The notion of rationality is crucial to Computer Science and Artificial Intelligence, Economics, Law, Philosophy, Psychology, Anthropology, etc. Most if not all of these disciplines presuppose the agent's capacity to infer in a logical manner. Theories about rationality tend toward two extremes: either they presuppose an unattainable logical capacity, or they tend to minimize the role of logic, in light of vast data on fallacious inferential performance. We analyze some presuppositions in the classical view of logic, and suggest (...) empirical and theoretical evidence for the place of inferential heuristics in a theory of rationality. We propose (1) to outline a new theory of rationality that includes the key notion of logical capacity as a necessary but realistic factor, (2) to expand the notion of inference to include non-deductive inference, specifically non-monotonic, and (3) to emphasize the logical role of inferential heuristics and constraints such as cognitive economy. (shrink)

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to (...) class='Hi'>logic available today that presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website. -/- Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject. -/- Provides an essential introduction to classical logic Emphasizes the how and why of logic Covers both formal and philosophical issues Presents all the major forms of proof--from trees to sequent calculus Features numerous exercises, with solutions available online The ideal textbook for undergraduates and graduate students . (shrink)

Gigerenzer and his co-workers make some bold and striking claims about the relation between the fast and frugal heuristics discussed in their book and the traditional norms of rationality provided by deductive logic and probability theory. We are told, for example, that fast and frugal heuristics such as “Take the Best” replace “the multiple coherence criteria stemming from the laws of logic and probability with multiple correspondence criteria relating to real-world decision performance.” This commentary explores just how (...) we should interpret this proposed replacement of logic and probability theory by fast and frugal heuristics. (shrink)

This paper is a proposal of continuation of the work of C. Rauszer. The logic of falsehood created by her may constitute the starting point for construction of logic formalising reductive reasonings. The extension of Heyting-Brouwer logic to its deductive-reductive form sheds new light upon those classical tautologies which are rejected in intuitionism. It turns out that among HBtautologies there can be found all the classical ones. Some of them are characteristic for deductive reasoning and (...) they are accepted by intuitionism. Others formulate the laws of reductive reasoning. Many of them, including the law of excluded middle has been rejected in Heyting’s intuitionism. Intuitionism only permits for those reductive tautologies, which at the same time bear deductive character. Thus, the complete HB intuitionism does not reject any of the classical tautologies. Every classical tautology appears in HB logic in its deductive or reductive part. Some are even present in both parts. At the end it is shown that the law of excluded middle α∨¬α is a law of the reductive part of the traditional, Heyting’s intuitionistic propositional calculus. (shrink)

Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.

The paper provides a qualified defence of Bruce Waller’s deductivist schema for a priori analogical arguments in ethics and law. One crucial qualification is that the schema represents analogical arguments as complexes composed of one deductive inference but also of one non-deductive subargument. Another important qualification is that the schema is informed by normative assumptions regarding the conditions that an analogical argument must satisfy in order for it to count as an optimal instance of its kind. Waller’s schema (...) is defended from criticisms formulated by Trudy Govier, Marcello Guarini and Lilian Bermejo-Luque. (shrink)

Legal terms, such as “ownership,”“contract,”“validity,”“negligence,” are used as middle terms in legal deduction. The paper distinguishes two problems regarding this use. One is the logical function of terms for deduction within a normative system. Specific problems dealt with in this connection are meaning, definition, and economy of expression. The other problem connected with middle terms is the “moulding” and possible manipulation of the meaning of legal terms, for arriving at desired conclusions in a given scheme of inference. It is indicated (...) how the moulding of contested legal concepts, if not restricted, will obscure the ratio of legal rules. This problem is relevant, inter alia, to arguments ex analogia in the law. (shrink)

Peirce's Law of Triviality: The Implementation of the Trivium of Logic, Rhetoric and Grammar. Basic Categories for Linguistics and Literature Studies from a Universal Semiotic Theory This article focuses on the aspects that refer to linguistics in the works of Charles S. Peirce. His pragmatic philosophy implemented many other sciences and among them is the traditional trivium of logic, grammar, and rhetoric, which Peirce divided into different kinds of logic, grammar, and rhetoric. While the impact of the (...) work of Peirce on theses sciences is weak, the integration of the sciences in his philosophy is interesting as a step in the history of science and his work is an example for ecclecticism and historism of science in the 19th century and the universalism of science deducted from a philosophy that uses the sign as an unitarian principle. Triple constructions are a very common feature in the writings of Peirce, and the trivium is an example of an academic construction Peirce implemented. (shrink)

On the face of it, we might think that logic and the law were made for each other. Their intellectual identities are grounded in a shared stock of concepts: argument, proof, evidence, inference, probability, relevance, presumption, precedent or analogy, plausibility, reasonability and explanation. Provided that we understand logic broadly enough to include not only mathematical theories of deduction and induction, but also more recent attempts by computer scientists to investigate defeasible and default reasoning, there is not an item (...) on this list that escapes the attention of logicians. If we also take note of brisk developments in dialogue logic and formal argumentation theory, the list of shared concepts enlarges accordingly, including among others, leading questions and cross-examination. (shrink)

Kelly suggested that it was useful to consider anyone as functioning as a scientist, in the business of applying theories, making hypotheses and predictions and testing them out in the practice of everyday life. One of Charles Peirce’s major contributions was to develop the disciplines of logic and the philosophy of science. We can deepen and enrich our understanding of Kelly’s vision by looking at what Peirce has to say about the process of science. For Peirce, the essence of (...) science was the application of the laws of inference. He developed a much broader concept of logic, elaborating the processes of deduction and induction and adding to these the logic of hypothetical inference, or ‘abduction’, even as Kelly broadened it further in his “departure from classical logic”. Examining the implications of these three forms of inference allows us to elaborate the dynamics involved in the process of construing, ordinacy and the cycles of experience, creativity and decision making. This is the second of a three part series examining the relationship between the work of Peirce and Kelly. The third will include a look at phenomenology, bipolarity, the self, dialogical process and sociological considerations. (shrink)

One of the most crucial questions in the philosophy of law deals with the very nature of legal reasoning. Does this reasoning belong to logic or to rhetoric? This debate, increasingly centered on rhetoric, is not merely a question of language use; it covers and indicates a more basic choice between formal legalism — focusing on rational deduction from the law — and pragmatic judiciarism — focusing on reasonable debate in the court.Today, it is necessary to circumscribe the respective (...) fields of logic and rhetoric in the language of law, while showing how they are sometimes complementary in the resolution of legal problems.But, even when we have acknowledged the need for a rhetoric accompanied by logic, we have to define that rhetoric cautiously. I confront a narrow rhetoric, often called argumentation, with a wider one of interrogative nature. There are two conceptions of rationality at stake. Their comparison enables us to raise the question of the foundation of law, as a locus to use arguments, as well as to solve social problems. (shrink)

Illuminates legal reasoning -- and its justification At least since plato and Aristotle, thinkers have pondered the relationship between philosophical arguments and the "sophistical" arguments offered by the Sophists -- who were the first professional lawyers. Judges wield substantial political power, and the justifications they offer for their decisions are a vital means by which citizens can assess the legitimacy of how that power is exercised. However, to evaluate judicial justifications requires close attention to the method of reasoning behind decisions. (...) This new collection illuminates and explains the political and moral importance in justifying the exercise of judicial power. Explores enduring questions Focusing on work over the past century, the essays address important recurring questions, such as: When a judge or a lawyer reasons to a conclusion about what is legally required in a given case, must he also ask what is morally required? To what extent do a judge's personal, political, or moral biases affect his legal reasoning? What is the impact of such biases? Can all such biases be avoided? Is legal reasoning similar to reasoning in mathematics, logic, and linguistics, the physical sciences, the social sciences, or literature and history? Do formal logical modes of argument play any roles in legal reasoning? Solid coverage, well organized The articles were chosen to present some of the most influential works on the topic, as well as less familiar works that are thought provoking and informative. Each volume also offers a representative range of theoretical approaches to its topic, contains an introduction that locates the subject within the larger framework oftheories of legal reasoning and jurisprudence, and includes bibliographical notes on further readings. Many 19th century legal theorists argued that deduction is the central mode of legal reasoning, and that legal argument is like a deductive proof in mathematics or logic. They were attracted to this "deductivist" concept because it suggested that legal reasoning could be politically and morally neutral. This volume brings together some of the most thought-provoking articles on both sides of the debate. It also contains several leading articles that explain the role of probabilistic judgments and presumptions in various types of legal arguments, including the laws of evidence and criminal procedure. The collection is a solid introduction to the basic modes of logical argument in legal reasoning. (shrink)

This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study (...) of Gentzen-type formulations of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)

a This is an outline of a coherence theory of law. Its basic ideas are: reasonable support and weighing of reasons. All the rest is commentary.a (TM) These words at the beginning of the preface of this book perfectly indicate what On Law and Reason is about. It is a theory about the nature of the law which emphasises the role of reason in the law and which refuses to limit the role of reason to the application of deductive (...) logic. In 1989, when the first edition of On Law and Reason appeared, this book was ground breaking for several reasons. It provided a rationalistic theory of the law in the language of analytic philosophy and based on a thorough understanding of the results, including technical ones, of analytic philosophy. That was not an obvious combination at the time of the booka (TM)s first appearance and still is not. The result is an analytical rigor that is usually associated with positivist theories of the law, combined with a philosophical position that is not natural law in a strict sense, but which shares with it the emphasis on the role of reason in determining what the law is. If only for this rare combination, On Law and Reason still deserves careful study. On Law and Reason also foreshadowed and influenced a development in the field of Legal Logic that would take place in the nineties of the 20th century, namely the development of non-monotonic (a defeasiblea (TM)) logics for the analysis of legal reasoning. In the new Introduction to this second edition, this aspect is explored in some more detail. (shrink)

TheTractatusfirst appeared in 1921, the same year that Post's “Introduction to a General Theory of Elementary Propositions” appeared in theAmerican Journal of Mathematics. As the latter is the first piece clearly to present and exploit the distinction between a deductive system and a truth-functional interpretation of such a system, we may conclude that Wittgenstein's views had been arrived at somewhat before a variety of logical concepts had received the clarification and refinement incipient on the now taken-for-granted distinction between proof (...) and model theory. One such concept, of considerable interest to Wittgenstein, was that of inference. The following constitutes an attempt to explicate his notion. In particular, I shall attempt to show that his repudiation of “laws of inference” is closely tied to his rejection of logical constants; and that both can be seen as the product of what might be termed a “metaphysics of completeness”—before, of course, any notion of completeness had achieved a measure of precision or currency. (shrink)

How does a Muslim jurist think the law and how, accordingly, he judges a fact? Using Alice in Wonderland as hermeneutical device to explore the logic of fiqh, this article identifies a divergence between Western and Islamic legal thinking in the application of abduction as key form of inference in the law of Islam. In particular, looking at the fact/law relation in symbolic terms, the article highlights how, while a dichotomy between fact and law characterizes Western legal thinking, fiqh (...) upholds a connection between the “real” and the “right”, where the effort in understanding sharī‘ah postulates the actualization of the “rule” in God’s creation. Thus, if sharī‘ahpre-scribes the Law, not only is the rule discovered through the sources, but the right has to be justified through a verdict de-scribing the fact, for the law to be validly stated for the given situation. In this sense, abduction as explanatory “hypothesis” and “inference to the best explanation” of sharī‘ah provides an account for the probabilistic nature of fiqh, its ramification through verdicts, as well as for the epistemic and narrative function of the tradition as core aspects of the logic of Islamic law. At the same time, doubts can be raised about the compatibility between this logic and the deductive logic of modern state law, as a sub-product of Western legal thinking. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 111-120 [Access article in PDF] Hobbes on Law, Nature, and Reason Kinch Hoekstra Balliol College, University of Oxford The reason of a thing is not to bee inquired after till you are sure the thing it selfe bee soe. Wee comonly are att (What's the reason of it?) before wee are sure of the thing. T'was an excellent question of my (...) Lady Cotton, when Sr. Robert Cotton was magnifying of a shoe, wch was Moses's or Noahs, & Wondering att the strange shape & fashion of it: but, Mr. Cotton, sayes shee, are you sure 'tis a shooe. 1A law of nature is a rule discovered by reason. 2 This is the key to John Deigh's attempt to show that "Hobbes's ethics is logically independent of his moral psychology." 3 By this he means that the "theorems" of Hobbes's ethics, the laws of nature, "have no other ground than the definition on which it [his ethics] is based." 4 Deigh thinks he establishes this conclusion by taking seriously both Hobbes's definition of a law of nature as "a Precept, or generall Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life," and his definition of reason as "nothing but Reckoning (that is, Adding and Substracting) of the Consequences of generall names." 5 Deigh puts these two definitions together to argue that Hobbes's ethics is a deductive science, and that those who instead think of his ethics as dependent on desire or as involving instrumental reason ("means-to-ends thinking," as he calls it) are mistaken. The particular virtue of this interpretation, Deigh says, is that without it we have to read Hobbes in the Leviathan as sometimes using "reason" in a way that is different from the way he defines it in chapter 5. 6I will argue that Deigh misunderstands the basis, status, and scope of Hobbesian natural law. In his attempt to save Hobbes from using "reason" equivocally, Deigh attributes mistakes and inconsistencies to him that are more serious and have less [End Page 111] textual justification than that apparent equivocation. A source of the misunderstanding is a simplification—accepted by Mark Murphy and many other interpreters—of Hobbes's conception of reason.Let us begin with Deigh's view of the scope of the law of nature, as he admits that his interpretation would be undermined were he wrong about this. "While the laws of nature are dictates of reason for people living in a state of nature," he says, "they are not truly laws in such circumstances and therefore not sources of obligation in them." 7 If Murphy is right that Hobbes does think they are obligatory outside of civil society, then it is, Deigh concedes, "a genuine problem" for his account. 8 In reply, Deigh refers to the two passages where Hobbes says that the laws of nature are "not properly Lawes," quoting the one from chapter 26, which explicitly recapitulates a claim from chapter 15. 9 In this earlier passage, however, Hobbes adds: "But yet if we consider the same Theoremes, as delivered in the word of God, that by right commandeth all things; then are they properly called Lawes." 10 Hobbes thinks that the laws of nature are always obligatory. He holds, for example, that the law of nature that covenants be kept obliges even "in the condition of meer Nature" or "condition of Warre," and that "the rule of Manners, without Civill Government, is the Law of Nature." 11 Hobbes says that although the laws of nature donot always oblige "in foro externo; that is, to the putting them in act," they do always "oblige in foro interno; that is to say, they bind to a desire they should take place." 12 Although they only require "a desire, and endeavour," Hobbes makes clear that these requirements are laws, and that they are binding and obligatory. 13If Deigh were right, sovereigns would not be obligated by... (shrink)

This article demonstrates the fallacy of legal deduction as a method which is supposed to guarantee the certainty and predictability of the law. The Author asserts that legal deduction is in fact not of a logical nature. Their premises are of an uneven character or else one of them must be created in a non-mechanical way. This in turn makes legal deduction that is comprehended as a mode of inference that is infallible, provided its premises are true / valid nothing (...) more than misunderstanding and fallacy. In addition, in this paper, the outcomes of legal deduction are shown to be highly dependent on the direct and indirect context under the threat of their being utterly absurd. Since the lack of fixity and clarity, these contexts, however, may lead one to madness, i. e. at least unless she or he abandons the idea that only logical types of inferences govern legal deduction and are solely responsible for its outcomes. (shrink)

Pragmatism, Logic and Law traces legal pragmatism as a distinct logical theory originated in late 19th century America, covering various issues, cases, personalities, and relevant intellectual movements within and outside law. It addresses pragmatism’s relation to legal liberalism, natural law, critical legal studies (CLS), and neopragmatism.

Since Leibniz first put forward the sufficient reason law in his philosophical work "The Monadology" (1914), the issue of the law of sufficient reason has aroused heated discussions in the field of logic in our country. The question of whether the law of sufficient reason is the basic law of formal logic was particularly heated in the domestic logic circle in 1978-1980. Since then, there has been little discussion, but from the newly compiled formal logic textbooks (...) published one after another, no consensus has been reached. Although they didn't agree on the question of "whether or not", the two sides elaborated their arguments in detail and put forward some new opinions, thus creating new conditions for solving this problem scientifically. Firstly, this paper analyzes the different viewpoints of both sides of the argument. Secondly, it analyzes whether the law of sufficient reason is the basic law of formal logic from whether Leibniz put forward the law of sufficient reason. Finally, on this basis, a new transformation method is put forward. After this transformation, the law of sufficient reason is an important basic law of deductive logic, which can be juxtaposed with the other three logical laws, such as identity, and coordinated with the "three laws" and complement each other. (shrink)

This paper argues against the deductive reconstruction of scientific prediction, that is, against the view that in prediction the predicted event follows deductively from the laws and initial conditions that are the basis of the prediction. The major argument of the paper is intended to show that the deductive reconstruction is an inaccurate reconstruction of actual scientific procedure. Our reason for maintaining that it is inaccurate is that if the deductive reconstruction were an accurate reconstruction, then scientific (...) prediction would be impossible. (shrink)

This book presents the current state of the art regarding the application of logical tools to the problems of theory and practice of lawmaking. It shows how contemporary logic may be useful in the analysis of legislation, legislative drafting and legal reasoning concerning different contexts of lawmaking. Elaborations of the process of lawmaking have variously emphasised its political, social or economic aspects. Yet despite strong interest in logical analyses of law, questions remains about the role of logical tools in (...) lawmaking. This volume attempts to bridge that gap, or at least to narrow it, drawing together some important research problems-and some possible solutions-as seen through the work of leading contemporary academics. The volume encompasses 20 chapters written by authors from 16 countries and it presents diversified views on the understanding of logic (from strict mathematical approaches to the informal, argumentative ones) and differentiated choices concerning the aspects of lawmaking taken into account. The book presents a broad set of perspectives, insights and results into the emerging field of research devoted to the logical analysis of the area of creation of law. How does logic inform lawmaking? Are legal systems consistent and complete? How can legal rules be represented by means of formal calculi and visualization techniques? Does the structure of statutes or of legal systems resemble the structure of deductive systems? What are the logical relations between the basic concepts of jurisprudence that constitute the system of law? How are theories of legal interpretation relevant to the process of legislation? How might the statutory text be analysed by means of contemporary computer programs? These and other questions, ranging from the theoretical to the immediately practical, are addressed in this definitive collection. (shrink)

Hempel never met Ramsey, but he knew his work. In his 1958 The Theoretician’s Dilemma: a study in the logic of theory construction, Hempel introduces the term Ramsey sentence, referring to Ramsey’s attempt in Theories to get rid of theoretical terms in formal accounts of scientific theories. In this paper, I draw the attention to another connection between Ramsey’s and Hempel’s works. Hempel’s Deductive-Nomological (DN) account of scientific explanation resembles very closely Ramsey’s account of a certain type of (...) conditional sentences. In the first part of the paper, by introducing a fictional story, I highlight the similarities and differences between the two. In the last part of the paper, I claim that the most relevant difference between Ramsey and Hempel can be used to offer original solutions to Hempel’s Raven Paradox. Two possibilities are presented, arguing that the second, which requires a reconsideration of the formalisation of laws, is the most promising. (shrink)

In the process that followed the evolution of ancient Greek thought from mythology to a systematic philosophy, Parmenides, the founder of the Elea school, built up his thoughts with theses that were the exact opposite of his time and perhaps common sense in general. His famous poem On Nature, in the light of the logical principles, inferences, and analyses it contains, has profoundly influenced both epistemologies in terms of structure and possibility, and ontologies within the framework of time, space, and (...) movement. In the mentioned period, the logical internal consistency of Parmenides and his followers, and the rational level in their arguments shaped the ancient period. The role he played especially in natural philosophy and metaphysics is undeniable. However, the ambiguities in the context of the theses and their interpretations of his poem, the only work that has been quoted, have not been resolved until today. The dimensions of this mystery are not only related to classical thought. Ontologies related to physics approaches, theoretical and institutional beliefs about them, and various cosmogony and language understandings can be related to Parmenides in some way. It is also possible to find in Parmenides's early forms some of the contents that form the basis of the philosophy of logic and has metaphysical roots constructed by Aristotle in the ancient period and for which he gained a well-deserved reputation. In addition to the deductive approach, especially the law of contradiction, the principle of identity, the law of excluded third, and the principles of sufficient reason are the most important concepts among those mentioned. These principles, which are not directly formulated, have been used in the context of Parmenides’ arguments about knowledge, existence, and related concepts. In our study, by touching on the significant points of the poem written by Parmenides, we will try to examine the conceptual uses and logical structures of the principles we have expressed and follow the traces of the process in question, and examine its effects. The main reason for this effort is that the content presented by Parmenides continues to be discussed today, maintained its influence in many areas mentioned above, and is an important cornerstone in the development of philosophy. (shrink)

Formal implication is usually represented by symbolization such as ‘ φx ⊃ Ψx,’ which may be read, “for all values of ‘x’, φx implies Ψx.” If the values of the variable ‘x’, in ‘φx’ and ‘Ψx’ be ‘x1’ ‘x2’ ‘x3’, etc., then … ‘φx’ formally implies ‘Ψx’ if and only if, whatever values of ‘x’, ‘xn’, be chosen, ‘φxn’ materially implies ‘Ψxn’ …However, this still leaves it doubtful which of two possible interpretations of expressions having the form ‘ φx ⊃ (...) Ψx’ is to be taken as correct. … It means one thing to say, “Every existent having the property φ … has also the property Ψ,” and it means quite a different thing to say, “Every thinkable thing which should have the property φ must also have the property Ψ.” The second of these holds only when having the properly φ logically entails having the property Ψ; when ‘Ψx’ is deductible from ‘φx’. … The first of them, however, holds not only in such cases … but also in every case where among existent things, one property is universally accompanied by another. (shrink)

The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas (...) can be distinctly recognized within it. One of such ideas is Boole’s view that logic is the study of the laws of thought. This is not to be meant in a psychologistic way. Frege himself states that the task of logic can be represented “as the investigation of the mind; [though] of the mind, not of minds” [17, p. 369]. Moreover Frege never charges Boole with being psychologistic and in a letter to Peano even distinguishes between the followers of Boole and “the psychological logicians” [16, p. 108]. In fact for Boole the laws of thought which are the object of logic belong “to the domain of what is termed necessary truth” [2, p. 404]. For him logic does not depend on psychology, on the contrary psychology depends on logic insofar as it is only through an investigation of logical operations that we could obtain “some probable intimations concerning the nature and constitution of the human mind” [2, p. 1]. Logic is normative, not descriptive. For, the laws of thought do not “manifest their presence otherwise than by merely prescribing the conditions of formal inference” [2, p. 419]. They are, “properly speaking, the laws of right reasoning only” [2, p. 408]. So they “form but a part of the system of laws by which the actual processes of reasoning, whether right or wrong, are governed” [2, p. 409]. Boole’s idea that logic is the study of the laws of thought was taken over by Hilbert. According to him logic is “a discipline which expresses the structure of all our thought” [31, p.. (shrink)

Frederic Kellogg has already published several works on legal pragmatism and on Oliver Wendell Holmes in particular.1 In this volume, he focuses on the early history of Holmes' views, on his readings in law and philosophy, and his interests in science in the years of the Metaphysical Club. Drawing on sources like Francis Bacon, John Stuart Mill and Chauncey Wright, Holmes developed an inductive approach to common law reasoning; eventually, as I discuss below, this approach needed refinement when he engaged (...) with constitutional interpretation. Other parts of the book focus on contemporary issues like legal indeterminacy, hard cases, the role of politics in legal interpretation, Rorty's neopragmatism, liberalism and... (shrink)

The formal systems of logic have ordinarily been regarded as independent of biology, but recent developments in evolutionary theory suggest that biology and logic may be intimately interrelated. In this book, William Cooper outlines a theory of rationality in which logical law emerges as an intrinsic aspect of evolutionary biology. This biological perspective on logic, though at present unorthodox, could change traditional ideas about the reasoning process. Cooper examines the connections between logic and evolutionary biology and (...) illustrates how logical rules are derived directly from evolutionary principles, and therefore have no independent status of their own. Laws of decision theory, utility theory, induction, and deduction are reinterpreted as natural consequences of evolutionary processes. Cooper's connection of logical law to evolutionary theory ultimately results in a unified foundation for an evolutionary science of reason. It will be of interest to professionals and students of philosophy of science, logic, evolutionary theory, and cognitive science. (shrink)

Logic is concerned with the design or structure of arguments. It describes the forms of valid argument and is concerned with the public presentation and reception of arguments. Hence it has a close connection with politics and the public sphere, and with rhetoric as the science of persuasion. Philosophers have analysed the objective conditions of validation, that is, the justifiability of assertions about the world. This quest for objective and scientific validity in argumentation about the nature of reality dominated (...) much of the development of logic in the 20th century. Logical arguments are held to be successful as a result of the ‘force of reason’ rather than because one's opponents have been bribed or coerced. Logic involves the study of the abstract, deductive moves in argumentation rather than an empirical study of how actual arguments are conducted. However, there is also a tension between rhetoric and philosophy; Plato drew a clear distinction between knowledge and persuasion. Logic is intended to give security to the former. The historical drift of logic is towards abstraction, especially the use of mathematical forms of representation. The study of logic is an important component of any project on encyclopaedic knowledge, that is, with knowledge that circulates in the public sphere, but the globalization of culture has raised an important problem about the universalistic claims of traditions of logic, namely, are there different forms of logical reasoning? (shrink)

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring in covering (...) laws can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization. (shrink)

Against recent commentators such as Annstrong, D’Arcy, Copleston, O’Connor, Bourke, and Grisez, I argue that the logic referred to by Thomas in his “Treatise on Law” should not be understood metaphorically. Instead, it involves a chain of syllogisms, beginning with the synderesis principle, followed by primary, secondary, and tertiary principles, and ends with a practical syllogism. In showing this, I attack the view that the synderesis principle, “good ought to be done and evil avoided,” is tautological. Second, I show (...) the syllogistic relation between this and the more subordinate moral principIes. Finally, I argue that the practical syllogism also involves a logical deduction, where the minor premise is a propositional attitude of perception, and the conclusion is an action which expresses a proposition. What emerges is a more precise account of how actions are related to natural law. (shrink)

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended (...) herein and the Trudy Govier's account are discussed as well. (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books (...) of the Bible, and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

BERTRAND RUSSELL ON MODALITY AND LOGICAL RELEVANCE - SECOND EDITION of 2015. Praise for the first edition of 1999: "In the twenty-nine years since Russell's death, much of the major scholarship has drawn heavily on his manuscripts and unpublished correspondence. The author shows that the published Russell is capable of new interpretations; in particular, that modal notions such as possibility have a greater place in various aspects of his logical and philosophical thought than has been previously imagined." -Ivor Grattan-Guinness, Foreword (...) to the first edition. EXCERPT FROM PUBLISHED REVIEW: "Dejnožka's book is the first full-length study of modality in Russell. It is useful for its very full survey of passages in which Russell makes use of or alludes to modal notions. Dejnožka's command of Russell's huge output is indeed impressive and his utilization of it thorough...." - Nicholas Griffin, Studia Logica. EXCERPT FROM PUBLISHED REVIEW: "Dejnožka's book raises a very important point in the history of formal logic. Until now the major studies on this topic have drawn heavily on the development of classical logic as standardized by Gottlob Frege and Bertrand Russell. Dejnožka challenges the reader to open his mind for a new interpretation of Russell's work, in particular that modal and relevance notions have a greater place in his philosophy of logic than has been stressed before.... "Dejnožka rightly observes that many of Russell's insights on modality are a result of his discussions with Hugh MacColl, who was indeed the first to seriously attempt to develop formal modal logic. This particularly applies to Russell's conception of a modal logic without modal operators....That is, classical logic can be used to simulate modal expressions. Thus, the notions of (logical) necessity and possibility are not 'fundamental notions'....On this basis, Dejnožka develops a higher level of modality, where the quantification scope extends to the predicates yielding what Russell calls 'fully general propositions'.... "The best studied translation method is known as the standard translation, and it is quite compatible with Dejnožka's suggestions.... "Dejnožka's book is full of material which stimulates [one] to rethink Russell's philosophy of logic and...it is greatly to the author's credit that he brings to light such a wealth of crucial issues in the history and philosophy of logic. - Shahid Rahman, History and Philosophy of Logic. BOOK DESCRIPTION: This book is the only exhaustive study of Russell on modality and logical relevance ever written. This is the second edition, revised over a period of over sixteen years, and over twice as long. Russell initially rejects the possibility of a modal logic in an unpublished paper written ca. 1903-05 and read to an audience in 1905. But the very next year, he adopts the theory of modality he had rejected, and he repeats that theory in published works for many years to come. That theory, together with other texts scattered among Russell's writings, implies eight modal logics which Russell himself never expressly accepted. And Russell's express acceptance of the early Wittgenstein's theory of entailment ("following from") as truth-ground containment implies a deductive relevance logic in Russell's writings which Russell himself never expressly accepted. The book ends with a look at John Maynard Keynes and Anglo-American evidence law as the origins of Russell's theory of probability as degree of logical relevance. Thus the book is written toward the reunion of modern classical logicians with modal logicians and relevantists. On the reunion of modern classical logicians with relevantists, please see also The Concept of Relevance and the Logic Diagram Tradition (2012). Thus I hope to have created two new fields of Russell studies. I may have created a new legal field as well: the history of logical relevance in evidence law: 132 pages (368-500) in chapter 10. (shrink)

This special issue on Logic and Law consists of four research papers and one interview focusing on epistemological reflections on relationships between logic and law, whether in a reductionist or complementary approach. Logic aims to elucidate through formal frameworks, yet it often grapples with the intricate nuances of everyday legal discourse. While law endeavors to delineate permissible conduct within defined jurisdictions, it often encounters challenges stemming from the ambiguity of terms, leading to frequent judicial interpretations and the (...) perception that proliferating exceptions undermines the efficacy of the rule itself. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:LAW AND THOMISTIC EXEMPLARISM JOHN PETERSON University of Rhode Island Kingston, Rhode Island CIVIL LAW differs from empirical law in that the former prescribes regularities in human action while the latter describes and predicts regularities in the world apart from human action. By an empirical or descriptive law scientists mean a law that is knowable on the basis of observed regularities. An example is Boyle's law. That at a (...) constant temperature the volumes occupied by a constant mass of gas are in inverse ratio to the pressures they support is an observed regularity. This law also describes and predicts a regular occurrence in the world apart from human action. The same is true of Galileo's law that the acceleration of free fall on Earth is thirty-two feet per second per second. But the law that citizens ought to pay taxes in proportion to their incomes prescribes a type of action human beings are obliged to take at regular intervals. A notable difference is that predictability is much lower in the case of civil law than it is in the case of empirical law. You can infallibly predict that the inverse ratio of volumes to pressures in a gas will hold in the next case or that the next free fall will accelerate at thirtytwo feet per second per second. But that your neighbors will pay their fair share of taxes next year is a risky guess. This is part of what it means to say that empirical natural laws are in the world in a way that the laws of society and the state are not. Events, activities, or relationships in the world do not fail to conform to laws whereas actions of citizens often fail to conform to the laws of the state. From empirical laws scientists distinguish theoretical laws. These more general laws are usually called theories or hypotheses. Unlike empirical laws, theories are never generalizations drawn from observations of phenomena. Moreover, theories are often the explanation of empirical laws. So the latter both enter 81 82 JOHN PETERSON into the explanation of a phenomenon and are for their own part explained by theories. Empirical laws are thus both explanans and explanandum as regards phenomena and theories respectively. Thus, Galileo's law of acceleration both enters into the explanation of the particular event of the free fall of this stone at thirty-two feet per second per second and is itself partly explain~d by Newton's laws of motion and his law of gravity.1 But whether or not causal-deductive explanation includes empirical laws that are themselves explained by theoretical laws, all such explanation includes both explanandum and explanans. The former is always some empirical phenomenon. And the latter, as Carl Hempel and Paul Oppenheim point out, is generally made up of two parts, a law or laws and statements of fact or antecedent conditions.2 In the following schema the first two lines comprise the explanans and the last line the explanandum. Thus: C1, C2,..., Cn (statements of conditions) L1, L2,... Ln (laws) E (description of phenomenon to be explained)3 While much causal-deductive explanation in science follows this pattern, not all of it does. For while the explanans must include a law, it need not include a statement that is not a law. For example, Hempel and Oppenheim cite the case in which the regularities that govern the motion of the double stars are explained solely in terms of the laws of celestial mechanics.4 In any case, whether it is the explanandum of a theory or the explanans of a particular observed phenomenon, an empirical law has these three characteristics: first, it is originally based on observations; second, no term in the statement of it fails to occur in the observation statements from which (in the order of knowl1 Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation," in Janet A. Kourany, ed., Scientific Knowledge: Basic Issues in the Philosophy ofScience (Belmont, Cal.: Wadsworth, 1987), 31. 2 Ibid., 31.·1 Ibid., 32. 4 Ibid., 31. LAW AND THOMISTIC EXEMPLARISM 83 edge) it is based; and third, no values of its variable terms are determined in relation... (shrink)

The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe with the Nuisance Principle (NP) discussed by neo-Fregean philosophers of mathematics. This paper uses the Burali–Forti paradox to demonstrate this incompatibility, and another closely related, without appeal to principles related to the axiom of choice—a result hitherto (...) unestablished. It discusses both the general interest of this result, its interest to neo-Fregean philosophy of mathematics, and the potential significance of the Burali–Fortian method of proof. (shrink)

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects the division (...) of the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

The deductive system in Boole's Laws of Thought (LT) involves both an algebra, which we call proto-Boolean, and a "general method in Logic" making use of that algebra. Our object is to elucidate these two components of Boole's system, to prove his principal results, and to draw some conclusions not explicit in LT. We also discuss some examples of incoherence in LT; these mask the genius of Boole's design and account for much of the puzzled and disparaging commentary (...) LT has received. Our evaluation of Boole's logical system does not differ substantially from that advanced in Hailperin's exhaustive study, Boole's Logic and Probability. Unlike the latter work, however, we make direct use of the polynomials native to LT rather than appealing to formalisms such as multisets and rings. (shrink)

The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I (...) argue that the DN-account of ground can be defended against the well-known objections to the DN-approach to scientific explanation. The goal of the paper is to show that the DN-account of metaphysical explanation is a well-motivated and defensible theory. (shrink)

Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or argument forms. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by claiming that there is more than (...) one way for an argument to be valid. In this book, Erik Stei defends logical monism, the view that there is exactly one correct logic. He provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic. (shrink)

Today, mechanisms and mechanistic explanation are very popular in philosophy of science and are deemed a welcome alternative to laws of nature and deductive‐nomological explanation. Starting from Mitchell's pragmatic notion of laws, I cast doubt on their status as a genuine alternative. I argue that (1) all complex‐systems mechanisms ontologically must rely on stable regularities, while (2) the reverse need not hold. Analogously, (3) models of mechanisms must incorporate pragmatic laws, while (4) such laws themselves need not always refer (...) to underlying mechanisms. Finally, I show that Mitchell's account is more encompassing than the mechanistic account *Received August 2008; revised January 2010. †To contact the author, please write to: Centre for Logic and Philosophy of Science, Ghent University, Blandijnberg 2, B‐9000 Belgium; e‐mail: [email protected]. (shrink)

This work is an introductory textbook for deductive logic being primarily concerned with truth-functional logic, but also containing an introduction to syllogisms with the application of Venn diagrams, an introduction to quantification theory, and a brief discussion of axiom systems. Harrison employs six logical operators in his truth-functional calculus, including both inclusive and exclusive disjunction. The six operators are initially defined by truth tables, but in the natural deduction presentation negation and conjunction are taken as primitive and (...) the other connectives are defined in terms of these two. The conditional and indirect methods of proof are included with the approach being essentially the same as that given in Copi’s Symbolic Logic. Categorical statements and syllogisms are analyzed from both hypothetical and existential viewpoints. The treatment of quantification theory includes two-place predicates and employs the four standard rules for generalization and instantiation. The book contains an abundance of explanations, examples, and exercises. Selected answers, usually for the odd numbered problems, are given in an appendix.—T. G. N. (shrink)

As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. (...) Intuitionistic logic satisfies the semantic requirement that we should either eschew the notion of truth altogether and replace it by provability in principle, or constrain it by provability in principle (Dummett [1973] 1978). (Handout: 1-5). Some philosophers have argued that the traditional antirealist desideratum of decidability in principle is too weak, so that semantic antirealism properly construed must be committed to effective decidability. As such, it either leads to strict finitism (Wright [1982] 1993) [Handout: 6] or to a much stronger kind of logical revisionism than the one considered by intuitionists (whether or not they accept the manifestability argument): substructural logics, and in particular linear logics, rather than intuitionistic logic, satisfy the semantic requirements of strict antirealism (Dubucs and Marion 2004) [Handout: 8-9]. I shall develop two different kinds of replies. The first is concerned with the notion of meaning per se and looks to strict finitism directly, although not on the ground that it would provide a correct way of dealing with Soritic-type paradoxes (the original and primary focus of discussion in Wright [1982] 1993). The second is concerned with the justification of structural and logical rules in a natural deduction system à la Gentzen. It will deal in particular with the criticism of the structural rules of Weakening and Contraction [Handout: 10 and 11]. The first kind of reply, which Dummett has partially taken into consideration, is that if we jettison the effectively vs. in principle distinction, as applied to manifestability-type arguments, we end up with an unsatisfactory explanation of how the meaning of statements covering the practically unsurveyable or pro tempora undecided cases is fixed. The idea is that if we have a method which may be used over some small range, we have determined a way of applying the method everywhere in principle and that this is enough as far as fixing meaning is concerned. Decidability in principle is just what we need with respect to manifestation of grasp of meaning. In this perspective, antirealism shouldn't be strict and manifestability-type arguments need not be applied as far as the strict finitist would want to [Handout: 7]. It follows that there is no reason to think that practical feasibility should be built in assertibility conditions and proofs be construed dynamically as acts in the strict antirealist's acception of that term [Handout: 8]. I shall then look at one radical antirealist principle disqualifying structural rules, namely Token Preservation, arguing against Bonnay and Cozic's criticisms of Dubucs and Marion (Bonnay and Cozic 3 2007) that some conceptual support may be provided for Token Preservation, which doesn't rely on a causal misreading of the turnstile [Handout: 13, 14]. I shall then assess the merits and limits of radical antirealism and the logic of feasible proofs with respect to the original Dummettian argument in favour of semantic antirealism (provided it has indeed revisionist implications for logic), whether the radical antirealist merely stipulates what human feasibility amounts to, or dispenses with structural rules in order to argue in favour of a curb on the epistemic idealizations they unwarrantedly embed. It will be noted here that there is a great difference, conceptually speaking, between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules, and the rejection of classical logic via the criticism of the introduction and elimination rules which fix the meaning of the classical constants. The kind of logical revisionism envisaged by intuitionists from Heyting on is in many respects stronger than the one envisaged by advocates of linear logic, should they ground their arguments on an endorsement of strict antirealism. The crucial case of excluded middle is telling. Because of the splitting of the constants in linear logic (Handout: 12], two distinct laws of excluded middle may be formulated (Handout: 15), but the traditional arguments of Brouwer and Heyting against the classical law yield a stronger revision than the substructural revision with its admission of these two (very) weak versions of the law. (Project: a clearer conception is needed of how the introduction and elimination rules for the logical connectives in the intuitionistic calculus depend on the structural rules which the radical antirealist wishes to reject.). (shrink)

This article investigates the nature of Aristotelian syllogistics and shows that the categorical syllogism is fundamentally about showing the connection, in the premises of the syllogism, between the major and minor terms as stated in the conclusion. It discusses how this is important for the use of the syllogism in scientific demonstration. The article then examines modern deductive logic with an eye to they way in which it contrasts with Aristotelian syllogistics. It shows howmodern logic is about (...) making necessary connections between each proposition by means of external or second order rules. In the syllogism, on the other hand, the necessity between the premises as a whole unit and the conclusion is based on the internal middle term. The article concludes with a discussion of Günther Patzig’s claim that Aristotelian syllogisms are best thought of as tautological propositions. If this were the case, then the differences asserted to exist between syllogistic and modern logic would not hold. However, it is shown that Patzig’s assimilation of syllogistics to modern deductive logic is illegitimate. (shrink)

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, (...) there are hundreds of uses of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”. (shrink)