The Pinocchio paradox, devised by Veronique Eldridge-Smith in February 2001, is a counter-example to solutions to the Liar that restrict the use or definition of semantic predicates. Pinocchio’s nose grows if and only if what he is stating is false, and Pinocchio says ‘My nose is growing’. In this statement, ‘is growing’ has its normal meaning and is not a semantic predicate. If Pinocchio’s nose is growing it is because he is saying something false; otherwise, it is (...) not growing. ‘Because’ stands here for a non-semantic relation; it might be supposed to be causal or of some other nature, but it is not semantic. The paradox is discussed in relation to Tarski’s and Kripke’s theories of truth. Although the paradox is not necessarily a counter-example to a theory of a truth predicate, it is a problem for a theory of truth of the kind preserved by validity. (shrink)

The Liar paradox is an obstacle to a theory of truth, but a Liar sentence need not contain a semantic predicate. The Pinocchio paradox, devised by Veronique Eldridge-Smith, was the first published paradox to show this. Pinocchio’s nose grows if, and only if, what Pinocchio is saying is untrue. What happens if Pinocchio says that his nose is growing? Eldridge-Smith and Eldridge-Smith : 212-5, 2010) posed the Pinocchio paradox against the Tarskian-Kripkean solutions to (...) the Liar paradox that use language hierarchies. Eldridge-Smith : 306-8, 2011) also set the Pinocchio paradox against semantic dialetheic solutions to the Liar. Beall argued the Pinocchio story was just an impossible story. Eldridge-Smith : 749-752, 2012b) responded that unless the T-schema is a necessary truth of some sort, the Pinocchio principle is possible. Luna : 77–86, 2016) argues that the Pinocchio contradiction proves the principle is false. D’Agostini & Ficara discuss a more plausible physical truth-tracking trait, the Blushing Liar, and argue that the Pinocchio contradiction is not a metaphysical dialetheia. I respond to Luna, and D’Agostini & Ficara, and prove that the Pinocchio paradox is a counterexample to hierarchical solutions to the Liar. (shrink)

Semantic dialetheists astutely dodge Explosion, the logical contagion of everything being true if a single contradiction is true. A dialetheia is contained in their semantics, and sustained by a paraconsistent logic. Graham Priest has shown that this is a solution to the Liar paradox. I use the Pinocchio paradox, devised by Veronique Eldridge-Smith, as a counter-example. The Pinocchio paradox turns on the truth of Pinocchio, whose nose grows if and only if what he is saying is not (...) true, saying ‘My nose is growing’. It is not just a matter of interpretation whether Pinocchio’s nose is and is not growing. (shrink)

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction. (shrink)

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution of (...) identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate. A logic for truth implementing this restriction is a monotonic extension of a classical first order logic, or indeed a formalizable fragment of natural language. Proofs of Tarski’s Indefinability of Truth theorem are invalid in this logic. This approach generalizes to invalidate proofs of Liar-like paradoxes, particularly the predicate form of the Knower paradox. Consequently, such a logic can be further extended in a way that avoids Montague’s theorem for such a system. Yet, the semantic status of a Liar sentence is not fully resolved. It is no longer overdetermined; it is now underdetermined. (shrink)

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...) for modal hypodoxes as duals to known paradoxes. I also try to continue this search further by mapping the relations between some paradoxes and hypodoxes in duality squares. This investigation increases the known extension of the concept of hypodox, and the duality relation between paradoxes and hypodoxes assists in finding some of these. (shrink)

There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective pathologies lie. Having different (...) pathologies, they are paradoxes of different kinds. Furthermore, each of these satisfaction paradoxes has an analogue with the same pathology in set theory. Therefore, these analogues are respectively of the same two kinds. This level of abstraction is significant in that it tracks two related but different pathologies. Thus, not all paradoxes of semantics and set theory share the same pathology: there are at least two kinds of paradox cutting across the semantic and set-theoretic distinction. (shrink)

The Pinocchio paradox poses one dialetheia too many for semantic dialetheists (Eldridge-Smith 2011). However, Beall (2011) thinks that the Pinocchio scenario is merely an impossible story, like that of the village barber who shaves just those villagers who do not shave themselves. Meanwhile, Beall maintains that Liar paradoxes generate dialetheia. The Barber scenario is self-contradictory, yet the Pinocchio scenario requires a principle of truth for a contradiction. In this and other respects the Pinocchio paradox is a version of (...) the Liar, unlike the Barber. One wonders why some Liars would be impossible if others generate dialetheias. (shrink)

For a dialetheist, it is rational to believe that true contradictions exist. However, we argue that a dialetheist faces a complex dilemma given some bridge principles for rational beliefs that connect possibility and probability, including the so-called ‘Regularity Principle’. Either her belief is not doxastically possible even for her, or she must assign positive credence to the proposition that dialetheia exists. The former makes her belief prima facie self-defeating. The latter seems to compel her to choose between several more fine-grained (...) options, each of which seems undesirable for a regular and rational probability theory. It is unclear how a dialetheist would stay rationally regular, so we pose this challenge, seeking a response from a dialetheist. (shrink)

One way of resolving a paradox is to defuse it to a hypodox. This way is relatively unknown though. The goal of this paper is to explain this way with varied examples. The hypodoxes are themselves a broad class: both the Truth-teller and the 21st birthday of someone born on 29th February can be construed as hypodoxes. The most familiar kind of relation between paradoxes and hypodoxes is exemplified by the relation between the Liar and the Truth-teller. This article concerns (...) a second kind where a paradox is defused to a hypodox by restricting or rejecting some granted principles. The Liar paradox has this second kind of relation to a Liar hypodox, which will be introduced. In some cases, defusing a paradox to a hypodox is only a partial resolution, as the hypodox itself may then need resolving. Even so, such a partial resolution decomposes a complex problem into more easily understood problems. Moreover, I compare the result of defusing a paradox to a hypodox with the results of resolving paradoxes in other ways. I give four examples. The first is mainly pedagogic, concerning a birthday. The second is a lightweight legal case, presenting a parking voucher paradox. The third is a formal system in which a Liar and Liar-like sentences are hypodoxical. The fourth is a philosophical critique of ways of solving Bertrand’s chord paradox. (shrink)

Is the set of all self-membered sets, S, a member of itself? In naive set theory, this is Russell’s hypodox. By the Laws of Excluded Middle and Non-contradiction, S is a member of itself xor it is not, but no principle of classical logic or naive set theory determines which. (Herein, ‘xor’ extends English with a specifically exclusive disjunction.) As a hypodox, the Truth-teller is a sentence that says of itself simply that it is true; by the above mentioned principles, (...) the Truth-teller is true xor not true, but no principle of classical logic or naive truth determines which. Many concepts that have paradoxes have related hypodoxes, although the focus here is on these two. I argue that the Truth-teller does not rely on a principle of truth, in particular it does not rely on the T-schema. I also argue that Russell’s hypodox does not rely on Comprehension. Yet I relate Russell’s paradox and hypodox based on involution functions. The Liar and the Truth-teller are also related by means of involutions. Relations based on these involution functions can be represented in duality squares. Although hypodoxes are not paradoxes, these involution functions and duality relations warrant some commonality in a correct solution to a paradox and its dual hypodox. Using this and some other premises, I provide novel arguments supporting non-classical solutions for the Liar paradox and the significance of Russell’s hypodox for solutions to Russell’s paradox. (shrink)

In ‘Many-valued Logics’, a lecture broadcast over New Zealand's public radio in 1957, Arthur N. Prior (1914–1969) complained that conjunctions are put ‘to something like forced labour’ in Łukasiewicz's three-valued semantics, Ł3. In this paper, we discuss what Prior might have meant by this.

In ‘The Unsatisfied Paradox’ (The Reasoner 6(12), p.184-5), Peter Eldridge-Smith has argued that no unique solution for the logical paradoxes is likely to exist in the presence of the following two kinds of paradox: 1. The Unsatisfied kind. 2. The Satisfiable kind. We argue that both kinds of paradoxes typically contain some kind of self-reference used for an attempt of self-diagonalization, and that consequently they may solvable in the same way, namely, by the acknowledgement that no intensional object (...) is available to itself for reference or quantification. (shrink)

This paper argues that, contrary to P. Eldridge-Smith, the so-called Pinocchio paradox affords no argument against ‘simply semantic dialetheism’.

We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.

This book presents the framework for a new, comprehensive approach to cognitive science. The proposed paradigm, enaction, offers an alternative to cognitive science's classical, first-generation Computational Theory of Mind. _Enaction_, first articulated by Varela, Thompson, and Rosch in _The Embodied Mind_, breaks from CTM's formalisms of information processing and symbolic representations to view cognition as grounded in the sensorimotor dynamics of the interactions between a living organism and its environment. A living organism enacts the world it lives in; its embodied (...) action in the world constitutes its perception and thereby grounds its cognition. _Enaction_ offers a range of perspectives on this exciting new approach to embodied cognitive science. Some chapters offer manifestos for the enaction paradigm; others address specific areas of research, including artificial intelligence, developmental psychology, neuroscience, language, phenomenology, and culture and cognition. Three themes emerge as testimony to the originality and specificity of enaction as a paradigm: the relation between first-person lived experience and third-person natural science; the ambition to provide an encompassing framework applicable at levels from the cell to society; and the difficulties of reflexivity. Taken together, the chapters offer nothing less than the framework for a far-reaching renewal of cognitive science. Contributors: Renaud Barbaras, Didier Bottineau, Giovanna Colombetti, Diego Cosmelli, Hanne De Jaegher, Ezequiel A. Di Paolo. Andreas K. Engel, Olivier Gapenne, Véronique Havelange, Edwin Hutchins, Michel Le Van Quyen, Rafael E. Núñez, Marieke Rohde, Benny Shanon, Maxine Sheets-Johnstone, Adam Sheya, Linda B. Smith, John Stewart, Evan Thompson. (shrink)

Chaotic dynamics has been hailed as the third great scientific revolution in physics this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues which arise. In particular, he explores the new kinds of explanation of empirical phenomena which modern dynamics can (...) deliver. Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory. (shrink)

The aim of this literature review was to compose a narrative review supported by a systematic approach to critically identify and examine concerns about accountability and the allocation of responsibility and legal liability as applied to the clinician and the technologist as applied the use of opaque AI-powered systems in clinical decision making. This review questions if it is permissible for a clinician to use an opaque AI system in clinical decision making and if a patient was harmed as a (...) result of using a clinician using an AIS’s suggestion, how would responsibility and legal liability be allocated? Literature was systematically searched, retrieved, and reviewed from nine databases, which also included items from three clinical professional regulators, as well as relevant grey literature from governmental and non-governmental organisations. This literature was subjected to inclusion/exclusion criteria; those items found relevant to this review underwent data extraction. This review found that there are multiple concerns about opacity, accountability, responsibility and liability when considering the stakeholders of technologists and clinicians in the creation and use of AIS in clinical decision making. Accountability is challenged when the AIS used is opaque, and allocation of responsibility is somewhat unclear. Legal analysis would help stakeholders to understand their obligations and prepare should an undesirable scenario of patient harm eventuate when AIS were used. (shrink)

In this chapter we explain what the no-difference challenge is, focusing in particular on act consequentialism. We talk about how different theories of causation affect the no-difference challenge; how the challenge shows up in real-world cases including voting, global labour injustice, global poverty, and climate change; and we work through a number of the solutions to the challenge that have been offered, arguing that many fail to actually meet it. We defend and extend one solution that does, and present a (...) further solution of our own. (shrink)

Background: Studies have found that children with Autism Spectrum Disorder (ASD) are more likely to make errors in appropriately producing referring expressions (‘the dog’ vs. ‘the black dog’) than are controls but comprehend them with equal facility. We tested whether this anomaly arises because comprehension studies have focused on manipulating perspective-taking at a ‘generic speaker’ level. Method: We compared 24 autistic eight- to eleven-year-olds with 24 well-matched neuro-typical controls. Children interpreted requests (e.g. ‘Can I have that ball?’) in contexts which (...) would be ambiguous (i.e. because the child can see two balls) if perspective-taking were not utilized. In the interlocutor-specific perspective-taking condition, the target was the particular object which was new for the speaker. Children needed to take into account what the speaker had played with before and the fact that they were now expressing excitement about something new. In two control ‘speaker-generic’ conditions we tested children’s ability to take the visual perspective of the speaker (where any speaker who stood behind a particular barrier would have the same perspective). Results: The autistic group were significantly less likely to select the target and significantly more likely to request clarification in the ‘interlocutor-specific’ condition. Performance in the ‘interlocutor-generic’ (visual) perspective taking conditions did not differ between groups. Conclusion: Autistic children, even those who are not intellectually-impaired, tend to have more difficulty than neuro-typical peers in comprehending referring expressions when this requires understanding that people comment on what is new for them. (shrink)

When we from what may be called Aristotle's Cosmology turn to his work traditionally called the Metaphysics, we are faced with something—an inquiry or doctrine—of a surprisingly different character. There what we find is the exposition of a sort or degree of knowledge superior to that of the Sciences. This is what we call his metaphysics, but he does not so name it; he names it Wisdom, or Theoretical Wisdom. At times he calls it First Philosophy, or, again, Theology. It (...) is par excellence knowledge, the consummate achievement of theoretic or cognitive power. It is the supreme Science, scientia scientiarum. Of what is it knowledge? It is knowledge not about, but of, whatsoever is real, really real, and of its universal and necessary attributes. The latter are distinct from one another, and from that to which they indissolubly belong, and metaphysics apprehends all this in its distinctions and interconnections. Further, it is a knowledge of itself, a knowledge of knowledge, and so a Wissenschaftslehre, or“super-Logic.” Finally, it is knowledge commensurate with the real Universe as a whole, so that nothing which is genuinely a part of that escapes its view. (shrink)

By “voluntary actions” we mean the actions that are willed to be done in a prior volition, and which are realized by our own power, rather than by an external force. Running up the slope of a hill for exercise is a voluntary action, but falling down the slope is not. The volition, or the “decision” to undertake an action, may be the outcome of a deliberation about which of several actions to undertake, or it may be a spontaneous decision (...) to engage in a certain action, without being preceded by a deliberative process. (shrink)

In Episode 1, we introduced the very idea of a negation-incomplete formalized theory T . We noted that if we aim to construct a theory of basic arithmetic, we’ll ideally like the theory to be able to prove all the truths expressible in the language of basic arithmetic, and hence to be negation complete. But Gödel’s First Incompleteness Theorem says, very roughly, that a nice theory T containing enough arithmetic will always be negation incomplete. Now, the Theorem comes in two (...) flavours, depending on whether we cash out the idea of being ‘nice enough’ in terms of (i) the semantic idea of T ’s being a sound theory, or (ii) the idea of odel’s own T ’s being a consistent theory which proves enough arithmetic. And we noted that G¨. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Elizabeth Hanson-Smith AUGUSTINE'S CONFESSIONS: THE CONCRETE REFERENT The chief problem facing critics who would consider the Confessions as both a literary work and a philosophical treatise remains the connection between the first nine books, the autobiography, and the last four, the metaphysical speculations on time, eternity, epistemology, and theology. A persistent desire to justify the work as an aesthetic whole has led critics on a search for thematic (...) and structural unity; they have been more successful in the former endeavor than in the latter. The interpretation of the work's plot as a peregrinatio animae, a pilgrimage of the soul, is now generally accepted as definitive; but attempts to find structural unity within that broad outline have not progressed beyond Marrou's characterization of the work as a "musical composition."1 His analogy to music has not been anchored to any concrete structural features of the Confessions and does not illuminate the connections between its content and its form. I shall attempt to prove that a unified structural model for the development of the soul in the Confessions does indeed exist and is outlined in Augustine's earlier discursive work, the De quantitate animae.2 The seven degrees or steps (gradus) of the soul's ascent to God, as sketched in the De quantitate, are deliberately fleshed out and translated into a mimetic, narrative version in the Confessions. Placing the two works side by side gives us a unique opportunity to examine a typically medieval literary form, the educative journey, in its relationship to its philosophical premises. Such a study reveals the inner formal unity of the literary work and, further, provides us with significant evidence for a re-examination of Augustine's Neo-Platonism, his supposed dualism, and his influence on later works, both literary and philosophical. In the Confessions we see one of the earliest Christian blendings of several models: first, the educative journey, the archetypal pattern familiar from the Odyssey, the Aeneid, and even The Golden Ass of Apuleius. Augustine's version, like later medieval cosmologies, also 176 Elizabeth Hanson-Smith1 77 includes a vision of the cosmic order and its relationship to human order, elements of significance in pagan philosophical works such as the Timaeus and the Dream of Scipio. But Augustine's journey also depends upon the Judeo-Christian conception of history as a series of figurae or types of the Messiah: the protagonist of the Christian educative journey joins thefigurae of the Biblical past. Christ's incarnation as Mansoul and his life on earth are the pattern of universal history from Fall to Apocalypse; Christ's life becomes a figurative pattern for the actions of Everyman.3 The Confessions is one of the earliest Christian works to apply this pattern in a narrative context. Augustine was also preoccupied with the Hexaemeron, the six days of creation and the seventh of rest. He views the exegesis of Genesis as an explanation of all subsequent life; the Ages of Man recapitulate the days of creation, as do the sacraments and the seven steps in the ascent of the soul. Thus, to the figurative pattern of Christ's "pilgrimage" from creating Logos to Incarnate God and finally to judge at the Second Coming, Augustine applies the schematic seven-fold ascent found in the De quantitate: the soul passes through the ascending steps of animation, sense, art, religion, tranquillity, initiation, and contemplation—each of which is figured by or patterned on a stage in Christ's life, as represented by the sacraments, and each of which, further, reflects a segment of universal history. The seven steps are not simply the movement of the individual soul, but the progress of Mansoul on its journey to Apocalypse. The stylistic differences between the two works—one an exposition written as Socratic dialogue, the other a metaphorical personal narrative —will no doubt give rise to differing interpretations; but one may, I think, object to certain details I suggest while still agreeing that the De quantitate provides the structuring model. Let me first define the major areas of difference between the two works. In the De quantitate, each of the levels or steps of the soul takes on a discrete, separate... (shrink)

Saint Bonaventure's Journey of the Soul into God is one of the most important works in the Christian mystical tradition. In this volume, Randall Smith provides the first comprehensive commentary in English of Bonaventure's classic text. He situates the work within its historical, intellectual, and cultural contexts.

Dans cet article je propose d'exprimer et de défendre une conception des pratiques et du domaine de discours mathématiques qui soit sensible, d'une part, au pluralisme des relations entre pratiques inférentielles et intérêts, et d'autre part, à la structure objective et déterminante des concepts mathématiques. J'ébauche tout d'abord une caractérisation générale des pratiques, pour ensuite préciser certains phénomènes propres aux pratiques mathématiques. Suit un recensement des idées qui se dégagent des arguments pluralistes, et de celles qui sont à retenir. Mais (...) je défends par la suite la nécessité d'une forme de réalisme mathématique, qui toutefois ne peut être le réalisme d'objets que prônent les partisans de l'argument d'indispensabilité. Je défends plutôt un réalisme des concepts, soutenu par ce que je baptise l'« argument de la contrainte ». (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Abstract:The term “soul” is found throughout John Dewey’s work, particularly when discussing self-realization and meaningfulness. Soul can be easily associated with religious connotations, and yet it is well accepted that he did not imply such. So, then, what did he mean? In his early writings, he shifted away from theologically inspired language and toward a conception composed in naturalized terms. This, no doubt, can be confusing to uninitiated readers. While extensive analyses have been written on his philosophy of spirit and (...) metaphysics, they can leave one wondering: what is a conception of soul that is consistent with Dewey’s philosophy of experience and education, and how might it be made accessible to students in teacher preparation programs? The key for understanding this concept exists in his early work, but the characteristics need to be drawn out so they can be read more clearly into his later works. This article provides an analysis of (1) four of his early works and (2) scholarly explications on the subject in order to lay a framework for a Deweyan conception of soul as conceived within the individual, psycho-physiological makeup. (shrink)

Recognition of the place of good fortune in people's lives occupies an important place in the liberal egalitarian perspective on social justice. Elaboration of this notion sets the scene for a discussion of three senses of moral progress in human geography. The first is the creation of a more equal world, in which the morally arbitrary contingencies of good or bad fortune are transcended. The second is the undertaking of geographical research which might promote a process of equalization. The third (...) is the pursuit of professional practice and institutions sensitive to the needs of persons in places of misfortune. Moral progress in human geography involves a spatially extensive ethic of care, to combat contemporary forces encouraging parochialism and the perpetuation of inequality. (shrink)

This is a new release of the original 1938 edition.