scholarly journals Reasoning with Ambiguity

2021 ◽  
Vol 30 (1) ◽  
pp. 139-206
Author(s):  
Christian Wurm
Keyword(s):  
Sequent Calculus ◽  
Formal Analysis ◽  
Point Of View ◽  
The Other ◽  
Logical Point ◽  
Underlying Mechanisms ◽  
The One ◽  
Paradoxical Results

AbstractWe treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less obvious that ambiguous propositions entail other propositions (both ambiguous and unambiguous), and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound (and complete) reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the fact that $$\alpha $$ α entails $$\beta $$ β does not imply $$\beta $$ β can be substituted for $$\alpha $$ α in all contexts preserving truth. Without this distinction, we will always run into paradoxical results. We present the (cut-free) sequent calculus $$\mathsf {AL}^{\textit{cf}}$$ AL cf , which we conjecture implements sound and complete propositional reasoning with ambiguity, and provide it with a language-theoretic semantics, where letters represent unambiguous meanings and concatenation represents ambiguity.

La logique de la preuve dans la littérature bartoliste Quelques explications à partir de la Summa circa testes et examinationem eorum (Ms. Bruxelles, B.R., II 1442, fol. 101 ra – 103 rb)

2008 ◽  
Vol 76 (3-4) ◽  
pp. 249-271
Author(s):  
Yves Mausen
Keyword(s):  
Sensory Perception ◽  
Point Of View ◽  
The Other ◽  
Minor Premise ◽  
Other Hand ◽  
Logical Point ◽  
The One

Abstract The logic of evidence in Bartolistic literature, A reading of the Summa circa testes et examinationem eorum (Ms. Bruxelles, B.R., II 1442, fol.101 ra – 103 rb). – Bartolus teaches how to read testimonies from a logical point of view. On the one hand, the facts that the witness recounts constitute the minor premise of a syllogism, its conclusion being their legal characterization; therefore he is prohibited from pronouncing directly on any legal matter. On the other hand, given that the witness' knowledge of the facts has to stem from sensory perception, the information he provides has at least to constitute the minor premise of another syllogism, making for establishing the causa of his testimony.

Toward useful type-free theories. I

1984 ◽  
Vol 49 (1) ◽  
pp. 75-111 ◽  
Author(s):  
Solomon Feferman
Keyword(s):  
Ordinal Number ◽  
Point Of View ◽  
The Other ◽  
Class Relation ◽  
Ordinal Numbers ◽  
Logical Point ◽  
The One

There is a distinction between semantical paradoxes on the one hand and logical or mathematical paradoxes on the other, going back to Ramsey [1925]. Those falling under the first heading have to do with such notions as truth, assertion (or proposition), definition, etc., while those falling under the second have to do with membership, class, relation, function (and derivative notions such as cardinal and ordinal number), etc. There are a number of compelling reasons for maintaining this separation but, as we shall see, there are also many close parallels from the logical point of view.The initial solutions to the paradoxes on each side—namely Russell's theory of types for mathematics and Tarski's hierarchy of language levels for semantics— were early recognized to be excessively restrictive. The first really workable solution to the mathematical paradoxes was provided by Zermelo's theory of sets, subsequently improved by Fraenkel. The informal argument that the paradoxes are blocked in ZF is that its axioms are true in the cumulative hierarchy of sets where (i) unlike the theory of types, a set may have members of various (ordinal) levels, but (ii) as in the theory of types, the level of a set is greater than that of each of its members. Thus in ZF there is no set of all sets, nor any Russell set {x∣x∉x} (which would be universal since ∀x(x∉x) holds in ZF). Nor is there a set of all ordinal numbers (and so the Burali-Forti paradox is blocked).

To Discriminate in Order to Fight Discrimination

2017 ◽  
Author(s):  
Dolores Morondo Taramundi
Keyword(s):  
Human Rights ◽  
United Kingdom ◽  
The Other ◽  
The United Kingdom ◽  
European Court ◽  
Main Technique ◽  
Antidiscrimination Law ◽  
The One ◽  
Paradoxical Results ◽  
Conflicts Of Rights

This chapter analyses arguments regarding conflicts of rights in the field of antidiscrimination law, which is a troublesome and less studied area of the growing literature on conflicts of rights. Through discussion of Ladele and McFarlane v. The United Kingdom, a case before the European Court of Human Rights, the chapter examines how the construction of this kind of controversy in terms of ‘competing rights’ or ‘conflicts of rights’ seems to produce paradoxical results. Assessment of these apparent difficulties leads the discussion in two different directions. On the one hand, some troubles come to light regarding the use of the conflict of rights frame itself in the field of antidiscrimination law, particularly in relation to the main technique (‘balancing of rights’) to solve them. On the other hand, some serious consequences of the conflict of rights frame on the development of the antidiscrimination theory of the ECtHR are unearthed.

XXVII.—The Inheritance of Long and Short Wings in the Weevil, Sitona hispidula, with a Discussion of Wing Reduction among Beetles

1928 ◽  
Vol 55 (3) ◽  
pp. 665-735 ◽  
Author(s):  
Dorothy J. Jackson
Keyword(s):  
Experimental Work ◽  
Adult Stage ◽  
Point Of View ◽  
The Other ◽  
Wing Dimorphism ◽  
Wing Reduction ◽  
Hereditary Factors ◽  
The Subject ◽  
The One ◽  
Evolutionary Point

It is well known that in many orders of typically winged insects species occur which in the adult stage are apterous or have the wings so reduced in size that flight is impossible. Sometimes the reduction of wings affects one sex only, as in the case of the females of certain moths, but in the majority of cases it is exhibited by both sexes. In many instances wing dimorphism occurs irrespective of sex, one form of the species having fully developed wings and the other greatly reduced wings. In some species the wings are polymorphic. The problem of the origin of reduced wings and of other functionless organs is one of great interest from the evolutionary point of view. Various theories have been advanced in explanation, but in the majority of cases the various aspects of the subject are too little known to warrant discussion. More experimental work is required to show how far environmental conditions on the one hand, and hereditary factors on the other, are responsible for this phenomenon. Those species which exhibit alary dimorphism afford material for the study of the inheritance of the two types of wings, but only in a few cases has this method of research been utilized.

Translation and interpretation in Abhidharmakośa

Diogenes ◽  
2021 ◽  
Vol 29 (2) ◽  
Author(s):  
Mitko Momov
Keyword(s):  
Critical Review ◽  
Point Of View ◽  
Literal Meaning ◽  
The Other ◽  
Young Scholar ◽  
Other Hand ◽  
The One

Rosemberg (1991) has made a critical review of a long-standing discussion between Eastern philologists and Buddhist philosophers. The discussion is centered around the translation of the doctrine on the one hand, and its philosophical systematization on the other hand. When scientific-philological translation prevails, the literal meaning of Buddhist terminology is declared to be its basis. The young scholar, who had specialized in Japan, studied Buddhism from Japanese and Chinese sources and collected lexicographic material from non-Hindu sources. After comparing them, he encountered inaccuracies in the translation. In an attempt to overcome them, he preferred the point of view of the philosophy of Buddhism. The conclusion that he has drawn in the preface of this edition is that the study should begin with a systematization of antiquity.

Philosophical Ideas of Yanaihara Tadao:Nationalism, Pacifism and the Concept of the “Just War”

2021 ◽  
pp. 187-197
Author(s):  
Anna D. Bertova ◽  
Keyword(s):  
Just War ◽  
Second World War ◽  
Point Of View ◽  
The Other ◽  
Historical Period ◽  
World War ◽  
Postwar Japan ◽  
State Of Affairs ◽  
The One ◽  
Second World

Prominent Japanese economist, specialist in colonial politics, a professor of Im­perial Tokyo University, Yanaihara Tadao (1893‒1961) was one of a few people who dared to oppose the aggressive policy of Japanese government before and during the Second World War. He developed his own view of patriotism and na­tionalism, regarding as a true patriot a person who wished for the moral develop­ment of his or her country and fought the injustice. In the years leading up to the war he stated the necessity of pacifism, calling every war evil in the ultimate, divine sense, developing at the same time the concept of the «just war» (gisen­ron), which can be considered good seen from the point of view of this, imper­fect life. Yanaihara’s theory of pacifism is, on one hand, the continuation of the one proposed by his spiritual teacher, the founder of the Non-Church movement, Uchimura Kanzo (1861‒1930); one the other hand, being a person of different historical period, directly witnessing the boundless spread of Japanese militarism and enormous hardships brought by the war, Yanaihara introduced a number of corrections to the idealistic theory of his teacher and proposed quite a specific explanation of the international situation and the state of affairs in Japan. Yanai­hara’s philosophical concepts influenced greatly both his contemporaries and successors of the pacifist ideas in postwar Japan, and contributed to the dis­cussion about interrelations of pacifism and patriotism, and also patriotism and religion.

scholarly journals VII.—On the Geological History of the Cornish Serpentinous Rocks

1886 ◽  
Vol 3 (8) ◽  
pp. 359-367
Author(s):  
J. H. Collins
Keyword(s):  
East Coast ◽  
Point Of View ◽  
Open Cavity ◽  
The Other ◽  
Geological History ◽  
History Of ◽  
The One ◽  
Great Mass

My argument that at Porthalla there is a “passage” from hornblende-schist to serpentine; or rather that some beds of a common series have been changed into serpentine, others into hornblende-schist, and others again into a substance of intermediate character, is, I think, much strengthened by the fact that many such “apparent passages” are admitted to exist by all those who have examined the Lizard Coast with any degree of detail. De la Beche's description of that seen near the Lizard Town is as follows, and it would apply equally well to the others. “The hornblende slate,” he says, “supports the great mass of the Lizard serpentine with an apparent passage of the one into the other in many places—an apparent passage somewhat embarrassing,” that is, from his point of view; from mine it is perfectly natural. He goes on to say: “Whatever the cause of this apparent passage may have been, it is very readily seen at Mullion Cove, at Pradanack Point, at the coast west of Lizard Town, and at several places on the east coast between Landewednack and Kennick Cove, more especially under the Balk … and at the remarkable cavern and open cavity named the Frying-Pan, near Cadgwith.” At Kynance some of the laminse of serpentine are not more than one-tenth of an inch in thickness for considerable distances.

scholarly journals The theory of photographic processes, part II: On the chemical dynamics of development, including the microscopy of the image

1905 ◽  
Vol 76 (509) ◽  
pp. 217-234 ◽  
Keyword(s):  
Heterogeneous Systems ◽  
Point Of View ◽  
The Other ◽  
Chemical Dynamics ◽  
Practical Point ◽  
Previous Communication ◽  
The One

The investigation of development described in a previous communication was extended by the application of microscopic methods. The fact that both the silver haloid and the resulting silver are distributed through the film in the form of particles of minute but measurable size, allows us in this way to detect finer qualitative differences in, and to draw independent deductions on the processes of exposure and development. The size of the grain is important, both from the practical point of view and from the theoretical: in the one case as bearing on spectroscopical and astronomical photography, in the other on account of the great importance of the degree of surface-extension for heterogeneous systems. The method has been used previously by Abney, Abegg, Kaiserling, Ebert, and others, but by far the most systematic and important inquiry is that of K. Schaum and V. Bellach.

scholarly journals Williams on Ethics, Knowledge, and Reflection

Philosophy ◽  
2003 ◽  
Vol 78 (3) ◽  
pp. 337-354 ◽  
Author(s):  
A. W. Moore
Keyword(s):  
Moral Philosophy ◽  
Final Section ◽  
Point Of View ◽  
The Other ◽  
Ethical Knowledge ◽  
Ethical Point ◽  
The One

The author begins with an outline of Bernard William's moral philosophy, within which he locates William's notorious doctrine that reflection can destroy ethical knowledge. He then gives a partial defence of this doctrine, exploiting an analogy between ethical judgements and tensed judgements. The basic idea is that what the passage of time does for the latter, reflection can do for the former: namely, prevent the re-adoption of an abandoned point of view (an ethical point of view in the one case, a temporal point of view in the other). In the final section the author says a little about how reflection might do this.

scholarly journals The problems of syncretism

1969 ◽  
Vol 3 ◽  
Author(s):  
Helmer Ringgren
Keyword(s):  
Point Of View ◽  
The Other ◽  
Complete Fusion ◽  
Broad Definition ◽  
The One

That which happens when two religions meet is obviously different from case to case. It is possible for two "organized" religions to exist side by side for centuries without any exchange taking place. But otherwise, we are obviously moving along a continuum, the one pole of which is the repression of one of the two religions, the other a complete fusion of them. From another point of view, the results of syncretism may be grouped according to the degree in which the foreign elements are felt as essential or less essential. On this broad definition, the topic before us is vast. As a matter of fact few religions are totally "pure" or homogeneous and free from elements of syncretism or traces of an encounter with other religions.

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