Amodal completion is usually characterized as the representation of those parts of the perceived object that we get no sensory stimulation from. In the case of the visual sense modality, for example, amodal completion is the representation of occluded parts of objects we see. I argue that relationalism about perception, the view that perceptual experience is constituted by the relation to the perceived object, cannot give a coherent account of amodal completion. The relationalist has (...) two options: construe the perceptual relation as the relation to the entire perceived object or as the relation to the unoccluded parts of the perceived object. I argue that neither of these options are viable. (shrink)

Amodal completion is the representation of occluded parts of perceived objects. We argue for the following three claims: First, at least some amodal completion-involved experiences can ground knowledge about the occluded portions of perceived objects. Second, at least some instances of amodal completion-grounded knowledge are not sensitive, that is, it is not the case that in the nearest worlds in which the relevant claim is false, that claim is not believed true. Third, at least (...) some instances of amodal completion-grounded knowledge are not safe, that is, it is not the case that in all or nearly all near worlds where the relevant claim is believed true, that claim is in fact true. Thus, certain instances of amodal completion-grounded knowledge refute both the view that knowledge is necessarily sensitive and the view that knowledge is necessarily safe. (shrink)

Amodal completion is the representation of those parts of the perceived object that we get no sensory stimulation from. While amodal completion is rife and plays an essential role in all sense modalities, philosophical discussions of this phenomenon have almost entirely been limited to vision. The aim of this paper is to examine in what sense we can talk about amodal completion in olfaction. We distinguish three different senses of amodal completion – (...) spatial, temporal and feature-based completion – and argue that all three are present and play a significant role in olfaction. (shrink)

The problem of amodal perception is the problem of how we represent features of perceived objects that are occluded or otherwise hidden from us. Bence Nanay (2010) has recently proposed that we amodally perceive an object's occluded features by imaginatively projecting them into the relevant regions of visual egocentric space. In this paper, I argue that amodal perception is not a single, unitary capacity. Drawing appropriate distinctions reveals amodal perception to be characterized not only by mental imagery, (...) as Nanay suggests, but also by genuinely visual representations as well as beliefs. I conclude with some brief remarks on the role of object-directed bodily action in conferring a sense of unseen presence on an object's occluded features. (shrink)

Integration information theories posit that the integration of information is necessary and/or sufficient for consciousness. In this paper, we focus on three of the most prominent information integration theories: Information Integration Theory, Global Workspace Theory, and Attended Intermediate-Level Theory. We begin by explicating each theory and key concepts they utilize. We then argue that the current evidence indicates that the integration of information is neither necessary nor sufficient for consciousness. Unlike GWT and AIR, IIT maintains that conscious experience is both (...) necessary and sufficient for consciousness. We present empirical evidence indicating that simple features are experienced in the absence of feature integration and argue that it challenges IIT’s necessity claim. In addition, we challenge IIT’s sufficiency claim by presenting evidence from hemineglect cases and amodal completion indicating that contents may be integrated and yet fail to give rise to subjective experience. Moreover, we present empirical evidence from subjects with frontal lesions who are unable to carry out simple instructions and argue that they are irreconcilable with GWT. Lastly, we argue that empirical evidence indicating that patients with visual agnosia fail to identify objects they report being conscious of present a challenge to AIR’s necessity claim. (shrink)

Many philosophers take experience to be an essential aspect of perceptual justification. I argue against a specific variety of such an experientialist view, namely, the Looks View of perceptual justification, according to which our visual beliefs are mediately justified by beliefs about the way things look. I describe three types of cases that put pressure on the idea that perceptual justification is always related to looks-related reasons: unsophisticated cognizers, multimodal identification, and amodal completion. I then provide a tentative (...) diagnosis of what goes wrong in the Looks View: it ascribes a specific epistemic role to beliefs about looks that is actually fulfilled by subpersonal perceptual processes. (shrink)

Human beings have the ability to ‘augment’ reality by superimposing mental imagery on the visually perceived scene. For example, when deciding how to arrange furniture in a new home, one might project the image of an armchair into an empty corner or the image of a painting onto a wall. The experience of noticing a constellation in the sky at night is also perceptual-imaginative amalgam: it involves both seeing the stars in the constellation and imagining the lines that connect them (...) at the same time. I here refer to such hybrid experiences – involving both a bottom-up, externally generated component and a top-down, internally generated component – as make-perceive (Briscoe 2008, 2011). My discussion in this paper has two parts. In the first part, I show that make-perceive enables human beings to solve certain problems and pursue certain projects more effectively than bottom-up perceiving or top-down visualization alone. To this end, the skillful use of projected mental imagery is surveyed in a variety of contexts, including action planning, the interpretation of static mechanical diagrams, and non-instrumental navigation. In the second part, I address the question of whether make-perceive may help to account for the “phenomenal presence” of occluded or otherwise hidden features of perceived objects. I argue that phenomenal presence is not well explained by the hypothesis that hidden features are represented using projected mental images. In defending this position, I point to important phenomenological and functional differences between the way hidden object features are represented respectively in mental imagery and amodal completion. (shrink)

In this paper we argue that object perception may be affected by what we call “perceptual frames.” Perceptual frames are adaptations of the perceptual system that guide how perceptual objects are singled out from a sensory environment. These adaptations are caused by perceptual learning and realized through bottom-up functional processes such that sensory information is organized in a subject-dependent way leading to idiosyncratic perceptual object representations. Through domain-specific training, perceptual learning, and the acquisition of object-knowledge, it is possible to modulate (...) the adaptive perceptual system such that its ability to represent becomes bespoke. Different perceivers with different perceptual frames may, therefore, receive the same sensory information and perceive different perceptual objects due to the effects of framing. Consequently, we demonstrate the plausibility of this account by surveying empirical data concerning the functions of (1) multisensory integration, (2) amodal completion, and (3) predictive anticipation. Regarding (1), we argue that the perceptual system’s optimization processes employ perceptual frames to facilitate multisensory feature binding. Regarding (2), we argue that amodal completion can occur with or without the help of mental imagery, yet either instance of amodal completion requires perceptual frames. Regarding (3), we demonstrate that perceptually anticipating an object’s motion involves the implementation of perceptual frames. We conclude that framing effects are a matter of perceptual diversity and highlight the need to accommodate unique perspectives in the philosophy and science of perception. (shrink)

The dictionary tells you that a shadow is a dark area or volume caused by an opaque object blocking some light. The definition is correct, but we need to clarify a couple of its elements: darkness and blocking. The clarification leads to the view that to see a shadow is a degree of failing to see a surface. I will also argue that seeing a silhouette (i.e. a backlit object) is a particular way of failing to see an object. Thus (...) visual discriminability is not sufficient for seeing. Finally, I argue that comparative empirical research on shadows' contribution to amodal completion in apes and humans supports the view that humans, unlike apes, perceive shadows as shadows rather than as black objects, thus lending indirect support for my view that to see a shadow is a way and degree of failing to see a surface. (shrink)

Perception is a central means by which we come to represent and be aware of particulars in the world. I argue that an adequate account of perception must distinguish between what one perceives and what one's perceptual experience is of or about. Through capacities for visual completion, one can be visually aware of particular parts of a scene that one nevertheless does not see. Seeing corresponds to a basic, but not exhaustive, way in which one can be visually aware (...) of an item. I discuss how the relation between seeing and visual awareness should be explicated within a representational account of the mind. Visual awareness of an item involves a primitive kind of reference: one is visually aware of an item when one's visual perceptual state succeeds in referring to that particular item and functions to represent it accurately. Seeing, by contrast, requires more than successful visual reference. Seeing depends additionally on meta-semantic facts about how visual reference happens to be fixed. The notions of seeing and of visual reference are both indispensable to an account of perception, but they are to be characterized at different levels of representational explanation. (shrink)

Look at a red apple. Now close your eyes and visualize this apple. Your perceptual state and your imagery of the apple are very similar in some respects. They are also different in some respects. The aim of this paper is to address three questions about the relation between perception and imagination: -/- (a) How similar are perception and imagination and what explains this similarity? (b) How different are perception and imagination and what explains this difference? (c) How do perception (...) and imagination interact? (shrink)

I defend the thesis that most or all perceptual experiences are infused with imaginative contributions. While the idea is not new, it has few supporters. I begin by developing a framework for the underlying debate. Central to that framework is the claim that a perceptual experience is infused with imagination if and only if there are self-generated contributions to that experience that have ampliative effect on its phenomenal and directed elements. Self-generated ingredients to experience are produced by the subject as (...) opposed to being received from the world. Some form of stored content is an obvious starting point. Ampliative effects are aspects of perceptual experience that outstrip the content the senses get from the world. This conceptual framework is applied to three case studies: object-sameness and object-kind recognition (section 2), memory colour (section 3), and perceptual constancy and amodal completion (section 4). If the three cases and my overall analysis are accepted (a substantive if), then we have a forceful inductive argument for perception being infused with imagination. (shrink)

This chapter distinguishes between two kinds of ordinary multisensory experience that go beyond mere co-consciousness of features (e.g., the experience that results from concurrently hearing a sound in the hallway and seeing the cup on the table). In one case, a sensory experience in one modality creates a perceptual demonstrative to whose referent qualities are attributed in another sensory modality. For example, when you hear someone speak, auditory experience attributes audible qualities to a seen event, a person’s speaking motions. The (...) second kind of multisensory experience attributes features experienced in several sensory modalities to one and the same object via a process of amodal perceptual integration, i.e., integration that occurs separately from processing within the individual sensory modalities. Multisensory experiences arising from holding and seeing a tomato or from seeing the Indian curry boil and smelling it are examples of the second kind of multisensory experience. At the end of the chapter we look at synesthesia, a kind of atypical multisensory experience, and argue that one version of this phenomenon may be able to shed light on the neural mechanism underlying amodally integrated multisensory experience. (shrink)

The chapter deals with the notion of phenomenal realness, which was first systematically explored by Albert Michotte. Phenomenal realness refers to the impression that a perceptual object is perceived to have an autonomous existence in our mind-independent world. Perceptual psychology provides an abundance of phenomena, ranging from amodal completion to picture perception, that indicate that phenomenal realness is an independent perceptual attribute that can be conferred to perceptual objects in different degrees. The chapter outlines a theoretical framework that (...) appears particularly well-suited for dealing with corresponding phenomena. According to this framework, perception can be understood as a triggering of conceptual forms by sensor inputs. It is argued that the attribute of phenomenal realness is based on specific types of internal evaluation functions which deal with the segregation of causes conceived as ‘external’ from those conceived as ‘internal’. These evaluation functions integrate different internal sources of ‘knowledge’ about the potential causes for the activation of conceptual forms and provide markers by which conceptual forms can be tagged as ‘external world objects’. (shrink)

Higher animals need to identify and track material objects because they depend on interactions with them for nutrition, reproduction, and social interaction. This paper investigates the perception of material objects. It argues, first, that material objects are tagged, in all five external senses, as bearers of the features detected by them. This happens through a perceptual process, here entitled Generalized Completion, which creates the appearance of objects that have properties that transcend the activation of sensory receptors. The paper shows, (...) secondly, that material objects are privileged subjects for perceived motion and interaction. That is, they are perceived as subjects for these properties while their parts seem to be subjects only derivatively. Material objects are the only perceptual subjects that are both multisensory and privileged. (shrink)

Higher animals need to identify and track material objects because they depend on interactions with them for nutrition, reproduction, and social interaction. This paper investigates the perception of material objects. It argues, first, that material objects are tagged, in all five external senses, as bearers of the features detected by them. This happens through a perceptual process, here entitled Generalized Completion, which creates the appearance of objects that have properties that transcend the activation of sensory receptors. The paper shows, (...) secondly, that material objects are privileged subjects for perceived motion and interaction. That is, they are perceived as subjects for these properties while their parts seem to be subjects only derivatively. Material objects are the only perceptual subjects that are both multisensory and privileged. (shrink)

Western Buddhists often believe and proclaim that metaphysical speculation is irrelevant to Buddhist ethics or practice. This view is problematic even with respect to early Buddhism, and cannot be sustained regarding later Indian Buddhists. In Śāntideva’s famous Bodhicaryāvatāra, multiple claims about the nature of reality are premises for conclusions about how human beings should act; that is, metaphysics logically entails ethics for Śāntideva, as it does for many Western philosophers. This article explores four key arguments that Śāntideva makes from metaphysics (...) to ethics: actions are determined by their causes, and therefore we should not get angry; the body is reducible to its component parts, and therefore we should neither protect it nor lust after other bodies; the self is an illusion, and therefore we should be altruistic; all phenomena are empty, and therefore we should not be attached to them. The exploration of these arguments together shows us why metaphysical claims can matter a great deal for Buddhist ethics, practice and liberation. (shrink)

The Mahāyāna Buddhist thinker Śāntideva tells his audience to give out alcohol, weapons and sex for reasons of Buddhist compassion, though he repeatedly warns of the dangers of all these three. The article shows how Śāntideva resolves this issue: these gifts, and gifts in general, attract their recipients to the virtuous giver, in a way that helps the recipients to become more virtuous in the long run. As a consequence, Śāntideva does recommend the alleviation of poverty, but assigns it a (...) much smaller significance than is usually supposed. His views run counter to many engaged Buddhist discussions of political action, and lend support to the “modernist” interpretation of engaged Buddhist practice. (shrink)

This dissertation examines the idea of _ethical revaluation_ — taking things we normally see as good for our flourishing and seeing them as neutral or bad, and vice versa — in the Mahāyāna Buddhist thinker Śāntideva. It shows how Śāntideva’s thought on the matter is more coherent than it might otherwise appear, first by examining the consistency of Śāntideva’s own claims and then by applying them to contemporary ethical thought. In so doing, it makes four significant contributions. Śāntideva claims that (...) property and relationships are bad for us because they promote attachment, and that others’ wrongdoing is good for us because it allows us to generate patient endurance. Yet he also urges his readers to give property to others, and to prevent their wrongdoing. Is he caught in contradiction? The dissertation argues that he is not, because giving to others is not intended to benefit them materially, but rather to produce beneficial mental states in them, and preventing wrongdoing is intended to benefit the wrongdoer and not the victim. In both cases, Śāntideva emphasizes individual action in a way that makes social or political action more difficult to justify. The dissertation’s first contribution is to show how this interpretation of Śāntideva contrasts notably with standard presentations of Mahāyāna ethics. Its second contribution is to refute claims that Buddhists have no normative ethics. Śāntideva’s resolutions of these apparent contradictions also have relevance for contemporary ethical thought. Martha Nussbaum argues against an ethical revaluation similar to Śāntideva’s, on the grounds that such a revaluation makes it contradictory to argue for providing goods to others, preventing others’ wrongdoing or engaging in political action. Śāntideva’s views show that ethical revaluation is a more sustainable position than these criticisms of Nussbaum’s would imply; if it is to be rejected, it must be rejected on other grounds. To show this point is the dissertation’s third contribution. The fourth contribution is methodological; by finding similarities of concern and differences of opinion between Śāntideva and a contemporary thinker, it helps bridge the gap between normative and comparative religious ethics. (shrink)

Ken Wilber insists that valid knowledge must be derived from paradigms: sets of injunctions and social practices that lead to replicable experiences. In this article, I examine Wilber's claims that the theory still includes the essentials of premodern traditions, because the essentials of those traditions consist of a phenomenological core of practices leading to mystical experience. Drawing on the works of Robert Sharf and Wilhelm Halbfass and on close readings of primary texts, this article argues that mystical paradigms of replicable (...) experience are not in fact the essentials of these traditions--neither for the majority of practitioners nor even for their revered teachers or masters. The article concludes with a discussion of the implications of this point for constructive integral work. (shrink)

An encyclopedia article about Śāntideva, the 8th-century Indian Mahāyāna Buddhist philosopher known for his work on ethics. The article explores his history and written corpus and classifies his work (as he does) by way of the "perfections" (pāramitā) of the bodhisattva. It addresses his views on metaphysics and their implications for ethics and practice, as well as his views on gift-giving, anger and other emotions. It also briefly discusses his relationship to virtue ethics and consequentialism.

Contemporary engaged Buddhist scholars typically claim either that Buddhism always endorsed social activism, or that its non-endorsement of such activism represented an unwitting lack of progress. This article examines several classical South Asian Buddhist texts that explicitly reject social and political activism. These texts argue for this rejection on the grounds that the most important sources of suffering are not something that activism can fix, and that political involvement interferes with the tranquility required for liberation. The article then examines the (...) history of engaged Buddhism in order to identify why this rejection of activism has not yet been taken sufficiently seriously. (shrink)

When we see an object, we also represent those parts of it that are not visible. The question is how we represent them: this is the problem of amodal perception. I will consider three possible accounts: (a) we see them, (b) we have non-perceptual beliefs about them and (c) we have immediate perceptual access to them, and point out that all of these views face both empirical and conceptual objections. I suggest and defend a fourth account, according to which (...) we represent the occluded parts of perceived objects by means of mental imagery. This conclusion could be thought of as a (weak) version of the Strawsonian dictum, according to which “imagination is a necessary ingredient of perception itself”. (shrink)

Response to Gover (2015) on Trogdon and Livingston (2015) on artwork completion.

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

In the Eudemian Ethics II 1, 1219a34–b8, Aristotle defines happiness as ‘the activity of a complete life in accordance with complete virtue’. Most scholars interpret a complete life as a whole lifetime, which means that happiness involves virtuous activity over an entire life. This article argues against this common reading by using Aristotle’s notion of ‘activity’ (energeia) as a touchstone. It argues that happiness, according to the Eudemian Ethics, must be a complete activity that reaches its end at any and (...) every moment. The upshot of this reading is that life reaches completeness within a lifetime and that death cannot be the requirement for making life complete. (shrink)

The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, I (...) argue that large-scale simulations require that the explanandum phenomenon is identified; otherwise, the explanatory value of such explanations is difficult to establish, and testing the model empirically by comparing its behavior with the explanandum remains practically impossible. The completeness of the explanation, and hence of the explanatory value of the explanatory model, is to be assessed vis-à-vis the explanandum phenomenon, which is not to be conflated with raw observational data and may be idealized. I argue that idealizations, which include building models of a single phenomenon displayed by multi-functional mechanisms, lumping together multiple factors in a single causal variable, simplifying the causal structure of the mechanisms, and multi-model integration, are indispensable for complex systems such as brains; otherwise, the model may be as complex as the explanandum phenomenon, which would make it prone to so-called Bonini paradox. I conclude by enumerating dimensions of empirical validation of explanatory models according to new mechanism, which are given in a form of a “checklist” for a modeler. (shrink)

Investigation of a puzzle concerning complete yet authorless artworks.

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As (...) Humberstone notes, the issue of Post completeness in congruential modal logics is not well understood. The present article shows that in contrast to normal modal logics, the extent of the property of Post completeness among congruential modal logics depends on the background set of logics. Some basic results on the corresponding properties of Post completeness are established, in particular that although a congruential modal logic is Post complete among all modal logics if and only if its modality is truth-functional, there are continuum many modal logics Post complete among congruential modal logics. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional (...) decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

Defense of a psychological account of what it is for an artwork to be complete.

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with (...) implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

: In the first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object, the metaphysical exposition (...) will show that this representation is secondary to space considered as an original, undetermined and as such unrepresentable intuitive manifold. Now, following Kant, the representation of any kind of object involves diversity, synthesis and unity. In the case of our representation of space as formal intuition, this involves, firstly, a manifold a priori, i.e. space as pure form, delivered by the transcendental Aesthetic, secondly, a figurative, productive synthesis of that manifold, and, thirdly, the unity provided by the categories. Analysing our given representation of space – the task of the metaphysical exposition – amounts to dismantling its unity and determine its characteristics with respect to the categories. (shrink)

Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such. -/- Matthew, Mark, Luke, and John wrote Greek. ? Every evangelist wrote Greek. -/- Matthew, Mark, Luke, and John wrote Greek. Every evangelist is Matthew, Mark, Luke, or John. ? Every evangelist wrote Greek. -/- The above pair of premise-conclusion arguments is of a sort familiar to logicians and philosophers of science. In each case the first premise is (...) logically equivalent to the set of four atomic propositions: “Matthew wrote Greek”, “Mark wrote Greek”, “Luke wrote Greek”, and “John wrote Greek”. The universe of discourse is the set of evangelists. We presuppose standard first-order logic. -/- As many logic texts teach, the first of these two premise-conclusion arguments—sometimes called a complete enumerative induction— is invalid in the sense that its conclusion does not follow from its premises. To get a counterargument, replace ‘Matthew’, ‘Mark’, ‘Luke’, and ‘John’ by ‘two’,’four’, ‘six’ and ‘eight’; replace ‘wrote Greek’ by ‘are even’; and replace ‘evangelist’ by ‘number’. This replacement converts the first argument into one having true premises and false conclusion. -/- But the same replacement performed on the second argument does no such thing: it converts the second premise into the falsehood “Every number is two, four, six, or eight”. As many logic texts teach, there is no replacement that converts the second argument into one with all true premises and false conclusion. The second is valid; its conclusion is deducible from its two premises using an instructive natural deduction. -/- This paper “does the math” behind the above examples. The theorem could be stated informally: the above examples are typical. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

Modern fundamental science tends to avoid the principle of physical causality and realism, replacing it with heuristically postulated and separated mathematical constructions that impose their own rules before being adjusted to measurement results. While it is officially accepted as the single possible kind of rigorous knowledge, we argue that another, explicitly extended kind of science can provide the causally complete picture of reality avoiding the glaring gaps, growing problems and persisting stagnation of the artificially reduced knowledge paradigm. The logic of (...) science development and especially its current state call for the urgently needed transition to the extended, causally complete kind of knowledge and related sustainable progress at superior creativity levels of self-aware, reason-based society. (shrink)

Despite the vast literature on Rawls's work, few have discussed his arguments for the value of democracy. When his arguments have been discussed, they have received staunch criticism. Some critics have charged that Rawls's arguments are not deeply democratic. Others have gone further, claiming that Rawls's arguments denigrate democracy. These criticisms are unsurprising, since Rawls's arguments, as arguments that the principle of equal basic liberty needs to include democratic liberties, are incomplete. In contrast to his trenchant remarks about core civil (...) liberties, Rawls does not say much about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. -/- In this paper, I complete some of Rawls's arguments and show that he has grounds for including political liberties, particularly those of a democratic nature, in the principle of equal basic liberty. In doing so, I make some beginning steps toward illustrating the genuinely democratic nature of Rawls's arguments. Rawls believes that a few different arguments can be given for democratic institutions and that these arguments work together to support the value of democracy. In this paper, I focus on Rawls's arguments relating to self-respect. I focus on this set of arguments because they are among the strongest of Rawls's arguments for equal political liberty and its fair value. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

We show that early vision can use monocular cues to rapidly complete partially-occluded objects. Visual search for easily detected fragments becomes difficult when the completed shape is similar to others in the display; conversely, search for fragments that are difficult to detect becomes easy when the completed shape is distinctive. Results indicate that completion occurs via the occlusion-triggered removal of occlusion edges and linking of associated regions. We fail to find evidence for a visible filling-in of contours or surfaces, (...) but do find evidence for a "functional" filling-in that prevents the constituent fragments from being rapidly accessed. As such, it is only the completed structures—and not the fragments themselves—that serve as the basis for rapid recognition. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative extensions of K, (...) using a novel generalisation of the standard semantics. (shrink)

A theoretically rigorous approach to the key problems of Molinism leads to a clear distinction between semantic and metaphysical problems. Answers to semantic problems do not provide answers to metaphysical problems that arise from the theory of middle knowledge. The so-called ‘grounding objection’ to Molinism raises a metaphysical problem. The most promising solution to it is a revised form of the traditional ‘essence solution’. Inspired by Leibniz’s idea of a ‘notio completa’ (complete concept), we propose a mathematical model of ‘possibilistic’ (...) (Molinist) complete concepts. They ground middle knowledge within the very being of the agents themselves. Molinist Complete Concepts can thus serve to reject consequence-style arguments against Molinism. They also allow the Molinist to safeguard a robustly libertarian notion of the ability to do otherwise. (shrink)

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the (...) propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic. (shrink)

Propositional dynamic logic is complete but not compact. As a consequence, strong completeness requires an infinitary proof system. In this paper, we present a short proof for strong completeness of $$\mathsf{PDL}$$ relative to an infinitary proof system containing the rule from [α; β n ]φ for all $$n \in {\mathbb{N}}$$, conclude $$[\alpha;\beta^*] \varphi$$. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. Also, we (...) show that the universal canonical model of $$\mathsf{PDL}$$ lacks the property of modal harmony, the analogue of the Truth lemma for modal operators. (shrink)

In his 1802 article for the Critical Journal, “Relationship of Skepticism to Philosophy,” Hegel attempts to articulate a form of skepticism that is “at one with every true philosophy.” Focusing on the priority that Hegel gives to ancient skepticism over its modern counterpart, Michael Forster and other commentators suggest that it is Pyrrhonism that Hegel views as one with philosophy. Since Hegel calls attention to the persistence of dogmatism even in the work of Sextus Empiricus, however, I argue that it (...) is only a sublated form of Pyrrhonism, what in the Phenomenology of Spirit he calls “self-completing skepticism,” that Hegel takes to be part of genuine philosophical cognition. In this way, I hope to show that the insight that motivates Hegel’s engagement with skepticism in the 1802 essay comes to inform the philosophical itinerary of the Phenomenology of Spirit. (shrink)

The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that against it. In opposition to (...) those who argue that formulation is impossible because no account of what is to count as physical can be provided, I argue that as long as the purpose of the argument in which the account is to be used are borne in mind there are no significant difficulties. The account of the physical which I develop holds as physical whatever is needed to fix the likelihood of pre-theoretically given physical effects, and hypothesises in addition that no chemical, biological or psychological factors will be needed in this way. The thus formulated Completeness Thesis is coherent, and has significant empirical content. In opposition to those who defend the doctrine of emergentism by means of philosophical arguments I contend that those arguments are flawed, setting up misleading dichotomies between needlessly attenuated alternatives and assuming the truth of what is to be proved. Against those who defend emergentism by appeal to the evidence, I argue that the history of science since the nineteenth century shows clearly that the empirical credentials of the view that the world is causally closed at the level of a small number of purely physical forces and types of energy is stronger than ever, and the credentials of emergentism correspondingly weaker. In opposition to those who argue that difficulties with reductionism point to the implausibility of the Completeness Thesis I argue that completeness in no way entails the kinds of reductionism which give rise to the difficulties in question. I argue further that the truth of the Completeness Thesis is in fact compatible with a great deal of taxonomic disorder and the impossibility of any general reduction of non-fundamental descriptions to fundamental ones. In opposition to those who argue that the epistemological credentials of fundamental physical laws are poor, and that those laws should in fact be seen as false, I contend that truth preserving accounts of fundamental laws can be developed. Developing such an account, I test it by considering cases of the composition of forces and causes, where what takes place is different to what is predicted by reference to any single law, and argue that viewing laws as tendencies allows their truth to be preserved, and sense to be made of both the experimental discovery of laws, and the fact that composition enables accurate prediction in at least some cases. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive logical (...) connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

Richard Dawkins’s The Blind Watchmaker argues that evolution is a blind, mechanistic process devoid of purpose or intelligence. This paper provides a complete and total refutation of Dawkins’s claims using Aristotelian metaphysics and Ethical Empirical Rationalism (EER), a doctrine that integrates empirical truth, rational coherence, and ethical universality. Through a focus on Dawkins’s three primary errors, this paper demonstrates how Aristotle’s concepts of form, purpose, and agency offer a superior framework for understanding evolution. Using Cognita as an illustration, this paper (...) highlights how EER establishes a coherent, truth-centered approach to nature, in contrast to Dawkins’s reductionist perspective. (shrink)