ABSTRACTStudies examining the interpretation that is given to if–then statementstypically use what are referred to as basic conditionals, which give contextless relations between two unrelated concrete terms. However, there is some evidence that basic conditionals require a more abstract form of representation. In order to examine this, we presented participants with truth-table tasks involving either basic conditionals or conditionals referring to imaginary categories, and standard conditional inference tasks with abstract and familiar premises. As expected, fewer typical defective conditional (...) interpretations were given to basic conditionals. In addition, partial correlations showed a unique relationship between the interpretation of basic conditionals and abstract inferential reasoning. Results suggest that people process basic conditionals as a form of abstract reasoning, and that the interpretation of conditionals... (shrink)

The chapter provides illustrations of the link between Hegel's work and Vygotsky's and shows how the argument that Vygotsky employed an abstract decontextualised form of reason, is groundless. Kant sets out to resolve the dualism of world and mind by positing the categories of understanding. Although Kant's later work moved towards overcoming the rigid separation of concept and intuition and of spontaneity from receptivity, dualism remained. Hegel dealt with dualism from a radically different standpoint, and this transformed the (...) terms in which it can be posed. In contrast to Kant, he rejected the categorical separation of subject and object, thereby opening a philosophical space within which the antinomies of dualism could be transcended. Most reactions to Hegel after Marx were intermingled with reactions to Marx. Misinterpretation of Hegel is communicated to readings of Vygotsky, where the influence of Hegel is read as evidence of hierarchical conceptions of abstract reason. (shrink)

This study investigated individual differences in the belief bias effect, which is the tendency to accept conclusions because they are believable rather than because they are logically valid. It was observed that the extent of an individual's belief bias effect was unrelated to a number of measures of reasoning competence. Instead, as predicted by mental models theory, it was related to a person's ability to generate alternative representations of premises: the more alternatives a person generated, the less likely they were (...) to show a belief bias effect. In contrast to belief effects, which were predicted by the number of alternatives generated, scores on logical reasoning tasks were predicted by an individual's understanding of the concept of logical necessity. These two mediating variables, ability to generate alternatives and understanding of logical necessity, were themselves predicted by similar variables, such as cognitive motivation and abstract reasoning ability. Our findings strongly support the mental models interpretation of the belief bias effect, and suggest that individual differences in this effect are associated with a specific ability to generate alternatives, rather than with a general logical competence. (shrink)

We may think of the city as a kind of symbol of what most characterises our era: if it is true that our era is most characterised by complexity and uncertainty, it is also true that the city may be what can most clearly show what complexity and uncertainty actually mean. Our era’s harshest lesson is precisely that, when we move from the village to the city, specifically contemporary cities becoming not only exponentially big but also exponentially interconnected, complexity and (...) uncertainty increase as our era’s equally harsh global challenges, from climate change to pandemics to wars. Yet, contemporary cities’ global challenges may be not only harsh lessons but also unmissable opportunities. In what follows, as a philosopher, I shall work on at least two reasons why contemporary cities, specifically their future as what is likely to further increase complexity and uncertainty, may teach us something key from an epistemological perspective: first, to abstract more and, second, to be wiser, which are two epistemological capabilities that may be more crucial than ever in the future. (shrink)

According to conciliatory views on the significance of disagreement, it’s rational for you to become less confident in your take on an issue in case your epistemic peer’s take on it is different. These views are intuitively appealing, but they also face a powerful objection: in scenarios that involve disagreements over their own correctness, conciliatory views appear to self-defeat and, thereby, issue inconsistent recommendations. This paper provides a response to this objection. Drawing on the work from defeasible logics paradigm and (...) abstract argumentation, it develops a formal model of conciliatory reasoning and explores its behavior in the troubling scenarios. The model suggests that the recommendations that conciliatory views issue in such scenarios are perfectly reasonable—even if outwardly they may look odd. (shrink)

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour (...) in games with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature. (shrink)

This paper presents a new algorithm to find an appropriate similarityunder which we apply legal rules analogically. Since there may exist a lotof similarities between the premises of rule and a case in inquiry, we haveto select an appropriate similarity that is relevant to both thelegal rule and a top goal of our legal reasoning. For this purpose, a newcriterion to distinguish the appropriate similarities from the others isproposed and tested. The criterion is based on Goal-DependentAbstraction (GDA) to select a (...) similarity such that an abstraction basedon the similarity never loses the necessary information to prove the ground (purpose of legislation) of the legal rule. In order to cope withour huge space of similarities, our GDA algorithm uses some constraintsto prune useless similarities. (shrink)

Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds (...) of diagram manipulation: Sometimes diagrams are manipulated in order to profile known information in an optimal fashion. At other times diagrams are explored in order to gain new insights, solve problems or discover hidden meaning potentials. The latter cases often entail manipulations that either generate additional information or extract information by means of abstraction. Ideas are substantiated by reference to ethnographic, experimental and historical examples. (shrink)

Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient reasoners. (...) First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning. (shrink)

Molecular biologists use different kinds of reasoning strategies for different tasks, such as hypothesis formation, experimental design, and anomaly resolution. More specifically, the reasoning strategies discussed in this paper may be characterized as (1) abstraction-instantiation, in which an abstract skeletal model is instantiated to produce an experimental system; (2) the systematic scan, in which alternative hypotheses are systematically generated; and (3) modular anomaly resolution, in which components of a model are stated explicitly and methodically changed to generate alternative changes (...) to resolve an anomaly. This work grew out of close observation over a period of six months of an actively functioning molecular genetics laboratory. (shrink)

Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it is through (...) imagined variation of diagrams that one can universalize spatial inferences. In order to shift the discussion of Aristotle’s work on geometry from ontological to methodological questions, I argue in the first section that geometrical properties for Aristotle are necessary accidents of the particulars, canonically diagrams, in which they inhere. I then consider a line of research that shows how diagrams in ancient geometry are not illustrations of the textual proof but are in part constitutive of geometrical inference, an insight I claim can shed light on Aristotle’s philosophical project. Next I substantiate this assertion by giving an alternative interpretation of abstraction according to which it is a diagrammatic procedure that allows a part of a particular diagram to stand in for a universal. In the last section, I consider Aristotle’s account of mathematical cognition, arguing that there is evidence for the view that imagination is necessary both for the construction of figures, and for their presentation as abstractions subject to universal inference. (shrink)

This paper presents a methodology to design and implement programs intended to decide cases, described as sets of factors, according to a theory of a particular domain based on a set of precedent cases relating to that domain. We useDialectical Frameworks, a recent development in AI knowledge representation, as the central feature of our design method. ADFs will play a role akin to that played by Entity–Relationship models in the design of database systems. First, we explain how the factor hierarchy (...) of the well-known legal reasoning system CATO can be used to instantiate an ADF for the domain of US Trade Secrets. This is intended to demonstrate the suitability of ADFs for expressing the design of legal cased based systems. The method is then applied to two other legal domains often used in the literature of AI and Law. In each domain, the design is provided by the domain analyst expressing the cases in terms of factors organised into an ADF from which an executable program can be implemented in a straightforward way by taking advantage of the closeness of the acceptance conditions of the ADF to components of an executable program. We evaluate the ease of implementation, the performance and efficacy of the resulting program, ease of refinement of the program and the transparency of the reasoning. This evaluation suggests ways in which factor based systems, which are limited by taking as their starting point the representation of cases as sets of factors and so abstracting away the particular facts, can be extended to address open issues in AI and Law by incorporating the case facts to improve the decision, and by considering justification and reasoning using portion of precedents. (shrink)

dialectical frameworks constitute a recent and powerful generalisation of Dung's argumentation frameworks, where the relationship between the arguments can be specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas thus are suitable engines to be (...) employed. In this paper we give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning. (shrink)

Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to (...) classify states of information, information-bases, and evidential situations. (shrink)

Many animal species use tools, but human technical engagement is more complex. We argue that there is coevolution between technical engagement and advanced forms of causal cognition in the human lineage. As an analytic tool, we present a classification of different forms of causal thinking. Human causal thinking has become detached from space and time, so that instead of just reacting to perceptual input, our minds can simulate actions and forces and their causal consequences. Our main thesis is that, unlike (...) the situation for other primate species, an increasing emphasis on technical engagement made some hominins capable of reasoning about the forces involved in causal processes. This thesis is supported in three ways: We compare the casual thinking about forces of hominins with that of other primates. We analyze the causal thinking required for Stone Age hunting technologies such as throwing spears, bow hunting and the use of poisoned arrows, arguing that they may serve as examples of the expansion of casual cognition about forces. We present neurophysiological results that indicate the facilitation of advanced causal thinking. (shrink)

Probabilistic theories of reasoning assume that people use their prior knowledge to estimate the conditional probability of q given p and that this probability predicts the acceptance of modus ponens inferences. But how do people reason with unfamiliar conditionals for which they do not have prior knowledge? Reasoning without prior knowledge has been extensively investigated in experiments in which participants were instructed to reason deductively. But it is still not clear how people reason with unfamiliar conditionals when (...) they are instructed to reason as in daily life. Can probabilities also predict reasoning with unfamiliar content? In two experiments we instructed participants to reason as in everyday life and to evaluate conclusions from familiar and unfamiliar conditionals. Results showed that reasoning with familiar conditionals can be predicted by the conditional probability. For unfamiliar conditionals, however, this was not the case. Conclusions from unfamiliar conditionals were accepted more strongly than what could be expected according to their conditional probability. Our findings challenge probabilistic theories of reasoning and suggest that other approaches, such as a dual-strategy model, describe our results more adequately. (shrink)

In a 1998 Hume Studies book symposium, Peter Millican provided excellent critical comments on my Cognition and Commitment in Hume’s Philosophy, and I am grateful that he has done the same for Hume. Many of the new or revised interpretations in the latter book result, directly or indirectly, from his extraordinary stimulus, both in his writings and in person, as a philosophical scholar and interlocutor. His comments range over much of the book, but the majority of them concern chapter 2, (...) chapter 3, chapter 4, and chapter 8 (“Morality... (shrink)

La variedad de metodologías científicas dedicadas a obtener conocimiento, generar creencias y motivarla acción es amplia. La filosofía de la ciencia y de la educación ha valorado críticamente las virtudes de los diversos métodos científicos, en especial de los inductivos y deductivos. Sin embargo, la aparición de nuevos procedimientos vinculados a ciencias no académicas ha promovido el desarrollo de nuevas perspectivas reflexivas que analicen dichas virtudes. Desde los métodos controlados aleatorios hasta los procedimientosepidemiológicos o clínicos, la filosofía ha examinado las (...) virtudes y también los defectos de su puesta en práctica. El presente artículo asume que la modelación basada en evidencias empíricas es una práctica de alto interés en linguistica. Con el fin de sustanciar tal asunción, se comparan dos enfoques filosóficos de la modelación científicadistinguidos por sus respectivas líneas de investigación en torno a la noción de representación: el representacionaly el pragmático. Los enfoques se ilustran posteriormente con un caso de la linguística denominado análisissintáctico del lenguaje, dirigido a examinar muestras particulares recogidas como evidencias en fases iniciales de la modelación experimental. Como conclusión, se enfatiza que ambos enfoques filosóficos aportan elementosanalíticos realmente pertinentes para el tipo de razonamiento científico que pivota en torno a modelos y cuyo alcance en la enseñanza de las ciencias puede resultar de gran interés práctico. (shrink)

“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, philosophy and history of (...) science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for (...) selecting arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework. (shrink)

Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, who introduced (...) composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

The Abstract Conceptual Feature (ACF) framework predicts that word meaning is represented within a high‐dimensional semantic space bounded by weighted contributions of perceptual, affective, and encyclopedic information. The ACF, like latent semantic analysis, is amenable to distance metrics between any two words. We applied predictions of the ACF framework to abstract words using eyetracking via an adaptation of the classical “visual word paradigm” (VWP). Healthy adults (n = 20) selected the lexical item most related to a probe word (...) in a 4‐item written word array comprising the target and three distractors. The relation between the probe and each of the four words was determined using the semantic distance metrics derived from ACF ratings. Eye movement data indicated that the word that was most semantically related to the probe received more and longer fixations relative to distractors. Importantly, in sets where participants did not provide an overt behavioral response, the fixation rates were nonetheless significantly higher for targets than distractors, closely resembling trials where an expected response was given. Furthermore, ACF ratings which are based on individual words predicted eye fixation metrics of probe‐target similarity at least as well as latent semantic analysis ratings which are based on word co‐occurrence. The results provide further validation of Euclidean distance metrics derived from ACF ratings as a measure of one facet of the semantic relatedness of abstract words and suggest that they represent a reasonable approximation of the organization of abstract conceptual space. The data are also compatible with the broad notion that multiple sources of information (not restricted to sensorimotor and emotion information) shape the organization of abstract concepts. While the adapted “VWP” is potentially a more metacognitive task than the classical visual world paradigm, we argue that it offers potential utility for studying abstract word comprehension. (shrink)

In this paper, we study conditional preferences in abstract argumentation by introducing a new generalization of Dung-style argumentation frameworks (AFs) called Conditional Preference-based AFs (CPAFs). Each subset of arguments in a CPAF can be associated with its own preference relation. This generalizes existing approaches for preference-handling in abstract argumentation, and allows us to reason about conditional preferences in a general way. We conduct a principle-based analysis of CPAFs and compare them to related generalizations of AFs. Specifically, we (...) highlight similarities and differences to Modgil’s Extended AFs and show that our formalism can capture Value-based AFs. Moreover, we show that in some cases the introduction of conditional preferences leads to an increase in computational complexity. (shrink)

BackgroundDistorted gambling-related cognitions are tightly related to gambling problems, and are one of the main targets of treatment for disordered gambling, but their etiology remains uncertain. Although folk wisdom and some theoretical approaches have linked them to lower domain-general reasoning abilities, evidence regarding that relationship remains unconvincing.MethodIn the present cross-sectional study, the relationship between probabilistic/abstract reasoning, as measured by the Berlin Numeracy Test, and the Matrices Test, respectively, and the five dimensions of the Gambling-Related Cognitions Scale, was tested in (...) a sample of 77 patients with gambling disorder and 58 individuals without gambling problems.Results and interpretationNeither BNT nor matrices scores were significantly related to gambling-related cognitions, according to frequentist analyses, performed both considering and disregarding group in the models. Correlation Bayesian analyses largely supported the null hypothesis, i.e., the absence of relationships between the measures of interest. This pattern or results reinforces the idea that distorted cognitions do not originate in a general lack of understanding of probability or low fluid intelligence, but probably result from motivated reasoning. (shrink)

There is a widespread consensus within analytic metaphysics that the abstract versus concrete distinction, if valid at all, must be thought of as exhaustive and exclusive. I present four arguments designed to cast doubt on this consensus.

The article offers an account of the constructivist methodology in ethics and political philosophy as 1) deriving from an agnostic moral ontology and 2) proposing intersubjective justifiability as the criterion of justification for normative principles. It then asks whether constructivism, conceived in this way, can respond to the challenge of “content skepticism about practical reason”, namely whether it can provide sufficiently precise normative guidance whilst remaining faithful to its methodological commitment. The paper critically examines to alternative way of meeting (...) this challenge, namely John Rawls's original position and O'Neill's Kantian constructivism, analyses what is problematic about both, and endorses a third, possibly intermediate model. Within such a model, the basic features of the original position are accepted, but in a flexible and heuristic manner, thereby accommodating some of O'Neill's concerns. (shrink)

Abstract Finding the western just war criterion of reasonable chance of success to be a contribution to ethical decision making about armed conflict requires dealing with a number of critiques. Specifying ?probability? rather than the alternatives ?hope? or ?chance?, and raising standards of evidence involved, makes the term less vague. Expanding the concept of ?success? to include morally defensible aims that can be achieved without military victory enriches the understanding of the moral relationship between ends and means in armed (...) conflict. Asking decision makers to accept moral responsibility for the costs of possible failure is a unique contribution to the just war criteria. The enriched concept of reasonable probability of success thus offers morally significant insights to prewar jus ad bellum decisions, and can benefit ethical decision-making about whether to continue once fighting has begun. (shrink)

The main thesis of this book is that abstraction, far from being confined to higher forms of cognition, language and logical reasoning, has actually been a major driving force throughout the evolution of creatures with brains. It is manifest in emotive as well as rational thought. Wending its way through the various facets of abstraction, the book attempts to clarify - and relate - the often confusing meanings of the word 'abstract' that one may encounter even within the same (...) discipline. The unusual synoptic approach, which draws upon research in psychology, neural network theory, child language acquisition, philosophy and consciousness studies, as well as a variety of linguistic disciplines, cannot be compared directly to other books on the market that touch upon just one particular aspect of abstraction. It is aimed at a wide readership - anyone interested in the nature of abstraction and the cognitive processing and purpose behind it. (shrink)

TheConceptual Feature framework predicts that word meaning is represented within a high-dimensional semantic space bounded by weighted contributions of perceptual, affective, and encyclopedic information. The ACF, like latent semantic analysis, is amenable to distance metrics between any two words. We applied predictions of the ACF framework to abstract words using eyetracking via an adaptation of the classical “visual word paradigm”. Healthy adults selected the lexical item most related to a probe word in a 4-item written word array comprising the (...) target and three distractors. The relation between the probe and each of the four words was determined using the semantic distance metrics derived from ACF ratings. Eye movement data indicated that the word that was most semantically related to the probe received more and longer fixations relative to distractors. Importantly, in sets where participants did not provide an overt behavioral response, the fixation rates were nonetheless significantly higher for targets than distractors, closely resembling trials where an expected response was given. Furthermore, ACF ratings which are based on individual words predicted eye fixation metrics of probe-target similarity at least as well as latent semantic analysis ratings which are based on word co-occurrence. The results provide further validation of Euclidean distance metrics derived from ACF ratings as a measure of one facet of the semantic relatedness of abstract words and suggest that they represent a reasonable approximation of the organization of abstract conceptual space. The data are also compatible with the broad notion that multiple sources of information shape the organization of abstract concepts. While the adapted “VWP” is potentially a more metacognitive task than the classical visual world paradigm, we argue that it offers potential utility for studying abstract word comprehension. (shrink)

Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. (...) It also provides advice on which lines of discussion promise to be the most fruitful. (shrink)

Reasoning with the maximally consistent subsets of the premises is a well-known approach for handling contradictory information. In this paper we consider several variations of this kind of reasoning, for each one we introduce two complementary computational methods that are based on logical argumentation theory. The difference between the two approaches is in their ways of making consequences: one approach is of a declarative nature and is related to Dung-style semantics for abstract argumentation, while the other approach has a (...) more proof-theoretical flavor, extending Gentzen-style sequent calculi. The outcome of this work is a new perspective on reasoning with MCS, which shows a strong link between the latter and argumentation systems, and which can be generalized to some related formalisms. As a by-product of this we obtain soundness and completeness results for the dynamic proof systems with respect to several of Dung’s semantics. In a broader context, we believe that this work helps to better understand and evaluate the role of logic-based instantiations of argumentation frameworks. (shrink)

This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then selected (...) the top propositions—by a priori falsity—and strung them together to form ad hoc abstracts and compared these abstracts with the published summary. The results were startling: translation to logical form, followed by application of the Asimovian idea and Bar-Hillel/Carnap mathematics as elaborated into an AI/NLP proposal in Fulda (1986, 1988), produced excellent abstracts, thereby providing a proof-of-concept that merely by knowing the logical form of long text passages, one can produce reasonable abstracts of them—without actually understanding the text. We here report on a second experiment analyzing, in the exact same manner, the correspondence that followed the published text of the first experiment. While the results of this confirming experiment are less startling, they nevertheless provide additional confidence in the promise of the technique. In other words, were the results of these two experiments to generalize, that would show that logical form captures much more semantics than has heretofore been considered likely. Far from (as is commonly supposed) being merely the syntactical rewrite of text into formal notation, translation to logical form, even when undertaken with almost no knowledge about the particular predicates, individual constants, or other objects referred to in that form, might capture the core of the meaning in some important sense. -/- Note: There is a key difference in the /style/ of the texts analyzed in I and II in this long paper, divided into two only for practical reasons—space; the first text analyzed is written in a tight mathematical style, while the second is written in the discursive style of philosophy. -/- Finally, the unusual (for me) length of this two-part paper is justified by its being data-driven. (shrink)

Formal abstraction is a key instrument Aquinas employs to secure the possibility of mathematics conceived as a theoretical Aristotelian science. In this concept, mathematics investigates quantitative beings, which are grasped by means of formal abstraction in their necessary, universal, and changeless properties. Based on this, the paper divides into two main parts. In the first part (section II) I explicate Aquinas’s conception of (formal) abstraction against the background of the Aristotelian theory of science and mathematics. In the second part (section (...) III) I present and critically assess the problems associated with formal abstraction in mathematics. With all due respect to Aquinas’s genius, I find his conception of formal abstraction (as well as mathematics) unsatisfactory and list the main reasons for its failure in the conclusion. (shrink)

We present an abstract model of rationality that focuses on structural properties of attitudes. Rationality requires coherence between your attitudes, such as your beliefs, values, and intentions. We define three 'logical' conditions on attitudes: consistency, completeness, and closedness. They parallel the familiar logical conditions on beliefs, but contrast with standard rationality conditions like preference transitivity. We establish a formal correspondence between our logical conditions and standard rationality conditions. Addressing John Broome's programme 'rationality through reasoning', we formally characterize how you (...) can (not) become more logical by reasoning. Our analysis connects rationality with logic, and enables logical talk about multi-attitude psychology. (shrink)

Capacities for abstract thinking and problem‐solving are central to human cognition. Processes of abstraction allow the transfer of experiences and knowledge between contexts helping us make informed decisions in new or changing contexts. While we are often inclined to relate such reasoning capacities to individual minds and brains, they may in fact be contingent on human‐specific modes of collaboration, dialogue, and shared attention. In an experimental study, we test the hypothesis that social interaction enhances cognitive processes of rule‐induction, which (...) in turn improves problem‐solving performance. Through three sessions of increasing complexity, individuals and groups were presented with a problem‐solving task requiring them to categorize a set of visual stimuli. To assess the character of participants’ problem representations, after each training session, they were presented with a transfer task involving stimuli that differed in appearance, but shared relations among features with the training set. Besides, we compared participants’ categorization behaviors to simulated agents relying on exemplar learning. We found that groups performed superior to individuals and agents in the training sessions and were more likely to correctly generalize their observations in the transfer phase, especially in the high complexity session, suggesting that groups more effectively induced underlying categorization rules from the stimuli than individuals and agents. Crucially, variation in performance among groups was predicted by semantic diversity in members’ dialogical contributions, suggesting a link between social interaction, cognitive diversity, and abstraction. (shrink)

Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...) of success in reconstructing areas of mathematics other than arithmetic based on non-invariant abstraction principles. (shrink)

Material traces of the past are notoriously inscrutable; they rarely speak with one voice, and what they say is never unmediated. They stand as evidence only given a rich scaffolding of interpretation which is, itself, always open to challenge and revision. And yet archaeological evidence has dramatically expanded what we know of the cultural past, sometimes demonstrating a striking capacity to disrupt settled assumptions. The questions we address in Evidential Reasoning are: How are these successes realized? What gives us confidence (...) in the credibility and robustness, the trustworthiness, of the evidential claims based on archaeological data? And, what constitute best practices in building evidential claims, critically scrutinizing them and putting them to work in archaeological contexts? Rather than retreat to abstractions about how how science operates in the ideal, we approach this question by interrogating a number of close-to-the-ground case studies with the aim of teasing out the wisdom embodied in archaeological practice. The cases we consider – of fieldwork, strategies for working with old evidence, and the role of external resources – illuminate the role of various types of inferential scaffolding and bring into focus practice-grounded epistemic norms that we believe serve archaeologists better than the all-or-nothing ideals of truth and objectivity that dominate programmatic debate. (shrink)

Abstract“Reason of state” is a concept that is rarely used in contemporary legal and political philosophy, compared to everyday parlance; “public reason,” in contrast, is ubiquitous, especially in liberal philosophy, as a legitimacy‐conferring device. In this article it is argued that the unpopularity of the notion of “reason of state” is partly due to its notorious ambiguity. Three different usages of the notion can be identified: a “thin” usage (where “reason of state” is equivalent to (...) the common good); an “ironical” usage (where it is used pejoratively to denounce it as a pretext for application of illegitimate or illegal means); and a “pre‐emptive” usage (where “reason of state” functions as a legitimate second‐order exclusionary reason used to override otherwise mandatory first‐order rules of action). It is argued that only the “thin” usage is helpful in a by‐and‐large liberal‐democratic context. The article then discusses the main dilemmas related to the concept of public reason, especially in its most influential, Rawlsian interpretation, and defends the concept against common critiques. Finally, the two concepts of “reason of state” and public reason are compared, and it is argued that a “thin” usage of “reason of state” is functionally equivalent to public reason, and that both resonate with the theory of “input democracy” (focusing, as it does, on the legitimacy of reasons—or motivations—for applying coercive rules to individuals). The article also identifies a problematic feature of “reason of state”: its emphasis on the state as a privileged interpreter of such reasons and/or as identifying the pool of actors within which the “constituency” of public reason is ascertained. There are good reasons to resist both of these consequences: the former because of its potentially authoritarian consequences, the latter because of reasons provided by cosmopolitan political conceptions. (shrink)

Essays showing how environmental philosophy can have an impact on the world by integrating abstract reasoning with actual environmental practice.