During the first few decades of the twentieth century, legal theory on both sides of the Atlantic was characterized by a tremendous amount of skepticism toward the private law concepts of property and contract. In the United States and France, Oliver Wendell Holmes and François Gény led the charge with withering critiques of the abuse of deduction, exposing their forebears' supposedly gapless system of private law rules for what it was, a house of cards built on the ideological foundations of (...) laissez faire capitalism. The goal was to make the United States Constitution and the French civil code more responsive to the realities of industrialization. Unlike the other participants in this transatlantic critique, François Gény simultaneously insisted on the immutability of justice and social utility. His “ineluctable minimum of natural law” would guide judges and jurists toward the proper social ends, replacing deduction with teleology. The problem was that nearly all of Gény's contemporaries were perplexed by his conception of natural law, which lacked the substance of the natural rights tradition of the eighteenth and nineteenth centuries and the historicist impulse of the early twentieth. No one was more perplexed than Oliver Wendell Holmes, whose more thorough going skepticism led him to see judicial restraint as the only solution to the abuse of deduction. The ultimate framework for this debate was World War I, in which both Holmes and Gény thought they had found vindication for their views. Events on the battlefield reaffirmed Gény's commitment to justice just as they reignited Holmes' existential embrace of the unknown. In a sense, the limits of their skepticism would be forged in the trenches of the Great War. (shrink)

The article develops and justifies, on the basis of the epistemological argumentation theory, two central pieces of the theory of evaluative argumentation interpretation: 1. criteria for recognizing argument types and 2. rules for adding reasons to create ideal arguments. Ad 1: The criteria for identifying argument types are a selection of essential elements from the definitions of the respective argument types. Ad 2: After presenting the general principles for adding reasons (benevolence, authenticity, immanence, optimization), heuristics are proposed for finding missing (...) reasons, for deductive arguments, e.g., semantic tableaux are suggested. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

El trabajo consiste en una elucidación de los elementos que conforman el concepto de pena natural (poena naturalis) en el Derecho penal. Se puede caracterizar la pena natural como el daño o sufrimiento que recae sobre el autor de un delito, producto de la comisión del mismo, que debe ser descontado de la pena legal que ha de aplicársele. Si bien existe un mínimo acuerdo sobre esto, tanto en la jurisprudencia como en la doctrina penal se observan serios desacuerdos acerca (...) de los requisitos que se deben cumplir para reconocer que se está frente a una pena natural. Para elucidar los elementos, se utilizará el constructivismo conceptual de Ronald Dworkin, a fin de describir el desacuerdo y sus implicancias, reconocer los elementos principales de la pena natural y justificarlos bajo su mejor luz moral. ABSTRACT This study focuses on the clarification of the conceptual elements of poena naturalis in criminal law settings. The poena naturalis is the damage or suffering that falls on the convict for its commission. This damage must be deducted from the poena forensis to be applied. Although there is a minimum agreement about the concept of poena naturalis, in the jurisprudence and among legal scholars, there are serious disagreements about the elements of poena naturalis. To elucidate the elements, I will adopt Ronald Dworkin’s conceptual constructivism to describe the disagreement and its implications. At last, I will justify the main elements of the poena naturalis by their best moral light. (shrink)

A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical (...) logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study. (shrink)

After more than 60 years, Shannon’s research continues to raise fundamental questions, such as the one formulated by R. Luce, which is still unanswered: “Why is information theory not very applicable to psychological problems, despite apparent similarities of concepts?” On this topic, S. Pinker, one of the foremost defenders of the widespread computational theory of mind, has argued that thought is simply a type of computation, and that the gap between human cognition and computational models may be illusory. In this (...) context, in his latest book, titled Thinking Fast and Slow, D. Kahneman provides further theoretical interpretation by differentiating the two assumed systems of the cognitive functioning of the human mind. He calls them intuition (system 1) determined to be an associative (automatic, fast and perceptual) machine, and reasoning (system 2) required to be voluntary and to operate logical-deductively. In this paper, we propose a mathematical approach inspired by Ausubel’s meaningful learning theory for investigating, from the constructivist perspective, information processing in the working memory of cognizers. Specifically, a thought experiment is performed utilizing the mind of a dual-natured creature known as Maxwell’s demon: a tiny “man–machine” solely equipped with the characteristics of system 1, which prevents it from reasoning. The calculation presented here shows that the Ausubelian learning schema, when inserted into the creature’s memory, leads to a Shannon-Hartley-like model that, in turn, converges exactly to the fundamental thermodynamic principle of computation, known as the Landauer limit. This result indicates that when the system 2 is shut down, both an intelligent being, as well as a binary machine, incur the same minimum energy cost per unit of information (knowledge) processed (acquired), which mathematically shows the computational attribute of the system 1, as Kahneman theorized. This finding links information theory to human psychological features and opens the possibility to experimentally test the computational theory of mind by means of Landauer’s energy cost, which can pave a way toward the conception of a multi-bit reasoning machine. (shrink)

This memoir consists of two parts, of which the first deals with the foundations of the theory of the struggle for existence, and begins with the introduction of the important concept of quantity of life, besides that of population. The fundamental equations are then established for the case where the individuals of a biological association mutually devour each other, the reasoning being based on the principle of encounters and on the fundamental hypothesis of the existence of equivalents of the individuals (...) constituting the different species which form the association.Having now obtained the equations which determine the rates of change of the numbers of individuals and of the quantities of life of the species, the memoir proceeds to find the equations relating to the stationary state, by establishing theorems which are afterwards applied for the purpose of obtaining the three general laws of the fluctuations. This investigation of the equilibrium state is then followed by the determination of the integrals of the fluctuation equations, and the deduction from these of their most important consequences.The second part of the memoir contains the enumeration and demonstration of the general laws of the struggle for existence, which flow from the discussion of the principles and the integrals obtained in the first part. In this way there is established a new sort of dynamics, demographic dynamics, which, though substantially different from the dynamics of material systems, is developed from an analogous point of view.The second part begins with the principle of the conservation of demographic energy, according to which there are two sorts of energy, one actual and one potential, which transform mutually the one into the other. This principle is the analogue of the principle of conservation of mechanical energy. It is followed by the enunciation of the three laws relating to the biological fluctuations, the experimental verification of which has been investigated by several naturalists. The success which has attended their efforts is well known.Everybody knows the importance ofHamilton's principle in mechanics and in all the domains of physical science. An analogous variation principle can be found in biology, and from it one can deduce the fluctuation equations in the canonical Hamiltonian form and also in the form of a Jacobian partial differential equation. Their integrals in involution from the subject next studied, and in this way are found cases where the integration is reducible to quadratures.Hamilton's principle leads to the principle of least action . There exists also in biology a closely related principle, which may be called the principle of least vital action. Its analytical form is such that it requires the existence of a true minimum, a state of affairs which does not always hold good in the analogous case in mechanics.Die Abhandlung besteht aus zwei Teilen: Der erste ist den Grundlagen der Theorie des Kampfes ums Dasein gewidmet. Man beginnt damit, neben der Bevölkerung die Menge des Lebens einzuführen, welche eine sehr wichtige Rolle spielt. Man geht dann dazu über, die Grundgleichungen für den Fall aufzustellen, in welchem die Individuen einer biologischen Assoziation sich gegenseitig auffressen. Man wendet das Prinzip der Begegnungen an und stützt sich auf die Grundhypothese der Existenz von Individuenäquivalenten der verschiedenen Arten, welche die Assoziation bilden.Wenn man die Gleichungen, welche die Variationen der Individuenzahlen und der Lebensmengen der Arten liefern, gefunden hat, so schreitet man zu den statischen oder Gleichgewichtsgleichungen fort und findet so die Theoreme, die man alsdann benutzt, um die drei allgemeinen Gesetze der Fluktuationen zu erhalten.Nach dem Studium des Gleichgewichtes geht man dazu über, die verschiedenen Integrale der Fluktuationengleichungen zu finden und zieht endlich aus ihnen die wichtigsten Folgerungen.Im zweiten Teile werden die allgemeinen Gesetze des Kampfes ums Dasein, welche aus der Diskussion der Prinzipien und der im ersten Teil gewonnenen Integrale stammen, ausgesprochen und bewiesen. Man baut so eine neue Dynamik auf: die demographische Dynamik, welche, obschon sie wesentlich verschieden von derjenigen der materiellen Systeme ist, sich nach einem analogen Gesichtspunkt entwickelt.Man beginnt in diesem zweiten Teil mit dem Prinzip der Erhaltung der demographischen Energie, nach welchem zwei Energien, die aktuelle und die potentielle, sich ineinander verwandeln. Wir haben hier eine Analogie zum Prinzip der Erhaltung der mechanischen Energie. Dann werden die drei Gesetze der biologischen Fluktuationen formuliert. Für sie haben verschiedene Naturforscher experimentelle Bestätigungen gesucht. Man kennt den Erfolg ihrer Bemühungen.Alle Welt kennt die Bedeutung des Prinzips vonHamilton in der Mechanik und in allen Gebieten der Physik. Man kann ein dem Variationskalkül analoges Prinzip in der Biologie finden. Aus ihm kann man die Fluktuationsgleichungen in der kanonischen Form vonHamilton und in der Gestalt einer Gleichung mit partiellen Differentialquotienten vonJacobi herleiten. Ihre Integrale bilden den Gegenstand der folgenden Studien. Man findet Fälle, in denen die Integration sich auf Quadraturen reduziert.Das Prinzip vonHamilton zieht das Prinzip der kleinsten Wirkung oder das Prinzip vonMaupertuis nach sich. Auch in der Biologie gibt es ein mit dem vorgenannten zusammenhängendes Prinzip, welches man das Prinzip der kleinsten vitalen Wirkung nennen kann. Seine analytische Form ist derart, dass es sich um ein wahres Minimum handelt, das im analogen Fall in der Mechanik nicht immer zutrifft. (shrink)

Epistemology mirrors reality but notperfectly, and in the process molds reality butnot exactly as intended or anticipated. Horizontal interconnections also exist betweenand among epistemology, ideology, theory andpraxiology. However, these relations areneither deductive nor deterministic in naturebut are merely resonant, and then unclear,ambiguous and confounded. In this paper, thepoint is made that we need a grand reflectionon both our paradigms of reality and ourpredicaments of life as lived, to deal with thediscontent of humanity at this moment of thehistory of our (...) civilization, and to engage inpraxis ``to act on our world and to reconstructit'' to make it moral, just and more humane. Toundertake such a grand reflection, we need apractical philosophy of knowledge – that is, apractical epistemology – to bridge across themultiple epistemological approaches nowcrowding our discussions. An epistemictriangle formed by systems thinking,constructivist thinking, and dialecticalthinking is offered to serve as the startingpoint of crystallization for building a commonground for epistemologies. It is shown how suchan epistemological diagram could be first usedto develop a minimum ideological consensus andthen to bring orderliness to the chaos ofcontemporary themes of our civilization andissues of education and culture within andacross nations. Finally, an agenda foreducational leadership for educational practiceis offered to fit the needs of the globalcommunity of nations as we enter thetwenty-first century. (shrink)

A three dimensional hypercube representing all of the 4,096 dyadic computations in a standard bivalent system has been created. It has been constructed from the 16 functions arrayed in a table of functional completeness that can compute a dyadic relationship. Each component of the dyad is an operator as well as a function, such as “implication” being a result, as well as an operation. Every function in the hypercube has been color keyed to enhance the display of emerging patterns. At (...) the minimum, the hypercube is a “multiplication table” of dyadic computations and produces values in a way that shortens the time to do operations that normally would take longer using conventional truth table methods. It also can serve as a theorem prover and creator. With the hypercube comes a deductive system without the need for axioms. The main significance of the 3-D hypercube at this point is that it is the most fundamental way of displaying all dyadic computations in binary space, thus serving as a way of normalizing the rendition of uninterpreted, or raw, binary space. The hypercube is a dimensionless entity, a standard by which in binary spaces can be measured and classified, analogous to a meter stick. (shrink)

We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 37–53] in which two players, the Believer and the Doubter, compete by trying to prove a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the (...) sense that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play “passes through” negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinite-games. Our determinacy result immediately provides a novel and purely game-theoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinite-valued minimum model semantics of negation [P. Rondogiannis,W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 441–467]. This immediately implies that the unrefined game is equivalent to the well-founded semantics. (shrink)

An important link between model theory and proof theory is to construe a deductive disproof of S as an attempted construction of a countermodel to it. In the function logic outlined here, this idea is implemented in such a way that different kinds of individuals can be introduced into the countermodel in any order whatsoever. This imposes connections between the length of the branches of the tree that a disproof is and their number. If there are already n individuals (...) in the countermodel that is being constructed, the next individual has to be considered in its relations to each of the n old ones, creating 2^n different cases and accordingly at least 2^n different branches. Hence a disproof procedure of a polynomial length is normally not equivalent with an exponential one. Because every computation can be represented as a deduction with the same number of constant terms, the same holds for nondeterministic computations. Apparent exceptions seem to come about if a branch created by a new individual i is redundant. But when the disproof is a shortest one (contains the minimum number of different constant terms) then not introducing that idle term at all would result in an even shorter disproof, violating the shortness assumption. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Parmenides: The Road to Reality A New Verse Translation RICHARD MCKIM introduction i. In the history of Presocratic Greek philosophy, the poetry of Parmenides seems to loom up suddenly out of the blue like a spectral mountain peak. Depicting a vision of ultimate reality that transcends the sensory world, his towering verse manifesto revolutionized both how philosophers thought and what they thought about, with profound repercussions that still reverberate (...) today. Parmenides has not, however, been well served by his English translators. He wrote poetry and yet is almost always translated into prose. His poem describes a divinely inspired revelation and yet is persistently translated as if it were an exercise in deductive logic. His Greek can be strange and difficult but is never unintelligible, which is more than can be said for the Anglo-gibberish his translators too often force him to speak. Too many subscribe to the misguided notion that a “literal” translation, as close as possible to word-forword, best represents the original. In fact, the painful English that results, so far from being faithful to the Greek, actually betrays it, creating the obscurities it purports to reflect. Parmenides ’ reputation for being hard to understand is largely his translators’ fault, not his. I’ve undertaken to make amends by translating his poem as a poem, in a loose English approximation of the same meter. My goal is to capture some of what gets lost in prose—to mirror, however dimly, the vital role of poetic form in shaping Parmenides’ vision. The demands of meter make literal translation impossible—not at all a bad thing— while paradoxically freeing the translator to be more faitharion 27.2 fall 2019 ful. I’ve tried to use this freedom to demonstrate that Parmenides is not the obscurantist would-be logician of so many other translations but a philosopher who thinks in poetry, and whose thought is as clear and accessible as it is astonishing. ii. parmenides was a citizen of Elea, a Greek colonial town on the west coast of the ankle of Italy’s boot. Born around 515 BCE, he was an older contemporary of Socrates, who was born in 470 (according to Plato, the two men met when Parmenides was sixty-five). Several other so-called Presocratics were active even later—Democritus for one was Socrates’ junior by a decade. But the label is still useful: while Socrates reoriented philosophy toward moral values and politics, the later Presocratics maintained their predecessors’ focus on physics and cosmology. Their project was to account for the physical workings of the universe—its origins, its elements, and the forces or laws that govern its behavior— without falling back on the gods of traditional myth. But Parmenides splits their story in two. Before him, Presocratics took the reality of the sensory world for granted— a world of multiplicity and variety, motion and change, becoming and passing away. Parmenides radically rejected this assumption. The sensory world, he declared, is an illusion. What really exists is what he calls “being,” whose true nature can be perceived only by the mind. And by clearly perceiving what being must be like, the mind perceives that it can’t be anything like the world as our senses perceive it. Being is the exact opposite of the sensory world in every respect. It is timeless, motionless, changeless and imperishable, an eternal and indivisible One. After Parmenides, the reality of the sensory world needed defending. Subsequent Presocratics had to explain, at a minimum, how it could circumvent his ban on multiplicity and motion. Most notably, he provoked Leucippus and Democri106 parmenides: the road to reality tus into developing their theory of atomism—that the universe consists entirely of atoms in a void. Atoms are microscopic Parmenidean beings insofar as they’re indivisible, indestructible and immutable, but they can be infinite in number, they can move, collide and combine, thanks to the roominess of the infinite void, defined as the absence of being. Never mind that Parmenides ruled out the existence of such an absence—by inspiring atomism, he became, in his otherworldly way, the unwitting godfather of modern physics. As for metaphysics, it may be debatable whether he arrived at the idea... (shrink)

Essentials of Symbolic Logic is a concise and clearly written introduction to the topic. Based on years of use in colleges and universities, the book provides an accessible and thorough grounding in sentence logic and predicate logic. While technical jargon is kept to a minimum, all necessary logical concepts and vocabulary are explained clearly. A standard system of natural deduction is developed, and readers are given suggestions for developing strategies for creating derivations (proofs) in this system.

The third edition of _Essentials of Symbolic Logic_ is a concise and clearly written introduction to the topic. Based on years of use in colleges and universities, the book provides an accessible and thorough grounding in sentence logic and predicate logic. While technical jargon is kept to a minimum, all necessary logical concepts and vocabulary are explained clearly. A standard system of natural deduction is developed, and readers are given suggestions for developing strategies for creating derivations in this system. (...) An instructor’s website is available with solutions to all the exercises in the text, including the many new exercises which have been added to this new edition. (shrink)

After some preliminaries concerning the original character of Rawls's formulation of the problem of social justice the author discusses the question, whether the proposed principles of justice for the basic structure of society bear the marks of a liberal theory.The conclusion of this part (IA) is that Rawls seems to have in view a mixed society, or perhaps rather a society which transcends the contrast between liberalism and socialism.Some critics have ascribed to Rawls the view of man of classical liberalism (...) and for this reason have considered him a liberal. The author contends that these critics do not seem to have grasped the purely methodological significance of the concept of the original position. After some preliminaries concerning the original character of Rawls's formulation of the problem of social justice the author discusses the question, whether the proposed principles of justice for the basic structure of society bear the marks of a liberal theory.The conclusion of this part (IA) is that Rawls seems to have in view a mixed society, or perhaps rather a society which transcends the contrast between liberalism and socialism.Some critics have ascribed to Rawls the view of man of classical liberalism and for this reason have considered him a liberal. The author contends that these critics do not seem to have grasped the purely methodological significance of the concept of the original position. After a short interlude in which the conceptions of justice of Marx and Rawls are compared (IB) the author presents some considerations of a critical nature as regards the principles of justice (IC). The distinction between the general and the special conception of justice hinges on the lixical priority of freedom. Now, a contradiction seems to emerge between the fact that the choice in favor of the special conception is an absolute one, valid for all societies regardless of time and place, and the fact that the general conception is sometimes presented as a first phase in the evolution of a well-ordered society (sect.82). This is an indication that in Rawl's theory the priority of freedom is not as absolute as he thinks it to be. The decisive point in this respect seems to be the fact that the „fair value of liberty” (Sect. 36) would demand that a subsistence minimum is lexically prior to freedom. These seem to be serious inconsistencies for which nnno remedy can be found and which are apt to lead us back to „instuitionism” The author considers next (and this is his main point) the logical structure of Rawls's contract theory, which in his opinion stands in urgent need of clarification. It is argued that the concept of contract as such implies a certain indifference or indeterminateness as regards its result. At the other hand, the result (that which is agreed upon, i.e. the principles of justice) is ex hypothesi considered to explain „our considered judgements” in reflective equilibrium. In this way it appears that Rawl's central idea (rather implicitly) is : there exists a consensus as regards our considered judgements concerning justice and this consensus may be explained as resulting from a (hypothetical) contract. So the argument really is of a hypothetico-deductive nature and it would have been much better if Rawls had been clear about it himself. Some critical considerations follow. First attention is paid to the fact that strict observance is an essential element of the concept of contract and that from this point of view the three psychological laws (chapt. VIII) are of crucial importance to the theory. Their nature, however, is not altogether clear. They are neither empirical laws (because they presuppose a just institutional structure and a just society is said not to exist), nor are they a priori ones. So it is only left for us to say that they are construed as empirical laws. Now, the difficulty for Rawls with this must be that reliance on such laws is inconsistent with the rationality of the parties in the original position, because as a matter of fact these laws have not been tested empirically (the fact that they can not be tested in this way makes no difference at all). Secondly it is asked whether we are dealing with a contract doctrine at all. Starting from the question, whether in this theory the notion of contract (intended to explain our considered judgements as givens) really is an ultimate explanatory concept, it is argued that there are some anthropological presuppositions, which rather point in the direction of a theory of self-realization. This seems to be confirmed by some other features of the theory, e. g. the Aristotelian principle, the Kantian interpretation, the concept of natural rights, and society as a social union of social unions. In conclusion, neither Rawls's principles of justice nor his contract theory are sufficiently consistent to escape the need of reconsideration. (shrink)

This article presents a model of the production of human behaviour, grounded in a pragmatist perspective. The model has two components: a small set of considered behaviours, and a set of motivators which I group into four subsets: material, reproductive, and two sets of attributional motivators. The model is based on a minimum principle. A person performs that considered behaviour which comes closest to ideal in light of the person's motivators. I show that both declining marginal utility and satisfying (...) follow as deductions from the model. In addition, especially with the inclusion of attributional motivators, the model accounts for a variety of findings in social science. I also show how it can generate theory and testable empirical predictions. (shrink)

This article begins with four situations, the first three of which are common to many businesspeople and persons in the United States today and the fourth, unfortunately, is growing: Setting the minimum level at which workers are paid; going bankrupt to avoid paying for credit card purchases, claiming a questionable deduction in calculating one's federal income tax liability, and violating the law in every state by a major U.S. corporation.These cases support the idea that positive law is the operative (...) ethic for persons in a commercial setting. Reasons advanced for this phenomenon are ethical ambiguity, lack of personal responsibility, increasing technicality of contemporary society, and the fact that the law is now seen as the most that is expected of businesspersons. In arriving at the paper's conclusions, positive law theory is discussed. Data are presented to explain why these illustrations are not mere anecdotal examples but represent broad contemporary occurrences in the U.S. (shrink)

Mandatory minimum sentencing provisions have been a feature of the U.S. justice system since 1790. But they have expanded considerably under the war on drugs, and their use has expanded considerably under the Trump Administration; some states are also poised to expand drug-related mandatory minimums further in efforts to fight the current opioid epidemic. In this paper I outline and evaluate three prominent arguments for and against the use of mandatory minimums in the war on drugs—they appeal, respectively, to (...) proportionality, consistency, and efficiency. I ultimately defend the view that the use of mandatory minimums in the war on drugs is unjust. -/- . (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, (...) leading a number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

This book is part of aaThe Minimum You Need to Knowaa family of books by Logikal Solutions. As the family expands they will cover an increasing variety of topics. This book is designed to be used as a text book for classes in logic from high school to college level. It should be one of the first courses you have on IT and this should be one of the first books you read when starting in IT. Not only does (...) this book cover flow charting and pseudocode, it teaches the reader to think before they start mapping out the logic to solve a problem. The author of this book is an industry veteran with nearly 20 years in the field. It has been his experience that recent graduates, from any country, are nearly useless at problem solving. If they cannot point, click, and drag, they cannot solve the problem. This book is an attempt to teach them how to solve the problem. An instructoraas guide is available for schools looking to make this book the basis of coursework. (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 distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of (...) the semantic approach. In structuralist theory of science, as founded by Sneed and Stegmüller, the focus is on global propositions concerning the question of whether or not certain empirical systems satisfy a set-theoretic predicate that encodes the axioms of a scientific theory. Hence, an analysis of deductive reasoning from atomic premisses with the help of a given theory is missing. The objective of the present paper is to develop a deductive system on the basis of the structuralist framework. This system comes with a novel formulation of empirical propositions in structuralism. (shrink)

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

Minimum deterrence, though consistent with the nonaggression principle, is inadequate to deter states from invading anarchist territory and provides inadequate means of territorial defense when deterrence fails. In order to be effective, and thus attract clients, private defense agencies may want to adopt a military posture that incorporates first-strike counterforce and second-strike countervalue capabilities. To this end, they must acquire weapons of mass destruction—including tactical and strategic nuclear weapons—and long-range delivery vehicles capable of penetrating deep into enemy territory. They (...) must also decline to extend the nonaggression principle to states and individuals outside the voluntary defense network. Paradoxically, advertising such a posture while possessing a nuclear arsenal will save lives on both sides by minimizing the probability that anarchists must ever wage a defensive war at all. (shrink)

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and (...) that it is in good epistemic standing. (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)

The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the (...) fact that we have learned natural languages which are themselves syntactically structured. According to this view, symbols of natural language are external to the cognitive processing system and what the cognitive system must learn to do is produce and comprehend such symbols. In this paper I pursue that idea by arguing that ability in natural deduction itself may rely on pattern recognition abilities that enable us to operate on external symbols rather than encodings of rules that might be applied to internal representations. To support this suggestion, I present a series of experiments with connectionist networks that have been trained to construct simple natural deductions in sentential logic. These networks not only succeed in reconstructing the derivations on which they have been trained, but in constructing new derivations that are only similar to the ones on which they have been trained. (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

This article discusses interactive minimum cost spanning tree problems and argues that the standard approach of using a transferable utility game to come up with a fair allocation of the total costs has some flaws. A new model of spillover games is presented, in which each player’s decision whether or not to cooperate is properly taken into account.

Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof?The answer is an emphatic yes, as I explain in this chapter. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...) is in good epistemic standing. (shrink)

The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

Deductive inference seems to reveal semantic connections between their premise(s) and conclusion that were there all along. This looks inconsistent with Wittgenstein's later views on meaning. The paper argues that W's treatment of aspects suggests a Wittgensteinian treatment of deduction that accommodates the troublesome phenomenon without conceding its force.

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

By deduction, we often extend both our knowledge and our justified belief. Moreover, in achieving knowledge or justified belief of some proposition, we commonly acquire justification for believing many of its entailed consequences, such as at least some of those that self-evidently follow from it. These and related facts have led some philosophers to endorse strong closure principles, for instance: If a person, S, is justified in believing a proposition, p, and p entails q, then S is justified in believing (...) q. Others have denied such principles, whether for justification or, with the appropriate additions, for knowledge. The debate continues. There is, however, this much consensus: there are difficult problems about the scope of closure, and epistemology should develop theories that can resolve them. (shrink)

A minimum voting age is defended as the most effective and least disrespectful means of ensuring all members of an electorate are sufficiently competent to vote. Whilst it may be reasonable to require competency from voters, a minimum voting age should be rejected because its view of competence is unreasonably controversial, it is incapable of defining a clear threshold of sufficiency and an alternative test is available which treats children more respectfully. This alternative is a procedural test for (...) minimum electoral competence. A procedural test for minimum electoral competence also succeeds in fulfilling adults’ duties to promote children’s rational and moral engagement with democracy. A minimum voting age should therefore be rejected, all things considered. A procedural test for minimum literacy and independent voting is the most justified means to ensure competency from voters and to promote the democratic agency of children. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...) `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic. (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 aim of this paper is to present and discuss the issue of the adequacy of the Minimum Intelligent Signal Test (MIST) as an alternative to the Turing Test. MIST has been proposed by Chris McKinstry as a better alternative to Turing’s original idea. Two of the main claims about MIST are that (1) MIST questions exploit commonsense knowledge and as a result are expected to be easy to answer for human beings and difficult for computer programs; and that (...) (2) the MIST design aims at eliminating the problem of the role of judges in the test. To discuss these design assumptions we will present Peter D. Turney’s PMI-IR algorithm which allows for MIST-type questions to be answered. We will also present and discuss the results of our own study aimed at the judge problem for MIST. (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)

In this paper, I shall examine attempts to furnish formal models for deductive scientific explanation. All such attempts have had certain defects. The most serious of these defects is to be found in the fact that the extant models seem to be formally restrictive in ways that do not allow any obvious generalization of their conditions which will encompass the full range of all those scientific explanations which must be considered plausible candidates for translation into deductive models.

It is often assumed that Fichte's aim in Part I of the System of Ethics is to provide a deduction of the moral law, the very thing that Kant – after years of unsuccessful attempts – deemed impossible. On this familiar reading, what Kant eventually viewed as an underivable 'fact' (Factum), the authority of the moral law, is what Fichte traces to its highest ground in what he calls the principle of the 'I'. However, scholars have largely overlooked a passage (...) in the System of Ethics where Fichte explicitly invokes Kant's doctrine of the fact of reason with approval, claiming that consciousness of the moral law grounds our belief in freedom (GA I/5:65). On the reading I defend, Fichte's invocation of the Factum is consistent with the structure of Part I when we distinguish (a) the feeling of moral compulsion from (b) the moral law itself. (shrink)

What are the worst conditions under which someone can be virtuous and happy? In this paper, I argue that a minimum threshold of favorable circumstances is necessary for moral virtue and human flourishing or happiness. Stoic and Aristotelian traditions make different and important claims about the role of external circumstances in our moral lives. Retrieving the ancient dispute benefits contemporary ethics. For one, the relevance of external circumstances is an important question for the development of present-day virtue ethics. For (...) another, identifying the minimal ingredients for virtue and happiness is helpful for wider ethical concerns such as discussions of our moral obligations to future generations. After explaining the ancient dispute, I describe categories of circumstances that seem intuitively relevant to virtue and happiness. Then, I investigate which are necessary and examine commonsense examples. I conclude that a minimum threshold of favorable circumstances from the following categories is necessary: the necessities for biological life, cognitive ability, and moral education. (shrink)

This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.

Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a (...) contextual DDT iff it is protoalgebraic and gives rise to a dually Brouwerian semilattice of compact deductive filters in every finitely generated algebra of the corresponding type. Any such system is filter distributive, although it may lack the filter extension property. More generally, filter distributivity and modularity are characterized for all finitary systems with a local contextual DDT, and several examples are discussed. For algebraizable logics, the well-known correspondence between the DDT and the equational definability of principal congruences is adapted to the contextual case. (shrink)