Paradox

5 Key excerpts on "Paradox"

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  Philosophy of Language

  50 Puzzles, Paradoxes, and Thought Experiments

  • Michael P. Wolf(Author)
  • 2023(Publication Date)
  • Routledge

    (Publisher)

  Semantic Paradoxes Passage contains an image

  Introduction

  DOI: 10.4324/9781003183167-24

  Much of the more formal work in the philosophy of language has been driven by a set of semantic Paradoxes, which are the subject of this section. When people speak of something as a Paradox in everyday language, they simply mean that a situation is unexpected or confusing. The more precise conception of Paradox at work in this section involves a sentence or set of sentences that appears to be well-formed (or even true) and yet entails a contradiction. That may sound harmless (just remember not to say that sentence), but if there were genuine Paradoxes, that would have disastrous consequences for our classical understanding of truth, rationality, and logic. The classical notion of truth presumes that no well-formed declarative sentence can lack a truth value or be both true and false. Classical logic in the Western tradition purports to give us rules of inference that would never lead us from true premises to false conclusions in deductive arguments. If there were genuine Paradoxes that entailed contradictions, it would be possible to derive any conclusion we liked from any set of premises, as we see in entry #16. If any conclusion can be derived from anything, then logic tells us nothing and we lack a rational basis for any belief that we might hold. Entries #17–18 present additional Paradoxes that deepen this threat.

  What can we do in the face of such Paradoxes? A good first tactic would be to show that the Paradoxes were illusory – predicated on some mistake or misunderstanding – and thus readily dismissed. Each entry considers some refutations of this sort, but as you will read, the Paradoxes have shown great staying power. More substantial changes to our understanding of truth and logic may be necessary. The most substantial of these possible revisions are considered in entry #20. There, we look at logical systems that would have three, four or potentially more possible truth values instead of just the familiar two (true and false) as a means to disarm the Paradoxes. We also look at paracomplete logical systems that leave some Paradoxical sentences without truth values at all, and paraconsistent

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  The Politics of Logic

  Badiou, Wittgenstein, and the Consequences of Formalism

  • Paul Livingston(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  9 It is, in other words, language as a totality of possible signification that determines sense as unidirectional meaning or reference to being; but this linguistic determination and staging of sense also evinces sense as the condition for a transcendence of the specific limits of language in the excessive dimension that again allows an unlimited affirmation of bidirectional becoming.

  Deleuze proceeds to characterize this “excessive” and original dimension of sense through a series of specific Paradoxes that demonstrate how it underlies (though it is distinct from) the denotative, deictic, and significative (or inferential and propositional) dimensions of language as it is ordinarily spoken. First, there is the Paradox of inference already given by Lewis Carroll in his dialogue “What the Tortoise Said to Achilles” in 1895 (see Chapter 2 ).10 As we have seen, this Paradox appears to show that the application of the logical rule involved in the most ordinary chains of reasoning cannot be justified, on pain of a bottomless infinite regress of justifications. Deleuze concludes that the ascent from the proposition, as conditioned by its logical relations, to its underlying logical conditions will never have a finite end; it is therefore necessary either simply to affirm the irreducibility of this Paradox or to affirm sense as a constitutive dimension of the “unconditioned” which halts the regress and provides an ultimate foundation for the possibility of significative meaning. Thus there is, as a fundamental and constitutive feature of linguistic meaning, an essential gap between rules and their application that must apparently result from any

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  Wittgenstein and Psychotherapy

  From Paradox to Wonder

  • J. Heaton(Author)
  • 2014(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  2 Paradoxes

  Paradoxes are best characterized as unacceptable conclusions derived by apparently acceptable reasoning from apparently acceptable premises. They have positive and negative aspects. The positive is that they may be true from a different point of view, the negative is that they are absurd or contradictory. A Paradox is a heightened ambiguity. The Paradoxical is an impasse, an apparent impossibility, which needs courage to face. It can be a driving force in human development because the contradictions it embodies cannot be absolute; it is neither absolutely false nor absolutely incomprehensible (Sainsbury, 2009; Cook, 2013).

  It was Russell’s Paradox that drove Wittgenstein to give up aeronautical engineering and take up philosophy. This Paradox is concerned with the set of all sets that are not members of themselves. If this set is a member of itself, then it is not a member of itself, and if it is not a member of itself, then it is. So we have a contradiction. If we are interested in sets then it seems natural to talk about ‘the set of all sets’; even a great logician such as Frege assumed this. But what is this monstrous object? How can we describe it? If we try, by dividing it into two distinct categories: sets that are members of themselves and sets that are not, the Paradox shows we end up talking nonsense. What this demonstrates is that if we assume that words have a fixed meaning and then we use them out of their usual surroundings, they will lead to nonsense. It showed the dangers and ease of careless talk. Words are like living organisms, they only make sense if placed rightly. Wittgenstein applied this fundamental insight to philosophical problems (Pears, 2006).

  One of the most famous is Zeno’s Paradox of Achilles and the Tortoise. The argument aims to show that if, in a race, the tortoise starts some distance ahead, Achilles, a fast runner, would be powerless to catch up. Achilles has to go a greater distance than the tortoise, so it seems that if he catches the tortoise at some point of time, he has to have traversed more measurement points than the tortoise in the same amount of time. It seems as if while Achilles is occupied in making up his handicap, the tortoise advances a little bit further. This continues ad infinitum

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  Bertrand Russell Memorial Volume

  • George W Roberts(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  3 Russell’s Paradox and Some Others William C. Kneale (1) In a recent paper (1972 1) I argue (i) that a language which makes possible the characteristically human form of social life must allow for talk not only about its own sounds, but also about communication by means of those sounds, (ii) that failure to recognise this had led many philosophers into a dangerous confusion between sentences and propositions, (iii) that attempts to formulate logic as a theory of grammatically well-formed sentences involve neglect of the token-reflexive device and misunderstanding of the role of definite descriptions and (iv) that the Paradox of the Liar holds no terrors for those who realise how the notion of truth is related to that of a proposition. My reason for concluding with an attempt to solve the old problem by means acceptable to a student of natural languages was, of course, a wish to counter Tarski’s thesis that natural languages are all inconsistent through failure of their users to observe the distinction between language and metalanguage which he considers essential for solution of the Liar Paradox

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  A Passage to Anthropology

  Between Experience and Theory

  • Kirsten Hastrup(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  Chapter 2

  The language Paradox

  On the limits of words

  The relationship between the language and the world is at the core of epistemology. It has been probed into from various philosophical angles, which have suggested as many ways of seeing it. In this chapter I shall limit my discussion to some areas that have particular pertinence for anthropology. My approach is pragmatic in the sense that I aim at identifying current concerns of anthropology as practice, rather than at tracing the history of anthropological thought about language. This, of course, is related to my wish to expand on the present. My principal focus in this chapter is on local or natural language, bút it reflects back upon anthropological language as well.

  As indicated by the heading of this chapter, I believe that there are serious limitations on local words and writings as sources of genuine anthropological understanding. The Paradox of language to which I refer lies in the fact that while it may indeed sometimes be difficult in real life to determine whether we are dealing with a social or a linguistic phenomenon, because language somehow is to the social as a measuring rod is to the measured, linguistics alone cannot unlock the complexities of social life (Ardener 1989b: 180). Language, spoken or written, measures bút does not represent. As measuring rod it imposes its own scale upon the plasticity of the social. This applies to local language as much as scholarly works.

  This reflects back upon the understanding of the relationship between language, culture and identity that always had a prominent position on the anthropological agenda. The discussion of this particular item has taken a new turn with the emergence of world-wide literacy, virtually if not actually or statistically. Literacy implies that part of any culture is now stored in writings, ranging from laws to poetry, and the question naturally arises how we should deal with this kind of material. The traditional ethnographic practice of eavesdropping outside the local walls of silence has been supplemented by a reading over broad native shoulders.1

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