Ioannis G. Ntagkas

Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalised valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalised valuation. A key ingredient throughout is the idea that, in a situation where no normal truth-value can be given to a proposition asserting that the value of a physical quantity A lies in a set D of real numbers , it is nevertheless possible to ascribe a partial truth-value which is determined by the set of all coarse-grained propositions that assert that some function f(A) lies in f(D), and that are true in a normal sense. The set of all such coarse-grainings forms a sieve on the category of self-adjoint operators, and is hence fundamentally related to the theory of presheave.

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 concludes.

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5.

Control consciousness is the awareness or experience of seeming to be in control of one’s actions. One view, which I will be arguing against in the present paper, is that control consciousness is a form of sensory consciousness. In such a view, control consciousness is exhausted by sensory elements such as tactile and proprioceptive information. An opposing view, which I will be arguing for, is that sensory elements cannot be the whole story and must be supplemented by direct contributions of nonsensory, motor elements. More specifically, I will be arguing for the view that the neural basis of control consciousness is constituted by states of recurrent activation in relatively intermediate levels of the motor hierarchy

Deviant phenomenal knowledge is knowing what it’s like to have experiences of, e.g., red without actually having had experiences of red. Such a knower is a deviant. Some physicalists have argued and some anti-physicalists have denied that the possibility of deviants undermines anti-physicalism and the Knowledge Argument. The current paper presents new arguments defending the deviant-based attacks on anti-physicalism. Central to my arguments are considerations concerning the psychosemantic underpinnings of deviant phenomenal knowledge. I argue that physicalists are in a superior position to account for the conditions in virtue of which states of deviants constitute representations of phenomenal facts.

The philosophical technical term "supervenience" is frequently used in the philosophy of mind as a concise way of characterizing the core idea of physicalism in a manner that is neutral with respect to debates between reductive physicalists and nonreductive physicalists. I argue against this alleged neutrality and side with reductive physicalists. I am especially interested here in debates between psychoneural reductionists and nonreductive functionalist physicalists. Central to my arguments will be considerations concerning how best to articulate the spirit of the idea of supervenience. I argue for a version of supervenience, "fine-grained supervenience," which is the claim that if, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties. I argue further that despite initial appearances to the contrary, such a construal of supervenience can be embraced only by reductive physicalists

Among our conscious states are conscious thoughts. The question at the center of the recent growing literature on cognitive phenomenology is this: In consciously thinking P, is there thereby any phenomenology—is there something it’s like? One way of clarifying the question is to say that it concerns whether there is any proprietary phenomenology associated with conscious thought. Is there any phenomenology due to thinking, as opposed to phenomenology that is due to some co-occurring sensation or mental image? In this paper we will present two arguments that a “yes” answer to this question of cognitive phenomenology can be obtained via appeal to the HOT theory of consciousness, especially the version articulated and defended by David Rosenthal.

I respond to the separate commentaries by Jacob Berger, Charlie Pelling, and David Pereplyotchik on my paper, “Color-Consciousness Conceptualism.” I resist Berger’s suggestion that mental colors ever enter consciousness without accompaniment by deployments of concepts of their extra-mental counterparts. I express concerns about Pelling’s proposal that a more uniform conceptualist treatment of phenomenal sorites can be gained by a simple appeal to the partial overlap of the extensions of some concepts. I question the relevance to perceptual consciousness of the arguments for demonstrative concepts that Pereplyotchik attacks

Though the following problem is not explicitly raised by her, it seems sufficiently similar to an issue of pertinence to Akins's "Black and White and Color" (this volume) to merit the moniker, Akins's Problem : Can there be a visual experience devoid of both color phenomenology and black-and-white phenomenology? The point of the present paper is to draw from Akins's paper the materials needed to sketch a case for a positive answer to Akins's Problem. I am unsure about how much of what follows Akins will want to endorse, but I hope this helps move us forward in our collective pursuit of a theory of visual consciousness.

I develop an argument that believing in the survivability of a mind uploading procedure conveys value to its believers that is assessable independently of assessing the truth of the belief. Regardless of whether the first-order metaphysical belief is true, believing it conveys a kind of Darwinian fitness to the believer. Of course, a further question remains of whether having that Darwinian property can be a basis—in a rational sense of being a basis—for one’s holding the belief. I’ll also make some remarks in the present article toward answering that latter question.

Many so-called problems in contemporary philosophy of mind depend for their expression on a collection of inter-defined technical terms, a few of which are qualia, phenomenal property, and what-it’s-like-ness. I express my scepticism about Keith Frankish’s illusionism, the view that people are generally subject to a systematic illusion that any properties are phenomenal, and scout the relative merits of two alternatives to Frankish’s illusionism. The first is phenomenal meta-illusionism, the view that illusionists such as Frankish, in holding their view, are themselves thereby under an illusion. The second is qualia quietism, the view that nothing worth saying is said by employing any of the aforementioned inter-defined technical terms.

I argue against a class of philosophical views of color perception, especially insofar as such views posit the existence of color sensations. I argue against the need to posit such nonconceptual mental intermediaries between the stimulus and the eventual conceptualized perceptual judgment. Central to my arguments are considerations of certain color illusions. Such illusions are best explained by reference to high-level, conceptualized knowledge concerning, for example, object identity, likely lighting conditions, and material composition of the distal stimulus. Such explanations obviate the need to appeal to nonconceputal mental links in the causal chains eventuating in conceptualized color discriminations.

Cognitive Science is a major new guide to the central theories and problems in the study of the mind and brain. The authors clearly explain how and why cognitive science aims to understand the brain as a computational system that manipulates representations. They identify the roots of cognitive science in Descartes - who argued that all knowledge of the external world is filtered through some sort of representation - and examine the present-day role of Artificial Intelligence, computing, psychology, linguistics and neuroscience. Throughout, the key building blocks of cognitive science are clearly illustrated: perception, memory, attention, emotion, language, control of movement, learning, understanding and other important mental phenomena. Cognitive Science: presents a clear, collaborative introduction to the subject is the first textbook to bring together all the different strands of this new science in a unified approach includes illustrations and exercises to aid the student

This is Philosophy. In keeping with the mission of the series, This is Philosophy: Philosophy of Mind will be both accessible to the average student and technology oriented, integrating with supplemental online material. Also, while the proposed book will cover all of the topics one would expect in a traditional philosophy of mind course, it will be up to date and cover recent advances that are sadly missing from many competitor volumes. My proposed volume will not be limited to what has become a very oldfashioned approach to teaching philosophy of mind, which is to focus solely on the mindbody problem via Cartesian substance dualism and the twentieth-century reactions to it (behaviorism, identity theory, functionalism, and eliminativism). In recent decades philosophers of mind have made exciting progress toward, for example, explanations of consciousness, and explications of the nature of perception and emotion. It is increasingly clear that the progress made is now part of canonical philosophy of mind

The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the third author has provided evidence that there is an ultimate inner model—Ultimate-L—and he has isolated a natural conjecture associated with the model—the Ultimate-L Conjecture. This conjecture implies that that the first alternative holds—HOD is “close” to V. This is the future in which pattern prevails. In this paper we introduce a very different program, one aimed at establishing the second alternative—the “far” side of the HOD Dichotomy. This is the program of large cardinals beyond choice. Kunen famously showed that if AC holds then there cannot be a Reinhardt cardinal. It has remained open whether Reinhardt cardinals are consistent in ZF alone. It turns out that there is an entire hierarchy of choiceless large cardinals of which Reinhardt cardinals are only the beginning, and, surprisingly, this hierarchy appears to be highly ordered and amenable to systematic investigation, as we shall show in this paper. The point is that if these choiceless large cardinals are consistent then the Ultimate-L Conjecture must fail. This is the future where chaos prevails.

The independence results in set theory invite the search for new and justified axioms. In Chapter 1 I set the stage by examining three approaches to justifying the axioms of standard set theory and argue that the approach via reflection principles is the most successful. In Chapter 2 I analyse the limitations of ZF and use this analysis to set up a mathematically precise minimal hurdle which any set of new axioms must overcome if it is to effect a significant reduction in incompleteness. In Chapter 3 I examine the standard method of justifying new axioms---reflection principles---and prove a result which shows that no reflection principle can overcome the minimal hurdle and yield a significant reduction in incompleteness. In Chapter 4 I introduce a new approach to justifying new axioms---extension principles---and show that such principles can overcome the minimal hurdle and much more, in particular, such principles imply PD and that the theory of second-order arithmetic cannot be altered by set size forcing. I show that in a sense these principles are inevitable. In Chapter 5 I close with a brief discussion of meta-mathematical justifications stemming from the work of Woodin. These touch on the continuum hypothesis and other questions which are beyond the reach of standard large cardinals

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a series of limitative results concerning this approach. These results collectively show that general reflection principles are either weak ) or inconsistent. The philosophical significance of these results is discussed

In 1985 the second author showed that if there is a proper class of measurable Woodin cardinals and $V^{B1} $ and $V^{B2} $ are generic extensions of V satisfying CH then $V^{B1} $ and $V^{B2} $ agree on all $\Sigma _1^2 $ -statements. In terms of the strong logic Ω-logic this can be reformulated by saying that under the above large cardinal assumption ZFC + CH is Ω-complete for $\Sigma _1^2 $ Moreover. CH is the unique $\Sigma _1^2 $ -statement with this feature in the sense that any other $\Sigma _1^2 $ -statement with this feature is Ω-equivalent to CH over ZFC. It is natural to look for other strengthenings of ZFC that have an even greater degree of Ω-completeness. For example, one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for all of third-order arithmetic. Going further, for each specifiable segment $V_\lambda $ of the universe of sets (for example, one might take $V_\lambda $ to be the least level that satisfies there is a proper class of huge cardinals), one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for the theory of $V_\lambda $ . If such theories exist, extend one another, and are unique in the sense that any other such theory B with the same level of Ω-completeness as A is actually Ω-equivalent to A over ZFC, then this would show that there is a unique Ω-complete picture of the successive fragments of the universe of sets and it would make for a very strong case for axioms complementing large cardinal axioms. In this paper we show that uniqueness must fail. In particular, we show that if there is one such theory that Ω-implies CH then there is another that Ω-implies¬CH