CogSci2004 Symposium Abduction and Creative Inferences in Science Lorenzo Magnani (lorenzo.magnan... more CogSci2004 Symposium Abduction and Creative Inferences in Science Lorenzo Magnani ([email protected]) - Organizer, University of Pavia, Italy Atocha Aliseda ([email protected]), UNAM. Mexico City, Mexico Thomas Addis ([email protected]) and David Gooding ([email protected]), University of Portsmouth, Portsmouth, UK and University of Bath, Bath, UK John Woods ([email protected]) and Dov Gabbay ([email protected]), University of British Columbia, CA and King’s College London, UK Joke Meheus ([email protected]), Ghent University, Ghent, Belgium Matti Sintonen and Sami Paavola ([email protected],[email protected], - Discussants, University of Helsinki, Finland The symposium aims to explore abduction (inference to explanatory hypotheses), an important but neglected topic in scientific reasoning. The aim is to integrate philosophi- cal, cognitive, and computational issues. The main thesis is that abduction is a significant kind of scientific ...
Book Reviews/Comptes rendus 705 relation de nécessité qui lie la connaissance et la tolérance. De... more Book Reviews/Comptes rendus 705 relation de nécessité qui lie la connaissance et la tolérance. De plus, il serait naïf de croire que les tensions qui subsistent entre les divers groupes sont surtout de nature religieuse et que l'acquisition de connaissances relativement à la religion de l'«autre» ferait disparaître, comme par enchantement, ces tensions. Aux lendemains du onze septembre, ici comme à travers le monde, l'intolérance atteignit son paroxysme, le désir d'arborer des signes religieux fut soudainement ranimé chez plusieurs croyants, et les divers intégrismes connurent une recrudescence fulgurante. Mais ces phénomènes transcendent le cadre national et commandent une analyse politique globale. Leur ultime apaisement ne sera pas réalisé grâce à une meilleure connaissance théorique de l'autre culture ou de l'autre religion. Cet apaisement dépend aussi du règlement de conflits qui font rage à une échelle internationale. L'intolérance, le mépris et la discrimination sont des phénomènes complexes qui ne sont pas réductibles à l'analyse religieuse. Si des dissensions subsistent toujours entre islamistes et Québécois (occidentaux), ce n'est pas en premier lieu parce que les Québécois ont nécessairement une mauvaise connaissance de l'Islam. Nous devons recadrer ces tensions dans une perspective politique et sociologique plus large dès lors que l'on entend sérieusement y remédier. L'intégration au marché de travail, la reconnaissance des diplômes étrangers et un meilleur accueil des nouveaux arrivants, notamment par l'apprentissage du français, sont autant d'avenues à explorer.
IfColog journal of logics and their applications (FLAP), 2014
Commonsense reasoning often relies on the perception of similarity as well as dissimilarity betwe... more Commonsense reasoning often relies on the perception of similarity as well as dissimilarity between objects or situations. Such a perception may be expressed and summarized by means of analogical proportions, i.e., statements of the form "A is to B as C is to D". Analogy is not a mere question of similarity between two objects (or situations), but rather a matter of proportion or relation between objects. This view dates back to Aristotle and was enforced by Scholastic philosophy. Indeed, an analogical proportion equates a relation between two objects with the relation between two other objects. As such, the analogical proportion "A is to B as C is to D" poses an analogy of proportionality by (implicitly) stating that the way the two objects A and B, otherwise similar, differ is the same way as the two objects C and D, which are similar in some respects, differ. A propositional logic modeling of analogical proportions, viewed as a quaternary connective between the Boolean values of some feature pertaining to A, B, C, and D, has been recently proposed in [14]. This logical modeling amounts to precisely state that the difference between A and B is the same as the one between C and D, and that the difference between B and A is the same as the one between D and C. This view can then be proved to be equivalent to state that each time a Boolean feature is true for A and D (resp. A or D) it is also true for B and C (resp. B or C), and conversely. This latter point shows that a counterpart of a characteristic behavior of numerical geometrical proportions (a b = c d), or of numerical arithmetic proportions (a − b = c − d), namely that the product (resp. sum, in the second case) of the extremes is equal to the product (resp. the sum) of the means, is still observed in the logical setting. However, analogical proportions are not the only type of quaternary statements relying on the ideas of similarity and dissimilarity that can be imagined. They turn out to be a special case of so-called logical proportions [17]. Roughly speaking, a
Studies in Applied Philosophy, Epistemology and Rational Ethics, 2021
Psychological experiments have shown that humans do not reason according to classical logic. Ther... more Psychological experiments have shown that humans do not reason according to classical logic. Therefore, we might argue that logic-based approaches in general are not suitable for modeling human reasoning. Yet, we take a different view and are convinced that logic can help us as an underlying formalization of a cognitive theory, but claim rather that classical logic is not adequate for this purpose. In this chapter we investigate abduction and its link to human reasoning. In particular we discuss three different variations we have explored and show how they can be adequately modeled within a novel computational and integrated, cognitive theory, the Weak Completion Semantics.
Students of the literature on entailment [7], [1] are familiar with the von Wright-Geach definiti... more Students of the literature on entailment [7], [1] are familiar with the von Wright-Geach definition of entailment [6], [2]: p entails q if, and only if, by means of logic, 1 it is possible to come to know the truth of •"/ > D cp without coming to know the falsehood of p or the truth of q. A competitor of the Lewis account of entailment as strict implication, the von Wright-Geach definition has enjoyed little success. Perhaps one reason is that the definition is essentially epistemic, and entailment is not widely thought to be an epistemic notion. 2 The notion of entailment aside, however, the von Wright-Geach notion does intriguingly seem to be applicable to one interesting epistemic concept of obvious logical interest. In this article,* we suggest that the von Wright-Geach definiens, in effect, partially defines the concept of a non-circular demonstration, and we argue that the von Wright-Geach definiens can be extended in a natural way to yield a full definition for non-circular demonstration. Thus we think of the latter notion in a frankly epistemic way. We have argued in [8] and [9] that circularity of argument (petitio principii) is best thought of as an epistemic matter, and for those who agree with us on this point it may not seem too surprising that there is a connection between circularity and von Wright-Geach "entailment". For those who disagree with our thesis that petitio is essentially epistemic, we hope that establishing the connection in question may serve to diminish the disagreement. In either case, we think that this new application of the von Wright-Geach framework is interesting in its own right. In [9] we argued that the history of the subject, which has largely followed in the tradition set by Aristotle in various remarks in the Topics, De Sophisticis Elenchis, and the Rhetoric? suggests the wisdom of *Research for this paper was partly supported by Canada Council Leave Grant W750356. We would like to thank members of the Logic Seminar of Victoria University of Wellington, especially Max Cresswell, for discussions of some aspects of this paper.
There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arg... more There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arguments, hence to the existence of inductive fallacies. Although the passages are brief and few in number, it would appear that Hamblin’s resistance stems from doubts about the existence of relations of inductive consequence. This paper attempts to find a case in which such skepticism might plausibly be grounded. The case it proposes is highly conjectural, but important if true. Its greater importance lies in the threat it creates for the whole class of nonmonotonic logics.
The totality of evidence heard in a trial is usually collectively inconsistent, indeed often join... more The totality of evidence heard in a trial is usually collectively inconsistent, indeed often jointly incoherent. In those cases in which each party offers its own theory of the evidence, an abduction is forwarded which best explains a coherent subset of the evidence. Since these are themselves often jointly incoherent subsets S and S*, we have the following difficulty. Opposing theories are those which purport best to explain different sets of the evidence. In that sense, they aren’t rival theories. How could they be, since “E best explains S” and “~E best explains S*” could both be true? How can the defence’s theory of the case answer the prosecution’s if it does not in some sense contradict it? Examination of the empirical record suggests that when faced with this kind of incommensurability, jurors form their own evidential subsets, for which they themselves try to furnish seek for the best explanation. This at once raises a difficult question. On what basis does a juror select th...
In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken th... more In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken the practical turn and recovered something of its historic mission. In so doing, it has taken on in a quite general way a game-theoretic character, precisely as it was with the theory of syllogistic refutation in the Topics and On Sophistical Refutations, where Aristotle develops winning strategies for disputations. The approach that the present authors take toward the logic of practical reasoning is one in which cognitive agency is inherently strategic in its orientation. In particular, as is typically the case, individual agents set cognitive targets for themselves opportunistically, that is, in such ways that the attainment of those targets can be met with resources currently or forseeably at their disposal. This not to say that human reasoning is so game-like as to be utterly tendentious. But it does make the point that the human player of the cognitive game has no general stake in accepting undertakings that he has no chance of making good on. Throughout its long history, the traditional fallacies have been characterized as mistakes that are attractive, universal and incorrigible. In the present essay, we want to begin developing an alternative understanding of the fallacies. We will suggest that, when they are actually employed by beings like us, they are defensible strategies in game-theoretically describable pursuit of cognitive (and other) ends. In its recent return to reasoning that is agent-based and target-driven, logic has recovered something of its historic mission. In so doing, it has taken on in a quite general way a game-theoretic character, precisely as it was with
Summary. Do model-based approaches to reasoning have a stake in accounting for errors of reasonin... more Summary. Do model-based approaches to reasoning have a stake in accounting for errors of reasoning? If mainstream logic is anything to go on, a theory of bad reasoning is wholly subsumed by a theory of good reasoning, with the former construed as the complement of the latter. In an older tradition (e.g., Mill’s System of Logic), errors are best considered as a stand-alone component of any psychologically real approach to logic. Such is the assumption of this essay. Historically, logic’s almost exclusive preoccupation with error is to be found in what it may chance to say about fallacies. In the tradition that has come down to us since Aristotle, fallacies are errors of reasoning that are attractive, widely-distributed enough to be called “universal”, and difficult to correct, that is, possessed of signi.cant levels of incorrigibility.
Analogy is rife in the lives of certain species. It scarcely seems possible that we ourselves cou... more Analogy is rife in the lives of certain species. It scarcely seems possible that we ourselves could do without it. We have analogical predication, analogical pattern recognition, analogical explanation, analogical inference, and analogical argu-ment. Analogy is one of those ...
Studia Logica - An International Journal for Symbolic Logic - SLOGICA, 2008
Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “... more Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles.
In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidenc... more In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidence even in the face of a reasonable case for acquittal. This generates the highly counterintuitive-if not absurdconsequence that there being reason to think that the accused didn't do it is not reason to doubt that he did. This is the no-reason-todoubt problem. It has a technical solution provided that the evidence on which it is reasonable to think that the accused didn't do it is a different subset of the total evidence from that on which there is no reason to doubt that he did do it. It lies in the adversarial nature of criminal proceedings in the common law tradition that the subsets of the total evidence on which counsel base their opposing arguments are themselves different from and often incompatible with one another. While this solves the no-reason-to-doubt problem, it does so at the cost of triggering a second problem just as bad. It is the no-rival problem, according to which incompatible theories of the case based on incompatible subsets of the evidence cannot be rivals of one another. If neither party's case contradicts the other's then, by the burden of proof requirement, criminal convictions are impossible. Once having generated the dilemma, the object of the paper is to determine how it might be escaped.
CogSci2004 Symposium Abduction and Creative Inferences in Science Lorenzo Magnani (lorenzo.magnan... more CogSci2004 Symposium Abduction and Creative Inferences in Science Lorenzo Magnani ([email protected]) - Organizer, University of Pavia, Italy Atocha Aliseda ([email protected]), UNAM. Mexico City, Mexico Thomas Addis ([email protected]) and David Gooding ([email protected]), University of Portsmouth, Portsmouth, UK and University of Bath, Bath, UK John Woods ([email protected]) and Dov Gabbay ([email protected]), University of British Columbia, CA and King’s College London, UK Joke Meheus ([email protected]), Ghent University, Ghent, Belgium Matti Sintonen and Sami Paavola ([email protected],[email protected], - Discussants, University of Helsinki, Finland The symposium aims to explore abduction (inference to explanatory hypotheses), an important but neglected topic in scientific reasoning. The aim is to integrate philosophi- cal, cognitive, and computational issues. The main thesis is that abduction is a significant kind of scientific ...
Book Reviews/Comptes rendus 705 relation de nécessité qui lie la connaissance et la tolérance. De... more Book Reviews/Comptes rendus 705 relation de nécessité qui lie la connaissance et la tolérance. De plus, il serait naïf de croire que les tensions qui subsistent entre les divers groupes sont surtout de nature religieuse et que l'acquisition de connaissances relativement à la religion de l'«autre» ferait disparaître, comme par enchantement, ces tensions. Aux lendemains du onze septembre, ici comme à travers le monde, l'intolérance atteignit son paroxysme, le désir d'arborer des signes religieux fut soudainement ranimé chez plusieurs croyants, et les divers intégrismes connurent une recrudescence fulgurante. Mais ces phénomènes transcendent le cadre national et commandent une analyse politique globale. Leur ultime apaisement ne sera pas réalisé grâce à une meilleure connaissance théorique de l'autre culture ou de l'autre religion. Cet apaisement dépend aussi du règlement de conflits qui font rage à une échelle internationale. L'intolérance, le mépris et la discrimination sont des phénomènes complexes qui ne sont pas réductibles à l'analyse religieuse. Si des dissensions subsistent toujours entre islamistes et Québécois (occidentaux), ce n'est pas en premier lieu parce que les Québécois ont nécessairement une mauvaise connaissance de l'Islam. Nous devons recadrer ces tensions dans une perspective politique et sociologique plus large dès lors que l'on entend sérieusement y remédier. L'intégration au marché de travail, la reconnaissance des diplômes étrangers et un meilleur accueil des nouveaux arrivants, notamment par l'apprentissage du français, sont autant d'avenues à explorer.
IfColog journal of logics and their applications (FLAP), 2014
Commonsense reasoning often relies on the perception of similarity as well as dissimilarity betwe... more Commonsense reasoning often relies on the perception of similarity as well as dissimilarity between objects or situations. Such a perception may be expressed and summarized by means of analogical proportions, i.e., statements of the form "A is to B as C is to D". Analogy is not a mere question of similarity between two objects (or situations), but rather a matter of proportion or relation between objects. This view dates back to Aristotle and was enforced by Scholastic philosophy. Indeed, an analogical proportion equates a relation between two objects with the relation between two other objects. As such, the analogical proportion "A is to B as C is to D" poses an analogy of proportionality by (implicitly) stating that the way the two objects A and B, otherwise similar, differ is the same way as the two objects C and D, which are similar in some respects, differ. A propositional logic modeling of analogical proportions, viewed as a quaternary connective between the Boolean values of some feature pertaining to A, B, C, and D, has been recently proposed in [14]. This logical modeling amounts to precisely state that the difference between A and B is the same as the one between C and D, and that the difference between B and A is the same as the one between D and C. This view can then be proved to be equivalent to state that each time a Boolean feature is true for A and D (resp. A or D) it is also true for B and C (resp. B or C), and conversely. This latter point shows that a counterpart of a characteristic behavior of numerical geometrical proportions (a b = c d), or of numerical arithmetic proportions (a − b = c − d), namely that the product (resp. sum, in the second case) of the extremes is equal to the product (resp. the sum) of the means, is still observed in the logical setting. However, analogical proportions are not the only type of quaternary statements relying on the ideas of similarity and dissimilarity that can be imagined. They turn out to be a special case of so-called logical proportions [17]. Roughly speaking, a
Studies in Applied Philosophy, Epistemology and Rational Ethics, 2021
Psychological experiments have shown that humans do not reason according to classical logic. Ther... more Psychological experiments have shown that humans do not reason according to classical logic. Therefore, we might argue that logic-based approaches in general are not suitable for modeling human reasoning. Yet, we take a different view and are convinced that logic can help us as an underlying formalization of a cognitive theory, but claim rather that classical logic is not adequate for this purpose. In this chapter we investigate abduction and its link to human reasoning. In particular we discuss three different variations we have explored and show how they can be adequately modeled within a novel computational and integrated, cognitive theory, the Weak Completion Semantics.
Students of the literature on entailment [7], [1] are familiar with the von Wright-Geach definiti... more Students of the literature on entailment [7], [1] are familiar with the von Wright-Geach definition of entailment [6], [2]: p entails q if, and only if, by means of logic, 1 it is possible to come to know the truth of •"/ > D cp without coming to know the falsehood of p or the truth of q. A competitor of the Lewis account of entailment as strict implication, the von Wright-Geach definition has enjoyed little success. Perhaps one reason is that the definition is essentially epistemic, and entailment is not widely thought to be an epistemic notion. 2 The notion of entailment aside, however, the von Wright-Geach notion does intriguingly seem to be applicable to one interesting epistemic concept of obvious logical interest. In this article,* we suggest that the von Wright-Geach definiens, in effect, partially defines the concept of a non-circular demonstration, and we argue that the von Wright-Geach definiens can be extended in a natural way to yield a full definition for non-circular demonstration. Thus we think of the latter notion in a frankly epistemic way. We have argued in [8] and [9] that circularity of argument (petitio principii) is best thought of as an epistemic matter, and for those who agree with us on this point it may not seem too surprising that there is a connection between circularity and von Wright-Geach "entailment". For those who disagree with our thesis that petitio is essentially epistemic, we hope that establishing the connection in question may serve to diminish the disagreement. In either case, we think that this new application of the von Wright-Geach framework is interesting in its own right. In [9] we argued that the history of the subject, which has largely followed in the tradition set by Aristotle in various remarks in the Topics, De Sophisticis Elenchis, and the Rhetoric? suggests the wisdom of *Research for this paper was partly supported by Canada Council Leave Grant W750356. We would like to thank members of the Logic Seminar of Victoria University of Wellington, especially Max Cresswell, for discussions of some aspects of this paper.
There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arg... more There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arguments, hence to the existence of inductive fallacies. Although the passages are brief and few in number, it would appear that Hamblin’s resistance stems from doubts about the existence of relations of inductive consequence. This paper attempts to find a case in which such skepticism might plausibly be grounded. The case it proposes is highly conjectural, but important if true. Its greater importance lies in the threat it creates for the whole class of nonmonotonic logics.
The totality of evidence heard in a trial is usually collectively inconsistent, indeed often join... more The totality of evidence heard in a trial is usually collectively inconsistent, indeed often jointly incoherent. In those cases in which each party offers its own theory of the evidence, an abduction is forwarded which best explains a coherent subset of the evidence. Since these are themselves often jointly incoherent subsets S and S*, we have the following difficulty. Opposing theories are those which purport best to explain different sets of the evidence. In that sense, they aren’t rival theories. How could they be, since “E best explains S” and “~E best explains S*” could both be true? How can the defence’s theory of the case answer the prosecution’s if it does not in some sense contradict it? Examination of the empirical record suggests that when faced with this kind of incommensurability, jurors form their own evidential subsets, for which they themselves try to furnish seek for the best explanation. This at once raises a difficult question. On what basis does a juror select th...
In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken th... more In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken the practical turn and recovered something of its historic mission. In so doing, it has taken on in a quite general way a game-theoretic character, precisely as it was with the theory of syllogistic refutation in the Topics and On Sophistical Refutations, where Aristotle develops winning strategies for disputations. The approach that the present authors take toward the logic of practical reasoning is one in which cognitive agency is inherently strategic in its orientation. In particular, as is typically the case, individual agents set cognitive targets for themselves opportunistically, that is, in such ways that the attainment of those targets can be met with resources currently or forseeably at their disposal. This not to say that human reasoning is so game-like as to be utterly tendentious. But it does make the point that the human player of the cognitive game has no general stake in accepting undertakings that he has no chance of making good on. Throughout its long history, the traditional fallacies have been characterized as mistakes that are attractive, universal and incorrigible. In the present essay, we want to begin developing an alternative understanding of the fallacies. We will suggest that, when they are actually employed by beings like us, they are defensible strategies in game-theoretically describable pursuit of cognitive (and other) ends. In its recent return to reasoning that is agent-based and target-driven, logic has recovered something of its historic mission. In so doing, it has taken on in a quite general way a game-theoretic character, precisely as it was with
Summary. Do model-based approaches to reasoning have a stake in accounting for errors of reasonin... more Summary. Do model-based approaches to reasoning have a stake in accounting for errors of reasoning? If mainstream logic is anything to go on, a theory of bad reasoning is wholly subsumed by a theory of good reasoning, with the former construed as the complement of the latter. In an older tradition (e.g., Mill’s System of Logic), errors are best considered as a stand-alone component of any psychologically real approach to logic. Such is the assumption of this essay. Historically, logic’s almost exclusive preoccupation with error is to be found in what it may chance to say about fallacies. In the tradition that has come down to us since Aristotle, fallacies are errors of reasoning that are attractive, widely-distributed enough to be called “universal”, and difficult to correct, that is, possessed of signi.cant levels of incorrigibility.
Analogy is rife in the lives of certain species. It scarcely seems possible that we ourselves cou... more Analogy is rife in the lives of certain species. It scarcely seems possible that we ourselves could do without it. We have analogical predication, analogical pattern recognition, analogical explanation, analogical inference, and analogical argu-ment. Analogy is one of those ...
Studia Logica - An International Journal for Symbolic Logic - SLOGICA, 2008
Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “... more Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles.
In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidenc... more In criminal cases at common law, juries are permitted to convict on wholly circumstantial evidence even in the face of a reasonable case for acquittal. This generates the highly counterintuitive-if not absurdconsequence that there being reason to think that the accused didn't do it is not reason to doubt that he did. This is the no-reason-todoubt problem. It has a technical solution provided that the evidence on which it is reasonable to think that the accused didn't do it is a different subset of the total evidence from that on which there is no reason to doubt that he did do it. It lies in the adversarial nature of criminal proceedings in the common law tradition that the subsets of the total evidence on which counsel base their opposing arguments are themselves different from and often incompatible with one another. While this solves the no-reason-to-doubt problem, it does so at the cost of triggering a second problem just as bad. It is the no-rival problem, according to which incompatible theories of the case based on incompatible subsets of the evidence cannot be rivals of one another. If neither party's case contradicts the other's then, by the burden of proof requirement, criminal convictions are impossible. Once having generated the dilemma, the object of the paper is to determine how it might be escaped.
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