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In this note we consider Gentzen's first ordinal notation, used in his first published proof of the consistency of Peano Arithmetic (1936). It is a decimal notation, quite different from our current notations. We give a rule to translate this notation into our usual set-theoretic notation and we show some of its peculiarities. Then we indicate how to decode Gentzen's assignment of ordinal notations to derivations and give some examples. Finally, we go through his proof of their decrease after the application of his reduction procedure, giving further examples.  相似文献   
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Pistone  Paolo  Tranchini  Luca  Petrolo  Mattia 《Studia Logica》2022,110(2):545-592
Studia Logica - In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative...  相似文献   
184.
Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: although its rules are intuitively unstable, they pass the test of existence of expansions. Although most authors view instabilities of this kind as too subtle to be detected by the requirement of existence of expansions, we first discuss a case showing that this requirement can indeed detect instabilities of this kind, and then show how the expansions for disjunction-like connectives have to be reformulated to rule out quantum disjunction. We show how the alternative pattern for expansions can be formulated for connectives and quantifiers whose rules satisfy a scheme originally developed by Prawitz and Schroeder-Heister. Finally we compare our proposal with a recent one due to Jacinto and Read.  相似文献   
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Past research at the nexus of motor control and perception investigated the role of perspective taking in many behavioral and neuroimaging studies. Some investigators addressed the issue of one's own vs. others' action imagination, but the possible effects of a front or a back view in imagining others' actions have so far been neglected. We report two 'single trial' experiments in which a total of 640 participants were asked to imagine a person performing a manual action - either in a front or in a back view - and then to indicate the hand used by the imagined person during movement execution. In such a task, we assume the existence of two distinct biases: a perceptual-mnemonic bias due to subjects' visual experience of others' actions, encouraging them to imagine right-handed movements, and a motor bias due to subjects' experience of self-made actions, encouraging them to imagine movements performed with the same hand as their dominant hand. We hypothesized that a greater involvement of motor representations in the back view compared to the front view could result in an increased correspondence between one's own manual preference and the hand used by the imagined agent in the former condition. The results of both experiments were consistent with this hypothesis, suggesting that while imagining others' actions we employ motor simulations in different degrees according to the perspective adopted.  相似文献   
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Since about two decades neuroscientists have systematically faced the problem of consciousness: the aim is to discover the neural activity specifically related to conscious perceptions, i.e. the biological properties of what philosophers call qualia. In this view, a neural correlate of consciousness (NCC) is a precise pattern of brain activity that specifically accompanies a particular conscious experience. Almost all studies aimed at investigating the NCC have been carried out in the visual system. One of the most promising paradigms is based on sensory stimuli which elicit bistable percepts, as they allow to decouple subjective perception from the characteristics of the physical stimulation. Such kind of perception can be produced in the visual modality by using particular images (e.g. Rubin's vase/face figure) or by presenting two dissimilar stimuli separately to the two eyes (binocular rivalry). The stimuli compete for perceptual dominance and each image is visible in turn for a few seconds, while the other is suppressed. The use of this methodology has led to important findings concerning visual consciousness, which are briefly discussed. For the investigation of auditory consciousness, a similar stimulation paradigm can be achieved by using dichotic listening, consisting in two different stimuli presented each to one ear, which compete for perception (binaural rivalry). The principal aim of the present mini-review is to discuss the few contributes facing the issue of auditory consciousness and to advance the use of dichotic listening and binaural rivalry as valid tools for its investigation.  相似文献   
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According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view.  相似文献   
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During intractable conflicts, “competitive victimhood” refers to the subjective belief that one's own ingroup has suffered more than the outgroup. Although competitive victimhood is considered an important inhibitor of reconciliation processes, no research has attempted to examine ways of reducing it. The present study aims to fill this gap. Kosovar Albanians students (N = 170) were asked to report their perception of ingroup and outgroup victimhood during the protracted violence between Serbs and Albanians in Kosovo. Our findings revealed that frequent and high‐quality extended contact with outgroup members and identification with a common ingroup reduced competitive victimhood. The effects of extended contact and common ingroup identification were fully mediated by increased perspective taking and trust toward the outgroup, and by decreased outgroup infrahumanization. The implications of these results for restoring fractured intergroup relations are discussed.  相似文献   
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