Current trends in soviet logic

A survey of the outstanding developments in Soviet philosophical logic shows that the formal and dialectical logicians have resolved most of the issues that divided them in the early 1950s. In orientation they are both converging on the avant‐garde of English‐speaking logicians who regard formalization as irrelevant for solving the essential problems of philosophical logic. Soviet dialecticians consider their logic to be a rapprochement with epistemology that will result in a logic that is concerned with the content and genetic development of concepts. Such a logic will provide a methodology of science that can encompass the creative growth of science, in contrast to the positivists’ fixation on the ‘logic of the finished research report’.     

Johnson and the Soundness Doctrine

Why informal logic? Informal logic is a group of proposals meant to contrast with, replace, and reject formal logic, at least for the analysis and evaluation of everyday arguments. Why reject formal logic? Formal logic is criticized and claimed to be inadequate because of its commitment to the soundness doctrine. In this paper I will examine and try to respond to some of these criticisms. It is not my aim to examine every argument ever given against formal logic; I am limiting myself to those that, as a matter of historical fact, were instrumental in the replacement of formal logic by informal logic and initially established informal logic as a separate discipline (in particular, Toulmin’s attacks on what he calls the “analytic ideal” will not form part of the discussion and were not instrumental in this way, only becoming appreciated later). If the criticism of the soundness doctrine is defective, then the move from formal logic to informal logic was not theoretically well-motivated. It is this motivation that I wish to bring into question, rather than the adequacy or inadequacy of formal or informal logic as such. While I will tend to the view that formal logic is as adequate as it is reasonable to expect, the real issue is whether it is inadequate for the reasons that, as a matter of historical fact, were used to motivate its rejection.     

Louis Couturat,modern logic,and the international auxiliary language

ABSTRACT

To some extent, the early twentieth century revival of universal languages was the work of logicians and mathematicians. Pioneers of modern logic such as Frege, Russell and Peano wanted to overcome the diversity and deficiencies of natural languages. Through the rigour of formal logic, they aimed at providing scientific thinking with a reliable medium free from the ambiguity and inconsistencies of ordinary language. This article shows some interconnections between modern logic and the search for a common tongue that would unite scientists and people of all nations. The French mathematician and philosopher Louis Couturat is a key figure in understanding the interplay between these two movements. Through his work in composing the Ido language as an alternative to Esperanto, Couturat gave a new life to the Leibnizian idea of a universal characteristics. In addition, his multifaceted work provides a valuable insight into some political implications of early analytic philosophy.     

A Debate About Anderson's Logic

This article is about the history of logic in Australia. Douglas Gasking (1911–1994) undertook to translate the logical terminology of John Anderson (1893–1962) into that of Ludwig Wittgenstein's (1921) Tractatus. At the time Gilbert Ryle (1900–1976), and more recently David Armstrong, recommended the result to students; but it is reasonable to have misgivings about Gasking as a guide to either Anderson or Wittgenstein. The historical interest of the debate Gasking initiated is that it yielded surprisingly little information about Anderson's traditional (syllogistic or Aristotelian) logic and its relation to classical (first-order predicate or Russellian) logic, the ostensible topic; but the materials now exist to interpret Anderson's logic in classical logic, possibly as an algebra of classes. This would be of little interest to contemporary logicians, but it might shed some light on Anderson's philosophy.     

The doctrine of distribution

Peter Geach describes the ‘doctrine of distribution’ as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ‘distributive supposition’ in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ‘taken universally’, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected.     

Bhāvaviveka's Arguments for Emptiness

In defending the teaching of emptiness, Bhāvaviveka offers some very strange arguments, which initially may appear so weak that we may be hard pressed to understand how anyone could endorse them. To make sense of these passages, it is helpful to compare them to an argument found in the writings of the Naiyāyika Uddyotakara. These arguments have a certain formal feature which makes them count as valid from the point of view of the rules and norms of some forms of Indian logic. Once we understand the logical structure of the arguments offered by Uddyotakara and Bhāvaviveka, we will not only have a better grasp on their philosophical views, but we will also be in a better position to understand how and why those views were rejected by later figures in the Indian tradition, such as Dharmakīrti and ?āntarak?ita.     

Book Reviews

Avicenna (d. 1037) and Tūsī (d. 1274) have different doctrines on the contradiction and conversion of the absolute proposition. Following Avicenna's presentation of the doctrine in Pointers and reminders, and comparing it with what is given in Tūsī's commentary, allow us to pinpoint a major reason why Avicenna and Tūsī have different treatments of the modal syllogistic. Further comparison shows that the syllogistic system Rescher described in his research on Arabic logic more nearly fits Tūsī than Avicenna. This in turn has consequences for analysing Avicenna's logic, and for writing the history of a fascinating period of change and diversity in the discipline in the medieval Islamic world.     

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     

Framework for formal ontology

The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments, and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented.     

‘Do to Me According to What Has Gone Out of Your Mouth’*: A Reformation Debate on the Tragedy of Jephthah and his Daughter

A challenging biblical passage is the narrative of Jephthah and his daughter in the Book of Judges. The consensus of the exegetical tradition is that in fulfillment of a rash vow, Jephthah sacrificed his daughter as a burnt offering. Yet some early Reformation exegetes argued instead that she entered into a life of dedication to the Lord. They argued on the basis of the grammar of Jephthah’s vow, a point which they found in one strand of rabbinical tradition. However, there developed a counter-argument reaffirming the patristic and medieval consensus, and that appealed to an alternative rabbinical tradition. The present essay will examine the competing arguments found in Protestant commentaries published between c.1530 and c.1650. In the end, the patristic and medieval consensus prevailed, and the alternative reading was rejected; but both sides agreed that the one noble character in this tale was the nameless daughter of Jephthah.     

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.     

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.     

Arthur Prior and medieval logic

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important r?le played by Prior??s research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be familiar with the medieval logicians and their work. In this article we give an overview of Prior??s work in ancient and medieval logic.     

Syllogistic: Old Wine in New Bottles

In the late nineteenth century there were two very active lines of research in the field of formal logic. First, logicians (mostly in English-speaking countries) were engaged in formulating a generally traditional logic as an algebra, a part of mathematics; second, logicians (mostly on the continent) were busy building a non-traditional logic that could serve, not as a part of, but as the foundation of, mathematics. By the end of the First World War the former line had been pretty well abandoned while the second continued to expand. However, that old abandoned line, stretching from Aristotle, through the Scholastics and then Leibniz to the nineteenth century algebraists, had not been completely forgotten. One of those logicians who has recently worked on the restoration (and, importantly, the extension) of that line is Fred Sommers. His Term Logic preserves a number of traditional insights (especially involving the theory of logical syntax), while also enjoying a power to account for formal inference at least comparable to that of the standard logic now in place.     

Evaluating Arguments Based on Toulmin’s Scheme

Toulmin’s scheme for the layout of arguments (1958, The Uses of Argument, Cambridge University Press, Cambridge) represents an influential tool for the analysis of arguments. The scheme enriches the traditional premises-conclusion model of arguments by distinguishing additional elements, like warrant, backing and rebuttal. The present paper contains a formal elaboration of Toulmin’s scheme, and extends it with a treatment of the formal evaluation of Toulmin-style arguments, which Toulmin did not discuss at all. Arguments are evaluated in terms of a so-called dialectical interpretation of their assumptions. In such an interpretation, an argument’s assumptions can be evaluated as defeated, e.g., when there is a defeating reason against the assumption. The present work builds on recent research on defeasible argumentation (cf. e.g. the work of Pollock, Reiter, Loui, Vreeswijk, Prakken, Hage and Dung). More specifically, the author’s work on the dialectical logic DEFLOG and the argumentation tool ARGUMED serve as starting points.     

Heterogeneous logic

This paper considers the question: what becomes of the notion of a logic as a way of codifying valid arguments when the customary assumption is dropped that the premisses and conclusions of these arguments are statements from some single language? An elegant treatment of the notion of a logic, when this assumption is in force, is that provided by Dana Scott's theory of consequence relations; this treatment is appropriately generalized in the present paper to the case where we do not make this assumption of linguistic homogeneity. Several applications of the resulting concept of a heterogeneous logic are suggested, but the main emphasis is on the formal development. One topic touched on is a certain contrast between the boolean and the intensional sentence-connectives in this more general setting.     

Fārābī and Avicenna on Contraposition

The rule of contraposition has been investigated thoroughly by Arabic logicians. In this paper, we study the work done by Fārābā and Avicenna, the fathers of Arabic logic. Fārābā studied contraposition of universal affirmatives, discussed its four forms, and discovered a relation between one form and the conversion of negative universals. Although Fārābā and logicians before him have used contraposition only for conditionals, as well as for indefinite and universal affirmative categorical propositions, Avicenna generalized the rule to all the four Aristotelian quantified categorical propositions. However, many of his ideas on contraposition were opposed by his 12th and 13th century followers, which are to be investigated later.     

Logic and Rhetoric in Legal Argumentation: Some Medieval Perspectives

While the formal treatment of arguments in the late medieval modi arguendi owes much to dialectic, this does not remove the substance and function of the argumentative modes discussed from the realm of rhetoric. These works, designed to teach law students skills in legal argumentation, remain importantly focused on persuasive features of argumentation which have traditionally been strongly associated with a rhetorical approach, particularly in efforts to differentiate from it dialectic as a more strictly scientific and logical form of reasoning. This also sheds some light on the relative roles logic and rhetoric play in the legal discourse of our own time. In their approach to persuasive legal discourse, the modi arguendi stand between the argumentative rhetorics of Antiquity and the rhetoricized dialectics of the Renaissance, and by linking the minute technicalities of professionalized law with broad general considerations of justice, utility, nature, and emotion, they mediate between the modem trend towards atomized field-specific rhetorics and the classical idea of a unified civic rhetoric.     

The Early Formation of Modal Logic and its Significance: A Historical Note on Quine,Carnap, and a Bit of Church

The aim of the paper is to show that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis’ systems and did not take Quine's arguments and remarks seriously—or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break was about the status of extensionality and modal logic (and analyticity was much more of a second issue). Since much of the works about the history of analytic philosophy is centered on the relationship of Quine and Carnap, their break about modality deserves much more attention—it also sheds some light on why should anyone wonder about Quine's early arguments against modal logic. The paper ends with some further considerations regarding the early formation of modal logic and hitherto unconsidered problematic issues.