The subject of the thesis is the relationship between aesthetic and God. It aims to discuss whether the sense of beauty is proof of the existence of God and to determine the plausibility of aesthetic proof. As a matter of fact that reality and the perception of beauty point to two-way consciousness. In this context, it will be inevitable to mention God's relation with consciousness in the emergence of beauty. In the first part, the concepts of (...) aesthetics will be analyzed, and their philosophical discussions will be investigated. In the second part, the source of beauty will be questioned, and beauty will be grounded way of a priori and a posteriori with God. Afterward, aesthetic proofs will be presented and an evaluation will be made in the context of naturalistic claims and objections. Among the traditional arguments in the philosophy of religion, aesthetic proof offers a value-oriented approach rather than a mechanical view. It appreciates beauty from an inclusive perspective and has an existential aspect. The study concentrates on the nature of beauty and aesthetics, philosophical discussions, and the rational value of aesthetic proof and concludes that it is rational to suppose that the existence of God can be ontologically and epistemologically explanatory for aesthetic properties. (shrink)

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal (...) processes of representing and assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

This article presents an ontological proof that God is impossible.I define an ‘impossibility’ as a condition which is inconceivable due to its a priori characteristics (e.g. a ‘square circle’). Accordingly, said conditions will not ever become conceivable, as they could in instances of a posteriori inconceivability (e.g. the notion that someone could touch a star without being burned). As the basis of this argument, I refer to an a priori observation (Primus, 2019) regarding our inability to imagine inconsistency (difference) (...) within any point of space. This observation renders the notion of absolute power to be inconceivable, a priori.I briefly discuss the moral implications of religious faith in the context of Purism: a moral rationalist paradigm. I conclude that whilst belief in God can be aesthetically expressed it should not be possessed as a material purpose, due to the illogicality of the latter category of belief and/or expression. With this article I provide conceptual delineation between harmless religious belief and expression—which, I argue, should be protected from persecution, as per any other artistic expression— and religious belief and expression which is materially harmful to society. Whilst I aim to protect religious freedom of expression on one hand, I duly aim to reduce instances of material faith in God(s) on the other. Finally, I aim to bring hope in the possibility for human salvation via technology—such that they should exist indefinitely as ‘demigods,’ defined by conditional, relative power over their environment. (shrink)

Is there a role for aesthetic judgements in science? One aspect of scientific practice, the use of thought experiments, has a clear aesthetic dimension. Thought experiments are creatively produced artefacts that are designed to engage the imagination. Comparisons have been made between scientific (and philosophical) thought experiments and other aesthetically appreciated objects. In particular, thought experiments are said to share qualities with literary fiction as they invite us to imagine a fictional scenario and often have a narrative form (...) (Elgin 2014). But philosophical discussions of aesthetics in science have focused mainly on the epistemic role of beauty and elegance when it comes to theories and mathematical proofs, and thought experiments have been widely overlooked. My aim in this chapter is to address how the aesthetic choices scientists make in the design of a thought experiment contribute to its function: to communicate, convince, or explain a theory or phenomenon. A key issue is whether any aesthetic features in science provide anything beyond catching our attention, or are at best, a mere heuristic aid. I respond to accounts that argue this way and show how formulation is important in scientific thought experiments and, similarly to literary fictions, there is more than one way of interpreting a thought experiment scenario. I end by considering which literary examples are most appropriate when making comparisons with thought experiments. As a result, the difference between representations in art and science raised in current discussions is not as stark as it has been made out to be, and science is a more heterogeneous practice than has been allowed. Part of the value of thought experiments in scientific practice includes the qualities they share with literary works. (shrink)

We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of (...) the proof, suggesting that a priori assumptions about the consistency of mathematical proof appraisals are unreasonable. (shrink)

It is widely agreed upon that aesthetic properties, such as grace, balance, and elegance, are perceived. I argue that aesthetic properties are experientially attributed to some non‐perceptible objects. For example, a mathematical proof can be experienced as elegant. In order to give a unified explanation of the experiential attribution of aesthetic properties to both perceptible and non‐perceptible objects, one has to reject the idea that aesthetic properties are perceived. I propose an alternative view: the affective (...) account. I argue that the standard case of experiential aesthetic property attribution is affective experience. (shrink)

The analogy between gustatory taste and critical or aesthetic taste plays a recurring role in the history of aesthetics. Our interest in this article is in a particular way in which gustatory judgments are frequently thought to be analogous to critical judgments. It appears obvious to many that to know how a particular object tastes we must have tasted it for ourselves; the proof of the pudding, we are all told, is in the eating. And it has seemed (...) just as obvious to many philosophers that aesthetic judgment requires first-person experience. In this article we argue that, despite its initial appeal, the claim that gustatory and critical judgments are analogous in this way is mistaken. The two sorts of judgments are, as a matter of fact, similar in their epistemology, but earlier theorists have got things entirely backward—neither gustatory judgment nor aesthetic judgment requires first-hand acquaintance with their objects. Our particular focus in this article is on arguing that first-person experience is not required to know how an item of food or drink tastes. In fact, there are a wide variety of ways in which we can acquire this knowledge. (shrink)

"Time. Perception. Imagination. Phenomenological Studies on the Question of Time by Augustine, Kant and Husserl". (rus), SPb, 2013. Summary: The monograph is devoted to the key elements of the philosophy of time which determine the necessity of historicism in the analysis of subjectivity. The main idea which defined the composition and design of this work is to trace how the Kantian definition of time as the “form of inner sense” is revealed in Husserl’s phenomenology. The original intention was to understand (...) all three components of this definition. Firstly, what is the inner form, in terms of phenomenology, what are the principles of its constitution and how one can talk about the property of formation? Secondly, what is the meaning of the term "inner" in philosophy, where the division into internal and external has always been a formality, not affecting the essence of things? And finally, what sort of “sensibility” is assumed in transcendental science, bound to become the basis of understanding the history and culture. Presumably, these three Kantian concepts constituted the original plan to analyze the nature of cognitive capabilities of the subject, claiming the gnoseological stage on which the philosophy of time is unfolded. In other words, this work deals with the historical and philosophical analysis of the phenomenological principles by which the concept of time as developed in the twentieth century emerged in the framework of phenomenology. The analyze of the structure of the subject assumes that time, perception and imagination combine in a special type of inner synthesis, which may not be relevant to certain aspects of the method but maintain the basis for a kind of anthropology of time, in continuation of the traditional “inner” contemplation. I consider the inner structure of time with the account of philosophy of St. Augustine, who in many respects not only anticipated the conclusions of phenomenology, but also in his reflections encompassed deeper layers of inner experience. The first chapter is devoted to the doctrine of St. Augustine, in which the theory of time is analyzed in conjunction with the doctrine of “inner word”, specifics of memory representations and notion of inner sense. Additionally, I consider St. Augustine’s reflections about numbers that constitute the basis of aesthetic perception of music (De Musica). Thus, the philosophy of St. Augustine already covers the whole spectrum of anthropology of time, including the question of relation between time and eternity, which remains practically unexplored in phenomenology and serves as the proof of that in interactions between philosophy and theology the tradition remains important. The second chapter of this study is devoted to analysis of the transcendental aesthetic of Kant, which includes all the methodological possibilities of considering the category of time as a formal condition for any experience, consequentially serving as a foundation for further logical development by Husserl, which includes the critical disengagement of the founder of phenomenology from Kant's transcendentalism. Particular attention is paid to the origin of the concept of inner sense, as well as possible interpretations of the function of imagination, which as a transcendental ability remains the most interesting type of synthesis. Handwritten fragments of Kant’s works are also of interest to the character of the imagery as considered in detail by Husserl. Chapter three discusses the phenomenology of inner time consciousness, represented in those important aspects, without which it is impossible to speak about the internal structure of temporal experience - the subjectivity of time, retention, "living present", and the character of synthesis. Particular attention is paid to Husserl's polemics with those representatives of psychological branch in the studies of consciousness, whose ideas greatly influenced the very motivation for creating the method. Apart from the well-known criticism of Brentano, the third chapter highlights the rarely analyzed psychological ideas that motivated the choice of Husserl’s terminology - the "Präsenzzeit” by W. Stern, the "psychological analysis" by A. Meinong, and the “fusion” (Verschmelzung) by K. Stumpf. Chapter four deals with the need to analyze the specifics of image as an element of consciousness and imagery as such, which includes a system of objectified acts. Thus is revealed the very nature of synthetic connections in the acts of consciousness, as well as the presumably imaginative character of the constitution of temporal form. (shrink)

In The Principles of Art, R. G. Collingwood pursues, on the one hand, a ‘definition’ of art, and, on the other, a ‘metaphysics’. The Principles is divided into three Books. Book I is devoted mostly to craft, while Book II pertains largely to metaphysics. The fact that Book II is twice the size of Book III, where the discussion of ‘art proper’ takes place, is proof enough that the metaphysical part of the Principles is not a mere excursus. Collingwood’s (...) ontology is indispensable for understanding his aesthetics, and vice versa. The crucial link is the imagination. What Collingwood calls ‘total imaginative experience’ is described in the Principles as the sine qua non of both thought and sensibility. The aim of this article is to examine the ontological import of Collingwood’s conception of the total imagination. (shrink)

It is a fact that there is ethical criticism about art. Art critics, the general public and even artists point out moral flaws in artworks while evaluating them. Philosophers, however, have maintained a hot debate on the meaning of such criticism. This debate can be understood as a disagreement about the kind of relation between the artistic value of artworks and their alleged moral value. While some claim that moral value can contribute to artistic value (moralism), others claim that there (...) cannot be such a contribution (autonomism). Since at least some works of architecture are artworks, that debate also concerns architecture. A moderate moralist view claims that some works of architecture have moral flaws/merits that bear on their artistic evaluation. In an apparently promising version, the contention is that some moral flaws/merits are aesthetically relevant. In this paper I argue against such contention and defend an autonomist view. Following some taxonomy remarks I distinguish the views in the debate and present two points in favour of autonomism: its simplicity and not having the burden of proof. Then I discuss Carroll’s merited response argument for moralism and I argue that in its best interpretation either it begs the question against autonomism or it is compatible with it. I conclude with some possible objections that may help further investigations on the subject. (shrink)

CATEGORY: Philosophy play; historical fiction; comedy; social criticism. -/- STORYLINE: Katherine, a neurotic American lawyer, meets Christianus for a philosophy session at The Late Victorian coffee shop in London, where they also meet Wendy the waitress and Baldy the player. Will Katherine be able to overcome her deep depression by adopting some of Christianus’s satisfactionist ideas? Or will she stay unsatisfied and unhappy by stubbornly sticking to her own neti-neti nothingness philosophy? And what roles do Baldy, Wendy, and the Okefenokee (...) Man-Monster have in this connexion? -/- TOPICS: In the course of this philosophy play, Katherine and Christianus discuss many things: friendship, a Renoir painting, global warming, elephant conservation, freemasons, Prince of Wales and his tiger-hunting experience in Nepal, Victorian Chartism and a Kennington Common daguerreotype, a Mortality Proof, and, last but not least, Baldy, Wendy, and the gory plot of the Okefenokee Man-Monster. -/- NOTES: This work features elaborate footnotes and comments (including full bibliographical references) by the author, to enhance the reader's experience of the play and its philosophizing characters. (shrink)

In this essay, I will look into Arthur Schopenhauer’s pessimism, which culminates in the view that since life is not worth living, it is better for us to deny it than try to affirm it. I will argue that his pessimism is not sustainable, and that it fails on its own propositions. In section 1, I will look at the importance of suffering as the central point in Schopenhauer’s pessimism. For Schopenhauer, the essence of the world, which he calls will, (...) is a never-ending, blind and purposeless striving that objectifies itself in the organic and inorganic world. Will, which can also be called the will to live, is constantly driving us from one desire to another, leaving us almost without rest in the constant state of need, hence suffering. I will argue against his position that only suffering is of a positive nature, while happiness can only be negative. According to Schopenhauer, the rare moments of happiness we experience consist only in the absence of suffering. I will also look into his view that absolute happiness is impossible to achieve and question this statement as a weak argument for pessimism. -/- Section 2 will focus on Schopenhauer’s use of the concepts of pain and suffering. As it seems that he uses them as co-extensive terms, I will explain why they are not co-extensive. -/- In section 3, I will discuss Schopenhauer’s view that the world has a moral meaning. Because of inevitable suffering, according to Schopenhauer, our only moral solution to the problem of suffering will be to deny suffering, consequently, life itself. And this is, for him, the hidden moral meaning of the world that only philosophy can uncover. -/- In section 4, I will look at the importance of aesthetic experience, which for Schopenhauer, represents the proof that the will can be abandoned and that the short periods of liberation from the will/suffering can be reached. As for Kant, for Schopenhauer, the aesthetic experience must be purposeless and unintentional and never contemplated or purposeful. Since our contemplated activities belong to the knowledge driven by the principle of practical reason that operates on the basis of our innate categories of time, space and causality and is related only to the phenomenal world, ideas that are the essence of artistic experience cannot be grasped by such knowledge. They can only be contemplated by objective knowledge by genius, who, in the process of artistic creation, abandons his individuality and disconnects from the phenomenal world completely, grasping the idea of a perceived object purely by its rare gift and not by reason. -/- In the final section, I will look at compassion, which can help us overcome suffering, according to Schopenhauer. By abandoning our selfishness through compassion, we can identify with the suffering of others and understand that we are the same as others. That will help us comprehend that our individuality is the main cause of suffering and trigger our attempt to overcome suffering through compassion. I will argue that compassion cannot be devoid of self-interest and, as such, still requires a strong presence of the will. I will also show why asceticism is, as the ultimate attempt to completely redeem suffering, antipodal to compassion. (shrink)

It is impossible to study philosophical methodology without being struck by the state of absolute chaos of the field’s methodological practices, methodological norms, and metaphilosophical beliefs. Not only are the methods of formal epistemology nothing like the methods of aesthetics, but even within specific debates and subfields, there are often significant disagreements about standards of proof, to say nothing about disagreements about the ultimate nature of the debate. The question facing metaphilosophers is whether this chaos is a feature or (...) a bug. Is the chaos a part of philosophy’s value as an incubator for new ideas or a sign that many philosophers have lost their way and are holding back philosophical progress? (shrink)

Kant’s argument in § 38 of the *Critique of Judgment* is subject to a dilemma: if the subjective condition of cognition is the sufficient condition of the pleasure of taste, then every object of experience must produce that pleasure; if not, then the universal communicability of cognition does not entail the universal communicability of the pleasure. Kant’s use of an additional premise in § 21 may get him out of this difficulty, but the premises themselves hang in the air and (...) have no independent plausibility. What Kant offers as a proof of our right to make judgments of taste is more charitably construed as an indirect argument for the adequacy of a speculative explanation of a *presumed* right to make judgments of taste. (shrink)

With the positively ending Elektra, Sophocles wanted to show the audience how political and moral independence, judgment and the courage to act are necessary - to a sometimes extreme extent - for the good of the family and the state. Even in the old democracy, virtue - which for Hegel was a principle of democracy - was not enough on its own. The downfall of democracy was probably due to a lack of individuality rather than the emergence of that individuality. (...) We find the negative result of Hegel's general assessment of the contribution of an individual to democracy not only in relation to ancient democracy. In a similar sense he expresses himself about contemporary conditions. In the Reform Bill article he describes how a French voter makes up a ninety-millionth part of the legislative power and will therefore pay little attention to his contribution to the general public. Although the Athenian democracy was smaller and different from the French one, its citizens probably needed proof of the need for individual participation in it too. Sophocles' Electra served this purpose. How Elektra and Orestes re-paved the way for an essential institution of democracy, the court of justice, will not have escaped the onlookers' attention. In this play it was shown that individuality could have negative as well as positive consequences. After all, it was only through the appearance of Electra and Orestes that justice could be saved and become a public matter again. (shrink)

Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices that contradict the (...) original intention of modern eristic. Eristic is not an art of being right or winning an argument, but an art of protecting oneself from the one who deliberately violates norms of discourse ethics to gain argumentative acceptance. For this reason, eristic must be seen as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Especially in the age of alternative facts and post-factual politics, this makes eristic a valuable discipline. (shrink)

Aesthetic reasons are reasons to do and think various things. For example, it makes sense to wonder if a tree stump on the lawn was left there for environmental rather than aesthetic reasons, or for no reason at all. Aesthetic considerations of this kind are often contrasted with non-aesthetic reasons—such as moral or epistemic reasons. For example, they seem connected to pleasure-in-experience in a distinctive way that differs from paradigmatic moral reasons. Relatedly, the authority of (...) class='Hi'>aesthetic reasons has often been thought to involve less of an “external demand” upon us than in the other cases. In this chapter, I suggest that such distinctiveness and modesty coheres well with an anti-realist treatment that views them as non-objective in nature. I then go on to consider an alternative, more robustly realist conception of aesthetic reasons. (shrink)

Aesthetic properties figure prominently in our daily lives, our conversations and many actions we take. Yet theoretical disagreement prevails over their nature, their variety, their epistemic and metaphysical status. This overview highlights the heterogeneity of aesthetic properties and examines repercussions for explanation. Aesthetic properties belong to natural objects or scenes, to artworks in any medium, to artefacts and built environments across historical eras; and they draw a wide variety of responses such as our perceptions, emotions or imaginative (...) thought. Historicism about artworks carries over to at least some aesthetic properties that depend on facts of their broader historical context just as works do. One issue is whether aesthetic properties can be demarcated solely in terms of non-aesthetic properties. If not, explanations of aesthetic properties need to draw on other aesthetic notions such as aesthetic experience, attention, judgement or value. The paper examines several accounts of aesthetic value to show how they extend to aesthetic properties. The paper concludes with an overview of the current metaphysical debate between realists and non-realists about aesthetic properties. (shrink)

This essay addresses one of the open questions of proof-theoretic semantics: how to understand the semantic values of atomic sentences. I embed a revised version of the explanatory proof system of Millson and Straßer (2019) into the proof-theoretic semantics of Francez (2015) and show how to specify (part of) the intended interpretation of atomic sentences on the basis of their occurrences in the premises and conclusions of inferences to and from best explanations.

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of (...) finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .

The standard of proof in criminal trials in many liberal democracies is proof beyond a reasonable doubt, the BARD standard. It is customary to describe it, when putting a number on it, as requiring that the fact finder be at least 90% certain, after considering the evidence, that the defendant is guilty. Strikingly, no good reason has yet been offered in defense of using that standard. A number of non-consequentialist justifications that aim to support an even higher standard (...) have been offered; all are morally unsound. Meanwhile, consequentialist arguments plausibly support a substantially lower standard — in some cases so low as to undermine the idea that punishment is what is at stake. In this paper, I offer a new retributive justification that supports excluding the instrumental benefits of punishment from the balance that sets the standard. The resulting balance supports a standard arguably in the ballpark of the customary understanding of BARD: a standard requiring that the fact finder have a high, though not maximally high, degree of confidence that the defendant is guilty. (shrink)

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...) of proof, instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to (...) allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation (...) schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

Gottfried Leibniz embarked on a research program to prove all the Aristotelic categorical syllogisms by diagrammatic and algebraic methods. He succeeded in proving them by means of Euler diagrams, but didn’t produce a manuscript with their algebraic proofs. We demonstrate how key excerpts scattered across various Leibniz’s drafts on logic contained sufficient ingredients to prove them by an algebraic method –which we call the Leibniz-Cayley (LC) system– without having to make use of the more expressive and complex machinery of first-order (...) quantificational logic. In addition, we prove the classic categorical syllogisms again by a relational method –which we call the McColl-Ladd (ML) system– employing categorical relations studied by Hugh McColl and Christine Ladd. Finally, we show the connection of ML and LC with Boolean algebra, proving that ML is a consequence of LC, and that LC is a consequence of the Boolean lattice axioms, thus establishing Leibniz’s historical priority over George Boole in characterizing and applying (a sufficient fragment of) Boolean algebra to effectively tackle categorical syllogistic. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established (...) to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

This paper traces the philosophical concept of life prior to Kant and uses this to contextualize his account of aesthetic judgment as a form of life. It argues on this basis that, according to Kant, the form that taste claims for itself, as explicated in its four moments, results in a demand being placed on the transcendental philosopher to admit the idea of an ultimate subjective basis of all cognitive activities in human beings, that is, a shared principle and (...) form of cognititive life htat is uniquely human. (shrink)

The paper highlights analytic aesthetics’ unacknowledged assumption that art is timeless, a view it inherited from Enlightenment thinkers such as Hume and Kant, who in turn inherited it from the Renaissance. This view, I contend, is no longer tenable because it is at odds with our experience of the art of the past. Analytic aesthetics bypasses this dilemma because it confines its attention to topics such as the nature of aesthetic pleasure, whether the appreciation of art should be disinterested (...) and so on, which it partitions off from historical change and encases in a world where time stands still and where, by consequence, the temporal nature of art, including art’s capacity to transcend time, can be ignored. (shrink)

Philosophers have predominantly regarded morality and aesthetics judgments as fundamentally different. However, whether this claim is empirically founded has remained unclear. In a novel task, we measured brain activity of participants judging the aesthetic beauty of artwork or the moral goodness of actions depicted. To control for the content of judgments, participants assessed the age of the artworks and the speed of depicted actions. Univariate analyses revealed whole-brain corrected, content-controlled common activation for aesthetics and morality judgments in frontopolar, dorsomedial (...) and ventrolateral prefrontal cortex. Temporoparietal cortex showed activation specific for morality judgments, occipital cortex for aesthetics judgments. Multivariate analyses revealed both common and distinct whole-brain corrected representations for morality and aesthetics judgments in temporoparietal and prefrontal regions. Overall, neural commonalities are more pronounced than predominant philosophical views would predict. They are compatible with minority accounts that stress commonalities between aesthetics and morality judgments, such as sentimentalism and a valuation framework. (shrink)

Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.

Analytic aesthetics has been obsessed with mature, art historically well-informed aesthetic judgment. But the vast majority of our engagement with art fails to take the form of this kind of judgment. Crucially, there seems to be a disconnect between taking pleasure in art and forming mature, well-informed judgments about it. My aim is to shift the emphasis away from aesthetic judgments to ways of engaging with works of art that are more enjoyable, more rewarding and happen to us (...) more often. (shrink)

Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...) process? What is the ontological status of a mathematical proof? Can computer assisted provers output a proof? Taking a naturalized world account, I will assess the relationship between mathematics, the physical world and consciousness by introducing a significant conceptual distinction between proving and proof. I will propose that proving is a phenomenological conscious experience. This experience involves a combination of what Kurt Gödel called intuition, and what Husserl called intentionality. In contrast, proof is a function of that process — the mathematical phenomenon — that objectively self-presents a property in the world, and that results from a spatiotemporal unity being subject to the exact laws of nature. In this essay, I apply phenomenology to mathematical proving as a performance of consciousness, that is, a lived experience expressed and formalized in language, in which there is the possibility of formulating intersubjectively shareable meanings. (shrink)

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings (...) of modal operators in terms of rules of inference. (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases (...) suggests standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

There is a long tradition of logic, from Aristotle to Gödel, of understanding a proof from the concepts of necessity and causality. Gödel's attempts to define provability in terms of necessity led him to the distinction of formal and absolute (abstract) provability. Turing's definition of mechanical procedure by means of a Turing machine (TM) and Gödel's definition of a formal system as a mechanical procedure for producing formulas prompt us to understand formal provability as a mechanical causality. We propose (...) a formalism which makes explicit the mechanical causal nature of a TM's work. We claim that Gödel's axiomatised ontotheology and his ontological proof give a clue for the understanding of the concept of absolute provability and the pattern of the corresponding absolute completeness proof, respectively. (shrink)

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical (...) proposition based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

Aesthetic considerations played a substantial and positive role in the development and acceptance of plate tectonics, the modern theory of the earth’s major geological features and the unifying framework of the earth sciences. Here I give an overview of how aesthetics influenced plate tectonics and take a detailed look at a handful of examples from this history where elegance and simplicity tipped the balance in favour of a given hypothesis. I discuss some implications of this case study for extant (...) accounts of aesthetics in science and argue that the positive role aesthetics played can be explained by recent accounts that posit an indirect and contingent link between knowledge and psychological mechanisms underlying aesthetic appreciation. (shrink)

Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in (...) Kyoto's school. For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them. (shrink)

Among semanticists and philosophers of language, there has been a recent outburst of interest in predicates such as delicious, called predicates of personal taste (PPTs, e.g. Lasersohn 2005). Somewhat surprisingly, the question of whether or how we can distinguish aesthetic predicates from PPTs has hardly been addressed at all in this recent work. It is precisely this question that we address. We investigate linguistic criteria that we argue can be used to delineate the class of specifically aesthetic adjectives. (...) We show that there are, in fact, good motivations for keeping PPTs and aesthetic predicates apart: the semantic structure of the former, but not the latter, entails an experiencer. There are many adjectives whose semantic structure arguably also entails an experiencer, yet which are readily used in expressing aesthetic judgments. Adjectives such as provocative or moving are a case in point, since as adjectives they arguably maintain the experiencer argument from the verb they are derived from. Nevertheless, when we describe, say, a sculpture as provocative, or a theater performance as moving, we clearly make aesthetic judgments. The difficult question, then, is to articulate the relationship between an aesthetic predicate (of which beautiful and ugly are paradigms) and other predicates that just happen to be used in making an aesthetic judgment. Tightly related to this point is the more general question of the relationship between an evaluative predicate and a predicate that occurs in an evaluative judgment. One of our aims is to make some progress in addressing these questions. (shrink)

Aesthetic theorists often interpret and understand works of art through the social and political context that creates and inspires the work. The recent economic recessions, and the accompanying austerity measures in many European countries, provide an interesting test case for this contextual understanding. Economists debate whether or not spending on entertainment and arts drops during times of recession and austerity. Some economists assume that spending will decline in times of austerity, but others point to evidence that spending on creative (...) arts and entertainment remains steady and even increases during a recession because of the relief and escapism that the arts provide. Tax incentives and production rights are often given to filmmakers in the United States; in hopes that such projects will enliven a local economy and provide work for a local creative community. In the context of recent austerity measures in Greece and Spain, new and creative ways for members of the arts community to bring about new projects, and fund them in ways that critique political leadership, have emerged. Following Richard Wollheim’s classic aesthetic theory of “criticism as retrieval,” we should be mindful of the cultural values that are at stake in the creativity-culture market now being created. In any case, some scholars estimate that austerity measures in many countries will last until 2020, giving us ample opportunity to be even more “creative” with both financial incentives and artistic achievements. Keywords: Austerity, Cultural Economy, Creative Class, Tax Incentives, Aesthetics, Microtheatres, Entertainment. (shrink)

Are aesthetic judgements cognitive, belief-like states or non-cognitive, desire-like states? There have been a number of attempts in recent years to evaluate the plausibility of a non-cognitivist theory of aesthetic judgements. These attempts borrow heavily from non-cognitivism in metaethics. One argument that is used to support metaethical non-cognitivism is the argument from Motivational Judgement Internalism. It is claimed that accepting this view, together with a plausible theory of motivation, pushes us towards accepting non-cognitivism. A tempting option, then, for (...) those wishing to defend aesthetic non-cognitivism, would be to appeal to a similar argument. However, both Caj Strandberg and Walter Sinnott-Armstong have argued that Internalism is a less plausible claim to make about aesthetic judgements than about moral judgements by raising objections against aesthetic internalism. In this paper, I will argue that both of these objections can be raised against internalism about moral judgements as well. As a result, internalism is no less plausible a claim to make about aesthetic judgements than about moral judgements. I will then show how a theory of internalism about normative judgements in general is capable of avoiding both of these objections. (shrink)

We argue that the aesthetic domain falls inside the scope of rationality, but does so in its own way. Aesthetic judgment is a stance neither on whether a proposition is to be believed nor on whether an action is to be done, but on whether an object is to be appreciated. Aesthetic judgment is simply appreciation. Correlatively, reasons supporting theoretical, practical and aesthetic judgments operate in fundamentally different ways. The irreducibility of the aesthetic domain is (...) due to the fact that aesthetic judgment is a sensory-affective disclosure of, and responsiveness to, merit: it is a feeling that presents an object, and is responsive to it, as worthy of being liked. Aesthetic judgment is thus shown to be, on the hand, first personal and non-transferable; and, on the other hand, a presentation of reality. We thereby capture what is right in both subjectivist and objectivist conceptions of aesthetic judgment. (shrink)

Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal aseity, and the (...) argument ex consensu gentium. Drawn from the work of eighteen philosophers, this book includes both canonical figures (such as Descartes, Spinoza, Newton, Leibniz, Locke, and Berkeley) and noncanonical thinkers (such as Norris, Fontenelle, Voltaire, Wolff, Du Châtelet, and Maupertuis). -/- Lloyd Strickland provides fresh translations of all selections not originally written in English and updates the spelling and grammar of those that were. Each selection is prefaced by a lengthy headnote, giving a biographical account of its author, an analysis of the main argument(s), and important details about the historical context. Strickland’s introductory essay provides further context, focusing on the various reasons that led so many thinkers of early modernity to develop proofs of God’s existence. -/- Proofs of God is perfect for both students and scholars of early modern philosophy and philosophy of religion. (shrink)

In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals (...) with the problem of undergeneration and Chapter 3 concerns the problem of overgeneration. Chapter 2 discusses that Tenant’s diagnosis of the counterexample which applies CR−rule and causes the undergeneration problem is not correct and presents a solution to the problem of undergeneration. Chapter 3 argues that Tennant’s diagnosis of the counterexample raising the overgeneration problem is wrong and provides a solution to the problem. Finally, Chapter 4 addresses what should be explicated in order for RND to be a proof-theoretic solution to the paradoxes. (shrink)

Aesthetics is thought of as not only a theory of art or beauty, but also includes sensibility, experience, judgment, and relationships. This paper is a study of Bernard Stiegler’s notion of Aesthetic War (stasis) and symbolic misery. Symbolic violence is ensued through a loss of individuation and participation in the creation of symbols. As a struggle between market values against spirit values human life and consciousness within neoliberal hyperindustrial society has become calculable, which prevents people from creating affective and (...) meaningful attachments to symbols in relation to our retentional apparatuses, technology and memory. Such tension can be thought of as a dissonance between overlapping domains of social life, private and public. New Media is a reflection of aesthetic dissonance, an experience such as being bored and entertained at the same time, between antagonistic experiences, values, and behavior. Moreover, new media is at once a medium of customizing aesthetic experience individually as well as the threat and practice of prioritizing calculability and modeling of consumer behavior in favor of capitalistic effectiveness, which results in the simultaneous categorization of an individual as a data point, putting those who do not fit an algorithm’s premises at a disadvantage. (shrink)

This paper is an English version of the paper that was published in German under the title: "Über die Aussichten erfolgreicher Beweise für Theismus oder Atheismus". My English paper was translated into German by Gabriele Schlegel. -/- The aim of this paper is to examine the prospects for proofs or successful arguments for the existence or non-existence of God.

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based (...) voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

A theory of aesthetic value should explain what makes aesthetic value good. Current views about what makes aesthetic value good privilege the individual’s encounter with aesthetic value—listening to music, reading a novel, writing a poem, or viewing a painting. What makes aesthetic value good is its benefit to the individual appreciator. But engagement with aesthetic value is often a social, participatory matter: sharing and discussing aesthetic goods, imitating aesthetic agents, dancing, cooking, dining, (...) or making music together. This article argues that we should understand aesthetic value in a way that centers these social forms of aesthetic engagement. To this end, the article argues that there is a social practice of aesthetic valuing, characterized as a participatory practice governed by the value of aesthetic community, which engages us in the social development of our capacities for discretionary valuing and volitional openness. Current theories of aesthetic value have trouble capturing the character of the practice of aesthetic valuing, and this motivates a novel communitarian theory of aesthetic value: aesthetic value is what is worthy of engagement in the social practice of aesthetic valuing. (shrink)

This essay surveys the main objections to aesthetic hedonism, the view that aesthetic value is reducible to the value of aesthetic pleasure or experience. Hedonism is the dominant view of aesthetic value, but a spate of recent criticisms has drawn its accuracy into question. I introduce some distinctions crucial to the criticisms, before using the bulk of the essay to identify and review six major lines of argument that hedonism's critics have employed against it. Whether or (...) not these arguments suffice to refute hedonism decisively, I argue that its privileged status, as the sole contender in aesthetic value theory, is detrimental to downstream research on aesthetic phenomena. The essay concludes with an overview of current work and promising avenues of inquiry into non-hedonic alternatives. (shrink)