Logic, Formal Methodology and Semantics in Works of Ryszard W��jcicki

For decades Ryszard Wójcicki has been a highly influential scholar in the community of logicians and philosophers. Our aim is to outline and comment on some essential issues on logic, methodology of science and semantics as seen from the perspective of distinguished contributions of Wójcicki to these areas of philosophical investigations.     

A Critical Examination of the Historical Origins of Connexive Logic

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic.     

Logic and the consistency of the world

The claim that nature is self-consistent has recently been contested by a number of paraconsistent logicians. In this paper I will survey the arguments which paraconsistent logicians have presented for the thesis that nature is actually inconsistent. My conclusion is that these arguments all fail.The paraconsistency programme has to date been concerned primarily with outlining the philosophical inadequacy of classical logic, and detailed discussions of issues bearing upon the philosophical adequacy of the paraconsistency position itself are not to be found as yet in the literature. This inadequacy will be illustrated here with respect to the question of the self-consistency of nature.     

Friedrich albert langes bewundernswerte logische studien

Friedrich Albert Lange (1828‐1875) author of a famous History of Materialism and Critique of Its Present Significance(1866, English transi.I–III 1877–79, repr.1925 with introduction by Bertrand Russell), was also interested in the epistemological foundations of formal logic.Part I of his intended two‐volume Logische Studienwas published posthumously in 1877 by Hermann Cohen“head”of the Marburg school of neo‐Kantianism.Lange, departing from Kant, claims that spatial intuition is the source of the apodeictic character not only of the truths of mathematics, but also of the truths of logic.He aims at showing this by basing validity and invalidity of syllogistic inferences on an interpretation of the standard forms (of proposition in assertoric syllogistic) with the help of the five kinds of possible relations (in fact what is known today as the Gergonne‐Euler relations) between extensions of concepts given to us as areas in a plane, i.e.in space.Generality is achieved by considering all possible variations within each type of spatial relation, exhibiting a connection between concept and intuition reminding Lange of the Kantian “schema”. Lange is well aware of the contemporary English “algebraic” logic, but he considers its approach as the appropriate one for a logic of content (Inhaltslogik)and not for a logic of extension (Umfangslogik)Lange did not live to enjoy the recognition by some leading logicians (amongst them John Venn, to whose reference in 1881 to Lange’s “admirable Logische Studien”the present paper owes it title), nor could he respond to the many critics of his proposed foundation of logic.Its radicality as well as its broad reception (and discussion up to at least 1959) seem to entitle Lange’s Logische Studiento an, if modest, place in the history of logic in the 19th century     

Returning to experience – Dewey’s second mission to China

ABSTRACT

In this essay, as a philosophical exercise in exploring some of the underlying assumptions that serve as an interpretive context for classical Chinese philosophy, I will first follow Dewey’s philosophical turn from a ‘knowledge paradigm’ to an ‘experience paradigm’ in which he seeks to overcome the dualism between subject and object. Secondly, I will interpret Dewey’s Darwinian challenge to the notions of Aristotelian ‘species’ (eidos) and ‘teleology’ (telos) and their ‘universality.’ In so doing, Dewey sought to restore time, change, relationality, and particularity to our philosophical agenda, ideas that are all recommended by the cosmology of the first among the Chinese philosophical canons, the Book of Changes (Yijing易经). And finally, I will try to offer an interpretation of traditional Chinese philosophy as a science in a Deweyan sense.     

The Venn-MacColl Dispute in Nature

During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about ‘symbolical logic’. The letters to the editor shed interesting light on the early reception of MacColl’s contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of the development of British algebraic logic in the confusing intermediary period between the 1870s and 1890s.     

Hegel's notion of Aufheben

The paper is an attempt to make sense of Hegel's notion of aufheben. The double meaning of aufheben and its alleged ‘rise above the mere “either‐or”; of understanding’ have been taken, by some, to constitute a criticism of the logic of either‐or. It is argued, on the contrary, that Hegel's notion of aufheben, explicated in its primary and philosophical context, turns out to be a substantiation of that logic. The intelligibility of the formula of either‐or depends, for example, on the categories of Being and Not‐Being. But if these categories are regarded as particular finite determinations themselves subject to the formula of either‐or, then the formula, far from being intelligible, ‘falls apart’. Hegel is arguing, in other words, that if we are to substantiate the logic of either‐or, we must, at the same time, ‘rise above’ that logic. The role of aufheben is then considered in the special sciences. Here it is argued that we must distinguish between empirical transitions, governed by the finite determinations of things, and logical or dialectical transitions, governed by considerations of the intelligibility of the notions involved. Applying the notion of aufheben to the former transitions suggests wrongly that empirical transitions have an objective or philosophic necessity. Finally, the place of ‘immanent transformation’ in the context of aufheben is examined. It is concluded that if there is to be a transformation, then a distinction must be drawn between thought and its content, but then the transformation cannot be regarded as immanent.     

Political emancipation and the domination of nature: The rise and fall of Soviet Prometheanism

Frolov, I. T. (1990) Man, Science, Humanism: A New Synthesis (Buffalo, NY, Prometheus Books), 342 pp.

Graham, L. R. (Ed.) (1990) Science and the Soviet Social Order (Cambridge, Mass., Harvard University Press), ix + 443 pp.

Understanding the place of science in Soviet culture is essential if we are to understand the distinctive character of the Soviet Union, its failings and contradictions, and its prospects for the future. This paper examines Soviet conceptions of the role of science in the socialist project. Focusing on Loren Graham's collection Science and the Soviet Social Order, the article critically assesses the claim that science and technology have been liberalizing influences on Soviet political culture. The paper concludes by considering Ivan Frolov's, Man, Science, Humanism, which attempts to reform Soviet conceptions of science by establishing a Marxist ‘scientific humanism’. Although Frolov challenges the idea of science as a means to subordinate nature, his approach is belied by his uncritical acceptance of a classic Soviet attitude to science; namely, the necessity of a total, systematic theory of humanity, nature and society. It is argued that the later stages of perestroika saw a marked loss of confidence in the power of science as a source of such ‘total theory’, and with this the history of Soviet Prometheanism appears to have come to a close.     

‘Caesura’ as Bion’s discourse on method1

The author contends that Caesura, one of Bion’s last works, can be read as the equivalent of Descartes’s Discourse on Method. In this compact and complex text, the dictate of ‘methodical’ and ‘hyperbolic doubt’– so called because it is taken to the extreme form of application to the faculty of thought itself – which, for Descartes, represents the fundamental principle of philosophical and scientific research, is reflected in the formula of ‘transcending the caesura’. Bion directs his attention successively to the pairs of opposing concepts that structure psychoanalytic discourse and demonstrates their paradoxical and non‐separative logic. The binary system of producing meaning is deconstructed through the systematic use of non‐pathological – i.e. not static but dynamic – reversible perspective. A viewpoint that appears natural, self‐evident and primary is plunged into crisis and proves to be founded on what the punctuation mark of the slash excludes. Yet the new point of view does not supplant its predecessor, but supplements it. The conceptual opposition is not overturned, but merely destabilized in such a way as to maintain a creative tension that generates new thoughts. By this technique of wrong‐footing the reader, Bion achieves what is tantamount to a Kuhnian revolution: the transition from Freud’s semiotic or evidential paradigm to an aesthetic one, centred on emotional experience – to a ‘science of at‐one‐ment’. Working with the antithetical concepts of censorship and caesura, the author illustrates some clinical implications of this radical shift.     

Essay Review

The incompleteness and artificiality of the ‘traditional logic’ of the textbooks is reflected in the way that syllogisms are commonly enumerated. The number said to be valid varies, but all the numbers given are of a kind that logicians should find irritating. Even the apparent harmony of what is almost invariably said to be the total number of syllogisms, 256, turns out to be illusory. In the following, it is shown that the concept of a distribution-value, which is related to the traditional theory of distribution, and the familiar concept of quantity together suffice to produce a far better way of enumerating syllogisms and a more complete understanding of the systematic features of syllogistic logic.     

Existential Import and an Unnecessary Restriction on Predicate Logics

Contemporary logicians continue to address problems associated with the existential import of categorical propositions. One notable problem concerns invalid instances of subalternation in the case of a universal proposition with an empty subject term. To remedy problems, logicians restrict first-order predicate logics to exclude such terms. Examining the historical origins of contemporary discussions reveals that logicians continue to make various category mistakes. We now believe that no proposition per se has existential import as commonly understood and thus it is unnecessary to restrict first-order predicate logics to non-empty classes. After introducing the problem, we trace some nineteenth century treatments of the issue to locate a source of misconstruing propositional import (1) in misconceptions of ‘implies’ and ‘affirms’ and name the process/product fallacy, along with (2) the translation of categorical sentences using quantifiers and accommodating an empty class. Next we treat some metalogical matters to orient our discussion by which we provide a more precise nomenclature about ‘sentence’ and ‘proposition’ to correct previous misconceptions; here we uncover a common category mistake in respect of a proposition’s efficacy. The semantic distinction between agent and force is helpful in this connection. We conclude by showing that logicians have reinserted existence as a predicate, a position previously excised by Kant, and that the Frege-Russell ambiguity thesis applies only to relationships within a categorical sentence between grammatical predicate and subject.     

Conventionalism,scientific discovery and the sociology of knowledge*

In this paper the basic aim of the so‐called ‘strong programme’ in the sociology of knowledge is examined. The ‘strong programme’ is considered (and rightly so) as an extreme version of the anti‐realist view of science. While the problem of scientific realism has normally been dealt with from the point of view of the ‘context of justification’ of theories, the paper focuses on the issues raised by law‐discovery. In this context Herbert Simon's views about the existence of a ‘logic of scientific discovery’ are discussed and criticized. The main thesis of the paper is that if the structure of both discovery and prediction is properly understood, then the basic anti‐realist claims become untenable. A fortiori, the ‘strong programme’ appears to be unable to explain some basic features of the structure of science.     

On what there is: Representation and history

Premise: our representational system has had a relatively invariant core throughout human history (cf. Sellars's manifest image). Major theses: (i) When philosophical argument establishes the existence of an entity, that entity is a representing, not a represented. (ii) Most of the documents in the history of philosophy are on a par (as dialogical resources) with current philosophical literature for establishing or controverting such existence claims. (iii) The use of mathematics (initially the mathematized neo-Platonism of classical mechanics) allowed modern physical science to break with the perennial system of representation; in consequence, a portion of the representings of modern physical scientists do not belong to the historically invariant core. This limits the dialogical resources of physical science and the applicability of arguments from perennial philosophy to science. It also explains the relative irrelevance of pre-17th century science to contemporary physical scientists in contrast to the relevance of pre-17th century philosophy to contemporary philosophers. It also supports thesis (iv), that logic (broadly conceived) in central to all serious philosophical enterprises, since logic is the central tool for exhibiting and criticizing the rationale(s) of our representational system(s). Support for these theses will be found in the paper.     

Logic as a Universal Medium or Logic as a Calculus? Husserl and the Presuppositions of “the Ultimate Presupposition of Twentieth Century Philosophy”

This paper discusses Jean van Heijenoort's (1967) and Jaakko and Merrill B. Hintikka's (1986, 1997) distinction between logic as a universal language and logic as a calculus, and its applicability to Edmund Husserl's phenomenology. Although it is argued that Husserl's phenomenology shares characteristics with both sides, his view of logic is closer to the model‐theoretical, logic‐as‐calculus view. However, Husserl's philosophy as transcendental philosophy is closer to the universalist view. This paper suggests that Husserl's position shows that holding a model‐theoretical view of logic does not necessarily imply a calculus view about the relations between language and the world. The situation calls for reflection about the distinction: It will be suggested that the applicability of the van Heijenoort and the Hintikkas distinction either has to be restricted to a particular philosopher's views about logic, in which case no implications about his or her more general philosophical views should be inferred from it; or the distinction turns into a question of whether our human predicament is inescapable or whether it is possible, presumably by means of model theory, to obtain neutral answers to philosophical questions. Thus the distinction ultimately turns into a question about the correct method for doing philosophy.     

Modality,Si! Modal Logic,No!

This article is oriented toward the use of modality in artificial intelligence (AI). An agent must reason about what it or other agents know, believe, want, intend or owe. Referentially opaque modalities are needed and must be formalized correctly. Unfortunately, modal logics seem too limited for many important purposes. This article contains examples of uses of modality for which modal logic seems inadequate.I have no proof that modal logic is inadequate, so I hope modal logicians will take the examples as challenges.Maybe this article will also have philosophical and mathematical logical interest.     

Ambiguity and contradiction: the outlines of Jung’s dialectics

This essay explores Jung’s thinking strategies, argumentation patterns, and concept formation processes, and reveals how they distinguish his work from normal present‐day science. Jung doesn’t much appreciate the law of noncontradiction, which is a cornerstone of classical logic, and he doesn’t refrain from using openly ambiguous theoretical terms. It will be pointed out that not only specific archetypes, but the notion of archetype itself, as well as other of Jung’s theoretical notions (energy, including libidinal energy, polarity, integration, wholeness, instinct, symbol, and so on), are consciously ambiguous and thus potentially contradictory. It is shown that this kind of dialectic research strategy and related contradiction‐tolerant and ambiguity‐tolerant methods connect his work to Post‐Kantian German Idealism, Schelling’s and Schopenhauer’s philosophy in particular. However, it was Hegel who, in his Science of Logic, presented a systematic overview of such dialectic principles of reasoning, which were, in the 19^th century, widely applied by German philosophers, theologians, and other scholars. Unfortunately, Jung decided not to study Hegel, but, instead, wrote derogatorily of his work. It will be argued that a Jungian who wants to be conscious of her own argumentation strategies and methods of concept formation should study Hegel’s complex and sophisticated dialectical logic. In addition, it is suggested that Jungian depth psychology might help us to amend the phenomenological deficits of Hegel’s system by providing it with a primal experiential source. This is needed because Hegel’s Geist, due to its intellectual emphasis, is a self‐conscious conceptual totality which advances progressively from stage to stage by guiding itself with the help of dialectical reason (Vernunft). It will be shown that if enriched with a proper kind of experiential givenness, which includes the Jungian unconsciousness (with libidinal energy, instincts, and archetypes), Hegelian metaphysics would be able to embrace a seriously aconceptual or preconceptual dimension. Aconceptual experience, which is, for Jung, mainly the instinctual layer of archetypes, remains essentially inaccessible, not only for normal scientific concepts, but for the concepts of any form of dialectics as well.     

New Foundations for Imperative Logic I: Logical Connectives,Consistency, and Quantifiers*

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me” is the conjunction of “kiss me” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, I argue. “If you love me, kiss me”, a conditional imperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three‐valued imperatives which mixes declaratives with imperatives. I develop such a logic.     

The Vietnamese mode of self‐reference: A model for Buddhist Egology

Buddhist egology concurs with the Husserlian claim that the enipirical ego is ‘constituted’. The Buddhist ‘deconstruction’ of the ego will not, however, pace Husserl, permit the pronoun ‘I’ to refer to a purported extra‐linguistic entity. The insights here distilled from the unique mode of self‐reference functional within the Vietnamese language secure for us an unmistakable confirmation of the Buddhist thesis and have profound consequences for the philosophical problems surrounding the existence and nature of the self and the existence of other minds.     

Insidious syncretism in the political philosophy of Huai‐nan‐tzu 1

This is a study of the ninth chapter of the Huai‐nan‐tzu, a Chinese philosophical text compiled in the mid‐second century BC. The chapter (entitled Chu‐shu [The techniques of the ruler]) has been consistently interpreted as a proposal for a benign government that is rooted in the syncretic Taoist principles of the Huai‐nan‐tzu and is designed to serve the best interests of the people. I argue, on the contrary, that the text makes skilful (and deliberately deceptive) use of vocabulary from the major philosophical traditions of the day, in an attempt to subdue all philosophical sectarianism and wrench various antecedent philosophical ideas into the justification of a supreme political state. The best interests of the people are understood as nothing more than their material needs, since the text also denies that the ruler's subjects are possessed of ‘minds’ in any philosophical sense. It is this process of systematically undermining other philosophical traditions that I call ‘insidious syncretism. ‘