Law Of Contradiction Research Articles

Remarks on Possibilia in Leibniz, 1672-1676

n a recent article Fabrizio Mondadori studies in detail the scholastic background for Leibniz's view of possibilia . Mondadori concludes that, sharply distinguishes between the question of the possibility, and the question of the reality, of possibilia , and explicitly suggests that the reality - but not the possibility - of possibilia depends on the (actual) existence of 1 The expression 'the possibility of possibilia' might seem a bit cumbersome for making a simple point, namely that possibility for Leibniz depends on the principle of contradiction alone, so that possibilities are defined by freedom from contradiction (or by self-consistency) and depend on nothing else. In particular, and against Descartes' voluntarist view of the eternal truths, for Leibniz, possibility is independent of God's will. According to Leibniz, God finds all possibilities fully formed in his understanding. This point provides a central premise in Leibniz's early reasoning in the confessio philosophi that God is not to be regarded as the Author of sin. Sins are understood and then permitted existence by God as part of the most harmonious series of things, but they are found (among the ideas of all things) in God's understanding and are not willed or made by God. Thus, Leibniz's God cannot make something possible impossible or vice versa. This is governed by purely logical considerations stemming from the law of contradiction. Even if indeed cumbersome, this terminology (the possibility of possibilia ) brings out some of the historical context (in its traditional jargon) and highlights the contrast with the question of the reality of possibilia . 2 The thesis that the reality of possibila depends on God means that, according to Leibniz, possibilities are not free floating or self-sufficient like platonic forms; rather, they are conceived in God's understanding and are among the objects of his understanding. This gives rise to a difficult question: if God does not think certain possibilities, are they to be considered possible or not? In somewhat different words, does it make sense to claim that God does not conceive certain possibilities, i.e., self-consistent concepts? While possibilities are certainly independent from God's will, and depend on the principle of contradiction, they do not seem to be entirely independent from some thinking agent. As Massimo Mugnai notes, there are no ideas without the intellectual activity of someone thinking (be it God or man or some other rational

Notes on the History of the Psychoanalytic Review

Notes on the History of the Psychoanalytic ReviewMichael EigenMichael Eigen1. 225 Central Park West, 101A New York, NY 10024Search for more papers by this authorPublished Online::January 2006https://doi.org/10.1521/prev.2005.92.6.805PDFPDF PLUS ShareShare onFacebookTwitterLinkedInRedditEmail ToolsAdd to favoritesDownload CitationsTrack Citations About"Notes on the History of the Psychoanalytic Review." , 92(6), pp. 805–806 Previous article Next article FiguresReferencesRelatedDetails Volume 92Issue 6Dec 2005 Information© N.P.A.P.PDF download

Moving Without Being Where You’re Not; A Non-Bivalent Way

The classical response to Zeno’s paradoxes goes like this: ‘Motion cannot properly be defined within an instant. Only over a period’ (Vlastos.) I show that this ob-jection is exactly what it takes for Zeno to be right. If motion cannot be defined at an instant, even though the object is always moving at that instant, motion cannot be defined at all, for any longer period of time identical in content to that instant. The nonclassical response introduces discontinuity, to evade the paradox of infinite proximity of any point of a distance with any ‘next’. But it introduces the wrong sort of discontinuity because, rather than assuming the discontinuity of motion, as Quantum Theory does, it assumes the discontinuity of space. Due then to the resulting spacetime disorder, though all else is certainly lost, the Tortoise now turns up at least as fast as Achilles and hence not even this much is rescued. Zeno rejects motion because he shows that a moving object must be where it is not. Hence motion, if to occur, must violate the Law of Contradiction (LNC). Applying the concept of quantum discontinuity, I produce an alternative. If an object is to move discontinuously between two boundary points, A and B, what actually obtains is, rather, that it is nowhere at all in-between A and B. And cannot therefore be at two places in-between A and B. And cannot therefore be where it is not. Thus, LNC is conserved. However, in these conditions, the Law of the Excluded Middle (LEM) fails. To mitigate the undesirability of this effect, I show that LEM fails because LNC holds. Thus, the resulting nonbivalent logic, which is also appropriate for quantized transitions of all kinds, will always turn up nonbivalent, because consistent. And this is not too bad, considering.

Beyond Turn-taking

The article discusses several epistemological and methodological issues related to the analysis of discourse in general and of educational talk in particular. The theoretical framework provided by conversation analysis (CA) is applied and critically discussed in the analysis of an empirical example of educational talk. Several questions seem pertinent: Can we - as analysts - have direct access to talk "as it actually occurs", independent of any kind of theorizing and predefined categorization? What is the epistemological status of the conversation analytic categories? What are the limitations of applying turn-taking as an analytical category in the study of talk? To what extent can we presume the knowledgeability of the interlocutors as a premise in our analysis? On the background of my own attempts at applying CA in the analysis of educational discourse, I argue for a widening of the perspective from a narrow, empiricist focus on conversational turn-takings and sequential organization of talk, for example in the handling of issues like silences and absences in talk. On the other hand, I also warn against the pitfalls of historicist, abstract social theory; here exemplified with some texts from theorists applying abstract philosophical categories from dialectical and historical materialism like "the law of contradiction" as explanatory tools in the study of situated action. In the study of educational meaning making we should avoid empiricist as well as historicist approaches and explanations.

Social Constructionism, Deconstructionism and Some Requirements of Discourse

Social constructionist metatheory allows that any coherent epistemology must be self-reflexive, but, while it denies that any assertion can be true, and that there are any independent realities to be referred to, it nevertheless treats discourse as having objective existence, and assumes that its own statements about discourse are true. Thus in asserting its own basic premise it contradicts it. Social constructionist metatheory borrows from deconstructionism and arrives at the same self-defeating scepticism. Derrida enlarges on Saussure's principle of the arbitrary relation between signifier and signified. Both linguists commence their accounts of the origin of language from a basis of epistemological idealism, thus undermining the stability of referential meaning. Derrida's attempt to reject the law of contradiction follows from his stress on the indeterminacy of meaning, and makes impossible the assertion of anything. His aphorism that there is nothing outside the text is revealed as his idiosyncratic version of classical idealism. Recognition of the possibility and necessity of objectivity in discourse is not, as some constructionists claim, author-itarian. It is essential for the effective criticism of social dogma.

On fuzzy preference relations

Triangular norms, conorms, and negation functions are used as interpretations for propositional connectives in a multiple-valued logic model for fuzzy binary relations of weak preference, strict preference, and indifference. It is shown that the Law of Contradiction is a necessary condition for the very existence of reflexive transitive fuzzy binary relations. Basic properties of indifference and strict preference relations are established including transitivity of a strict preference.

Priest, the Liar, and G�del

In a recent paper, Graham Priest proposed an analysis of the Liar Paradox according to which the Liar sentence is both true and not true.’ Such a position regarding the paradox requires a complete overhaul of our logical theory as well as the rejection of the Law of Contradiction. To justify this radical position, Priest advanced an argument based on Godel’s First Incompleteness Theorem. This argument is the topic of my paper. Priest argues that we humans have the means by which we come to know mathematical truths, viz., by constructing intuitively valid proofs of the mathematical propositions from

On Peirce's Denial of the Law of Contradiction

On Peirce's Denial of the Law of Contradiction

An Intentional Analysis of the Law of Contradiction

An Intentional Analysis of the Law of Contradiction

Popular Participation and the Dialectics of Cuban Development

The law of contradiction in things, that is, the law of the unity of opposites, is the fun damental law of nature and of society and therefore also the fundamental law of thought .... According to dialectical materialism, contradiction is present in all pro cesses of objectively existing things and of subjective thought and permeates all these processes from beginning to end (Mao Tse-Tung, 1937:128).

Blanshard and the Law of Contradiction

Blanshard and the Law of Contradiction

Plato's Separation of Reason from Desire

PLATO'S separation of reason from desire, in Republic 435-9, is made in ten propositions. Plato gives a name to none of these propositions. (Names for propositions, such as 'positivism' or 'Fermat's theorem', had not been invented in his day.) But we may find it convenient to name some of them. Some interpreters have found it convenient to name his first proposition 'The Law of Contradiction'. Others have rejected this name as involving a false description of the proposition laid down in 436 b-437 a. I shall call it here 'The Principle of Opposites'. (1) The Principle of Opposites, 436 b-437 a. This is stated first in 436 b, where I translate: 'It is clear that the same will not do or suffer opposites, at least with regard to the same and towards the same, at the same time.' This differs greatly from our Law of Contradiction in not being explicitly and specifically about propositions. Our Law of Contradiction is a statement about propositions and propositions only. But Plato's Principle of Opposites gives no explicit account whatever of what it is about or what it applies to. Its subject is indicated merely by the phrase 'the same', and therefore appears to be any nameable subject whatever. The only word that could be added to this phrase 'the same', without narrowing the reference, is the word 'entity', since this is the word for referring to any nameable subject whatever, without limitation to any class or category. We might roughly write 'the same thing' in the same sense, because 'thing' is often used in the same all-embracing and colourless reference as 'entity'; but we should be liable to be misunderstood, because 'thing' is often used in another sense, to mean substances as opposed to nonsubstantial entities such as qualities and relations. But does the context indicate that Plato really meant to say something about a narrower class than the class of all entities? Perhaps the verb of his Principle implicitly limits and classifies its subject. This verb is: 'do or suffer.' The subject must therefore be something that logically can do or suffer. Whether that is something less than all entities is hard to say. It certainly does not confine the scope of

Colin Lyas on the Coherence of Christian Atheism

IN A stimulating article 'On the Coherence of Christian Atheism'1 Colin Lyas claims that Gabrial Vahanian and Harvey Cox use the expression 'God is dead' non-literally in a theistic sense, that William Hamilton and Paul van Buren use it non-literally in an atheistic sense, and that Thomas Altizer uses it literally in an atheistic sense that purports to be Christian. Lyas finds Altizer's use of the expression particularly intriguing. He takes Altizer to mean that 'God, as a matter of fact, irreversibly died in Christ. This actually happened' (p. 7). 'God annihilated himself' (p. 9). 'The proposition has annihilated entails the proposition, could at one time and at a later time might no longer exist . . . If we ask X to annihilate himself we are asking that he should at one time and then bring it about that he does not at a later time' (p. 10). 'Once we concede that God does not any more, then since by definition a necessary being could not begin to exist, God's death is final' (p. 13). There is some confusion here. To say someone is dead is not to say he has been annihilated, certainly not that he has annihilated himself. Death usually leaves us with a corpse on our hands. The concept of self-annihilation has little empirical warrant. Even if one were to suppose that God annihilated himself, it would not follow that he could at one time and at another not. To apply, temporal predicates to God is inappropriate. The proposed divine selfannihilation must be atemporal. -it is in any case difficult to conceive annihilation as a temporal event. I cannot think of 'God' nor of 'God's having died' as 'a matter of fact'. The use of this latter expression deserves further attention. It seems a far cry from 'a matter of fact' to the classical notion of 'Pure Act'. The definitive evaluation of Altizer's Christian Atheism must await a satisfactory account of the ontological status of facts and matters of fact together with their conditions of possibility and some further elucidation of the notions of death and annihilation with reference to the Christian concept of God. Lyas thinks Altizer's language is 'often very obscure'. Sometimes it 'has a purely imaginative force'. His book 'poses a great problem to the ordinary understanding'. 'It is not clear exactly what Altizer's position is, nor what one could say to him that would lead him to see the falsity of his position', since he 'appears to reject both the law of identity and the law of contradiction' (pp. 4-5). The Gospel of Christian Atheisni expresses in words a coincidentia oppositorurn more suitably conveyed in images and symbols. 'It is the image as such, as a whole bundle of meanings, that is true and not any one of its meanings, nor one alone of its many frames of reference. To translate an image into a concrete terminology by restricting it to any one of its frames of reference is to do worse than mutilate it-it is to annihilate, to annul it as an instrument of cognition. We are not unaware that in certain cases the psyche may fixate an image on one single frame of reference-that of the concrete; but this is already a proof of psychic disequilibrium.'2 Salesian College. Battersea.

J. F. Staal. Negation and the law of contradiction in Indian thought: a comparative study. Bulletin of the School of Oriental and African Studies, University of London, vol. 25 part 1 (1962), pp. 52–71.

J. F. Staal. Negation and the law of contradiction in Indian thought: a comparative study. Bulletin of the School of Oriental and African Studies, University of London, vol. 25 part 1 (1962), pp. 52–71.

On "Can the Law of Contradiction be Contravened?"

A special supplement [of Kuang-ming Daily] published an article by Comrade Chu-ko Yin-t'ung entitled Can the Law of Contradiction Be Contravened?; in it he maintains that the law of contradiction, as well as the other laws of formal logic, must be observed in every situation. When thinking dialectically, the laws of formal logic must always be observed. His chief argument is that we have still not found an example in which the law of contradiction has been contravened. In addition to explaining the three generally accepted judgments resulting from dialectical thinking on the definitions, etc., of mechanical motion, he asserts that they actually contain no logical contradictions. There are, however, other arguments; and since, after the article was published, there were some who opposed it and some who agreed with it, I thought I would contribute to the discussion.

Dialectical Logic has Broken the Narrow Confines of Formal Logic (A Discussion with Comrade Chu-ko Yin-t'ung on "Can the Law of Contradiction Be Contravened?")

In connection with the discussion on the problem of logic, both within our country and abroad (the Soviet Union and the German Democratic Republic), it has already turned from the general, comparatively abstract, and difficult-to-resolve problem of the relationship between formal logic and dialectics to the more concrete problem of the functional scope of formal logic. Some people have even utilized special articles to inquire about a certain law in formal logic: the functional scope of the law of identity or the law of contradiction. The purpose of these philosophers or logicians is to try to define the functional scope of a certain law in formal logic as a starting point, and then to proceed to study the functional scope of formal logic in the entire thinking process of mankind. If the functional scope of formal logic in mankind's entire thinking process is clearly and precisely defined, the solution of this complicated problem of the relationship between formal logic and dialectics would certainly ...

Scepticism and conditions for description

Conditions for description are general rules to which language must conform if it is to serve descriptive purposes. It is argued that the existence of such rules renders scepticism about them incoherent. The only way we can decide whether or not there are such conditions is by seeing in practice whether or not there are certain rules such that we cannot in fact break them without making language unfit for describing. The case is similar to that of, e.g., the law of contradiction, which is itself a condition for description. If we find other conditions, the sceptic, like anyone else, will have to accept that he is bound by them no less than he is bound by the law of contradiction.

The self-contradictory and the inconceivable

THE law of contradiction, like any other logical law, may be interpreted in various ways. (1) It may be held that the relation of contradiction holds between objects; one object (or event or process) contradicts another object (event or process). The law of contradiction then states that nothing, physical or mental, is self-contradictory. On this interpretation the law of contradiction is stated thus: A cannot be both B and not-B at the same time (where 'A' and 'B' stand for any real thing, mental or physical). (2) Or, we may hold that the law of contradiction is a law of thought, not a law of things. On this interpretation, it is stated thus: A cannot be thought to be both B and not-B at the same time (where 'A' and 'B' stand for any real thing, mental or physical). (3) Or ,we may hold that the relation of contradiction holds neither between things nor between thoughts, but between sentences or propositions. It is only a sentence or proposition that can contradict another sentence or proposition. On this interpretation the law of contradiction is stated thus: NKpNp (where 'p' stands for a sentence or proposition). (4) Or, we may hold that the relation of contradiction holds neither between things, nor between thoughts, nor even between sentences or propositions. It is we who contradict ourselves. The law of contradiction, like any other logical law, is really a rule, an imperative, binding only on rational beings who want to think logically. The laws of logic thus apply only to performers who either obey or violate them.

Can the Law of Contradiction be Stated?

Can the Law of Contradiction be Stated? Get access Slbajiban Slbajiban Saugar University Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 21, Issue 5, April 1961, Pages 101–105, https://doi.org/10.1093/analys/21.5.101 Published: 01 April 1961

Can the Law of Contradiction Be Stated?

Can the Law of Contradiction Be Stated?