I respond to Kersten’s criticism in his article “Music and Cognitive Extension” of my approach to the musically extended emotional mind in Krueger (2014). I specify how we manipulate—and in so doing, integrate with—music when, as active listeners, we become part of a musically extended cognitive system. I also indicate how Kersten’s account might be enriched by paying closer attention to the way that music functions as an environmental artifact for emotion regulation.

This chapter offers the beginning of an enactive account of auditory experience—particularly the experience of listening sensitively to music. It investigates how sensorimotor regularities grant perceptual access to music qua music. Two specific claims are defended: (1) music manifests experientially as having complex spatial content; (2) sensorimotor regularities constrain this content. Musical content is thus brought to phenomenal presence by bodily exploring structural features of music. We enact musical content.

Why is listening to sad music pleasurable? Eerola et al. convincingly argue that we should adopt an integrative framework — encompassing biological, psycho-social, and cultural levels of explanation — to answer this question. I agree. The authors have done a great service in providing the outline of such an integrative account. But in their otherwise rich discussion of the psycho-social level of engagements with sad music, they say little about the phenomenology of such experiences — including features that may help (...) shed further light on this question. I suggest that emerging enactive perspectives on music and emotion can offer some useful resources. (shrink)

The extended mind thesis claims that mental states need not be confined to the brain or even the biological borders of the subject. Philosophers and cognitive scientists have in recent years debated the plausibility of this thesis, growing an immense body of literature. Yet despite its many supporters, there have been relatively few attempts to apply the thesis to religious studies, particularly studies of religious cognition. In this essay, I indicate how various dimensions of religious cognition might be thought of (...) as extended. In particular, I focus on the mutually-supporting relationship between religious cognition and material culture: the many things we use to organize and enact our religious practices and beliefs, from relics and rituals to songs and holy spaces. As we’ll see, taking the extended mind thesis seriously suggests that an investigation of religious material culture is, simultaneously, an investigation of religious cognition. (shrink)

In this paper, we introduce the Japanese philosopher Tetsurō Watsuji’s phenomenology of aidagara (“betweenness”) and use his analysis in the contemporary context of online space. We argue that Watsuji develops a prescient analysis anticipating modern technologically-mediated forms of expression and engagement. More precisely, we show that instead of adopting a traditional phenomenological focus on face-to-face interaction, Watsuji argues that communication technologies — which now include Internet-enabled technologies and spaces — are expressive vehicles enabling new forms of emotional expression, shared experiences, (...) and modes of betweenness that would be otherwise inaccessible. Using Watsuji’s phenomenological analysis, we argue that the Internet is not simply a sophisticated form of communication technology that expresses our subjective spatiality (although it is), but that it actually gives rise to new forms of subjective spatiality itself. We conclude with an exploration of how certain aspects of our online interconnections are hidden from lay users in ways that have significant political and ethical implications. (shrink)

Affordances are action-possibilities, ways of relating to and acting on our world. A theory of affordances helps us understand how we have bodily access to our world and what it means to enjoy such access. But what happens to bodies when this access is somehow ruptured or impeded? This question is relevant to psychopathology. People with psychiatric disorders often describe feeling as though they’ve lost access to affordances that others take for granted. Focusing on schizophrenia, depression, and autistic spectrum disorder, (...) I argue that thinking about the bodily consequences of losing access to everyday affordances can help us better understand these reports. An affordance-based approach to psychopathology can illuminate some of the causes, as well as the experiential character and content, of affective disorders in psychopathology. It can also draw our attention to some under-explored ethical and political dimensions of these issues needing further consideration. (shrink)

As technology improves, artificial systems are increasingly able to behave in human-like ways: holding a conversation; providing information, advice, and support; or taking on the role of therapist, teacher, or counsellor. This enhanced behavioural complexity, we argue, encourages deeper forms of affective engagement on the part of the human user, with the artificial agent helping to stabilise, subdue, prolong, or intensify a person’s emotional condition. Here, we defend a fictionalist account of human/AI interaction, according to which these encounters involve an (...) elaborate practise of imaginative pretence: a make-believe in which the artificial agent is attributed a life of its own. We attend, specifically, to the temporal characteristics of these fictions, and to what we imagine artificial agents are doing when we are not looking at them. (shrink)

A major part of philosophical work is engagement with argumentative texts. Engaging with an argumentative text involves correctly identifying the arguments presented in this text. In the context of teaching philosophy in school, the difficulty of correctly identifying arguments in philosophical texts is often underestimated. In this paper, I focus on one specific problem with argument identification that has been neglected in philosophy didactics thus far: the problem that there are many non-argumentative phenomena in an argumentative text that are easily (...) misidentified as expressing (part of) an argument. It is easy to fall for such phenomena if one is not aware of this problem, thereby misinterpreting the author’s intentions. This paper aims to present and discuss such phenomena, as well as to provide guidelines on how to help students recognize them. (shrink)

Opponents to consciousness in fish argue that fish do not feel pain because they do not have a neocortex, which is a necessary condition for feeling pain. A common counter-argument appeals to the multiple realizability of pain: while a neocortex might be necessary for feeling pain in humans, pain might be realized differently in fish. This paper argues, first, that it is impossible to find a criterion allowing us to demarcate between plausible and implausible cases of multiple realization of pain (...) without running into a circular argument. Second, opponents to consciousness in fish cannot be provided with reasons to believe in the multiple realizability of pain. I conclude that the debate on the existence of pain in fish is impossible to settle by relying on the multiple realization argument. (shrink)

As for most measurement procedures in the course of their development, measures of consciousness face the problem of coordination, i.e., the problem of knowing whether a measurement procedure actually measures what it is intended to measure. I focus on the case of the Perceptual Awareness Scale to illustrate how ignoring this problem leads to ambiguous interpretations of subjective reports in consciousness science. In turn, I show that empirical results based on this measurement procedure might be systematically misinterpreted.

Whether the prefrontal cortex is part of the neural substrates of consciousness is currently debated. Against prefrontal theories of consciousness, many have argued that neural activity in the prefrontal cortex does not correlate with consciousness but with subjective reports. We defend prefrontal theories of consciousness against this argument. We surmise that the requirement for reports is not a satisfying explanation of the difference in neural activity between conscious and unconscious trials, and that prefrontal theories of consciousness come out of this (...) debate unscathed. (shrink)

Is perceptual processing in dedicated sensory areas sufficient for conscious perception? Localists say ‘Yes—given some background conditions.’ Prefrontalists say ‘No: conscious perceptual experience requires the involvement of prefrontal structures.’ I review the evidence for prefrontalism. I start by presenting correlational evidence. In doing so, I answer the ‘report argument’, according to which the apparent involvement of the prefrontal cortex in consciousness stems from the requirement for reports. I then review causal evidence for prefrontalism and answer the ‘lesion argument’, which purports (...) to show that prefrontalism is wrong because lesions to the prefrontal cortex do not abolish consciousness. I conclude that multiple sources of evidence converge toward the view that the prefrontal cortex plays a significant role in consciousness. (shrink)

In this paper we adopt Sterelny's framework of the scaffolded mind, and his related dimensional approach, to highlight the many ways in which human affectivity is environmentally supported. After discussing the relationship between the scaffolded-mind view and related frameworks, such as the extended-mind view, we illustrate the many ways in which our affective states are environmentally supported by items of material culture, other people, and their interplay. To do so, we draw on empirical evidence from various disciplines, and develop phenomenological (...) considerations to distinguish different ways in which we experience the world affectively. (shrink)

Studying consciousness requires contrasting conscious and unconscious perception. While many studies have reported unconscious perceptual effects, recent work has questioned whether such effects are genuinely unconscious, or whether they are due to weak conscious perception. Some philosophers and psychologists have reacted by denying that there is such a thing as unconscious perception, or by holding that unconscious perception has been previously overestimated. This article has two parts. In the first part, I argue that the most significant attack on unconscious perception (...) commits the criterion content fallacy: the fallacy of interpreting evidence that observers were conscious of something as evidence that they were conscious of the task-relevant features of the stimuli. In the second part, I contend that the criterion content fallacy is prevalent in consciousness research. For this reason, I hold that if unconscious perception exists, scientists studying consciousness could routinely underestimate it. I conclude with methodological recommendations for moving the debate forward. (shrink)

We argue that a phenomenological approach to social space, as well as its relation to embodiment and affectivity, is crucial for understanding how the social world shows up as social in the first place—that is, as affording different forms of sharing, connection, and relatedness. We explore this idea by considering two cases where social space is experientially disrupted: Moebius Syndrome and schizophrenia. We show how this altered sense of social space emerges from subtle disruptions of embodiment and affectivity characteristic of (...) these conditions. These disruptions are instructive, we suggest, in that they highlight the foundational role that body and affect play in organizing social space—the lived context in which we first encounter one another as social agents. (shrink)

Anorexia Nervosa (AN) is an eating disorder characterised by self-starvation. Accounts of AN typically frame the disorder in individualistic terms: e.g., genetic predisposition, perceptual disturbances of body size and shape, experiential bodily disturbances. Without disputing the role these factors may play in developing AN, we instead draw attention to the way disordered eating practices in AN are actively supported by others. Specifically, we consider how Pro-Anorexia (ProAna) websites—which provide support and solidarity, tips, motivational content, a sense of community, and understanding (...) to individuals with AN—help drive and maintain AN practices. We use C. Thi Nguyen’s work on epistemic “echo chambers”, along with Maria Lugones’ work on “worlds” and “ease”, to explore the dynamics of these processes. Adopting this broader temporal and intersubjective perspective, we argue, not only helps to further illuminate the experiential character of AN but also has important clinical and therapeutic significance. (shrink)

In this paper, we develop an analysis of the structure and content of loneliness. We argue that this is an emotion of absence-an affective state in which certain social goods are regarded as out of reach for the subject of experience. By surveying the range of social goods that appear to be missing from the lonely person's perspective, we see what it is that can make this emotional condition so subjectively awful for those who undergo it, including the profound sense (...) of being unable to realise oneself, in collaboration with others. (shrink)

Consciousness is scientifically challenging to study because of its subjective aspect. This leads researchers to rely on report-based experimental paradigms in order to discover neural correlates of consciousness (NCCs). I argue that the reliance on reports has biased the search for NCCs, thus creating what I call 'methodological artefacts'. This paper has three main goals: first, describe the measurement problem in consciousness science and argue that this problem led to the emergence of methodological artefacts. Second, provide a critical assessment of (...) the NCCs put forward by the global neuronal workspace theory. Third, provide the means of dissociating genuine NCCs from methodological artefacts. (shrink)

To study consciousness, scientists need to determine when participants are conscious and when they are not. They do so with consciousness detection procedures. A recurring skeptical argument against those procedures is that they cannot be calibrated: there is no way to make sure that detection outcomes are accurate. In this article, I address two main skeptical arguments purporting to show that consciousness scientists cannot calibrate detection procedures. I conclude that there is nothing wrong with calibration in consciousness science.

In this paper, we draw on developmental findings to provide a nuanced understanding of background emotions, particularly those in depression. We demonstrate how they reflect our basic proximity (feeling of interpersonal connectedness) to others and defend both a phenomenological and a functional claim. First, we substantiate a conjecture by Fonagy & Target (International Journal of Psychoanalysis 88(4):917–937, 2007) that an important phenomenological aspect of depression is the experiential recreation of the infantile loss of proximity to significant others. Second, we argue (...) that proximity has a particular cognitive function that allows individuals to morph into a cohesive dyadic system able to carry out distributed emotion regulation. We show that elevated levels of psychological suffering connected to depressive background emotions may be explained not only in terms of a psychological loss, but also as the felt inability to enter into dyadic regulatory relations with others—an experiential constraint that decreases the individual’s ability to adapt to demanding situations. (shrink)

Local theories of consciousness state that one is conscious of a feature if it is adequately represented and processed in sensory brain areas, given some background conditions. We challenge the core prediction of local theories based on long-lasting postdictive effects demonstrating that features can be represented for hundreds of milliseconds in perceptual areas without being consciously perceived. Unlike previous empirical data aimed against local theories, localists cannot explain these effects away by conjecturing that subjects are phenomenally conscious of features that (...) they cannot report. We also discuss alternative explanations that localists could offer. (shrink)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

According to the global neuronal workspace model of consciousness, consciousness results from the global broadcast of information throughout the brain. The global neuronal workspace is mainly constituted by a fronto-parietal network. The anterior insular cortex is part of this global neuronal workspace, but the function of this region has not yet been defined within the global neuronal workspace model of consciousness. In this review, I hypothesize that the anterior insular cortex implements a cross-modal priority map, the function of which is (...) to determine priorities for the processing of information and subsequent entrance in the global neuronal workspace. (shrink)

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...) allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

Niche construction theory highlights the active role of organisms in modifying their environment. A subset of these modifications is the developmental niche, which concerns ecological, epistemic, social and symbolic legacies inherited by organisms as resources that scaffold their developmental processes. Since in this theory development is a situated process that takes place in a culturally structured environment, we may reasonably ask if implicit cultural biases may, in some cases, be responsible for maladaptive developmental niches. In this paper we wish to (...) argue for an affirmative answer. In order to do so, we first propose to conceptualize implicit bias as embodied perceptual habits, and then proceed to show that these habits are at least partially responsible for maladaptive developmental niches of children with Down syndrome and autism. With this framework we thus hope to bring together two fields of research that haven’t been explicitly connected: implicit bias and niche construction theory. Linking these two theories may bring benefits both to implicit bias researchers, who can extend this concept to characterize other sets of processes as biased, as well as to niche construction theorists, who will have a useful theoretical tool to diagnose maladaptive features of niches brought about by sociocultural biases. (shrink)

A foundationalist account of the justification of our empirical beliefs is committed to the following two claims: (1) Sense experience is a source of justification. (2) Some empirical beliefs are basic: justified without receiving their justification from any other beliefs. In this paper, I will defend each of these claims against an objection. The objection to (1) that I will discuss is due to Donald Davidson. He writes: The relation between a sensation and a belief cannot be logical, since sensations (...) are not beliefs or other propositional attitudes. What then is the relation? The answer is, I think, obvious: the relation is causal. Sensations cause some beliefs and in this sense are the basis or ground of those beliefs. But a causal explanation of a belief does not show how or why the belief is justified. [1] There are two important thoughts in this passage. The first of these is explicitly expressed, the second implied: (3) Sense-experiential states are devoid of propositional content. (4) Necessarily, if a mental state can play the role of a justifier, it has propositional content. (3) and (4) entail that a sense-experiential state cannot play the role of a justifier. If that is true, then (1) is false. This, in any case, seems to me to be Davidson's argument. In response to it, I accept (4) but reject (3). This is an unusual move for foundationalists, who tend to accept (3) and deny (4). Nevertheless, it is what I take to be the right move. (shrink)

The present paper is concerned with Helmholtz’s theory of measurement. It will be argued that an adequate understanding of this theory depends on how Helmholtz’s application of the concepts of perception and coincidence is interpreted. In contrast both to conventionalist and Kantian readings of Helmholtz’s theory, a more realistic interpretation will be suggested.

To study (un)conscious perception and test hypotheses about consciousness, researchers need procedures for determining whether subjects consciously perceive stimuli or not. This article is an introduction to a family of procedures called ‘confidence-based procedures’, which consist in interpreting metacognitive indicators as indicators of consciousness. I assess the validity and accuracy of these procedures, and answer a series of common objections to their use in consciousness research. I conclude that confidence-based procedures are valid for assessing consciousness, and, in most cases, accurate (...) enough for our practical and scientific purposes. (shrink)

Having a confirmation bias sometimes leads us to hold inaccurate beliefs. So, the puzzle goes: why do we have it? According to the influential argumentative theory of reasoning, confirmation bias emerges because the primary function of reason is not to form accurate beliefs, but to convince others that we’re right. A crucial prediction of the theory, then, is that confirmation bias should be found only in the reasoning domain. In this article, we argue that there is evidence that confirmation bias (...) does exist outside the reasoning domain. This undermines the main evidential basis for the argumentative theory of reasoning. In presenting the relevant evidence, we explore why having such confirmation bias may not be maladaptive. (shrink)

One of the leading cognitive models of auditory verbal hallucinations (AVHs) proposes such experiences result from a disturbance in the process by which inner speech is attributed to the self. Research in this area has, however, proceeded in the absence of thorough cognitive and phenomenological investigations of the nature of inner speech, against which AVHs are implicitly or explicitly defined. In this paper we begin by introducing philosophical phenomenology and highlighting its relevance to AVHs, before briefly examining the evolving literature (...) on the relation between inner experiences and AVHs. We then argue for the need for philosophical phenomenology (Phenomenology) and the traditional empirical methods of psychology for studying inner experience (phenomenology) to mutually inform each other to provide a richer and more nuanced picture of both inner experience and AVHs than either could on its own. A critical examination is undertaken of the leading model of AVHs derived from phenomenological philosophy, the ipseity disturbance model. From this we suggest issues that future work in this vein will need to consider, and examine how interdisciplinary methodologies may contribute to advances in our understanding of AVHs. Detailed suggestions are made for the direction and methodology of future work into AVHs, which we suggest should be undertaken in a context where phenomenology and physiology are both necessary, but neither sufficient. (shrink)

The experiences described in the VIP transcripts are incredibly varied and yet frequently explicitly labelled by participants as "voices." How can we make sense of this? If we reflect carefully on uses of the word "voice", we see that it can express at least two entirely different concepts, which pick out categorically different phenomena. One concept picks out a speech sound (e.g. "This synthesizer has a "voice" setting"). Another concept picks out a specific agent (e.g. "I hear two voices: one (...) is a ten year-old boy…"). This chapter explores how these two concepts are related to one another in the context of voice-hearing. (shrink)

Externalist theories hold that a comprehensive understanding of mental disorder cannot be achieved unless we attend to factors that lie outside of the head: neural explanations alone will not fully capture the complex dependencies that exist between an individual’s psychiatric condition and her social, cultural, and material environment. Here, we firstly offer a taxonomy of ways in which the externalist viewpoint can be understood, and unpack its commitments concerning the nature and physical realization of mental disorder. Secondly, we apply a (...) strongly externalist approach to the case of Autistic Spectrum Disorder, and argue that this condition can be illuminated by appeal to the hypothesis of extended cognition. We conclude by briefly considering the significance this strongly externalist approach may have for psychiatric practice and pedagogy. (shrink)

The aim of this paper is to show that the French philosopher and historian of science Abel Rey played a more influential role in the formative phase of the Vienna Circle than hitherto supposed. On the whole, it will be argued that Rey's contribution had political impact. His interpretation of "modern physics" in 1907 in the face of the alleged "bankruptcy of science" should be appreciated as a masterpiece of applied enlightenment thought. As such, it was especially paradigmatic for Philipp (...) Frank's "positivist" defense of the theory of relativity and quantum mechanics against the irrationalist tendencies of the 1920s and 1930s. (shrink)

This chapter presents the perceptual reality monitoring theory of consciousness (PRM). PRM is a higher-order theory of consciousness. It holds that consciousness involves monitoring the reliability of one’s own sensory signals. I explain how a perceptual reality monitoring mechanism computes the higher order representations that are crucial for consciousness. While PRM accounts for the difference between conscious and unconscious states, it does not explain, on its own, why experiences feel the way they do—the phenomenal character of experience. PRM is compatible (...) with multiple theories of phenomenal character. Here, I show how to combine it with ‘Mental Quality Space’ theory. I finish by presenting empirical evidence for PRM, as well as some of its predictions. (shrink)

Like many other philosophical disciplines, ethics is sometimes highly abstract. And many key notions of the discipline are vague, ambiguous or both. Abstractness, vagueness, and ambiguity invite confusion. My objective in this paper is to draw attention to a serious problem that, despite being widespread, has so far remained largely unrecognized: the confusion of different questions in teaching ethics. This confusion occurs, for example, when a philosopher’s viewpoint is presented as an answer to one question, but in fact, the philosopher (...) is addressing a different question with that viewpoint. In the first part of this paper, I will present and clarify several ethical questions that are often confused, and point out damaging consequences that the confusion of such questions entails. In the second part, I will demonstrate the confusion of ethical questions by drawing attention to cases of confused teaching of Schopenhauer’s ethics. Finally, for those interested, I outline how Schopenhauer’s ethics could be taught without confusion. (shrink)

According to infinitism, all justification comes from an infinite series of reasons. Peter Klein defends infinitism as the correct solution to the regress problem by rejecting two alternative solutions: foundationalism and coherentism. I focus on Klein's argument against foundationalism, which relies on the premise that there is no justification without meta-justification. This premise is incompatible with dogmatic foundationalism as defended by Michael Huemer and Time Pryor. It does not, however, conflict with non-dogmatic foundationalism. Whereas dogmatic foundationalism rejects the need for (...) any form of meta-justification, non-dogmatic foundationalism merely rejects Laurence BonJour's claim that meta-justification must come from beliefs. Unlike its dogmatic counterpart, non-dogmatic foundationalism can allow for basic beliefs to receive meta-justification from non-doxastic sources such as experiences and memories. Construed thus, non-dogmatic foundationalism is compatible with Klein's principle that there is no justification without meta-justification. I conclude that Klein's rejection of foundationalism. fails. Nevertheless, I agree with Klein that when in response to a skeptical challenge we engage in the activity of defending our beliefs, the number of reasons we can give is at least in principle infinite. I argue that this type of infinity is benign because, when we continue to give reasons, we will eventually merely repeat previously stated reasons. Consequently, I reject Klein's claim that the more reasons we give the more we increase the justification of our beliefs. (shrink)

Some moral value is transparent just in case an agent with average mental capacities can feasibly come to know whether some entity does, or does not, possess that value. In this paper, I consider whether legitimacy—that is, the property of exercises of political power to be permissible—is transparent. Implicit in much theorising about legitimacy is the idea that it is. I will offer two counter-arguments. First, injustice can defeat legitimacy, and injustice can be intransparent. Second, legitimacy can play a critical (...) function in our practical thought, which sometimes requires intransparency. (shrink)

We resist Schilbach et al.’s characterization of the “social perception” approach to social cognition as a “spectator theory” of other minds. We show how the social perception view acknowledges the crucial role interaction plays in enabling social understanding. We also highlight a dilemma Schilbach et al. face in attempting to distinguish their second person approach from the social perception view.

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...) be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k : Is (...) there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

This is a review of: God's Rational Warriors: The Rationality of Faith Considered.