All accepted proofs of the Four Colour Theorem (4CT) are computer-dependent; and appeal to the existence, and manual identification, of an ‘unavoidable’ set containing a sufficient number of explicitly defined configurations—each evidenced only by a computer as ‘reducible’—such that at least one of the configurations must occur in any chromatically distinguished, minimal, planar map. For instance, Appel and Haken ‘identified’ 1,482 such configurations in their 1977, computer-dependent, proof of (...) 4CT; whilst Neil Robertson et al ‘identified’ 633 configurations as sufficient in their 1997, also computer-dependent, proof of 4CT. However, treating any specific number of ‘reducible’ configurations in an ‘unavoidable’ set as sufficient entails a minimum number as necessary and sufficient. We now show that the minimum number of such configurations can only be the one corresponding to the ‘unavoidable’ set of a ‘reducible’, 4-sided configuration identified by Alfred Kempe in his, seemingly fatally flawed, 1879 ‘proof’ of 4CT. Although Kempe appealed to putative properties of ‘Kempe’ chains in a graphical representation to fallaciously argue that a 5-sided configuration was also in the ‘unavoidable’ set, and ‘reducible’, we shall show why the flaw in his ‘proof’ is not fatal when the argument is expressed geometrically; and that, essentially, Kempe correctly argued that any planar map which admits a chromatic differentiation with a five-sided area C that shares non-zero boundaries with four, all differently coloured, neighbours can be 4-coloured. (shrink)

All acknowledged proofs of the Four Colour Theorem (4CT) are computerdependent. They appeal to the existence, and manual identification, of an ‘unavoidable’ set containing a sufficient number of explicitly defined configurations—each evidenced only by a computer as ‘reducible’—such that at least one of the configurations must occur in any chromatically distinguished, putatively minimal, planar map. For instance, Appel and Haken ‘identified’ 1,482 such configurations in their 1977, computer-dependent, proof of (...) 4CT; whilst Neil Robertson et al ‘identified’ 633 configurations as sufficient in their 1997, also computer-dependent, proof of 4CT. However, treating any specific number of ‘reducible’ configurations in an ‘unavoidable’ set as sufficient entails a minimum number as necessary and sufficient. We now show that the minimum number of such configurations can only be the one corresponding to the ‘unavoidable’ set of the single, ‘reducible’, 4-sided configuration identified by Alfred Kempe in his, seemingly fatally flawed, 1879 ‘proof’ of 4CT. We shall further show that although Kempe fallaciously concluded that a 5-sided configuration was also in the ‘unavoidable’ set, and appealed to unproven properties of ‘Kempe’ chains in a graphical representation to then argue for its ‘reducibility’, neither flaw in his ‘proof’ is fatal when the argument is expressed geometrically; and that, essentially, Kempe correctly argued that any planar map which admits a chromatic differentiation with a five-sided area C that shares non-zero boundaries with four, all differently coloured, neighbours can be 4-coloured. (shrink)

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus (...) one can search for a properly mathematical proof of the statement. It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one. Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions. The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted. (shrink)

Although the Four Colour Theorem is passe, we give an elementary pre-formal proof that transparently illustrates why four colours suffice to chromatically differentiate any set of contiguous, simply connected and bounded, planar spaces; by showing that there is no minimal 4-coloured planar map M. We note that such a pre-formal proof of the Four Colour Theorem highlights the significance of differentiating between: (a) Plato's knowledge as justified true belief, which seeks a formal (...) proof in a first-order mathematical language in order to justify a belief as true; and (b) Piccinini's knowledge as factually grounded belief, which seeks a pre-formal proof, in Pantsar's sense, in order to justify the axioms and rules of inference of a first-order mathematical language which can, then, formally prove the belief as justifiably true under a well-defined interpretation of the language. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points (...) raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem. (shrink)

Luminance and color are strong and self-sufficient cues to pictorial depth in visual scenes and images. The present study investigates the conditions Under which luminance or color either strengthens or overrides geometric depth cues. We investigated how luminance contrasts associated with color contrast interact with relative height in the visual field, partial occlusion, and interposition in determining the probability that a given figure is perceived as ‘‘nearer’’ than another. Latencies of ‘‘near’’ responses were analyzed to test for effects of attentional (...) selection. Figures in a pair were supported by luminance contrast or isoluminant color contrast and combined with one of the three geometric cues. The results of Experiment 1 show that luminance contrasts associated with hue, when it does not interact with other hues, produces the same effects as achromatic luminance contrasts: The probability of‘‘near’’ increases with luminance contrast while the latencies for ‘‘near’’ responses decrease. Partial occlusion is found to be a strong enough pictorial cue to support a weaker red luminance contrast. Interposition cues lose out against cues of spatial position and partial occlusion. The results of Experiment 2, with isoluminant displays of varying color contrast, reveal that red color contrast on a light background supported by any of the three geometric cues wins over green or white supported by any of the three geometric cues. On a dark background, red color contrast supported by the interposition cue loses out against green or white color contrast supported by partial occlusion. These findings reveal that color is not an independent depth cue, but is strongly influenced by luminance contrast and stimulus geometry. Systematically shorter response latencies for stronger ‘‘near’’ percepts demonstrate that selective visual attention reliably detects the most likely depth cue combination in a given configuration. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

The quantization error in a fixed-size Self-Organizing Map (SOM) with unsupervised winner-take-all learning has previously been used successfully to detect, in minimal computation time, highly meaningful changes across images in medical time series and in time series of satellite images. Here, the functional properties of the quantization error in SOM are explored further to show that the metric is capable of reliably discriminating between the finest differences in local contrast intensities and contrast signs. While this capability of the QE (...) is akin to functional characteristics of a specific class of retinal ganglion cells (the so-called Y-cells) in the visual systems of the primate and the cat, the sensitivity of the QE surpasses the capacity limits of human visual detection. Here, the quantization error in the SOM is found to reliably signal changes in contrast or colour when contrast information is removed from or added to the image, but not when the amount and relative weight of contrast information is constant and only the local spatial position of contrast elements in the pattern changes. While the RGB Mean reflects coarser changes in colour or contrast well enough, the SOM-QE is shown to outperform the RGB Mean in the detection of single-pixel changes in images with up to five million pixels. This could have important implications in the context of unsupervised image learning and computational building block approaches to large sets of image data (big data). (shrink)

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light (...) on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. (shrink)

Conventional wisdom dictates that proofs of mathematical propositions should be treated as necessary, and sufficient, for entailing `significant' mathematical truths only if the proofs are expressed in a---minimally, deemed consistent---formal mathematical theory in terms of: * Axioms/Axiom schemas * Rules of Deduction * Definitions * Lemmas * Theorems * Corollaries. Whilst Andrew Wiles' proof of Fermat's Last Theorem FLT, which appeals essentially to geometrical properties of real and complex numbers, can be treated as meeting this criteria, it nevertheless leaves (...) two questions unanswered: (i) Why is x^n +y^n = z^n solvable only for n < 3 if x, y, z, n are natural numbers? (ii) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? Prevailing post-Wiles wisdom---leaving (i) essentially unaddressed---dismisses Fermat's claim as a conjecture without a plausible proof of FLT. -/- However, we posit that providing evidence-based answers to both queries is necessary not only for treating FLT as significant, but also for understanding why FLT can be treated as a true arithmetical proposition. We thus argue that proving a theorem formally from explicit, and implicit, premises/axioms using rules of deduction---as currently accepted---is a meaningless game, of little scientific value, in the absence of evidence that has already established---unambiguously---why the premises/axioms and rules of deduction can be treated, and categorically communicated, as pre-formal truths in Marcus Pantsar's sense. Consequently, only evidence-based, pre-formal, truth can entail formal provability; and the formal proof of any significant mathematical theorem cannot entail its pre-formal truth as evidence-based. It can only identify the explicit/implicit premises that have been used to evidence the, already established, pre-formal truth of a mathematical proposition. Hence visualising and understanding the evidence-based, pre-formal, truth of a mathematical proposition is the only raison d'etre for subsequently seeking a formal proof of the proposition within a formal mathematical language (whether first-order or second order set theory, arithmetic, geometry, etc.) By this yardstick Andrew Wiles' proof of FLT fails to meet the required, evidence-based, criteria for entailing a true arithmetical proposition. -/- Moreover, we offer two scenarios as to why/how Fermat could have laconically concluded in his recorded marginal noting that FLT is a true arithmetical proposition---even though he either did not (or could not to his own satisfaction) succeed in cogently evidencing, and recording, why FLT can be treated as an evidence-based, pre-formal, arithmetical truth (presumably without appeal to properties of real and complex numbers). It is primarily such a putative, unrecorded, evidence-based reasoning underlying Fermat's laconic assertion which this investigation seeks to reconstruct; and to justify by appeal to a plausible resolution of some philosophical ambiguities concerning the relation between evidence-based, pre-formal, truth and formal provability. (shrink)

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

1. Do models formulated in programming languages use explicit rules where connectionist models do not? 2. Are rules as found in programming languages hard, precise, and exceptionless, where connectionist rules are not? 3. Do connectionist models use rules operating on distributed representations where models formulated in programming languages do not? 4. Do connectionist models fail to use structure sensitive rules of the sort found in "classical" computer architectures? In this chapter we argue that the answer to each of these (...) questions is negative. (shrink)

Vagueness has gotten some attention in aesthetics, but deserves more. Vagueness is universally acknowledged to be ubiquitous. It has played a substantive role in some recent writing on the definition of art. It has figured importantly in analyses of the concept of literature, and (in connection with a thought experiment of Arthur Danto’s), of the ontology of art. Vagueness was a locus of contention in a debate between Alan Goldman and Eddy Zemach about the reality of aesthetic properties. This paper’s (...) aim is to advance that debate, by focusing on the relevance of vagueness to the familiar argument that moves from premises about aesthetic disagreement to the conclusion that aesthetic properties are not real. In what follows, it is argued that, vis-á-vis aesthetic disagreement, the vagueness of aesthetic properties can do important theoretical work for aesthetic realism. (shrink)

This article interrogates the bureaucratization of war, incarnate in the covert lethal drone. Bureaucracies are criticized typically for their complexity, inefficiency, and inflexibility. This article is concerned with their moral indifference. It explores killing, which is so highly administered, so morally remote, and of such scale, that we acknowledge a covert lethal program. This is a bureaucratized program of assassination in contravention of critical human rights. In this article, this program is seen to compromise the advance of global justice. Moreover, (...) the bureaucratization of lethal force is seen to dissolve democratic ideals from within. The bureaucracy isolates the citizens from lethal force applied in their name. People are killed, in the name of the State, but without conspicuous justification, or judicial review, and without informed public debate. This article gives an account of the risk associated with the bureaucratization of the State’s lethal power. Exemplified by the covert drone, this is power with formidable reach. It is power as well, which requires great moral sensitivity. Considering the drone program, this article identifies challenges, which will become more prominent and pressing, as technology advances. (shrink)

I argue that legitimacy discourses serve a gatekeeping function. They give practitioners telic standards for riding herd on social practices, ensuring that minimally acceptable versions of the practice are implemented. Such a function is a necessary part of implementing formalized social practices, especially including law. This gatekeeping account shows that political philosophers have misunderstood legitimacy; it is not secondary to justice and only necessary because we cannot agree about justice. Instead, it is a necessary feature of actual human social practices, (...) which must be implemented via practitioners' discretion in changing contexts. (shrink)

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this paper, we (...) consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the quantum state of the universe is more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research. (shrink)

This is an introductory handbook for some of the main themes around the notion of predication in Aristotle. It does not aim at being exhaustive, but only sketches some important lines about the subject; it contains an introductory essay, besides the translation (into Portuguese) and commentary of basic texts (such as Posterior Analytics I-22, Categories 1-5, Interpretation 1-6 etc.).

This paper examines Aristotle’s notion of priority with the specific aim of capturing the sort of priority that characterizes the primacy of substances in his metaphysics. I reject the traditional interpretation, which understands the ontological priority of substances in terms of independent existence. But there are rather two sorts of priority: the ontological priority of substances should be understood in terms of completeness, whereas the ontological priority of “substances-of-something” (the essences) is a causal-explanatory priority. Furthermore, an important piece of Aristotle’s (...) argument against Platonism is that these two sorts of priority – namely, the completeness priority and the causal-explanatory priority – should be kept distinct. (shrink)

According to Mathias Risse and Richard Zeckhauser, racial profiling can be justified in a society, such as the contemporary United States, where the legacy of slavery and segregation is found in lesser but, nonetheless, troubling forms of racial inequality. Racial profiling, Risse and Zeckhauser recognize, is often marked by police abuse and the harassment of racial minorities and by the disproportionate use of race in profiling. These, on their view, are unjustified. But, they contend, this does not mean that all (...) forms of racial profiling are unjustified; nor, they claim, need one be indifferent to the harms of racism in order to justify racial profiling. In fact, one of the aims of their paper is to show that racial profiling, suitably understood, “is consistent with support for far-reaching measures to decrease racial inequities and inequality.” Hence, one of their most striking claims, in an original and provocative paper, is that one can endorse racial profiling without being in any way indifferent to the disadvantaged status of racial minorities. In an initial response to these claims, I argued that Risse and Zeckhauser tend to underestimate the harms of racial profiling. I suggested two main reasons why they did so. The first is that they tend to identify the more serious harms associated with profiling with background racism, and therefore to believe that these are not properly attributable to profiling itself. The second reason is that they ignore the ways in which background racism makes even relatively minor harms harder to bear and to justify than would otherwise be the case. Hence, I concluded, racial profiling cannot be a normal part of police practice in a society still struggling with racism, although under very special conditions and with special regulation and compensation in place, it might be justified as an extraordinary police measure. I want to stand by those claims. However, Risse’s response to my arguments persuades me that I misinterpreted his earlier position in one significant respect. So I will start by explaining what interpretive mistake I believe that I made. I will then argue that despite Risse’s patient and careful response to my arguments, my initial concerns with his justification of profiling remain valid. -/- . (shrink)

Governments across the globe have squandered treasure and imprisoned millions of their own citizens by criminalising the use and sale of recreational drugs. But use of these drugs has remained relatively constant, and the primary victims are the users themselves. Meanwhile, antimicrobial drugs that once had the power to cure infections are losing their ability to do so, compromising the health of people around the world. The thesis of this essay is that policymakers should stop wasting resources trying to fight (...) an unwinnable and morally dubious war against recreational drug users, and start shifting their attention to the serious threat posed by our collective misuse of antibiotics. (shrink)

The way we answer the question, .what ought I to do?. goes to show what we believe about our life and the way to live that life. However we answer the question .what ought I to do?., we are prescribing a mode of -/- action and this action has a direct bearing on other people and our society at large. So the moral question has a direct connection with what society becomes. If we answer rightly then the impact on our (...) society will be salutary but if wrongly, the impact too will be fatal. So, what we do influences society for good or bad. -/- In this book, the meaning of morality and, ethics and how these can help in personal and national development will be examined. (shrink)

On most accounts, beliefs are supposed to fit the world rather than change it. But believing can have social consequences, since the beliefs we form underwrite our actions and impact our character. Because our beliefs affect how we live our lives and how we treat other people, it is surprising how little attention is usually given to the moral status of believing apart from its epistemic justification. In what follows, I develop a version of the harm principle that applies to (...) beliefs as well as actions. In doing so, I challenge the often exaggerated distinction between forming beliefs and acting on them.1 After developing this view, I consider what it might imply about controversial research the goal of which is to yield true beliefs but the outcome of which might include negative social consequences. In particular, I focus on the implications of research into biological differences between racial groups. (shrink)

Antibiotic resistance is one of the most pressing public health problems humanity faces. Research into new classes of antibiotics and new kinds of treatments – including risky experimental treatments such as phage therapy and vaccines – is an important part of improving our ability to treat infectious diseases. In order to aid this research, we will argue that we should permit researchers to pay people any amount of money to compensate for the risks of participating in clinical trials, including ‘challenge (...) studies’ that involve deliberately infecting patients. We think that standard worries about paying for participation in risky research are reducible to concerns that can be addressed with the right screening mechanisms. (shrink)

This study investigated the difference in the sports involvement of the first year and second year college students in terms power and performance and pleasure and participation. In a sample of seven hundred seventy first year and second year college student students collected between the months of November to December 2019, in terms of power and performance during sports activities, first year respondents gave an average rating of 3.06 (Agree) while the second-year respondents gave an average rating of 3.07 (agree). (...) The results suggest that the student-respondents were not after winning when they were involved in sports. Furthermore, first year respondents gave the highest mean score of 3.79 (strongly agree) in the item “I want to have fun during sports activities” while the second-year respondents gave the highest mean score of 3.75 (strongly agree) in the item “I believe that even poorly skilled students deserve the right to play”. Moreover, using the t-test at 0.05 level of significance power and performance with a computed t-test value of 1.54 and pleasure and participation with a computed t-test value of 1.170 were both lower than the tabular t-test value of 1.971 with the degree of freedom of 768. Therefore, the null hypothesis was accepted. Thus, there was no significant difference between the first year and second year college students’ sports involvement in terms of power and performance and pleasure and participation. The results suggest that students may be provided with various sports programs for competition or for leisure to foster holistic student development. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well (...) as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

Although the index is one of the best known features of Peirce's theory of signs there is little appreciation of Peirce's theory of the index amongst contemporary philosophers of language. Amongst Peirce scholars, the value placed on Peirce's account is greater, but is largely based on Thomas Goudge's paper, "Peirce's Index" (Goudge, 1965). Despite marking a crucial milestone in our comprehension of Peirce's theory, our understanding of indices and indexical reference has grown markedly over the last forty years. Time has (...) now come, then, to develop the work that Goudge began and to provide a full analysis of Peirce's account that makes its value to the philosophy of language clear. I undertake this enterprise here. (shrink)

Policy-making must always pay attention to race. That is the central claim of this chapter. Regardless of whether some particular policy debate is ostensibly “racial”, policy-makers must attend to questions of race, because race is a ubiquitous, but frequently unnoticed, feature of our world. I examine the type of philosophical question about race that I think philosophers and policy-makers would do well to examine and consider how the question “What is race?” is pertinent to policy debate. Examples will be drawn (...) from Australia, the United States, and Britain to illustrate these abstract arguments. (shrink)

My objective here is to give an account of self-deprecating humor—examining what works, what doesn't, and why—and to reflect on the significance of the audience response. More specifically, I will be focusing not only on the purpose or intention behind self-deprecating jokes, but considering how their consequences might render them successful or unsuccessful. For example, under what circumstances does self-deprecation tend to put listeners at ease, and when is this type of humor more likely to put people off? I will (...) also consider the ways in which self-deprecating jokes are similar to gallows humor, and the extent to which context counts. The target or "butt" of these jokes, in cases of self-deprecation as well as gallows humor, will be explored; as will whether or not the audience bears some responsibility or has a role to play in the ultimate success or failure of a joke. For instance, is the audience role a completely receptive and passive one? Is the joker/jokee relationship one which confers no responsibility on the listener whatsoever? Or, do listeners have an obligation to respond with appreciative laughter to mere attempts at humor, especially the self-deprecating sort, by accepting such levity in the spirit in which it is intended? Does this mean that being a good sport—responding generously or appreciatively when a well-intentioned joke fails to land—would be a habit worth cultivating? If so and courtesy laughter or a playful appreciation of self-deprecating humor is something that can be cultivated, what specifically would that entail? In sum, although I cannot fully or definitively answer each and every one of these questions, I do hope to provide some provisional responses. To better situate the nature of self-deprecation, I will not only provide a brief description of the gallows genre, I will also explore two traditional theories of humor. Those that are particularly relevant, to both gallows and self-deprecating humor are Freud's relief theory and the incongruity view. In addition, I will identify what I believe to be the three essential ingredients of successful self-deprecation and, finally, will conclude with the argument that audiences or listeners do have an important role to play. And, moreover, that generous, appreciative laughter can and should be cultivated—even though this is something that will largely depend on one's personal history and habits, dispositional character and cultural background. (shrink)

Is it possible for me to refer to someone other than myself with the word "I"? Or somewhere other than where I am with the word "here"? Or some time other than the present with the word "now"? David Kaplan, who provides the best worked out semantics for pure-indexical terms like "I," "here," and "now" suggests, quite intuitively, that I could not. Put simply, "I am here now" looks as though I can never utter it and have it turn out (...) false. But, intuitive as this seems, one need only hear the answering machine message, "Sorry! I am not here now," to see that there may be problems. If! can't fail to refer to where I am and when I'm there with "here" and "now," why is my apparently contradictory assertion so readily comprehensible? Many have been quick to abandon Kaplan's account of pure-indexicals in the face of such problems. The focus of this paper, though, is those who develop sophisticated accounts of how we determine different contexts for applying pure-indexicals. The hope is that this handles problem cases while allowing us to retain most of Kaplan's theory. However, this paper introduces and examines some additional uses of pure-indexicals which pose an interesting problem for the context-determination adaptation of Kaplan's account. It is argued that context-determination theorists cannot explain these cases in the same way that they explain standard problem cases, and that any reason they can offer for denying the relevance of such cases to accounts of pure-indexicals will apply equally well to the cases that motivate their theories, thus rendering context-determination accounts superfluous. In what follows, then, there is a brief summary of Kaplan's account, the problem cases that threaten it, and the context-determination theorist's response to these problem cases. The interesting and problematic uses of pure-indexicals that context-determination accounts cannot explain are then introduced, and an explanation is given of why there is no way for the context-determination theorist to exclude these cases from our accounts of pure-indexicals without also excluding the cases that motivate their own theory. (shrink)

It is reasonably well accepted that the explanation of intentional action is teleological explanation. Very roughly, an explanation of some event, E, is teleological only if it explains E by citing some goal or purpose or reason that produced E. Alternatively, teleological explanations of intentional action explain “by citing the state of affairs toward which the behavior was directed” thereby answering questions like “To what end was the agent’s behavior directed?” Causalism—advocated by causalists—is the thesis that explanations of intentional action (...) are both causal and teleological. By contrast, non-causalism—advocated by non-causalists—is the thesis that explanations of intentional action are teleological but not causal. Familiarly, the problem of causal deviance plagues causalism. But while some have supposed that the problem is grave enough that causalism is bound to suffer a global breakdown, the rumors of causalism’s demise are greatly exaggerated. In what follows, I note that every instance of causal deviance is also an instance of teleological deviance and that teleological deviance is a problem for causalist and non-causalist alike, a problem that causalists may be better able to deal with. Or so I argue. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

Justin Fisher (2007) has presented a novel argument designed to prove that all forms of mental internalism are false. I aim to show that the argument fails with regard to internalism about phenomenal experiences. The argument tacitly assumes a certain view about the ontology of phenomenal experience, which (inspired by Alva Noe) I call the “snapshot conception of phenomenal experience.” After clarifying what the snapshot conception involves, I present Fisher with a dilemma. If he rejects the snapshot conception, then his (...) argument against phenomenal internalism collapses. But if he embraces the snapshot conception, then internalists may argue that in light of the snapshot conception, their view is not so implausible—and that if Fisher still disagrees, he owes us an argument that shows why phenomenal internalism is false even given the snapshot conception. I conclude the paper by showing that Fisher cannot escape my criticism by adjusting his argument so that it no longer depends on the snapshot conception. (shrink)

PT. A noção de “pessoa”, pensada a partir do legado antropológico e filosófico do ocidente, afirma-se como uma unidade corporal e espiritual que determina a sua singularidade no seio da comunidade. A “pessoa” assim perspectivada assume uma importância destacada na reflexão ética das aplicações científicas de artificialização da vida humana. Muito concretamente, a noção de “pessoa” deve contribuir para a fundamentação ética das terapêuticas de transplantação. A transplantação representa um dos mais notáveis avanços da medicina do século XX e com (...) um impacto incontornável na prestação de cuidados de saúde. Os transplantes são considerados o tratamento mais eficaz para patologias crónicas que afectam a funcionalidade de determinados órgãos vitais, restituindo ao doente uma melhoria na sua saúde e/ou qualidade de vida. O sucesso desta terapêutica é, no entanto, condicionado pela disponibilização de pessoas que queiram fazer dádiva de si, do seu próprio corpo, para o bem-estar de outrem. Deste modo, a doação, realizada após a morte da pessoa ou ainda em vida, enfrenta vários desafios técnicos, mas também, e principalmente, desafios éticos. A nossa dissertação centra-se na reflexão ética da doação de órgãos e tecidos para transplante e no impacto que a dádiva de uma parte específica do corpo pode comportar na noção de “pessoa”. Deste modo, ao mesmo tempo em que se procura promover a doação de órgãos para aumentar o número de transplantes, também se vão delineando estratégias para salvaguardar a integridade corporal do dador e a eminente dignidade que o constitui como pessoa. As estratégias consistem fundamentalmente num diálogo entre o princípio de autonomia, que determina a singularidade da pessoa, e o princípio de solidariedade, que é desencadeado pela relação com o outro. Estes princípios éticos, articulados e uma vez cumpridos, são os alicerces da doação voluntária e altruísta, e impedem a instrumentalização e exploração da pessoa dadora. -/- EN. The western anthropological and philosophical notion of ‘person’ emerges as a corporal and spiritual entity, which determines his singularity at the level of community. From this perspective, the notion of ‘person’ holds an important place in ethical considerations concerning the scientific applications of artificial manipulation of human life. More precisely, the notion of ‘person’ must contribute towards the ethical basis of transplant therapeutics. The transplantation of human organs and tissues is one of the most notable advances in twentieth century medicine, and, as such, has had an unquestionable impact on health care practice. Transplants are now seen as the best treatment for chronic diseases that impair the function of some vital organs, improving the patient health and/or quality of life. The success of organs transplantation depends entirely upon the altruism of people giving their bodies for the well-being of others. Organ donation, performed during life or after death, raises not only technical, but also mainly ethical challenges. This work focuses on the ethical considerations associated with human organs and tissue donation for transplantation and on the impact that a donation of an organ has on the notion of ‘person’. At the same time that one recognizes the need to increase the number of organs for transplanting, there is also the need to preserve the donor’s corporal integrity and his eminent dignity. Strategies to preserve the donor’s corporal integrity and dignity must take into consideration the dialogue between the principle of autonomy, which is characterized by the singular entity, and the principle of solidarity, born out of one’s relationship with those around you. These ethical principles, once engaged and fulfilled, are the bases of a voluntary and altruistic donation, and prevent the donor from becoming a mere instrument and being exploited as such. (shrink)

Many philosophers have thought that our folk, or pre-reflective, view of persistence is one on which objects endure. This assumption not only plays a role in disputes about the nature of persistence itself, but is also put to use in several other areas of metaphysics, including debates about the nature of change and temporal passage. In this paper, we empirically test three broad claims. First, that most people (i.e. most non-philosophers) believe that, and it seems to them as though, objects (...) persist by enduring rather than perduring. Second, that most people have a view of change on which enduring but not perduring objects count as changing. Third, that one reason why the folk represent time as dynamical is because it seems to them, and they believe that, they endure through time. We found no evidence to support these claims. While there are certainly plenty of ‘folk’ endurantists in the population we tested, there are also plenty of ‘folk’ perdurantists. We did not find robust evidence that a majority of people believed that, or it seemed to them as though, objects endure rather than perdure. We conclude that many arguments in favour of endurantism that appeal to folk beliefs about, or experiences of, persisting objects and change rest on views about those beliefs and experiences that are empirically unsupported. There is no evidence to suggest that endurantism is the folk friendly view of persistence, and so we should stop treating it as such without argument. (shrink)

Many philosophers have thought that our folk, or pre-reflective, view of persistence is one on which objects endure. This assumption not only plays a role in disputes about the nature of persistence itself, but is also put to use in several other areas of metaphysics, including debates about the nature of change and temporal passage. In this paper, we empirically test three broad claims. First, that most people (i.e. most non-philosophers) believe that, and it seems to them as though, objects (...) persist by enduring rather than perduring. Second, that most people have a view of change on which enduring but not perduring objects count as changing. Third, that one reason why the folk represent time as dynamical is because it seems to them, and they believe that, they endure through time. We found no evidence to support these claims. While there are certainly plenty of ‘folk’ endurantists in the population we tested, there are also plenty of ‘folk’ perdurantists. We did not find robust evidence that a majority of people believed that, or it seemed to them as though, objects endure rather than perdure. We conclude that many arguments in favour of endurantism that appeal to folk beliefs about, or experiences of, persisting objects and change rest on views about those beliefs and experiences that are empirically unsupported. There is no evidence to suggest that endurantism is the folk friendly view of persistence, and so we should stop treating it as such without argument. (shrink)

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...) alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem. (shrink)

When a novel scientific theory conflicts with otherwise plausible moral assumptions, we do not treat that as evidence against the theory. We may scrutinize the empirical data more keenly and take extra care over its interpretation, but science is in some core sense immune to moral refutation. Can the same be said of philosophical theories (or the non-ethical, ‘metaphysical’ ones at least)? If a position in the philosophy of mind, for example, is discovered to have eye-widening moral import, does that (...) count against it at all? Actual responses by philosophers to the question of whether unanticipated moral consequences of metaphysical theories have evidential force are scattered, implicit, divergent, under-argued, and sometimes even self-undermining. The present discussion is, most immediately, an attempt to sort out the confusion. Beyond that, it exploits the new perspective this question gives us on a familiar topic: the relation of philosophy to science. (shrink)

A natural view of testimony holds that a source's statements provide one with evidence about what the source believes, which in turn provides one with evidence about what is true. But some theorists have gone further and developed a broadly analogous view of memory. According to this view, which this essay calls the “diary model,” one's memory ordinarily serves as a means for one's present self to gain evidence about one's past judgments, and in turn about the truth. This essay (...) rejects the diary model's analogy between memory and testimony from one's former self, arguing first that memory and a diary differ with respect to their psychological roles, and second that this psychological difference underwrites important downstream epistemic differences. The resulting view stands opposed to prominent discussions of memory and testimony, which either, like the diary model, treat memory by analogy to what we naively wish to say about testimony, or which instead attempt to extend to testimony the epistemically preservative role of memory. (shrink)

How should International Political Theory (IPT) relate to public policy? Should theorists aspire for their work to be policy- relevant and, if so, in what sense? When can we legitimately criticize a theory for failing to be relevant to practice? To develop a response to these questions, I will consider two issues: (1) the extent to which international political theorists should be concerned that the norms they articulate are precise enough to entail clear practical advice under different empirical circumstances; (2) (...) whether they should provide concrete practical advice on policy choice and institutional reform. These questions are related but distinct, and we should answer each quite differently. Regarding the first, I shall argue that it counts heavily against a theory if it is not precise enough to guide policy and reform given certain empirical assumptions. On the second, I will argue that theorists should be very cautious when engaging with questions of policy and institutional design. Some principles of IPT can be criticized for being insufficiently precise, but a degree of abstraction from concrete policy recommendations is a virtue, rather than a vice, of an element of IPT. I conclude that we should aim to be precise without being concrete. To help fix ideas and anchor my argument, I will discuss these issues with reference to a principle that John Rawls has advocated in his influential work The Law of Peoples (Rawls 1999a): a duty of assistance to societies that lack the capacity to satisfy the basic needs or protect the basic rights of their people. (shrink)

Climate change and other harmful large-scale processes challenge our understandings of individual responsibility. People throughout the world suffer harms—severe shortfalls in health, civic status, or standard of living relative to the vital needs of human beings—as a result of physical processes to which many people appear to contribute. Climate change, polluted air and water, and the erosion of grasslands, for example, occur because a great many people emit carbon and pollutants, build excessively, enable their flocks to overgraze, or otherwise stress (...) the environment. If a much smaller number of people engaged in these types of conduct, the harms in question would not occur, or would be substantially lessened. However, the conduct of any particular person (and, in the case of climate change, of even quite large numbers of people) could make no apparent difference to their occurrence. My carbon emissions (and quite possibly the carbon emissions of much larger groups of people dispersed throughout the world) may not make a difference to what happens to anyone. When the conduct of some agent does not make any apparent difference to the occurrence of harm, but this conduct is of a type that brings about harm because many people engage in it, we can call this agent an overdeterminer of that harm, and their conduct overdetermining conduct. In this essay we explore the moral status of overdetermining harm. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

An internalist slogan says that justification depends on internal factors. But which factors are those? This paper examines some common motivations favoring internalism over externalism, and says they are compatible with including dispositional and even past mental states in the internal.

Many philosophical theories of self-knowledge can be understood as attempts to explain why self-ascriptions enjoy a certain kind of authority that other-ascriptions lack (the Authority Thesis). The aim of this paper is not to expand the stock of existing explanations but to ask whether the Authority Thesis can be adequately specified. To this end, I identify three requirements that must be met by any satisfactory specification. I conclude that the search for an adequate specification of the Authority Thesis leads to (...) a dilemma: it either yields an interpretation under which the thesis is philosophically interesting but false, or it produces an interpretation under which the thesis is actually true but of minor philosophical interest. (shrink)

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy by (...) giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

A reflection on the merits of an a priori poeto-epistemology in relation to tacitly held assumptions about the a fortiori validity of computational logic to transcend the limits of contradiction and infinite regression and establish a valid ontology.

The article talks about the emergence of the theory of imperialism and neocolonialism, the reasons that gave rise to it, and its effects on the development of humanity in the current period. Imperialism is a multifaceted, multidimensional problem. It is a political issue, it has philosophical, scientific and technological foundations, it has economic, sociological, geographical, ethnic, religious and educational dimensions. But the fact that it is primarily a human problem makes it a multifaceted problem. Surely we can increase these reasons. (...) But no matter how much we multiply, colonization of one society by another society, confiscation of its wealth, enslavement and cultural separation is the most visible form of this. But this experience is not unprecedented in human history. Because human history has been a kind of exploitation, enslavement and attempts to create superiority. As Camus said, "Man emerges as the most dangerous being for his species". Attitudes to imperialism may vary between tribal and celestial cultures. After all, the culture of heaven is a culture cultivated by divine teaching. Exploitation and slavery are the dominant attitudes of tribal cultures. In these cultures, the relationship between man and man is based on power, wealth and nobility. In celestial cultures, the relationship between man and man was determined by nomos, divine laws. Heavenly culture is the product of a will that emerges for "good will" to prevail. It should be known that colonialism is a tribal behavior wherever and whenever it occurs. Because they do not see other societies as equal to themselves, it is a desire to dominate, exploit and enslave those who are not like themselves. From this perspective, colonialism can be seen as one of the oldest forms of behavior in history. This situation appears as the victory of the strong over the weak. Since transcendental attachment does not occur, they are in a position to absolutize their self. As a result, they see themselves as masters to be served, they see in themselves the right to such an inclination. It can be misleading to associate the colonial movement with human nature. It is more about the degradation and degeneration of human nature, it is about self-cultivation. It is a matter of outlook. The heavenly cultures, where the powerless were protected and spared, showed themselves not in a colonial style, but in a protective and compassionate way. We can see this patronizing relationship in the states established within the celestial cultures. (shrink)

Along the strike of this article we’ll try to perform two tasks. The first one is to review the world existence but not in form of concept but in form of modern scientific-philosophic system of views on the Universe structure and on the processes of formation and development of non-organic world, worlds of life and intelligence. The second one is to answer the question “what is the essence of human life?” through the scientific-philosophic understanding of the world existence.

It is widely thought that chance should be understood in reductionist terms: claims about chance should be understood as claims that certain patterns of events are instantiated. There are many possible reductionist theories of chance, differing as to which possible pattern of events they take to be chance-making. It is also widely taken to be a norm of rationality that credence should defer to chance: special cases aside, rationality requires that one’s credence function, when conditionalized on the chance-making facts, should (...) coincide with the objective chance function. It is a shortcoming of a theory of chance if it implies that this norm of rationality is unsatisfiable. The primary goal of this paper is to show, on the basis of considerations concerning computability and inductive learning, that this shortcoming is more common than one would have hoped. (shrink)