmatism enjoyed renewed attention after Willard Van Orman Quine and Wilfrid Sellars used a revised pragmatism to criticize logical positivism in the 1960s. Inspired by the work of Quine and Sellars, a brand of pragmatism known sometimes as neopragmatism gained influence through Richard Rorty, the most influential of the late 20th century pragmatists along with Hilary Putnam and Robert Brandom. Contemporary pragmatism may be broadly divided into a strict analytic tradition and a "neo-classical" pragmatism (such as Susan Haack) that adheres to the work of Peirce, James, and Dewey.
Lewis' main arguments in Mind and the World Order: Outline of a Theory of Knowledge (1929) was that science does not merely provide a copy of reality but must work with conceptual systems and that those are chosen for pragmatic reasons, that is, because they aid inquiry. Lewis' own development of multiple modal logics is a case in point. Lewis is sometimes called a proponent of conceptual pragmatism because of this. Another development is the cooperation of logical positivism and pragmatism in the works of Charles W. Morris and Rudolf Carnap. The influence of pragmatism on these writers is mostly limited to the incorporation of the pragmatic maxim into their epistemology.
The other is reductionism, the theory that each meaningful statement gets its meaning from some logical construction of terms which refers exclusively to immediate experience. Quine's argument brings to mind Peirce's insistence that axioms are not a priori truths but synthetic statements. === Logic === Later in his life Schiller became famous for his attacks on logic in his textbook, Formal Logic. By then, Schiller's pragmatism had become the nearest of any of the classical pragmatists to an ordinary language philosophy. Schiller sought to undermine the very possibility of formal logic, by showing that words only had meaning when used in context.
The least famous of Schiller's main works was the constructive sequel to his destructive book Formal Logic. In this sequel, Logic for Use, Schiller attempted to construct a new logic to replace the formal logic that he had criticized in Formal Logic. What he offers is something philosophers would recognize today as a logic covering the context of discovery and the hypothetico-deductive method. Whereas Schiller dismissed the possibility of formal logic, most pragmatists are critical rather of its pretension to ultimate validity and see logic as one logical tool among others—or perhaps, considering the multitude of formal logics, one set of tools among others. This is the view of C. I. Lewis.
During the late 1900s and first decade of 2000, pragmatism was embraced by many in the field of bioethics led by the philosophers John Lachs and his student Glenn McGee, whose 1997 book The Perfect Baby: A Pragmatic Approach to Genetic Engineering (see designer baby) garnered praise from within classical American philosophy and criticism from bioethics for its development of a theory of pragmatic bioethics and its rejection of the principalism theory then in vogue in medical ethics.
In addition, applied scholarship of public administration that assesses charter schools, contracting out or outsourcing, financial management, performance measurement, urban quality of life initiatives, and urban planning in part draws on the ideas of classical pragmatism in the development of the conceptual framework and focus of analysis. The health sector's administrators' use of pragmatism has been criticized as incomplete in its pragmatism, however, according to the classical pragmatists, knowledge is always shaped by human interests.
The administrator's focus on "outcomes" simply advances their own interest, and this focus on outcomes often undermines their citizen's interests, which often are more concerned with process. On the other hand, David Brendel argues that pragmatism's ability to bridge dualisms, focus on practical problems, include multiple perspectives, incorporate participation from interested parties (patient, family, health team), and provisional nature makes it well suited to address problems in this area. === Effects on feminism === Since the mid-1990s, feminist philosophers have re-discovered classical pragmatism as a source of feminist theories.
Works by Seigfried, Duran, Keith, and Whipps explore the historic and philosophic links between feminism and pragmatism. The connection between pragmatism and feminism took so long to be rediscovered because pragmatism itself was eclipsed by logical positivism during the middle decades of the twentieth century. As a result, it was lost from feminist discourse. Feminists now consider pragmatism's greatest strength to be the very features that led to
These are "persistent and early criticisms of positivist interpretations of scientific methodology; disclosure of value dimension of factual claims"; viewing aesthetics as informing everyday experience; subordinating logical analysis to political, cultural, and social issues; linking the dominant discourses with domination; "realigning theory with praxis; and resisting the turn to epistemology and instead emphasizing concrete experience". Feminist philosophers point to Jane Addams as a founder of classical pragmatism. Mary Parker Follett was also an important feminist pragmatist concerned with organizational operation during the early decades of the 20th century.
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