Leibniz's Logic

Lenzen, Wolfgang

doi:10.1016/s1874-5857(04)80014-1

Cited by 39 publications

(12 citation statements)

References 4 publications

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“…As has been shown at some length in [7] and [8], the basic system of Leibniz's logic of concepts uses the following primitive elements: Two further operators may be defined as follows:…”

Section: Leibniz's Algebra Of Conceptsmentioning

confidence: 99%

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Leibniz's laws of consistency and the philosophical foundations of connexive logic

Lenzen

2019

LLP

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As an extension of the traditional theory of the syllogism, Leibniz's algebra of concepts is built up from the term-logical operators of conjunction, negation, and the relation of containment. Leibniz's laws of consistency state that no concept contains its own negation, and that if concept A contains concept B, then A cannot also contain Not-B. Leibniz believed that these principles would be universally valid, but he eventually discovered that they have to be restricted to selfconsistent concepts. This result is of utmost importance for the philosophical foundations of connexive logic, i.e. for the question how far either "Aristotle's Thesis", ¬(α → ¬α), or "Boethius's Thesis", (α → β) → ¬(α → ¬β), should be accepted as reasonable principles of a logic of conditionals.

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“…As has been shown at some length in [7] and [8], the basic system of Leibniz's logic of concepts uses the following primitive elements: Two further operators may be defined as follows:…”

Section: Leibniz's Algebra Of Conceptsmentioning

confidence: 99%

“…He suggested to use instead the explicitly quantified variant "for all B: not: A est B ∼ B". As a matter of lowing principles put forward by Leibniz in [8]:…”

Section: Of a Concept A As Obtaining Whenevermentioning

confidence: 99%

Leibniz's laws of consistency and the philosophical foundations of connexive logic

Lenzen

2019

LLP

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“…For, on Lenzen's modal interpretation of falsehood, this principle amounts to the claim that ¬ϕ is equivalent to ¬3ϕ, but this means that 3 is trivial. Thus, Lenzen's contention that the logic of propositional terms is a nonclassical logic of strict implication fails to account for fundamental laws of truth and falsehood that Lenzen 1987Lenzen , 2004similarly, Juniewicz 1987: 51. See Lenzen 1987: 13, 2004: 36, 2005similarly, Rescher 1954: 10, Levey 2011: 122-3, Bonevac and Dever 2012: 202-4.…”

Section: T(a) F(a)mentioning

confidence: 99%

THE LOGIC OF LEIBNIZ’SGENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM

Malink

Vasudevan

2016

The Review of Symbolic Logic

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The Generales Inquisitiones de Analysi Notionum et Veritatum is Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in the Generales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to a simple class of enriched Boolean algebras which we call auto-Boolean algebras. Moreover, we show that Leibniz’s calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning about terms.

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“…The transformations offered at G VII 212 and A6.4.780 allows one to transform even negative singular, universal and particular truths into truths of the form 'A1, A2...An is (not)'. 25 SeeLenzen (2004).…”

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confidence: 99%

Leibniz and the Problem of Temporary Truths

Merlo¹

2017

The Leibniz Review

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Not unlike many contemporary philosophers, Leibniz admitted the existence of temporary truths, true propositions that have not always been or will not always be true. In contrast with contemporary philosophers, though, Leibniz conceived of truth in terms of analytic containment: on his view, the truth of a predicative sentence consists in the analytic containment of the concept expressed by predicate in the concept expressed by the subject. Given that analytic relations among concepts are eternal and unchanging, the problem arises of explaining how Leibniz reconciled one commitment with the other: how can truth be temporary, if concept-containment is not? This paper presents a new approach to this problem, based on the idea that a concept can be consistent at one time and inconsistent at another. It is argued that, given a proper understanding of what it is for a concept to be consistent, this idea is not as problematic as it may seem at first, and is in fact implied by Leibniz's general views about propositions, in conjunction with the thesis that some propositions are only temporarily true.

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Leibniz's Logic

Cited by 39 publications

References 4 publications

Leibniz's laws of consistency and the philosophical foundations of connexive logic

Leibniz's laws of consistency and the philosophical foundations of connexive logic

THE LOGIC OF LEIBNIZ’SGENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM

Leibniz and the Problem of Temporary Truths

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