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

Investigation of a puzzle concerning complete yet authorless artworks.

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

Gottlob Frege’s conception of works of art has received scant notice in the literature. This is a pity since, as this paper undertakes to reveal, his innovative philosophy of language motivated a theoretically and historically consequential, yet unaccountably marginalized Wittgenstinian line of inquiry in the domain of aesthetics. The element of Frege’s approach that most clearly inspired this development is the idea that only complete sentences articulate thoughts and that what sentences in works of drama and literary art express are (...) ‘mock thoughts’ (Schiengedanken). The early Wittgenstein closely followed Frege’s lead on this theme. One sees this, for example, in the Tractatus, where Wittgenstein announces that only sentential propositions model (‘picture’) states of affairs whereas works of art are objects we perceive sub specie aeternitatis (1961, 83). By the 1930s, however, Wittgenstein began to revise his view beyond his initial Frege-inspired standpoint. He came to insist that works of art can convey thoughts as well, but that thoughts do not model (picture) the world of facts and hence do not convey information about measurable objects and events. Rather, his contention was that aesthetically configured thoughts that artworks communicate impart information about our perspective on reality and reconfigure our view of life. To be more explicit, successful (gelungene) or ‘good’ works of art (ibid.), in Wittgenstein’s view, can supply aesthetically instructive ‘gestures’ that open to living experience promising new ways of being. It is in this respect, he held, that artists ‘have something to teach’ (1980, 36). (shrink)

I consider James Hamilton’s discussion of what I term the complete autonomy thesis, according to which no theatrical performance is a performance of some other work. While agreeing with Hamilton that theatrical performances are often artworks in their own right and that theatrical performance is not a derivative or subsidiary art form, I argue that the complete autonomy thesis overshoots the evidence. Some theatrical performances are autonomous, but many belong to an established tradition of close adherence to the texts of (...) dramatic literature. In such cases, we should say both that the performance itself is an artwork and that it is a performance of some literary work. I suggest that this way of understanding things promotes appreciation of both performances themselves and the dramatic works of literature that are employed in their creation. (shrink)

Since the beginning of the 21st century, technologies like neural networks, deep learning and “artificial intelligence” (AI) have gradually entered the artistic realm. We witness the development of systems that aim to assess, evaluate and appreciate artifacts according to artistic and aesthetic criteria or by observing people’s preferences. In addition to that, AI is now used to generate new synthetic artifacts. When a machine paints a Rembrandt, composes a Bach sonata, or completes a Beethoven symphony, we say that this is (...) neither original nor real art, but simply the complex imitation and reproduction of existing products of human culture. We face the old question concerning the nature of creativity: what kind of recombination of ideas, unusual analogies, and conceptual connections are considered the mark of originality? Can AI produce artworks? Could machines reach a point at which we consider them genuinely creative? We also need to investigate the challenges posed by AI-art to the notion of authoriality: Who is the author of an artificially generated artifact? An artificial system could be considered just an artist’s and a programmer’s tool. However, we are also fascinated by the idea of autonomous artificial creativity in the aesthetic domain, as a manifestation of highly intelligent behavior. This paper will try to define some key questions around what could it mean to consider a machine creative or even equipped with artistic intentionality. (shrink)

At a time when professional art criticism is on the wane, the ancient quarrel between art and philosophy demands fresh answers. Professional art criticism provided a basis upon which to distinguish apt experiences of art from the idiosyncratic. However, currently the kind of narratives from which critics once drew are underplayed or discarded in contemporary exhibition design where the visual arts are concerned. This leaves open the possibility that art operates either as mere stimulant to private reverie or, in the (...) more contentful cases, as propaganda. The ancient quarrel between art and philosophy is that art influences surreptitiously while philosophy presents reasons that invite rational scrutiny. As such, in contrast to philosophy, art would undermine our agency. In July 2017, a group of philosophers gathered at the Art Gallery of NSW (AGNSW), in Sydney, Australia, in the presence of two AGNSW curators to explore the basis of their own experiences of selected artworks. Here, those commentaries are reproduced. Each reveal that objective grounds for an experience of art can be based in the community from which one draws one’s terms of reference. In our commentaries we see the expertise of the respective philosophical communities but other communities of culture or expertise might serve the same purpose and hence resolve the ancient quarrel. Before hearing these commentaries, I explain what is at stake when the ancient quarrel between art and philosophy is understood in contemporary terms. This Issue of the Curator also includes an article on the community-based art criticism that emerges from these commentaries followed by an exhibition review which reveals the incorrigible impulse (also demonstrated in the commentaries) to find the basis for the most apt experience of an artwork. A response by the AGNSW curators completes this issue. (shrink)

Is it not surprising that we look with so much pleasure and emotion at works of art that were made thousands of years ago? Works depicting people we do not know, people whose backgrounds are usually a mystery to us, who lived in a very different society and time and who, moreover, have been ‘frozen’ by the artist in a very deliberate pose. It was the Classical Greek philosopher Aristotle who observed in his Poetics that people could apparently be moved (...) even by the imitation of a person or an act. And although we are usually well aware that it is a simulacrum, not a real situation, it nevertheless sometimes seems as if we ourselves are standing there on the stage or in the painting, so intense and emotional is our response, even though we are just spectators. Aristotle concludes from this that we have intellectual capacities which allow us put ourselves in another’s place and consequently to react to simulated situations as though they are actually happening to us, here and now. In this process, he contends, observation, memory, imagination and emotions are crucial elements. In the past it was not customary to invoke human mental faculties to explain our response to works of art. The Ancient Greeks, after all, knew little about the human body or brain and usually referred to the extended world of the gods in their endeavours to comprehend the ‘inner world’ of human beings. In our time the situation is completely different—such an allusion to the brain no longer surprises us. Whether it is about the mystery of the consciousness, the question of free will or accounts of bizarre psychological aberrations or disorders, we have become accustomed to references to parts of the brain, to images of brain scans, to reports about neural networks and the like. However, because there are so many factors that play a part in our appreciation of works of art we need a complex explanation for it, and it is not enough to look only at certain properties of the brain that are determined by evolution. Those properties are shared by every human being, and so are rather useless in explaining people’s different reactions to the same work of art. Evidently the brains of individuals differ so much that they make it possible for people to respond differently to one and the same artwork. This, of course, raises questions concerning the painted emotions that can be seen in this exhibition. Virtually everyone, after all, is fascinated by such paintings and usually recognizes the emotions they represent. The reactions to these painted emotions are also often similar. This is probably why artworks like this are generally highly valued, then and now, here and elsewhere: from the enigmatically smiling Egyptian Queen Nefertiti and the startled Rembrandt to a seemingly despairing African mask. Aristotle observed that in the theatre players imitate actions that are associated with emotions in a number of ways and that these emotions are shared in a particular fashion by the playwright, the actors and the audience. The audience may even be carried away by these emotions to such an extent that they are in a sense purged of them and can subsequently leave the theatre relieved. Are such emotional reactions perhaps related to the fact that emotions are universal and that brains respond similarly to them? Is this why we can so readily identify painted emotions? May we therefore also assume that the properties of the brain determined by evolution help us to explain these emotions? In answering these questions we shall discuss a number of insights into emotions in psychology and brain science and explore some theories about the possible function of emotions and their expression. (shrink)

In this paper the author reviews the most debated theories of art in contemporary aesthetics and offers a new, intentional-attributive definition of art. He begins by expanding on Weitz’s theory, after which he presents arguments that refute Weitz's claim that it is logically impossible to define art. The author then examines the institutional, the historical, and the aesthetic definitions of art and shows that all of these have weaknesses and none stands up completely to criticism. Taking into consideration the shortcomings (...) of the examined definitions, he suggests his own definition of art: for all x, x is an artwork if the author of x mainly intended to reveal such properties of x, the perception of which would evoke experiences, containing ends in themselves. (shrink)

I propose a distinction between design intentions, activities and products, as opposed to artistic intentions, activities and artworks. Examples of design products would include a specific type of car (or any other invention or device) as well as closer relatives of art such as decorative wall designs. In order to distinguish artistic from design intentions, I present an example in which two sculptors independently work on a single object to produce two sculptures, which are distinct just because the artistic intentions (...) of the sculptors are distinct. This case is then contrasted with an attempted parallel example for design intentions, which fails to produce two correspondingly distinct design products in spite of the different design intentions of its designers. I argue that this failure occurs because designs are types, for which any single token of a given type could not simultaneously be a token of some other type of the same general kind; whereas the possibility of my sculptural 'double artwork' example shows that such artworks cannot be types. I then further investigate the concept of a design, and conclude by arguing that an extension of my sculptural example shows that literary artworks also cannot be types. (shrink)

I sketch here an intuitive picture of repeatable artworks as created types, which are individuated in part by historical paths (re)production. Although attractive, this view has been rejected by a number of authors on the basis of general claims about abstract objects. On consideration, however, these general claims are overgeneralizations, which whilst true of some abstracta, are not true of all abstract objects, and in particular, are not true of created types. The intuitive picture of repeatable artworks as created types (...) is, then, left in place. (shrink)

To hold that artworks are valuable for their own sake—regardless of whatever secondary value they may have, such as entertainment, formation, education, or a pleasurable experience—is to hold that their final worth is not derived from external or secondary ends. I call this collective set of views the end-in-itself view. Nicholas Stang recently leveled a twofold charge of reductio ad absurdum and operating from a double standard against the EI view. In this article, I refute Stang by showing that the (...) charges do not obtain for at least one variation of the EI view that holds artworks to be valuable for their own sake as internally purposive ends-in-themselves. (shrink)

What makes a photograph an artwork, as opposed to a mere document? I defend a cluster account such that aesthetic value, aptness to interpretation, the artist’s intention and institutional uptake may contribute to the arthood of a body of photographs, with no single condition being necessary. With regard to Lawler’s works, I suggest that Lawler’s intention that they be art plays a definitive role because of the works’ resemblance to non-art photography. For some of her photographs, however, it appears (...) that such an intention is absent; and if this is correct, then, given their other features, those photographs are not artworks. (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)

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 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)

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)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (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)

Many artists, art critics, and poets suggest that an aesthetic appreciation of artworks may modify our perception of the world, including quotidian things and scenes. I call this Art-to-World, AtW. Focusing on visual artworks, in this paper I articulate an empirically-informed account of AtW that is based on content related views of aesthetic experience, and on Goodman’s and Elgin’s concept of exemplification. An aesthetic encounter with artworks demands paying attention to its aesthetic, expressive, or design properties that realize its purpose. (...) Attention to these properties make percipients better able to spot them in other entities and scenes as well. The upshot is that an aesthetic commerce with artworks enlarges the scope of what we are able to see and has therefore momentous epistemic consequences. (shrink)

This essay examines the difficulties faced by the claim that artworks are simple physical objects (or, in the case of non-visual art forms, simple structures of another sort) and examines alternative proposals regarding their ontological nature.

Artworks have at least some necessary content properties, as do abstract entities such as propositions. But no concrete item, whether an object, event, process etc., could have any necessary content property. So no artwork could be identical with a concrete item. Hence artworks must be abstract. I also argue that artworks are only contingently connected with concrete items, just as propositions are only contingently linked to their linguistic tokens.

A sustained challenge to the view that artworks are physical objects relates to the alleged inability of physical objects to possess representational properties, which some artworks clearly do possess. I argue that the challenge is subject to confusions about representational properties and aesthetic experience. I show that a challenge to artwork-object identity put forward by Danto is vulnerable to a similar criticism. I conclude by noting that the identity of artworks and physical objects is consistent with the insight that (...) attending exclusively to the object’s individual physical properties may prevent us from grasping the nature of the work. // Contre l’opinion voulant que les œuvres d’art soient des objets physiques, d’aucuns font régulièrement valoir la présumée incapacité des objets physiques à possedér des propriétés représentationnelles, propriétés que certaines œuvres d’art possèdent a l’evidence. Je fais valoir que cette remise en question est sujette à des confusions à propos des propriétés représentationnelles et de l’experience esthétique. Je montre que de même, la remise en question par Danto de l’identité œuvre d’art-objet prête le flanc à une critique similaire. Je conclus pour finir que l’identité entre œuvres d’art et objets physiques est compatible avec l’intuition voulant que prêter attention exclusivement aux propriétés physiques d’un certain objet peut nous empêcher de saisir la nature de l’œuvre. (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)

Some of our aesthetic experiences are of artworks. Some others are of everyday scenes. The question I examine in this paper is about the relation between these two different kinds of aesthetic experience. I argue that the experience of artworks can dispose us to experience everyday scenes in an aesthetic manner both short-term and long-term. Finally, I examine what constraints this phenomenon puts on different accounts of aesthetic experience.

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.

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)

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)

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)

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 question of how people change artworks is important for the metaphysics of art. It’s relatively easy for anyone to change a painting or sculpture, but who may change a literary or musical work is restricted and varies with context. Authors of novels and composers of symphonies often have a special power to change their artworks. Mary Shelley revised Frankenstein, and Tchaikovsky revised his Second Symphony. I cannot change these artworks. In other cases, such as those involving jazz standards and (...) folk songs, performers and ordinary folks have more power to change artworks. My preferred explanation of these facts is the created-abstract-simples view, according to which literary and musical works, unlike paintings and sculptures, are created abstract objects that have no parts. On this view, the way to change a literary or musical work is for an individual, empowered by social practices, to change rules about how a literary work should be published or a musical work should be performed. A. R. J. Fisher and Caterina Moruzzi object that the created-abstract-simples view doesn’t allow for literary and musical works to genuinely change, and Nemesio Garcia-Carríl Puy objects that the view doesn’t allow for these artworks to be repeatable. This paper clarifies the created-abstract-simples view and defends the view against these objections. -/- . (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)

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)

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)

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)

In this paper I will try to trace a discussion about status of art in some recent theories, which pay special attention to the fact that artworks are the kind of things to which representational, expressive, and aesthetic properties are ascribed. First, I will briefly mention some already established criticisms—developed by Richard Wollheim1—against the idea that artworks cannot be identified with physical objects. These criticisms have the further aim of providing an account of art experience that includes our perceiving representational (...) and expressive properties as well as aesthetic ones in artworks. In Wollheim's view, a misconstruction of the nature of these properties and of our perception of them in artworks has been the main reason for the view he intensely criticizes. Thus, he offers a different understanding of these properties, which also involves a new account of perception that does not require an idealisation of our experience of art. (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)

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)

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)

The artefacts produced by artists during their creation of works of art are very various: paintings, writings, musical scores, and so on. I have a general thesis to offer about the relations of artefacts and artworks, but within the confines of this article I shall mainly discuss cases drawn from the art of painting, central specimens of which seem to be autographic in Nelson Goodman's sense, namely such that even the most exact duplication of them does not count as producing (...) the same work of art. My view will be that an artwork (such as a painting) and its associated artefact are not identical, and nor is the artefact in any sense part of the painting in question,2 but that nevertheless it is still possible to maintain the view that paintings are autographic (which view I shall call l the autographic thesis). I shall proceed initially through presentation of some counter-examples to common assumptions as to the relations of artefacts and artworks, and then present an alternative 'representational' theory of their relations. (shrink)

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)

In the following essay, I argue that in the case of some works of art, moral evaluation should not play a role in artistic appraisal. While I reject the strong ethicist’s view—the view that moral evaluation may inform the artistic evaluation of any artwork—I will not do so in favor of the aestheticist’s position. The aestheticist argues for a rigid distinction between the moral and aesthetic evaluation of an artwork. On this view, the moral status of the work (...) is independent of and irrelevant to artistic value. This view would allow us, for example, to evaluate Leni Reifenstahl’s film The Triumph of the Will as a superior work of cinematic art, while at the same time condemning it on moral grounds. Rather than support a strict separation of aesthetic and moral elements in an artwork, I will suggest that in the case of certain types of artwork, it is inappropriate to use moral criteria in their artistic evaluation—even though the work’s moral content contributes to its artistic value. This is the case in artworks that (1) are “interrogative” in form and (2) have moral dilemmas as their principal theme. Briefly put, an interrogative artwork is one that poses a question or problem that remains unresolved in the work. I will begin by explaining in more detail what I mean by an interrogative artwork. Using the example of Duchamp’s “ready-made” sculpture Fountain, I will argue that it is inappropriate to artistically evaluate such works by appeal to criteria that they themselves call into question. I will then turn to the specific issue of morally interrogative artworks. I will consider Mark Twain’s The Adventures of Huckleberry Finn as a paradigmatic case of an interrogative artwork that poses an unresolved moral problem, and will contrast my own rejection of the moral appraisal of the novel to Wayne Booth’s attempt to provide a morally informed positive assessment of the novel. (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)

Theoretically rigorous approach to the key problems of Molinism.

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)