On Being in a Quandary

2021 ◽  
pp. 209-260
Author(s):  
Crispin Wright
Keyword(s):  
Intuitionistic Logic ◽  
Subject Matter ◽  
Classical Logic ◽  
The Other ◽  
Sorites Paradox ◽  
Metaphysical Realism ◽  
Specific Kind ◽  
Epistemic Conception ◽  
Broad Form

This chapter addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox, and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalized, contributes towards the solution of the other two. The key to this response is a generalized conception of indeterminacy as a specific kind of intellectual bafflement—Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, for example, matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight.

Intuitionism and the Sorites Paradox

2021 ◽  
pp. 393-422
Author(s):  
Crispin Wright
Keyword(s):  
Subject Matter ◽  
Classical Logic ◽  
Proof Theory ◽  
Philosophy Of Mathematics ◽  
Sorites Paradox ◽  
Major Premise ◽  
Stable Boundary

This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vague concepts that transcend our capacity to know them. Its treatment of their subject matter is thus broadly comparable to the Platonist philosophy of mathematics. An intuitionist philosophy of vagueness, as do many philosophies of the semantics and metaphysics of vague expressions, finds this idea merely superstitious and rejects it. The vagueness-intuitionist, however, credits the epistemicist with a crucial insight: that vagueness is indeed a cognitive, rather than a semantic, phenomenon—something that is not a consequence of some kind of indeterminacy, or open-endedness in the semantics of vague expressions but rather resides in our brute inability to bring, for example, yellow and orange right up against one another, so to speak, so as to mark a sharp and stable boundary. A solution to the Sorites paradox is developed that is consonant with this basic idea but, by motivating a background logic that observes (broadly) intuitionistic restrictions on the proof theory for negation, allows us to treat the paradoxical reasoning as a simple reductio of its major premise, without the unwelcome implication, sustained by classical logic, of sharp cut-offs.

Completeness of global intuitionistic set theory

1997 ◽  
Vol 62 (2) ◽  
pp. 506-528 ◽  
Author(s):  
Satoko Titani
Keyword(s):  
Set Theory ◽  
Intuitionistic Logic ◽  
Classical Logic ◽  
Mathematical Object ◽  
The Other ◽  
Logical System ◽  
Logical Operators ◽  
Logical Symbol ◽  
Image Position ◽  
Intuitionistic Set Theory

Gentzen's sequential system LJ of intuitionistic logic has two symbols of implication. One is the logical symbol → and the other is the metalogical symbol ⇒ in sequentsConsidering the logical system LJ as a mathematical object, we understand that the logical symbols ∧, ∨, →, ¬, ∀, ∃ are operators on formulas, and ⇒ is a relation. That is, φ ⇒ Ψ is a metalogical sentence which is true or false, on the understanding that our metalogic is a classical logic. In other words, we discuss the logical system LJ in the classical set theory ZFC, in which φ ⇒ Ψ is a sentence.The aim of this paper is to formulate an intuitionistic set theory together with its metatheory. In Takeuti and Titani [6], we formulated an intuitionistic set theory together with its metatheory based on intuitionistic logic. In this paper we postulate that the metatheory is based on classical logic.Let Ω be a cHa. Ω can be a truth value set of a model of LJ. Then the logical symbols ∧, ∨, →, ¬, ∀x, ∃x are interpreted as operators on Ω, and the sentence φ ⇒ Ψ is interpreted as 1 (true) or 0 (false). This means that the metalogical symbol ⇒ also can be expressed as a logical operators such that φ ⇒ Ψ is interpreted as 1 or 0.

scholarly journals Control effects as a modality

2009 ◽  
Vol 19 (1) ◽  
pp. 17-26 ◽  
Author(s):  
HAYO THIELECKE
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Propositional Logic ◽  
The Other ◽  
Classical Propositional Logic ◽  
Double Negation ◽  
Other Hand

AbstractWe combine ideas from types for continuations, effect systems and monads in a very simple setting by defining a version of classical propositional logic in which double-negation elimination is combined with a modality. The modality corresponds to control effects, and it includes a form of effect masking. Erasing the modality from formulas gives classical logic. On the other hand, the logic is conservative over intuitionistic logic.

scholarly journals On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 385
Author(s):  
Hyeonseung Im
Keyword(s):  
Programming Languages ◽  
Intuitionistic Logic ◽  
Reference Point ◽  
Classical Logic ◽  
Proof System ◽  
Double Negation

A double negation translation (DNT) embeds classical logic into intuitionistic logic. Such translations correspond to continuation passing style (CPS) transformations in programming languages via the Curry-Howard isomorphism. A selective CPS transformation uses a type and effect system to selectively translate only nontrivial expressions possibly with computational effects into CPS functions. In this paper, we review the conventional call-by-value (CBV) CPS transformation and its corresponding DNT, and provide a logical account of a CBV selective CPS transformation by defining a selective DNT via the Curry-Howard isomorphism. By using an annotated proof system derived from the corresponding type and effect system, our selective DNT translates classical proofs into equivalent intuitionistic proofs, which are smaller than those obtained by the usual DNTs. We believe that our work can serve as a reference point for further study on the Curry-Howard isomorphism between CPS transformations and DNTs.

scholarly journals Another Name for Liberty: Revelation, ‘Objectivity,’ and Intellectual Freedom in Barth and Marion

Open Theology ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 430-450
Author(s):  
Kristóf Oltvai
Keyword(s):  
A Priori ◽  
The Other ◽  
Christian Theology ◽  
Intellectual Freedom ◽  
Specific Kind ◽  
Absolute Truth ◽  
Saturated Phenomenon ◽  
Other Hand ◽  
The Difference ◽  
The Relationship

Abstract Karl Barth’s and Jean-Luc Marion’s theories of revelation, though prominent and popular, are often criticized by both theologians and philosophers for effacing the human subject’s epistemic integrity. I argue here that, in fact, both Barth and Marion appeal to revelation in an attempt to respond to a tendency within philosophy to coerce thought. Philosophy, when it claims to be able to access a universal, absolute truth within history, degenerates into ideology. By making conceptually possible some ‚evental’ phenomena that always evade a priori epistemic conditions, Barth’s and Marion’s theories of revelation relativize all philosophical knowledge, rendering any ideological claim to absolute truth impossible. The difference between their two theories, then, lies in how they understand the relationship between philosophy and theology. For Barth, philosophy’s attempts to make itself absolute is a produce of sinful human vanity; its corrective is thus an authentic revealed theology, which Barth articulates in Christian, dogmatic terms. Marion, on the other hand, equipped with Heidegger’s critique of ontotheology, highlights one specific kind of philosophizing—metaphysics—as generative of ideology. To counter metaphysics, Marion draws heavily on Barth’s account of revelation but secularizes it, reinterpreting the ‚event’ as the saturated phenomenon. Revelation’s unpredictability is thus preserved within Marion’s philosophy, but is no longer restricted to the appearing of God. Both understandings of revelation achieve the same epistemological result, however. Reality can never be rendered transparent to thought; within history, all truth is provisional. A concept of revelation drawn originally from Christian theology thus, counterintuitively, is what secures philosophy’s right to challenge and critique the pre-given, a hermeneutic freedom I suggest is the meaning of sola scriptura.

Individualisation as a social-cultural process and morality

2020 ◽  
Vol 29 ◽  
pp. 11-33
Author(s):  
Janusz Mariański
Keyword(s):  
Subject Matter ◽  
Moral Values ◽  
Moral Relativism ◽  
The Other ◽  
Human Being ◽  
Cultural Process ◽  
Self Development ◽  
The Subject ◽  
Moral Choices ◽  
Individual Human

In this article, the issue of structural individualisation, which is one of the results of social modernisation, is adopted as the subject-matter. In the processes of individualisation, it is, first and foremost, the importance of an individual human being and matters relevant to their life, including the obligation to make constant choices in all the aspects of life, that is placed emphasis upon. In the aspect of values, the process of individualisation means transfer from values seen as responsibilities (related to duties) to values connected with self-fulfilment (self-development). The consequence of individualisation is the significant changes in the realm of morality: departing from traditional moral values and standards, permissivism and moral relativism, the destruction of normativity, and the secularisation of morality. On the other hand, it creates the opportunity to determine one's own moral choices and shapean autonomous moral personality.

XVII.—Recent Translations of Old English Poetry.

PMLA ◽  
1903 ◽  
Vol 18 (3) ◽  
pp. 445-458
Author(s):  
James M. Garnett
Keyword(s):  
Old English ◽  
Subject Matter ◽  
The Other ◽  
English Poetry ◽  
William Morris ◽  
Anglo Saxon ◽  
Old English Poetry ◽  
The Past

The desire was expressed some years ago that we might soon have in English a collection of translations of Old English poetry that might fill the place so well filled in German by Grein's Dichtungen der Angelsachsen. This desire is now in a fair way of accomplishment, and much has been done during the past ten years, the period embraced in this paper. As was naturally to be expected from the work previously done in criticism of both text and subject-matter, Beowulf has attracted more than ever the thoughts and efforts of translators, for we had in 1892 the rhythmical translation of Professor J. Lesslie Hall and the prose version of Professor Earle; in 1895 (reprinted in cheaper form in 1898) the poetical translation of William Morris and A. J. Wyatt, the editor of Beowulf; in 1901 the prose version of Dr. J. R. Clark Hall, author of A Concise Anglo-Saxon Dictionary; and only the other day, in 1902, the handy prose version of Professor C. B. Tinker.

scholarly journals Misreading and re-reading: interpretation in comparative religion

1999 ◽  
Vol 17 (1) ◽  
pp. 87-98
Author(s):  
René Gothóni
Keyword(s):  
Subject Matter ◽  
The Other ◽  
Personal Beliefs ◽  
The Social ◽  
Marco Polo ◽  
The Subject ◽  
Holistic Conception ◽  
Sinhalese Buddhism ◽  
The Buddha ◽  
Christian Discourse

Religion should no longer only be equated with a doctrine or philosophy which, although important, is but one aspect or dimension of the phenomenon religion. Apart from presenting the intellectual or rational aspects of Buddhism, we should aim at a balanced view by also focusing on the mythical or narrative axioms of the Buddhist doctrines, as well as on the practical and ritual, the experiential and emotional, the ethical and legal, the social and institutional, and the material and artistic dimensions of the religious phenomenon known as Buddhism. This will help us to arrive at a balanced, unbiased and holistic conception of the subject matter. We must be careful not to impose the ethnocentric conceptions of our time, or to fall into the trap of reductionism, or to project our own idiosyncratic or personal beliefs onto the subject of our research. For example, according to Marco Polo, the Sinhalese Buddhists were 'idolaters', in other words worshippers of idols. This interpretation of the Sinhalese custom of placing offerings such as flowers, incense and lights before the Buddha image is quite understandable, because it is one of the most conspicuous feature of Sinhalese Buddhism even today. However, in conceiving of Buddhists as 'idolaters', Polo was uncritically using the concept of the then prevailing ethnocentric Christian discourse, by which the worshippers of other religions used idols, images or representations of God or the divine as objects of worship, a false God, as it were. Christians, on the other hand, worshipped the only true God.

scholarly journals Relative Earnings and Manpower Allocation in Developing Economies

1969 ◽  
Vol 9 (1) ◽  
pp. 14-34 ◽  
Author(s):  
Lloyd G. Reynolds
Keyword(s):  
Economic Growth ◽  
Subject Matter ◽  
Structural Changes ◽  
Developing Economies ◽  
Developed Countries ◽  
The Other ◽  
Labour Economics ◽  
Economic Behaviour ◽  
Agriculture Industry ◽  
Starting Point

The less developed countries (LDC) present two kinds of challenge to economists. First, they invite us to develop hypotheses about how economic growth begins and about structural changes during the early decades of growth. Second, they provide a fresh terrain on which specialists in particular subject-matter areas can test accepted notions about economic behaviour. For investigations in labour economics, the structure of earnings provides a convenient starting point. (It is best to say "earnings" rather than "wages" because most workers in the LDC's are self-emplqyed.) Analysis of earnings requires an examination of manpower supplies and requirements. This leads into the economics of agriculture, industry, government, and other labour demanding sectors on one side, and into a study of education and other skill-producing agencies, on the other. Thus by starting with the earnings structure, one is led rather directly into the heart of the economy.

scholarly journals On density of truth of the intuitionistic logic in one variable

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Zofia Kostrzycka
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Propositional Logic ◽  
Propositional Variable ◽  
Intuitionistic Propositional Logic ◽  
International Audience

International audience In this paper we focus on the intuitionistic propositional logic with one propositional variable. More precisely we consider the standard fragment $\{ \to ,\vee ,\bot \}$ of this logic and compute the proportion of tautologies among all formulas. It turns out that this proportion is different from the analog one in the classical logic case.

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