This volume of new essays presents groundbreaking interpretations of some of the most central themes of Wittgenstein's philosophy. A distinguished group of contributors demonstrates how Wittgenstein's thought can fruitfully be applied to contemporary debates in epistemology, metaphilosophy and philosophy of language. The volume combines historical and systematic approaches to Wittgensteinian methods and perspectives, with essays providing detailed analysis that will be accessible to students as well as specialists. The result is a rich and illuminating picture of a key figure in (...) twentieth-century philosophy and his continuing importance to philosophical study. (shrink)

Review of the book "Engaging Putnam".

Public reason liberalism is the political theory which holds that coercive laws and policies are justified when and only when they are grounded in reasons of the public. The standard interpretation of public reason liberalism, consensus accounts, claim that the reasons persons share or that persons can derive from shared values determine which policies can be justified. In this paper, I argue that consensus approaches cannot justify fair educational policies and preserving cultural goods. Consensus approaches can resolve some controversies about (...) teaching values in the educational system, such as curriculum choice. But they cannot determine which culture goods, e.g., architecture, artwork, or language ought to be preserved in the education system. Consensus approaches cannot fairly resolve competing claims about these kinds of disputes. -/- I propose that convergence accounts of public reason, which allow individuals to draw on their own comprehensive doctrines in limited ways, can remedy these weaknesses in the mainline public reason tradition. The convergence approach can justify a pluralist state that can advance valuable community goods. John Henry Newman’s advocacy of liberal arts education finds resonance in other cultures, notably among Confucians, illustrating that there can be a shared moral vision and inquiry into the good life across deep substantive disagreements about educational values and policies, once we expand our notion of justification to be more inclusive. (shrink)

A state-based reason for one to intend to perform an action F is a reason for one to intend to F which is not a reason for one to F. Are there any state-based reasons to intend? According to the Explanatory Argument, the answer is no, because state-based reasons do not satisfy a certain explanatory constraint. I argue that whether or not the constraint is correct, the Explanatory Argument is unsound, because state-based reasons do satisfy the constraint. The considerations that (...) undermine the Explanatory Argument also generate a strong, positive case for the existence of state-based reasons to intend. (shrink)

This chapter considers possible moral grounds for recognizing and realizing economic and social rights (ESRs) as human rights. It begins by suggesting that ESRs fall into three families: (1) welfareoriented ESRs, which protect adequate income, education, health, and safe and healthful working conditions; (2) freedom-oriented ESRs, which prohibit slavery, ensure free choice of employment, and protect workers’ freedoms to organize and strike: and (3) fairness-oriented ESRs, which require nondiscrimination and equal opportunity in the workplace along with fair remuneration for one’s (...) work. To accommodate the normative diversity found in these three families, the chapter suggests a pluralistic justicatory framework that appeals to three kinds of moral reasons: human welfare, freedom, and fairness. A final section considers the possibility of subsuming all three of these approaches to justication under the idea of human dignity or the associated idea of equal respect for persons. (shrink)

In this paper, I aim to discuss what puns, metaphysically, are. I argue that the type-token view of words leads to an indeterminacy problem when we consider puns. I then outline an alternative account of puns, based on recent nominalist views of words, that does not suffer from this indeterminacy.

Kant was engaged in a lifelong struggle to achieve what he calls in the 1756 Physical Monadology (PM) a “marriage” of metaphysics and geometry (1:475). On one hand, this involved showing that metaphysics and geometry are complementary, despite the seemingly irreconcilable conflicts between these disciplines and between their respective advocates, the Leibnizian-Wolffians and the Newtonians. On the other hand, this involved defining the terms of their union, which meant among other things, articulating their respective roles in grounding Newtonian natural science. (...) In this paper, consider how Kant’s project of marrying metaphysics and geometry evolves from the pre-Critical to the Critical period and how key discussions in the Prolegomena are related to the lifelong marriage project. (shrink)

Amie Thomasson’s work provides numerous ways to rethink and improve our approach to metaphysics. This chapter is my attempt to begin to sketch why I still think the easy approach leaves room for substantive metaphysical work, and why I do not think that metaphysics need rely on any ‘epistemically metaphysical’ knowledge. After distinguishing two possible forms of deflationism, I argue that the easy ontologist needs to accept (implicitly or explicitly) that there are worldly constraints on what sorts of entities could (...) exist, and could co-exist. I argue this leaves room for a substantive role for metaphysics if (following the work of E.J. Lowe) we take metaphysics to be concerned with the possible ways that reality could be. I explain how this conception does not need to appeal to any ‘epistemically metaphysical’ knowledge, and need only make use of conceptual and/or empirical means to arrive at views on what could exist (and co-exist). Thus, the answer I propose to the question posed in the title, at least in my view, is no-one. Or, at least, no-one should be afraid of conceptual analysis. Not even metaphysicians. (shrink)

The Münchhausen trilemma is the following: When trying to prove a fundamental truth, you run into one of, two of, or all three of the following issues: -/- 1: Circular reasoning 2: Infinite regress 3: An arbitrary starting point -/- But what if these are not in fact “problems”, but three different ways to observe the fundamental truth? Reconciling the three and showing how they function together is what I endeavor to articulate here.

Today, we find ourselves living during the most Religious era in all of human history. If this statement is true, it is also how we can predict the end of the human story.

The teachings and actions of Jesus Christ (Yeshua Ha'Mashiach) and the apostles recorded in the New Testament are analyzed in regard to their ethical and political philosophy, with analysis of context vis-à-vis the Old Testament (Tanakh, or Hebrew Bible) being given. From this analysis, it is shown that Jesus is a libertarian anarchist, i.e., a consistent voluntaryist. The implications this has for the world are profound, and the ramifications of Jesus's anarchism to Christians' attitudes toward government (the state) and its (...) actions are explicated. (shrink)

There is a meaning crisis correlated with the exponential rate of technology; As it disrupts our lives and forces society and its individuals to adapt increasingly quickly, we lose meaning. The challenge to deal with this immediately becomes philosophical, as we have never before needed to define and understand what “meaning” is on such a conscious level.

This volume brings together diverse sets of standpoints on liberalism in an era of growing skepticism and distrust regarding liberal institutions. The essays in the volume: - Relate concerns for liberal institutions with classical themes in perfectionist politics, such as the priority of the common good in decision-making or the role of comprehensive doctrines. - Analyse how perfectionist intuitions about the political life affect our concepts of public reason or public justification. - Outline various moral duties we have toward other (...) persons that underlie the liberal institutions or notions of rights functioning across the contemporary political landscape. - Explore various aspects of pluralism from within influential religious or philosophical traditions, applying insights from those traditions to issues in contemporary politics. The comprehensive volume will be of great interest to scholars, students, and researchers of politics, especially those in political philosophy and political theory. (shrink)

In this paper I take issue with James Conant’s claim that Johannes Climacus seeks to engage his reader in the Postscript by himself enacting the confusions to which he thinks his reader is prone. I contend that Conant’s way of reading the Postscript fosters a hermeneutic of suspicion that leads him (and those who follow his approach) to be unduly suspicious of some of Climacus’ philosophical activity. I argue that instead of serving as a mirror of his (...) reader’s faults, Climacus is better conceived of as a Socratic figure whose own philosophical activity represents a positive alternative to the Hegelian style of doing philosophy that is under attack in the Postscript. I close the paper by arguing that Climacus adopts two very different experimental stances in his two books: while in Fragments Climacus adopts the stance of someone who has “forgotten” about Christianity, in the Postscript he openly declares that he is not a Christian and then proceeds to investigate the question, appropriately cast in the first person, “How do I,Johannes Climacus, become a Christian?” I maintain that we will not be in a position to appreciate what makes the Postscript a profound work of philosophy until we obtain a better understanding of the various respects in which Climacus is a Socratic figure. (shrink)

(1st draft for review) -/- WARNING: -/- Reading this book comes with certain dangers to be mindful of; Please consider the following suggestions to avoid them: -/- 1: Do not try to perceive infinity; Any kind of success here leads to psychosis. 2: Do not try to resolve the paradoxes; To understand the greater truth of this book, paradoxes must be accepted as true. 3: Do not read this book if your faith is unstable and having it challenged could potentially (...) put you into existential crisis. (shrink)

Analysis is given of the Omega Point cosmology, an extensively peer-reviewed proof (i.e., mathematical theorem) published in leading physics journals by professor of physics and mathematics Frank J. Tipler, which demonstrates that in order for the known laws of physics to be mutually consistent, the universe must diverge to infinite computational power as it collapses into a final cosmological singularity, termed the Omega Point. The theorem is an intrinsic component of the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) describing (...) and unifying all the forces in physics, of which itself is also required by the known physical laws. With infinite computational resources, the dead can be resurrected--never to die again--via perfect computer emulation of the multiverse from its start at the Big Bang. Miracles are also physically allowed via electroweak quantum tunneling controlled by the Omega Point cosmological singularity. The Omega Point is a different aspect of the Big Bang cosmological singularity--the first cause--and the Omega Point has all the haecceities claimed for God in the traditional religions. -/- From this analysis, conclusions are drawn regarding the social, ethical, economic and political implications of the Omega Point cosmology. (shrink)

It is shown that libertarian anarchism (i.e., consistent liberalism) is unavoidably true.

This project has been supported by the Australian Government through the Australian Research Council (project number CS170100008); the Department of Industry, Innovation and Science; and the Department of Prime Minister and Cabinet. ACOLA collaborates with the Australian Academy of Health and Medical Sciences and the New Zealand Royal Society Te Apārangi to deliver the interdisciplinary Horizon Scanning reports to government. The aims of the project which produced this report are: 1. Examine the transformative role that artificial intelligence may play in (...) different sectors of the economy, including the opportunities, risks and challenges that advancement presents. 2. Examine the ethical, legal and social considerations and frameworks required to enable and support broad development and uptake of artificial intelligence. 3. Assess the future education, skills and infrastructure requirements to manage workforce transition and support thriving and internationally competitive artificial intelligence industries. (shrink)

One cannot understand the extreme schizophrenia and sadomasochistic psychopathy of mankind--and hence the appeal that etatism holds for many--without incorporating the crucial insight provided by psychologist Julian Jaynes in his 1976 monograph The Origin of Consciousness in the Breakdown of the Bicameral Mind. And here I'm not speaking of so-called "aberrant" human psychology, but rather simply standard human psychology that all humans are born with due to natural evolution.

In How We Get Along, philosopher David Velleman compares our social interactions to the interactions among improvisational actors on stage. He argues that we play ourselves - not artificially but authentically, by doing what would make sense coming from us as we really are. And, like improvisational actors, we deal with one another in dual capacities: both as characters within the social drama and as players contributing to the shared performance. In this conception of social intercourse, Velleman finds rational grounds (...) for morality, though not a rational guarantee. He maps a middle course between skepticism and rationalism, arguing that practical reasoning is 'pro-moral' without requiring moral action. The result is what he calls a 'Kinda Kantian metaethics'. How We Get Along is the summation of Velleman's thinking to date, incorporating and unifying previous work on agency, the self, the emotions, narrative and Kantian moral theory. (shrink)

According to the view that there is moral encroachment in epistemology, whether a person has knowledge of p sometimes depends on moral considerations, including moral considerations that do not bear on the truth or likelihood of p. Defenders of moral encroachment face a central challenge: they must explain why the moral considerations they cite, unlike moral bribes for belief, are reasons of the right kind for belief (or withheld belief). This paper distinguishes between a moderate and a radical version of (...) moral encroachment. It shows that, while defenders of moderate moral encroachment are well-placed to meet the central challenge, defenders of radical moral encroachment are not. The problem for radical moral encroachment is that it cannot, without taking on unacceptable costs, forge the right sort of connection between the moral badness of a belief and that belief’s chance of being false. (shrink)

Subject-sensitive invariantism posits surprising connections between a person’s knowledge and features of her environment that are not paradigmatically epistemic features. But which features of a person’s environment have this distinctive connection to knowledge? Traditional defenses of subject-sensitive invariantism emphasize features that matter to the subject of the knowledge-attribution. Call this pragmatic encroachment. A more radical thesis usually goes ignored: knowledge is sensitive to moral facts, whether or not those moral facts matter to the subject. Call this moral encroachment. This paper (...) argues that, insofar as there are good arguments for pragmatic encroachment, there are also good arguments for moral encroachment. (shrink)

A number of theistic philosophers have recently denied that God is subject to moral and rational norms. At the same time, many theists employ epistemological and inductive arguments for the existence of God. I will argue that ‘no-norms’ theists cannot make use of such arguments: if God is not subject to norms – particularly rational norms – then we can say nothing substantive about what kind of worlds God would be likely to create, and as such, we cannot predict the (...) likelihood of any particular evidence given theism. What is more, I argue that this lack of constraint on God's creative act raises a serious sceptical challenge for no-norms theism. (shrink)

Recent debates between representational and relational theories of perceptual experience sometimes fail to clarify in what respect the two views differ. In this essay, I explain that the relational view rejects two related claims endorsed by most representationalists: the claim that perceptual experiences can be erroneous, and the claim that having the same representational content is what explains the indiscriminability of veridical perceptions and phenomenally matching illusions or hallucinations. I then show how the relational view can claim that errors associated (...) with perception should be explained in terms of false judgments, and develop a theory of illusions based on the idea that appearances are properties of objects in the surrounding environment. I provide an account of why appearances are sometimes misleading, and conclude by showing how the availability of this view undermines one of the most common ways of motivating representationalist theories of perception. (shrink)

Experimental philosophy brings empirical methods to philosophy. These methods are used to probe how people think about philosophically interesting things such as knowledge, morality, and freedom. This paper explores the contribution that qualitative methods have to make in this enterprise. I argue that qualitative methods have the potential to make a much greater contribution than they have so far. Along the way, I acknowledge a few types of resistance that proponents of qualitative methods in experimental philosophy might encounter, and provide (...) reasons to think they are ill-founded. (shrink)

In this chapter I argue that there are three different senses of 'lie' in Kant's moral philosophy: the lie in the ethical sense (the broadest sense, which includes lies to oneself), the lie in the 'juristic' sense (the narrowest sense, which only includes lies that specifically harm particular others), and the lie in the sense of right (or justice), which is narrower than the ethical sense, but broader than the juristic sense, since it includes all lies told to others, including (...) those who are bent on harming innocent others. (shrink)

The default theory of aesthetic value combines hedonism about aesthetic value with strict perceptual formalism about aesthetic value, holding the aesthetic value of an object to be the value it has in virtue of the pleasure it gives strictly in virtue of its perceptual properties. A standard theory of aesthetic value is any theory of aesthetic value that takes the default theory as its theoretical point of departure. This paper argues that standard theories fail because they theorize from the default (...) theory. (shrink)

Naïve realism, often overlooked among philosophical theories of perception, has in recent years attracted a surge of interest. Broadly speaking, the central commitment of naïve realism is that mind-independent objects are essential to the fundamental analysis of perceptual experience. Since the claims of naïve realism concern the essential metaphysical structure of conscious perception, its truth or falsity is of central importance to a wide range of topics, including the explanation of semantic reference and representational content, the nature of phenomenal consciousness, (...) and the basis of perceptual justification and knowledge. One of the greatest difficulties surrounding discussions of naïve realism, however, has been lack of clarity concerning exactly what affirming or denying it entails. In particular, it is sometimes unclear how naïve realism is related to the claim that perceptual experience is in some sense direct or unmediated, and also to what extent the view is compatible with another widely discussed thesis in the philosophy of perception, the claim that perceptual experiences are states with representational content. In this essay, I discuss how recent work on these issues helps to clarify both the central commitments of naïve realism, as well as its relation to representationalist theories of perception. Along the way, I will attempt to shed light on the different ways in which each approach tries to address the various theoretical challenges facing a philosophical theory of perception, and also to assess the prospects for views that attempts to combine features of each approach. (shrink)

This paper defends the usefulness of the concept of philosophical progress and the common assumption that philosophy and science aim to make the same, or a comparable, kind of progress. It does so by responding to Yafeng Shan's (2022) arguments that the wealth of research on scientific progress is not applicable or useful to philosophy, and that philosophy doesn't need a concept of progress at all. It is ultimately argued that while Shan's arguments are not successful, they reveal the way (...) forward in developing accounts of philosophical progress. (shrink)

The collaboration of Language and Computing nv (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is guided by the hypothesis that quality constraints on ontologies for software ap-plication purposes closely parallel the constraints salient to the design of sound philosophical theories. The extent of this parallel has been poorly appreciated in the informatics community, and it turns out that importing the benefits of phi-losophical insight and methodology into application domains yields a variety of improvements. L&C’s LinKBase® (...) is one of the world’s largest medical domain ontologies. Its current primary use pertains to natural language processing ap-plications, but it also supports intelligent navigation through a range of struc-tured medical and bioinformatics information resources, such as SNOMED-CT, Swiss-Prot, and the Gene Ontology (GO). In this report we discuss how and why philosophical methods improve both the internal coherence of LinKBase®, and its capacity to serve as a translation hub, improving the interoperability of the ontologies through which it navigates. (shrink)

ABSTRACT: In a previous article (O’Shea 2006) I provided a concise overview of the reception of Kant’s philosophy among analytic philosophers during the periods from the ‘early analytic’ reactions to Kant in Frege, Russell, Carnap and others, to the systematic Kant-inspired works in epistemology and metaphysics of C. I. Lewis and P. F. Strawson, in particular. In this chapter I use the recently reinvigorated work of Wilfrid Sellars (1912–1989) in the second half of the twentieth century as the basis for (...) presenting some of the most familiar ‘analytic Kantian’ themes that continue to animate current debates. I also argue that the complex relationships between Sellars’ philosophy and Kant’s thought are often misunderstood. Overall the chapter examines Sellars’ analytic appropriations of Kant in three topic-areas of significant current philosophical debate: (1) conceptual analysis and the structure of human knowledge; (2) laws of nature, the causal modalities, and the pragmatic or relative a priori; and (3) the disputes concerning Kant and nonconceptual content. (shrink)

The notion of innateness is widely used, particularly in philosophy of mind, cognitive science and linguistics. Despite this popularity, it remains a controversial idea. This is partly because of the variety of ways in which it can be explicated and partly because it appears to embody the suggestion that we can determine the relative causal contributions of genes and environment in the development of biological individuals. As these causes are not independent, the claim is metaphysically suspect. This paper argues that (...) there is a plausible reconstruction of the notion of innateness. This involves defining it sufficiently broadly to cover most of the current usages as well as making it an informational rather than a causal property. This has two consequences. Firstly, innateness becomes a matter of degree. Secondly, we have to abandon the idea, originally proposed by ethologists, that innate traits are necessarily the products of genetic information. (shrink)

We report the results of a study that investigated the views of researchers working in seven scientific disciplines and in history and philosophy of science in regard to four hypothesized dimensions of scientific realism. Among other things, we found that natural scientists tended to express more strongly realist views than social scientists, that history and philosophy of science scholars tended to express more antirealist views than natural scientists, that van Fraassen’s characterization of scientific realism failed to cluster with more standard (...) characterizations, and that those who endorsed the pessimistic induction were no more or less likely to endorse antirealism. (shrink)

Various studies show moral intuitions to be susceptible to framing effects. Many have argued that this susceptibility is a sign of unreliability and that this poses a methodological challenge for moral philosophy. Recently, doubt has been cast on this idea. It has been argued that extant evidence of framing effects does not show that moral intuitions have an unreliability problem. I argue that, even if the extant evidence suggests that moral intuitions are fairly stable with respect to what intuitions we (...) have, the effect of framing on the strength of those intuitions still needs to be taken into account. I argue that this by itself poses a methodological challenge for moral philosophy. (shrink)

In the past decade, a number of empirical researchers have suggested that laypeople have compatibilist intuitions. In a recent paper, Feltz and Millan have challenged this conclusion by claiming that most laypeople are only compatibilists in appearance and are in fact willing to attribute free will to people no matter what. As evidence for this claim, they have shown that an important proportion of laypeople still attribute free will to agents in fatalistic universes. In this paper, we first argue that (...) Feltz and Millan’s error-theory rests on a conceptual confusion: it is perfectly acceptable for a certain brand of compatibilist to judge free will and fatalism to be compatible, as long as fatalism does not prevent agents from being the source of their actions. We then present the results of two studies showing that laypeople’s intuitions are best understood as following a certain brand of source compatibilism rather than a “free-will-no-matter-what” strategy. (shrink)

Conscious recollection, of the kind characterised by sensory mental imagery, is often thought to involve ‘episodically’ recalling experienced events in one’s personal past. One might wonder whether this overlooks distinctive ways in which we sometimes recall ordinary, persisting objects. Of course, one can recall an object by remembering an event in which one encountered it. But are there acts of recall which are distinctively objectual in that they are not about objects in this mediated way (i.e., by way of being (...) about events in which they featured)? This question has broad implications, not least for understanding the nature and role of imagery in remembering, the requirements of memory-based singular thought about objects, and the sense in which remembering involves ‘mental time travel’ through which one ‘relives’ past events. In this paper, I argue that we sometimes do recall objects from our past without remembering events in which they featured. The positive view of such cases I go on to propose draws on a wide body of empirical work in its support and accommodates a more nuanced picture of the role of imagery in remembering. In a slogan: remembering might essentially involve a kind of ‘re-experiencing’, but it need not involve ‘reliving’. (shrink)

These comments, which include informal offhand asides made during delivery, derive from an ‘Author Meets Critics’ session on Robert Brandom’s book, From Empiricism to Expressivism: Brandom Reads Sellars’ (2015), held at Kent State University and published subsequently in Sellars and Contemporary Philosophy (2017).

Most agree that, in some special scenarios, prudence can speak against feeling a fitting emotion. Some go further, arguing that the tension between fittingness and prudence afflicts some emotions in a fairly general way. This paper goes even further: it argues that, when it comes to anxiety, the tension between fittingness and prudence is nearly inescapable. On any plausible theory, an enormous array of possible outcomes are both bad and epistemically uncertain in the right way to ground fitting anxiety. What’s (...) more, the fittingness of an emotion is a demanding, not a permissive, normative status. So the norms of fitting emotion demand a great deal of anxiety. For almost any realistic agent, it would be deeply imprudent to feel anxiety in a way that meets the demands set by norms of fitting emotion. (shrink)

If, as Richard Wollheim says, the Acquaintance Principle is ‘a well-entrenched principle in aesthetics,’ it would be surprising if there were not something true at which those who have asserted it have been aiming. I argue that the Acquaintance Principle cannot be true on any traditional epistemic interpretation, nor on any usability interpretation of the sort Robert Hopkins has recently suggested. I then argue for an interpretation of the principle that treats acquaintance as the end to which judgments of aesthetic (...) value are the means as opposed to the other way around. (shrink)

Arthur Danto argued from the premiss that artworks are essentially cognitive to the conclusion that they are incidentally aesthetic. I wonder why Danto, and the very many of us he persuaded, came to believe that the cognitive and the aesthetic oppose one another. I argue, contrary to Danto’s historical claims, that the cognitive and the aesthetic did not come into opposition until the late nineteenth or early twentieth century, and that they were brought into opposition for reasons of art-critical expediency (...) rather than philosophical necessity. I conclude that a robustly cognitive notion of the aesthetic remains an option for us. (shrink)

Recent decades have seen a surge in interest in metaphilosophy. In particular there has been an interest in philosophical methodology. Various questions have been asked about philosophical methods. Are our methods any good? Can we improve upon them? Prior to such evaluative and ameliorative concerns, however, is the matter of what methods philosophers actually use. Worryingly, our understanding of philosophical methodology is impoverished in various respects. This article considers one particular respect in which we seem to be missing an important (...) part of the picture. While it is a received wisdom that the word “ intuition ” has exploded across analytic philosophy in recent decades, the article presents evidence that the explosion is apparent across a broad swathe of academia. It notes various implications for current methodological debates about the role of intuitions in philosophy. (shrink)

Sometimes, the fact that an attitude is fitting seems like a demand to have that attitude. But in other cases, the fact that an attitude is fitting seems more like a permission to have the attitude. I defend a proposal that can accommodate both of these appearances. I argue that there is a kind of emotionlessness, which I call apathy, that can be fitting or unfitting in just the same way that emotion can. I further argue that, in some cases, (...) it can be fitting to respond a single object either with emotion or with apathy. When both apathy and emotion are fitting options, the fittingness of the emotion is a permission-like status; failures to have the fitting emotion are not failures of fit. But when an emotion is fitting and apathy is unfitting, the fittingness of the emotion is a demand-like status; failures to have the emotion are failures of fit. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

The task of visual search is to determine as rapidly as possible whether a target item is present or absent in a display. Rapidly detected items are thought to contain features that correspond to primitive elements in the human visual system. In previous theories, it has been assumed that visual search is based on simple two-dimensional features in the image. However, visual search also has access to another level of representation, one that describes properties in the corresponding three-dimensional scene. Among (...) these properties are three dimensionality and the direction of lighting, but not viewing direction. These findings imply that the parallel processes of early vision are much more sophisticated than previously assumed. (shrink)