scholarly journals An enquiry into the ontological and logical foundations of sustainability: Toward a conceptual integration of the interface ‘Nature/Humanity’

2019 ◽  
Vol 2 ◽  
Author(s):  
Augustin Berque
Keyword(s):  
Conceptual Integration ◽  
Logical Foundations ◽  
Law Of Excluded Middle ◽  
Excluded Middle

Non-technical summary Implementing the logical and ontological principles (dualism, mechanicism, reductionism, law of excluded middle, etc.) of modernity has brought forth an unsustainable world. An overcoming of these principles is proposed by mesology (Umweltlehre, fûdoron), centring on the concept of trajection and the existential operator as (als, en tant que).

scholarly journals An enquiry into the ontological and logical foundations of sustainability: Toward a conceptual integration of the interface ‘Nature/Humanity’

2019 ◽  
Vol 2 ◽  
Author(s):  
Augustin Berque
Keyword(s):  
Conceptual Integration ◽  
Logical Foundations ◽  
Law Of Excluded Middle ◽  
Excluded Middle

Non-technical summary Implementing the logical and ontological principles (dualism, mechanicism, reductionism, law of excluded middle, etc.) of modernity has brought forth an unsustainable world. An overcoming of these principles is proposed by mesology (Umweltlehre, fûdoron), centring on the concept of trajection and the existential operator as (als, en tant que).

Reconsidering Kant’s Rejection of Indirect Arguments in Transcendental Philosophy

2021 ◽  
pp. 1-19
Author(s):  
Marcel Buß
Keyword(s):  
Immanuel Kant ◽  
Explanatory Power ◽  
Transcendental Philosophy ◽  
Point Of View ◽  
Transcendental Arguments ◽  
Mathematical Proofs ◽  
Law Of Excluded Middle ◽  
The Law ◽  
Excluded Middle ◽  
Insight Into

Abstract Immanuel Kant states that indirect arguments are not suitable for the purposes of transcendental philosophy. If he is correct, this affects contemporary versions of transcendental arguments which are often used as an indirect refutation of scepticism. I discuss two reasons for Kant’s rejection of indirect arguments. Firstly, Kant argues that we are prone to misapply the law of excluded middle in philosophical contexts. Secondly, Kant points out that indirect arguments lack some explanatory power. They can show that something is true but they do not provide insight into why something is true. Using mathematical proofs as examples, I show that this is because indirect arguments are non-constructive. From a Kantian point of view, transcendental arguments need to be constructive in some way. In the last part of the paper, I briefly examine a comment made by P. F. Strawson. In my view, this comment also points toward a connection between transcendental and constructive reasoning.

On Weakening the Law of Excluded Middle

Dialogue ◽  
1966 ◽  
Vol 5 (2) ◽  
pp. 232-236
Author(s):  
Douglas Odegard
Keyword(s):  
Law Of Excluded Middle ◽  
The Law ◽  
Excluded Middle

Let us use ‘false’ and ‘not true’ (and cognates) in such a way that the latter expression covers the broader territory of the two; in other words, a statement's falsity implies its non-truth but not vice versa. For example, ‘John is ill’ cannot be false without being nontrue; but it can be non-true without being false, since it may not be true when ‘John is not ill’ is also not true, a situation we could describe by saying ‘It is neither the case that John is ill nor the case that John is not ill.’

The Law of Excluded Middle

Mind ◽  
1978 ◽  
Vol LXXXVII (2) ◽  
pp. 161-180 ◽  
Author(s):  
NEIL COOPER
Keyword(s):  
Law Of Excluded Middle ◽  
The Law ◽  
Excluded Middle

Do Easterners and Westerners Treat Contradiction Differently?

2015 ◽  
Vol 15 (1-2) ◽  
pp. 45-63 ◽  
Author(s):  
Hugo Mercier ◽  
Jiehai Zhang ◽  
Yuping Qu ◽  
Peng Lu ◽  
Jean-Baptiste Van der Henst
Keyword(s):  
Cultural Differences ◽  
External Validity ◽  
Cross Cultural ◽  
The Other ◽  
Cross Cultural Differences ◽  
Middle Way ◽  
Points Of View ◽  
Law Of Excluded Middle ◽  
Excluded Middle ◽  
Influential Theory

Peng and Nisbett (1999) put forward an influential theory of the influence of culture on the resolution of contradiction. They suggested that Easterners deal with contradiction in a dialectical manner, trying to reconcile opposite points of view and seeking a middle-way. Westerners, by contrast, would follow the law of excluded middle, judging one side of the contradiction to be right and the other to be wrong. However, their work has already been questioned, both in terms of replicability and external validity. Here we test alternative interpretations of two of Peng and Nisbett’s experiments and conduct a new test of their theory in a third experiment. Overall, the Eastern (Chinese) and Western (French) participants behaved similarly, failing to exhibit the cross-cultural differences observed by Peng and Nisbett. Several interpretations of these failed replications and this failed new test are suggested. Together with previous failed replications, the present results raise questions about the breadth of Peng and Nisbett’s interpretation of cross-cultural differences in dealing with contradiction.

Frege's theorem in a constructive setting

1999 ◽  
Vol 64 (2) ◽  
pp. 486-488 ◽  
Author(s):  
John L. Bell
Keyword(s):  
Set Theory ◽  
Natural Numbers ◽  
The Family ◽  
Power Set ◽  
Law Of Excluded Middle ◽  
The Law ◽  
Image Position ◽  
Excluded Middle ◽  
Intuitionistic Set Theory

By Frege's Theorem is meant the result, implicit in Frege's Grundlagen, that, for any set E, if there exists a map υ from the power set of E to E satisfying the conditionthen E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in Section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map υ be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory, the followingTheorem. Let υ be a map with domain a family of subsets of a set E to E satisfying the following conditions:(i) ø ϵdom(υ)(ii)∀U ϵdom(υ)∀x ϵ E − UU ∪ x ϵdom(υ)(iii)∀UV ϵdom(5) υ(U) = υ(V) ⇔ U ≈ V.Then we can define a subset N of E which is the domain of a model of Peano's axioms.

scholarly journals Validating Brouwer's continuity principle for numbers using named exceptions

2017 ◽  
Vol 28 (6) ◽  
pp. 942-990 ◽  
Author(s):  
VINCENT RAHLI ◽  
MARK BICKFORD
Keyword(s):  
Equivalence Relation ◽  
Dependent Types ◽  
Proof Assistant ◽  
Continuity Theorem ◽  
Continuity Principle ◽  
Fan Theorem ◽  
Law Of Excluded Middle ◽  
The Law ◽  
Intuitionistic Mathematics ◽  
Excluded Middle

This paper extends the Nuprl proof assistant (a system representative of the class of extensional type theories with dependent types) withnamed exceptionsandhandlers, as well as a nominalfreshoperator. Using these new features, we prove a version of Brouwer's continuity principle for numbers. We also provide a simpler proof of a weaker version of this principle that only uses diverging terms. We prove these two principles in Nuprl's metatheory using our formalization of Nuprl in Coq and reflect these metatheoretical results in the Nuprl theory as derivation rules. We also show that these additions preserve Nuprl's key metatheoretical properties, in particular consistency and the congruence of Howe's computational equivalence relation. Using continuity and the fan theorem, we prove important results of Intuitionistic Mathematics: Brouwer's continuity theorem, bar induction on monotone bars and the negation of the law of excluded middle.

A proof–technique in uniform space theory

2003 ◽  
Vol 68 (3) ◽  
pp. 795-802 ◽  
Author(s):  
Douglas Bridges ◽  
Luminiţa Vîţă
Keyword(s):  
Uniform Space ◽  
Weak Form ◽  
Space Theory ◽  
Proof Technique ◽  
Uniform Spaces ◽  
Constructive Theory ◽  
Law Of Excluded Middle ◽  
The Law ◽  
Excluded Middle

AbstractIn the constructive theory of uniform spaces there occurs a technique of proof in which the application of a weak form of the law of excluded middle is circumvented by purely analytic means. The essence of this proof–technique is extracted and then applied in several different situations.

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