Ioannis G. Ntagkas

The Republic rarely speaks of piety; yet religious concerns inform more of its treatment of poetry than readers acknowledge. A pair of tripartite rankings in Book 10 has puzzled interpreters: first the triad Form-couch-painting, then the ostensibly equivalent triad of a flute’s or bridle’s user-maker-imitator. The tripartitions work better together if one recognizes the divinity at work behind Athena’s gifts the flute and bridle. This mythic reading reveals the imitator to stand, yet again, in opposition to the gods; but it also points toward an ambiguity about knowledge that Plato has forcibly excluded from his discussion.

Two great evaluative questions about The Birth of Tragedy ask how accurate the book is about Greece’s “tragic age,” and how nostalgic it is for that age. Wilamowitz raised the question of accuracy as soon as the book was published, and the issue has never gone away. As for nostalgia, even without accepting extreme versions of the charge, you can still worry that BT portrays Socrates as such a calamity—a monstrosity, and therefore a freakish birth, something that did not have to happen—as to invite the pious wish that he had never come along, and that the tragic age of Greece could have lived a little longer.Both evaluative questions are implicated in a perennial interpretive question: who is Nietzsche’s god ..

When the Phaedrus produces an account of eros that goes beyond earlier oversimplifying terms, it rests its analysis on a distinction between human and divine. The dialogue’s attempts to articulate this distinction repeatedly fail. In part they rest on the difference between right and left, but in ways that problematize that difference as well. In the end this difficulty in definition casts a shadow over the prospect of the effective reciprocation of love, because the loved one will not be able to tell the difference between a lover in pursuit crazed by divine eros and the lover who is crazed in the ordinary and destructive fashion.

Plato, often cited as a founding father of Western philosophy, set out ideas in the _Republic_ regarding the nature of justice, order, and the character of the just individual, that endure into the modern day. _The_ _Routledge Guidebook to Plato’s Republic_ introduces the major themes in Plato’s great book and acts as a companion for reading the work, examining: The context of Plato’s work and the background to his writing Each separate part of the text in relation to its goals, meanings and impact The reception the book received when first seen by the world The relevance of Plato’s work to modern philosophy, its legacy and influence. With further reading included throughout, this text follows Plato’s original work closely, making it essential reading for all students of philosophy, and all those wishing to get to grips with this classic work.

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions.

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond.

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

Often coherentism is taken to be the view that justification is solely a function of the coherence among a person's beliefs. I offer a counterexample to the idea that when so understood coherence is sufficient for justification. I then argue that the counterexample will still work if coherence is understood as coherence among a person's beliefs and experiences. I defend a form of nondoxastic foundationalism that takes sensations and philosophical intuitions as basic and sees nearly all other justification as depending on inference to the best explanation. I take up Wilfrid Sellars's Dilemma, which starts with the idea that the foundations must be either propositional in nature or not. The argument continues: if they are, they stand in need of justification; if they are not, they cannot confer justification. It concludes that there cannot be foundations that confer justification on other beliefs. I deny both horns of this dilemma, arguing that philosophical intuitions are propositional but do not stand in need of justification and that sensations are not propositional but can confer justification on perceptual beliefs

I begin by distinguishing four different versions of the argument from evil that start from four different moral premises that in various ways link the existence of God to the absence of suffering. The version of the argument from evil that I defend starts from the premise that if God exists, he would not allow excessive, unnecessary suffering. The argument continues by denying the consequent of this conditional to conclude that God does not exist. I defend the argument against Skeptical Theists who say we are in no position to judge that there is excessive, unnecessary suffering by arguing that this defense has absurd consequences. It allows Young Earthers to construct a parallel argument that concludes that we are in no position to judge that God did not create the earth recently. In the last section I consider whether theists can turn the argument from evil on its head by arguing that God exists. I first criticize Alvin Plantinga’s theory of warrant that one might try to use to argue for God’s existence. I then criticize Richard Swinburne’s Bayesian argument to the same conclusion. I conclude that my version of the argument from evil is a strong argument against the existence of God and that several important responses to it do not defeat it.

The review presents the International Workshop “Transcendental Turn in Contemporary Philosophy-3: Nature of Transcendental Philosophy” held in Moscow on 19-22 April, 2018. The workshop was co-sponsored by the State Academic University for the Humanities, the Russian State University for the Humanities and the Foundation for the Humanities. The review examines the main topics of the workshop, summarises the main presentations and explicates the problem area of modern interpretations of Kant and the development of transcendentalism in the twentieth and twenty-first centuries. The presentations, questions and discussions centred around the main problems of transcendentalism: the differences between the phenomenon and the thing in itself, between the first and second editions of the Critique of Pure Reason, the relationship between realist and constructivist aspects of Kantian transcendentalism, the transformation of Kantian transcendental philosophy in Neo-Kantianism and phenomenology and more.

ABSTRACTThe paper takes up a conception of substances according to which substances are simple property bearers, properties being modes, particular qualitative ways individual substances are. What a substance does or would do is determined by its qualities. Efficient causation is to be understood as the manifesting of powers possessed by substances owing to their qualitative natures. Although complexes, entities with substantial parts, are not substances, they would be no less real, no less participants in the causal fray. What the substances and properties are is an empirical matter, however, to be settled, if at all, by physics. For all we know, the substances might be particles, or fields, or the universe as a whole. Efficient causation appears to require pluralism: distinct interacting substances. In a non-pluralistic universe, causal truths would be relegated to the manifest image: true still, but made true by non-causal features of the universe perhaps revealed by the scientific image. There remains the final reflection, how shallow, puny, and imperfect are efforts to sound the depths in the nature of things. In philosophical discussion, the merest hint of dogmatic certainty as to finality of statement is an exhibition of folly. : x)

It is an old charge against Locke that his commitment to a common substratum for the observable qualities of particular objects and his empiricist theory about the origin of ideas are inconsistent with one another. How could we have an idea of something in which observable qualities inhere if all our ideas are constructed from ideas of observable qualities? In this paper, I propose an interpretation of the crucial passages in Locke, according to which the idea of substratum is formed through an elaborate mental process which he calls “supposition.” It is the same process we use when we form the idea of infinity − another problematic idea for an empiricist. In the end, Locke was more liberal than most empiricists in subscribing to the existence of ideas far removed from experience, because he accepted supposition as a legitimate way of constructing new ideas.

This article presents two learning processes in order to explain how children at an early age can transform a complex sensory input to concepts and categories. The first process constructs the perceptual structures that emerge in children’s cognitive development by detecting invariants in the sensory input. The invariant structures involve a reduction in dimensionality of the sensory information. It is argued that this process generates the primary domains of space, objects and actions and that these domains can be represented as conceptual spaces. Once the primary domains have been established, the second process utilizes covariances between different dimensions of the domains in order to identify natural clusters of entities. The clusters are then are used to determine concepts as regions in the spaces. As an application, the processes are used to resolve the so-called ‘complex first paradox’ that emerges from the fact that children, in general, learn nouns earlier than adjectives, even though nouns are semantically more complex than adjectives.

This article is a rejoinder to Hernández-Conde’s (Synthese 194(10):4011–4037, 2017) criticism of the convexity criterion in the theory of conceptual spaces. His arguments in general claim that the convexity criterion could be false and that it therefore is problematic for the theory. However, this is a misunderstanding since the convexity criterion is put forward as an empirically testable law for concepts. The long list of cases where the convexity criterion could be false that Hernández-Conde presents rather exhibits the rich empirical content of the criterion.

Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the cells of an optimally designed similarity space.

Why is a red face not really red? How do we decide that this book is a textbook or not? Conceptual spaces provide the medium on which these computations are performed, but an additional operation is needed: Contrast. By contrasting a reddish face with a prototypical face, one gets a prototypical ‘red’. By contrasting this book with a prototypical textbook, the lack of exercises may pop out. Dynamic contrasting is an essential operation for converting perceptions into predicates. The existence of dynamic contrasting may contribute to explaining why lexical meanings correspond to convex regions of conceptual spaces. But it also explains why predication is most of the time opportunistic, depending on context. While off-line conceptual similarity is a holistic operation, the contrast operation provides a context-dependent distance that creates ephemeral predicative judgments that are essential for interfacing conceptual spaces with natural language and with reasoning