The fallibility of deduction is the thesis that a thoughtful speaker-reasoner can wrongly believe that an inference is deductively valid. The author presents an argument to the effect that the fallibility of deduction is incompatible with the widespread view that deduction is epistemically unfruitful (the conclusion is contained in the premises, and the transition from premises to conclusion never extends knowledge). If the fallibility of deduction is a fact, the argument presented is a refutation of the (...) doctrine of the unfruitfulness of deduction. But its relevance goes further, because the argument reveals a connection between two different problems: a solution to the problem of fruitfulness (how can deductive inferences increase our knowledge?) is a starting point for a solution to the problem of fallibility (how can deductive inferences be wrong?). To solve the problem of fruitfulness, Michael Dummett proposed some general ideas concerning meaning and inference. Starting from these meaning-theoretical ideas, one can develop an explanation of the fallibility of deduction. The general explanatory strategy does not depend on the choice between a theory of meaning centered on truth, verification, inferential role, or on other key notions. (shrink)

Current conceptions of the nature of human reasoning make it no longer tenable to assess children's inference by reference to the norms of logical inference. Alternatively, the complexity of the mental models employed in children's inferences can be analysed. This approach is applied to transitive inference, class inclusion, categorical induction, theory of mind, oddity, categorical syllogisms, analogy, and reasoning deficits. It is argued that a coherent account of children's reasoning emerges in that there is correspondence between tasks at the same (...) level of complexity across different domains, and that the inferences of younger children, while impressive and important, are consistently simpler than those of older children. (shrink)

The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

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)

Transitive inference (TI) plays a part in many aspects of reasoning, and is usually assessed using variants on a particular task dubbed the “IP-paradigm”. Advocates of this paradigm assume it ensures that subjects must use deduction to solve the inferential questions. The present task with 63 adults strengthened this claim by removing all possible perceptual cues and limiting as far as possible all cues from the training procedure itself. Response speed and accuracy were measured as premises were learned. Findings (...) show that when over-training and non-logical cues are avoided, adults nevertheless reach high levels of overall performance. However, key indexes of Lexical Marking, Relative-End-Anchoring, and Symbolic Distance are largely absent or in the opposite direction to the generally accepted view at the start of training, and are present only for response time (RT) at the end of training. The widely accepted strategy of retrieval from an integrated mental representation does emerge; but only after an initial associative process and a deductive process. Regarding three comparisons critical for demonstrating deductive TI, the inference was more demanding than its antecedents both in terms of accuracy and RT, and both after initial and final training. Existing theories of TI account for some of these findings, but what is required is a theory accommodating them all. (shrink)

This paper is concerned with certain connections and oppositions that Brudner perceives between liberty, equality and community. As I understand his project, he begins with a strong atomist conception of the worth of individuals, which he calls libertarian, and claims to show how egalitarian and communitarian ideas of individual worth are unavoidably contained in the original idea and must be developed out of it in order to arrive at a coherent and conceptually stable view. This is the inclusive conception, which (...) retains the libertarian and egalitarian moments as subordinate but essential aspects of a liberal ethical community. This paper is sceptical of the validity of the proposed deduction. It concentrates on a few passages, which purport to show how an initial position has implications that nevertheless are in contradiction with the premises from which they are derived. As a result of this concentration, the paper, unavoidably, ignores a great wealth of illuminating material that, together with the impressive sweep of the project as a whole, fully justifies the attention the book is receiving, even if, as I believe, the overall argument does not succeed. (shrink)

Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT ) were measured as is typically done. We also measured RT confined to correct responses ( cRT ). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was (...) not at all evident for nRT ; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B ? D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held. (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)

The role of foundation with respect to transitive closure in the Zermelo system Z has been investigated by Boffa; our aim is to explore the role of antifoundation. We start by showing the consistency of "Z antifoundation transitive closure" relative to Z (by a technique well known for ZF). Further, we introduce a "weak replacement principle" (deductible from antifoundation and transitive closure) and study the relations among these three statements in Z via interpretations. Finally, we give some adaptations for ZF (...) without infinity. (shrink)

The principles of Kant's pure physics (conservation of quantity of matter, inertia, equality of action and reaction) are a priori in the same sense as are the principles of the understanding. We account for the empirical content of physics by showing that the pure principles operate as rules for generating wellformed empirical descriptions, and as rules for analysis of motion. The relationship between the metaphysics of matter and empirical descriptions is neither deductive, nor as loose as Buchdahl alleges. Belief that (...) a priori principles will apply to empirical cases requires acceptance of methodological presuppositions, chief among which is the principle of affinity. (shrink)

Recent studies have shown that deductive reasoning skills are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive (...) reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions. (shrink)

In a 1798 letter to Christian Garve, Kant claims that without a transition [Übergang] from the metaphysical foundations of natural science to physics there will be a ‘gap’ in the Critical philosophy. He does not make clear, however, exactly what this gap is or how the transition is supposed to fill the gap. The Übergang section of Kant's Opus postumum has received considerable attention of late due to the many drafts it contains of Kant's Ether Deduction. Commentators have also (...) hoped to find a solution there to the gap problem. Little attention has been paid, however, to Kant's project in Convolut 10 of the OP which he began in August 1799 immediately after completing the Übergang section. Assuming that the Ether Deduction is sound and proves a priori the existence of a transcendental material condition for experience, Convolut 10 discusses what changes would have to be made to the transcendental formal conditions of experience in their empirical function given the addition of this transcendental material condition. Kant claims in Convolut 10 that these changes are necessary to finally effect a transition from the metaphysical foundations of natural science to physics and, as I will argue, such a transition will be tantamount to bridging the gap in the Critical philosophy mentioned in the letter to Garve. (shrink)

This thesis is about how deduction is analytic and, at the same time, informative. In the first two chapters I am after the question of the justification of deduction. This justification is circular in the sense that to explain how deduction works we use some basic deductive rules. However, this circularity is not trivial as not every rule can be justified circularly. Moreover, deductive rules may not need suasive justification because they are not ampliative. Deduction preserves (...) meaning, that is, the meaning of non-logical vocabulary of any theory which is developed by deductive reasoning remains unchanged. It means that deduction adds no information to what we already had in our premises. This is why deduction is analytic. -/- However, there are many ways deduction can be informative. In the next three chapters, I will pick a specific kind of deductive reasoning, namely arithmetical reasoning, and will attempt to understand the nature of information we obtain by this kind of reasoning. There is a difference between simple deductive moves such as inferring `Socrates is mortal' from `All human are mortal' and `Socrates is human', and inferring that a relation is reflexive given that it is directed, symmetric and transitive. The latter is more complicated and not as easy to prove as the former. Therefore it is informative and the proof we construct to prove it puts us in an epistemic position that we were not in before having the proof. To be more specific, I show that concepts we need to confirm the conclusion are made in the process of proving the conclusion. (shrink)

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent (...) logic with deterministic or non-deterministic matrices is not applicable to \({\mathbf{NC}}_{\mathbf{3}}\) and its binary extensions. (shrink)

This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its (...) extensions which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication. (shrink)

This essay examines the grammatical structure underlying the use of the word "conscious". Despite the existence of this grammatical structure, I reject the assumption that actual consciousness has a similar structure. Specifically, I reject the claim that consciousness consists of three subtypes: state consciousness, transitive consciousness, and creature consciousness. I offer an inductive argument and a deductive argument that no such psychological entities exist. The inductive argument: given the lack of evidence or arguments for the entities and given that a (...) tripartite consciousness structure evolved from a tripartite grammatical habit, it would be far too coincidental if the grammatical distinction mirrored a psychological distinction. The deductive argument shows that absurd conclusions follow from assuming the existence of three distinct psychological entities. Furthermore, the verbal habits that motivate the distinction are rendered more intelligible under a "Unitary Thesis", the idea that verbal distinctions involving use of the word "conscious" are unified in their reliance on a single ontological unit, that of conscious experience. (shrink)

In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.

In almost all countries, the transition from a centrally planned economy to a market economy caused high unemployment. The governments attempted to ease the changeover to a market economy for the unemployed by introducing several passive and active labour market policies. This paper first points out which effects were to be expected of such policies from the perspective of Austrian Economics. These theoretical hypotheses are then tested empirically. It turns out that the hypotheses deducted from Austrian Economics theory are impressively (...) corroborated by the empirical evidence.Dans presque tous les pays, la transition d’une économie centralement planifiée vers une économie de marché ont provoqué un chômage élevé. Les gouvernements ont essayé d’adoucir la transition vers une économie de marché pour les chômeurs en introduisant plusieurs politiques passives et actives sur le marché du travail. Tout d’abord, cet article souligne quels étaient les effets attendus de telles politiques à la lumière de l’économie autrichienne. Ces hypothèses théoriques sont ensuite testées de manière empirique. Il en ressort que les hypothèses déduites de la théorie économique autrichienne sont corroborées de manière significative par les preuves empiriques. (shrink)

In another paper, one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what is expected: often, what is expected from a theory of the system's microscopic constituents. We take reduction as deduction, aided by appropriate definitions. Then the main idea of our reconciliation of (...) emergence and reduction is that one makes the deduction after taking a limit of an appropriate parameter $N$. Thus our first main claim will be that in some situations, one can deduce a novel behaviour, by taking a limit $N\to\infty$. Our main illustration of this will be Lee-Yang theory. But on the other hand, this does not show that the $N=\infty$ limit is physically real. For our second main claim will be that in such situations, there is a logically weaker, yet still vivid, novel behaviour that occurs before the limit, i.e. for finite $N$. And it is this weaker behaviour which is physically real. Our main illustration of this will be the renormalization group description of cross-over phenomena. (shrink)

Given the harmony principle for logical operators, compositionality ought to ensure that harmony should obtain at the level of whole contents. That is, the role of a content qua premise ought to be balanced exactly by its role as a conclusion. Frege's contextual definition of propositional content happens to exploit this balance, and one appeals to the Cut rule to show that the definition is adequate. We show here that Frege's definition remains adequate even when one relevantizes logic by abandoning (...) an unrestricted Cut rule. The proof exploits the fact that in the relevantized logic, which abandons the unrestricted rule of Cut, any failure of the transitivity of deduction is offset by the epistemic gain involved in learning that a stronger-than-expected result holds. (shrink)

Attributed to Alexander of Aphrodisias -the leading ancient commentator on Aristotle -the Quaestiones exemplify the process through which Aristotle's thought was organized and came to be interpreted as "Aristotelianism." This volume of R.W. Sharples's translation, together with his earlier translation of Quaestiones 1.1-2.15, makes the Quaestiones available in its entirety for the first time in a modern language. The Quaestiones are concerned with problems of physics and metaphysics, psychology and divine providence. Readers interested in Aristotle's psychological views will find the (...) second half of the Quaestiones particularly valuable. Ten of the problems discussed involve issues raised in Aristotle's On the Soul, including the unity of apperception and the transition from first to second actuality in the act of contemplation. An additional twelve problems relate to aspects of physical theory such as infinity, necessity, and potentiality. Quaestio 2.21 concerns divine providence and helps supplement our knowledge of Alexander's position. A study of the Quaestiones also suggests how interpretations of Aristotle were influenced by doctrines of Hellenistic philosophy. Translated first into Arabic and then into Latin, excerpts from the Quaestiones played a significant role in the transmission of ancient Greek philosophy to the medieval world. (shrink)

ABSTRACT This paper deals with the linguistic phenomenon of vagueness. Based on certain observations regarding the intuitions and linguistic practices of the philosophically informed speaker, we make a series of assumptions concerning the nature and characteristics of the phenomenon. Vagueness is treated as an emerging phenomenon, caused, in essence, by the messy way in which linguistic communities reach classificatory equilibria. Any talk of ‘meaning’, ‘truth’, and such is treated as an indirect way of attempting to describe such equilibria, and it (...) is in regard to these that ascriptions of truth are here relativised. Given such assumptions, we then proceed to formulate and study a semantic theory for languages that contain vague predicates. Finally, we describe two proof systems, one based on trees, and a natural deduction system in the style of Fitch, and outline the appropriate proofs of soundness and completeness. (shrink)

Some logic students falter at the transition from the mechanical method of truth tables to the less-mechanical method of natural deduction. This short paper introduces a word game intended to ease that transition.

In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a (...) notion of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak. (shrink)

In a fluent, clear, and lively style this translation by two of Maslov's junior colleagues brings the work of the late Soviet scientist S. Yu. Maslov to a wider audience. Maslov was considered by his peers to be a man of genius who was making fundamental contributions in the fields of automatic theorem proving and computational logic. He published little, and those few papers were regarded as notoriously difficult. This book, however, was written for a broad audience of readers and (...) describes elegant examples of applications in such fields as computer science, artificial intelligence, operations research, economic modeling, and biological modeling, among others. The book also brings to light the work by the American mathematician E. L. Post, which inspired Maslov's own work in the development of a general theory and which has been long neglected by mathematicial logicians and systems theorists in the United States. The book's first chapter introduces the Rules of the Game. Part I, Mathematics of Calculi, covers E. L. Post's canonical systems, deductive systems and algorithms, and probabilistic calculi and deductive information. Part II, Horizonal Modeling, takes up a "toy" economy, the calculi of technological possibilities, and the development of rules. Part III, Vertical Modeling, deals with the topics of "to fight and to search" and the consequences of the asymmetry of cognitive mechanisms. Vladimir Lifschitz is affiliated with the Department of Computer Science at Stanford University, and Michael Gelfond with the Department of Electrical Engineering and Computer Science at the University of Texas, El Paso. Theory of Deductive Systems and Its Applicationsis included in the Foundation of Computing Series, edited by Michael Garey. (shrink)

We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a calculus of natural (...) class='Hi'>deduction. Transitivity of set inclusion turns out to be a necessary condition for the validity of imperfect syllogisms. As a consequence, it can be established what the main metalogical difference between a perfect and an imperfect syllogism is. The validity of the laws of conversion is also obtained by direct proofs. Finally, it is shown that and explained why some imperfect syllogisms satisfy the definition of a perfect syllogism. (shrink)

Introduction. The article is focused on studying the self-knowledge techniques used in Buddhism and their application in teaching philosophy. The relevance of the study is due to the search for new approaches to studying philosophy, including approaches related to philosophical practice, as well as the interest of modern scientists in the problem of consciousness. The problem of consciousness is interdisciplinary and its study is of practical importance for philosophers, psychologists, linguists, specialists in artificial intelligence. Buddhism as a philosophical doctrine provides (...) rich material for the study of the phenomenon of consciousness, which does not lose its relevance today. A feature of the Buddhist approach to consciousness is that it has an axiological orientation that is directly related to the problem of self-knowledge. The practices of self-knowledge used in Buddhism enable a person to become happier and more harmonious, which is so important for each of us. The aim of the study is to conduct a philosophical analysis of Buddhist practices of self-knowledge and self-transformation in order to use them in the educational process. Methods: the author uses general scientific methods of analysis and synthesis, deduction and induction; phenomenological method to identify the intentions that are key for consciousness. The author also uses the hermeneutical method to interpret Buddhist texts. The method of introspection as self-observation of consciousness is used in Buddhist meditation techniques. The scientific novelty of the study is that we approach the study of extensive material on Buddhism in the context of the problem of selfknowledge, which is inextricably linked with the Buddhist concept of consciousness. The revealed and studied Buddhist techniques of self-knowledge have been adapted for teaching philosophy. Results. A philosophical analysis of the literature on Buddhism in the context of the problem of self-knowledge was carried out. As a result of the analysis, Buddhist techniques for working with consciousness, such as meditation, the method of pondering Zen koans, the method of getting rid of material attachments, or the practice of austerities, were studied and described. A philosophical analysis of various Buddhist meditation techniques showed that they are based on the Buddhist concept of consciousness, which denies the existence of an individual “I”, considers the “I” to be nothing more than a combination of various dharmas, therefore the purpose of meditation in Buddhism is to identify oneself with one’s own “I”, to achieve a state of voidness in which we must comprehend our true identity. The method of pondering Zen koans is also one of the techniques for working with one’s consciousness in Buddhism. As a result of deliberation of these paradoxical miniatures, a person goes beyond the boundaries of logical thinking; there is a transition from the level of profane consciousness to the level of deep consciousness. The basis of the method of getting rid of material attachments or the practice of austerities in Buddhism is the concept of the middle path. We have established a similarity between the method of getting rid of material attachments, the concept of the middle path and minimalism as a way of life. Findings. Elements of the Buddhist practices of self-transformation can be successfully used in the teaching of philosophy at the university as a practical aspect of studying this discipline, forming students with the idea of philosophy as a way of life leading to positive self-transformation. Studying the practical aspects of Buddhist philosophy contributes to the formation of tolerance, awareness, education of humanism and altruism, and the skills of psycho-emotional self-regulation. (shrink)

There is a paradigm shift occurring. The transition underway is from a rigid, mechanistic, and materialistic worldview to a process organismic worldview supporting a foundation of interconnectedness, cooperation, and the intersection of science and spirituality. A new paradigm must start with abductive hypotheses. I present the following as a presentation of abductive hypotheses. In semiotics abduction is a kind of reverse deduction to discover a law or some factor that would render some phenomenon intelligible. The importance of abduction is (...) that it is creative; it escapes the confines of deduction and induction. In this paper we’re not putting forth claims of truth or arguments for a position, but we are putting forth claims of usefulness; what do we need to be investigating to support this new paradigm? (shrink)

This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and (...) in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes C, (...) that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

Introduction. The relevance of the research topic is determined by the necessity to study financial phenomena and processes in order to understand the economic essence of public finance in the life of society. The strategic imperative for the formation of public finance is the development of an appropriate provision for its implementation, adequate to the complex and changeable circumstances of the territory development. The main purpose of the study is to identify the features of performing the functions of public finance (...) for regions with a specific mode of operating. Methods. When solving the tasks, the author uses general logical methods: analysis, synthesis, induction, deduction, analogy; empirical level methods: observation, description, measurement, modeling, as well as private and special methods of scientific research: comparative analysis, system approach, the Robinsonade model (Crusoe model). Scientific novelty of the research. The scientific novelty of the results lies in solving an important scientific problem - identifying the features of implementing the allocative function of public finance in the regions with a specific mode of operating (as exemplified by the Donetsk People’s Republic, where there is a special military and political situation, a mobilization type of economy, a transitional period due to the integration of the Republic into the system of the Russian Federation federal relations) in order to improve the system of public finance management in such regions. Results. The main results of the study consist in characterizing the process of implementing the allocation function of public finance, which makes it possible to determine the maximum effect of economic actions of the subjects in the current conditions, as well as to lay the foundations for analyzing the following distribution function of public finance. Conclusions. The author makes a conclusion that in the context of strengthening the role of public finance, not only in ensuring the economic development of the Donetsk People’s Republic, but also in the post-crisis recovery and stabilization of business activity, the implementation of the allocation function of public finance becomes important. (shrink)

Originally published in 1982, this was an extensive and up-to-date review of research into the psychology of deductive reasoning, Jonathan Evans presents an alternative theoretical framework to the rationalist approach which had dominated much of the published work in this field at the time. The review falls into three sections. The first is concerned with elementary reasoning tasks, in which response latency is the prime measure of interest. The second and third sections are concerned with syllogistic and propositional reasoning respectively, (...) in which interest has focused on the explanation of frequently observed logical errors. In an extended discussion it is argued that reasoning processes are content specific, and give little indication of the operation of any underlying system of logical competence. Finally, a dual process theory of reasoning, with broad implications and connections with other fields of psychology, is elaborated and assessed in the light of recent evidence. (shrink)

In metaphysics, the view that material constitution is transitive is ubiquitous, an assumption expressed by both proponents and critics of constitution views. Likewise, it is typically assumed within the philosophy of mind that physical realization is a transitive relation. In both cases, this assumption of transitivity plays a role in discussion of the broader implications of a metaphysics that invokes either relation. Here I provide reasons for questioning this assumption and the uses to which this appeal to transitivity (...) is put. As my title suggests, I shall focus on the case of material constitution, using a brief discussion of realization at the outset to motivate the discussion of the transitivity of material constitution at the core of the paper. (shrink)

The resources and resource potential of the innovative component of nanoeconomics are analyzed. The factors of production – classical types of resources such as land, labor, capital and technology – are described. Ways of influencing the security resources of nanoeconomics within the innovation paradigm are evaluated. The purpose of the study is to identify the factor of nanoeconomics in the formation of resource security potential in the innovation paradigm. To achieve this goal, the following tasks were set: to characterize the (...) importance of the land resource as a factor in the potential of economic nanosystems; to highlight the importance of capital as a factor of nanoproduction and an indicator of the innovation paradigm; to determine the labor resource in the development of innovative nanosystems; to analyze the intellectual potential of nanoeconomic development of the innovation paradigm; to identify clusters of innovative nanopotential in the regions of countries with transition economies. Each resource is examined separately with the first analysis of a resource security assessment such as land. The other resource under consideration is labor. Demographic factors become decisive in describing the development of labor resources. The capital factor allows the formation of independent economic systems, when the state budget affects the possibility of developing science, education and health care. A number of methods were applied during the study: methods of induction and deduction (to assess the importance of the innovation paradigm for the development of nanoeconomics); system analysis and structural approach (to determine the aggregate state of production factors); method of comparing the quality of production factors in market economies and in developed countries; an observation method (for assessing the state of resources in different countries); method of cluster analysis (to determine the existence of innovation-territorial regions in countries with economies in transition). The analysis is carried out to identify the conditions of the impact of production factors on the innovative paradigm of nanoeconomics. It reveals theoretical approaches to the formation of nanoeconomics and its active development. As a result of the study of intellectual and resource potential of security, a cluster analysis was carried out to assess the conditions for the formation of innovation-territorial regions. This study allows to understand the role of production security factors in the formation of the innovation paradigm and the efficiency of the development of nanoeconomics. The way of providing the basis for the development of nanoeconomics in the form of efficient use of production factors is considered as a perspective. (shrink)

How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not (...) directly stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)

The way in which vision represents objects as being the same despite movement and qualitative changes has been extensively investigated in contemporary psychology. However, the formal properties of the visual sameness relation are still unclear, for example, whether it is an identity-like, equivalence relation. The paper concerns one aspect of this problem: the transitivity of visual sameness. Results obtained by using different experimental paradigms are analysed, in particular studies using streaming/bouncing stimuli, multiple object tracking experiments and investigations concerning object-specific (...) preview benefit, and it is argued that the transitive interpretation of visual sameness is the most plausible given the current stage of knowledge. What is more, it is claimed that the way in which visual sameness is represented suggests that in some cases it should be characterized as a “primitive sameness”, similarly as in philosophical theories postulating “thisness”. (shrink)

According to the traditional nomological-deductive methodology of physics and chemistry [Hempel and Oppenheim, 1948], explaining a phenomenon means subsuming it under a law. Logic becomes then the glue of explanation and laws the primary explainers. Thus, the scientific study of a system would consist in the development of a logically sound model of it, once the relevant observables (state variables) are identified and the general laws governing their change (expressed as differential equations, state transition rules, maximization/minimization principles,. . . ) (...) are well determined, together with the initial or boundary conditions for each particular case. Often this also involves making a set of assumptions about the elementary components of the system (e.g., their structural and dynamic properties) and modes of local interaction. In this framework, predictability becomes the main goal and that is why research is carried out through the construction of accurate mathematical models. Thus, physics and chemistry have made most progress so far by focusing on systems that, either due to their intrinsic properties or to the conditions in which they are investigated, allow for very strong simplifying assumptions, under which, nevertheless, those highly idealized models of reality are deemed to be in good correspondence with reality itself. Despite the enormous success that this methodology has had, the study of living and cognitive phenomena had to follow a very different road, because these phenomena are produced by systems whose underlying material structure and organization do not permit such crude approximations. Seen from the perspective of physics or chemistry, biological and cognitive systems are made of an enormous number of parts or elements interacting in non-linear and selective ways, which makes very difficult their tractability through mathematical models. In addition, many of those interacting elements are hierarchically organized, in a way that the “macroscopic” (observable) parts behave according to rules that cannot be, in practice, derived from simple principles at the level of their “microscopic” dynamics.. (shrink)

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

This is a textbook covering the basics of formal logic and elementary metatheory. Its distinguishing feature is that it has more emphasis on metatheory than comparable introductory textbooks. It was originally written to accompany lectures in an introductory to intermediate logic course at the University of Oxford, but it is designed to be used independently.

The main purpose of this paper is to show that left-monotone risk aversion, a meaningful refinement of strong risk aversion, characterizes decision makers for whom deductible insurance is optimal. A second goal is to prove that the deductible’s computation is particularly tractable in the case of Yaari’s decision makers.

The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory.

Semantic studies on diagrammatic notations (Barwise & Etchemendy, ; Shimojima, ; Stenning & Lemon, ) have revealed that the “non-deductive,” “emergent,” or “perceptual” effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, ; Kulpa, ; Larkin & Simon, ; Lindsay, ) are all rooted in the exploitation of spatial constraints on graphical structures. Thus, theoretically, this process is a key factor in inference with diagrams, explaining the frequently observed reduction of inferential load. The purpose of this study was to examine (...) the empirical basis for this theoretical suggestion, focusing on the reality of the constraint-exploitation strategy in actual practices of diagrammatic reasoning. Eye movements were recorded while participants used simple position diagrams to solve three- or four-term transitive inference problems. Our experiments revealed that the participants could exploit spatial constraints on graphical structures even when (a) they were not in the position of actually manipulating diagrams, (b) the semantic rule for the provided diagrams did not match their preferences, and (c) the constraint-exploitation strategy invited a partly adverse effect. These findings indicate that the hypothesized process is in fact robust, with the potential to broadly account for the inferential advantage of diagrams. (shrink)

De jure coreference in a discourse is typically understood as explicit coreference that speakers are required to recognize in order to count as having correctly understood the discourse. For example, in an utterance of the sentence ‘Tom went to the market because he needed soy milk’, the two underlined terms are typically coreferential in a way that appreciating their coreference is required to fully understand the utterance. Often, de jure coreference is understood as an equivalence relation, so in particular it (...) is thought of as a transitive relation. However, Pinillos (Philos Stud 154(2):301–324, 2011) provides examples that apparently challenge the transitivity of de jure coreference. In this paper, I argue for two claims. First, while it is inconclusive whether the relevant terms in Pinillos’s examples satisfy his third condition, it is much clearer that they fail to satisfy his first two conditions. Given that Pinillos’s conditions capture important characteristics of de jure coreference, his examples do not successfully show the non-transitivity of de jure coreference. Second, I present an alternative account of his examples, one that shows which representation the anaphoric pronoun in an example of the sort that he presents is de jure coreferential with. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Hegel's Concept of Life: Self-Consciousness, Freedom, Logic by Karen NgMarina F. BykovaKaren Ng. Hegel's Concept of Life: Self-Consciousness, Freedom, Logic. Oxford: Oxford University Press, 2020. Pp. iii + 319. Hardback, $85.00.In her insightful book, Karen Ng defends the fundamental significance of Hegel's concept of life, which she considers "constitutive" not merely of his dynamic account of reason but also of his "idealist program" itself (3–4), the very core (...) structure that grounds his idealism (151, 291). Integrating this concept into his philosophy allows Hegel to resolve three systematic problems indicated in the subtitle of the book: self-consciousness, freedom or self-determination, and logical form.The book offers a systematic account of the logical concept of life by defending three interconnected claims, helpfully summarized in chapter 1. The first, rather general claim clarifies Ng's interpretive point of departure. She maintains that the "core tenets" of Hegel's philosophy can be understood through the "purposiveness theme" inherited from Kant's a priori principle of purposiveness in his Critique of Judgment (5, 43). Ng advances this claim in chapter 2, where she argues that it is working through Kant's concept of inner purposiveness of natural ends from the teleological power of judgment that leads Hegel to develop his own account of Concept, which is foundational for his entire philosophical system (61–64).Chapter 3 continues the examination of Hegel's immediate predecessors in relation to the interpretation of his "speculative identity thesis" (8), which constitutes the second claim. According to Ng, Hegel first introduces this thesis—which remains central to all his works—in the Differenzschift. In this work, Hegel, siding with Schelling, criticizes Fichte's subjective version of idealism, more specifically for his explanation of the relation between subject and object as constructed and facilitated by subjective consciousness itself, thus rendering "nature lifeless and dead" (88). Opposing this approach, in the Phenomenology of Spirit, Hegel interprets the identity of object and subject as facilitated by the relation and opposition between self-consciousness and life. Thus, the speculative identity thesis assumes a fundamental significance of life for self-consciousness. Unfolding this thesis is at the core of Hegel's absolute method in the Science of Logic as well. On Ng's reading, Hegel's speculative thesis along with his account of self-consciousness also have their roots in the purposiveness theme inherited from Kant. What is at work here is Kant's claim that the principle of purposiveness is a necessary condition for judgment, which Hegel develops into a claim about the concept of life as being constitutive for self-consciousness.In the rest of the book (chapters 4–8), devoted to a close analysis of Hegel's Science of Logic, Ng advances her third and perhaps most original claim: understanding Hegel's [End Page 527] Subjective Logic "as his own version of a 'critique of judgment'" (18). She demonstrates that this part of the Logic offers a positive account of the concept of life that Hegel develops in his critical interaction with Kant. The most illustrative in this respect is the "Subjectivity" section of the Logic, in which the form of life is presented as the ground and presupposition of Hegel's theory of concepts and judgments. According to Ng, such a reading makes evident that "life opens up the space of reasons" (234, 281).Chapter 4 takes up Hegel's immanent deduction of the Concept argument, revealing that the key to understanding it is the concept of reciprocity (Wechselwirkung) (127), most fully recognizable as an internal purposiveness of the Concept itself.Ng traces the purposiveness theme through the entirety of the Subjective Logic, establishing its significance for understanding the deduction of the Concept and for the transition to the Idea. In her analysis, she closely follows Hegel's division of the Subjective Logic and addresses Subjectivity, Objectivity, and the Idea in chapters 5–8, respectively. With chapter 5, Ng moves to a discussion of how Hegel finds judgment to arise from the "original judgement of life," the initial unity and division of subject and object within life (172). Chapter 6 extends this discussion by elucidating the tension Hegel... (shrink)