We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical (...) reflector, that Snell’s law of reflection is not a consequence of least time path principle and, that Leibniz’s method of derivation of Snell’s law of reflection is invalid. In (1), we prove that, if a light ray is reflected at point P on a line, along the least time path APB, then at every point Pi on that line, rays from A are reflected to point B, satisfying Snell’s law. However, paths, APB and APiB do not have equal travel times. In (2), we prove that, if a light ray is reflected along the least time path APB, from focus A to focus B incident at point P on an ellipse, satisfies Snell’s law, then points Pi, not lying on the ellipse, also reflect light rays from A to B, satisfying Snell’s law. However, the paths APB and APiB do not have equal travel times. Thus, both examples prove that least time path is not a criterion for reflection and, that Snell’s law of reflection is not a consequence of least time path principle. (shrink)

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned (...) areas. (shrink)

Enneads I: 8.14 poses significant problems for scholars working in the Plotinian secondary literature. In that passage, Plotinus gives the impression that the body and not the soul is causally responsible for vice. The difficulty is that in many other sections of the same text, Plotinus makes it abundantly clear that the body, as matter, is a mere privation of being and therefore represents the lowest rung on the proverbial metaphysical ladder. A crucial aspect to Plotinus’s emanationism, however, is that (...) lower levels of a metaphysical hierarchy cannot causally influence higher ones and, thus, there is an inconsistency in the Egyptian’s magnum opus, or so it would seem. Scholars have sought to work through this paradox by positing that Plotinus is a “paleolithic Platonist” or Socratic. The advantage of this approach is that one may be able to resolve the tension by invoking Socrates’s eliminativist solution to the problem of weakness of will, as found in The Protagoras. In the following article, I argue that such attempts are not wrong-headed just underdetermined. They take up the standard reading of Socratic moral intellectualism, namely the “informational” interpretation and, therefore, fail to render a coherent view of Plotinus’s moral philosophy. The following paper, in contrast, utilizes a new reading of intellectualism advanced by Brickhouse and Smith, which, when subtended with a “powers approach” to causality, resolves the aforementioned, problematic passage of Enneads. (shrink)

Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to (...) define point-free concept of connectedness that for the regular open regions of E coincides with the standard topological notion of connectedness, i.e., a region of the plane E is connected in the sense of topology if and only if it has no separable proper part. Moreover, it is shown that the contact relation algebra REL(O*E, C) and the relation algebra REL(O*E, NTPP) generated by the non-tangential proper parthood relation NTPP, coincide. This entails that the allegedly purely topological notion of connectedness can be defined in mereological terms. (shrink)

Victor Vasarely's (1906–1997) important legacy to the study of human perception is brought to the forefront and discussed. A large part of his impressive work conveys the appearance of striking three-dimensional shapes and structures in a large-scale pictorial plane. Current perception science explains such effects by invoking brain mechanisms for the processing of monocular (2D) depth cues. Here in this study, we illustrate and explain local effects of 2D color and contrast cues on the perceptual organization in terms of (...) figure-ground assignments, i.e. which local surfaces are likely to be seen as “nearer” or “bigger” in the image plane. Paired configurations are embedded in a larger, structurally ambivalent pictorial context inspired by some of Vasarely's creations. The figure-ground effects these configurations produce reveal a significant correlation between perceptual solutions for “nearer” and “bigger” when other geometric depth cues are missing. In consistency with previous findings on similar, albeit simpler visual displays, a specific color may compete with luminance contrast to resolve the planar ambiguity of a complex pattern context at a critical point in the hierarchical resolution of figure-ground uncertainty. The potential role of color temperature in this process is brought forward here. Vasarely intuitively understood and successfully exploited the subtle context effects accounted for in this paper, well before empirical investigation had set out to study and explain them in terms of information processing by the visual brain. (shrink)

The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...) notes that the appearance of writing, symbolic language and the depiction of the picture of the world through mathematics, led us into the sphere of discrete mathematical mathematics. (shrink)

The Church seeks to be inclusive; one that opens her doors to everyone. For many Filipino Catholics (FCs) in Japan, their ecclesial existence is marked by a history of negotiation as “guests” hosted by the Japanese Catholics (JCs). Within this field of host–guest interplay, this paper explores the dynamics of sociospatial seclusion by employing the ideation of marginality pro ered by Loic Wacquant’s study on urban ghettos. The paper argues that the guest-identity of FCs must not be understood as a (...) unilateral action imposed upon by the dominant hosts against the former’s subjugated narrative as powerless victims. Instead, its maintenance is perpetuated by FCs’ elective and chosen ethnic clustering. In attempt to obtain better analytical clarity of this dynamics, this paper employs the functional value of the Cartesian plane as a mapping device in plotting historical events of interplay within a spatial field. The techne inherent in the Cartesian plane is embedded with the episteme of Wacquant’s ideation. Fused together, its utility as a heuristic device is herewith proposed. It is hoped that this theoretical construct can also be useful to any analysis of marginality contained within a host–guest interplay. (shrink)

As all philosophical concepts, also the concept of person constitutes itself referring to a particular problem. The analysis drafted by Marcel Mauss regarding the genesis of the aforementioned category permits to analyse the problematic nucleus to which such concept refers to, disclosing that it responds to the necessity of solving the ancient problem of the link between mind and body in a specific perspective. In this respect, Bergsonian theory of images represents a solid attempt of passing not only the habitual (...) solution of the problem represented by the concept of person, but also the problem itself whereto refers. The deleuzian reading of Henri Bergson’s theory leads him to define the impersonal and pre-individual field sketched out by Bergson as a plane of immanence, and this last as “a life”. The ultimate aim of this paper is to analyse the nature of such plane and to suggest an interpretation of the latest Gilles Deleuze’s piece of writing, "L’immanence: une vie..." that unveils its profound Bergsonism. (shrink)

The plane was going to crash, but it didn't. Johnny was going to bleed to death, but he didn't. Geach sees here a changing future. In this paper, I develop Geach's primary argument for the (almost universally rejected) thesis that the future is mutable (an argument from the nature of prevention), respond to the most serious objections such a view faces, and consider how Geach's view bears on traditional debates concerning divine foreknowledge and human freedom. As I hope to (...) show, Geach's view constitutes a radically new view on the logic of future contingents, and deserves the status of a theoretical contender in these debates. (shrink)

Imagination plays a rich epistemic role in our cognitive lives. For example, if I want to learn whether my luggage will fit into the overhead compartment on a plane, I might imagine trying to fit it into the overhead compartment and form a justified belief on the basis of this imagining. But what explains the fact that imagination has the power to justify beliefs, and what is the structure of imaginative justification? In this paper, I answer these questions by (...) arguing that imaginings manifest an epistemic status: they are epistemically evaluable as justified or unjustified. This epistemic status grounds their ability to justify beliefs, and they accrue this status in virtue of being based on evidence. Thus, imaginings are best understood as justified justifiers. I argue for this view by way of showing how it offers a satisfying explanation of certain key features of imaginative justification that would otherwise be puzzling. I also argue that imaginings exhibit a number of markers of the basing relation, which further motivates the view that imaginings can be based on evidence. The arguments in this paper have theoretically fruitful implications not only for the epistemology of imagination, but for accounts of reasoning and epistemic normativity more generally. (shrink)

Difference and Repetition might be said to have brought about a Deleuzian Revolution in philosophy comparable to Kant’s Copernican Revolution. Kant had denounced the three great terminal points of traditional metaphysics – self, world and God – as transcendent illusions, and Deleuze pushes Kant’s revolution to its limit by positing a transcendental field that excludes the coherence of the self, world and God in favour of an immanent and differential plane of impersonal individuations and pre-individual singularities. In the process, (...) he introduces numerous conceptual innovations into philosophy: the becoming of concepts; a transformation of the form of the question; an insistence that philosophy must start in the middle; an attempt to think in terms of multiplicities; the development of a new logic and a new metaphysics based on a concept of difference; a new conception of space as intensive rather than extensive; a conception of time as a pure and empty form; and an understanding of philosophy as a system in heterogenesis – that is, a system that entails a perpetual genesis of the heterogeneous, an incessant production of the new. -/- Keywords: concepts, becoming, multiplicity, singularity, the middle [au milieu], difference, intensity, time, system, the new. (shrink)

Libertarian self-ownership views in the tradition of Locke, Nozick, and the left-libertarians have supposed that we enjoy very powerful deontological protections against infringing upon our property. Such a conception makes sense when we are focused on property that is very important to its owner, such as a person’s kidney. However, this stringency of our property rights is harder to credit when we consider more trivial infringements such as very mildly toxic pollution or trivial risks such having planes fly overhead. Maintaining (...) that our rights against all infringements are very powerful threatens to implausibly make such pollution and trivial risk broadly impermissible. This paper suggests that self-ownership views have tended to inappropriately conflate the seriousness of different types of infringements and that treating all infringements so seriously is implausible because it would make too much impermissible. I consider several ways to avoid this result within a self-ownership framework and conclude that the best approach is to allow that the strength of the protection against infringements should be tied to the seriousness of the harm of the infringement. (shrink)

Focused on evolutionary and continuous human development the global, the regulatory system should be formed in the conceptual (the constant research for the detection, identification and evaluation of global imperatives) and application (development and implementation of activities and coordination tools of influence to ensure the existence of human civilization in a secure politically, economically, socially and environmentally balanced world) planes. On the author's calculations of its formation in functionally complete, holistic view is expected by 2030 due to historically conditioned transformations (...) in the nature of social relations. (shrink)

In the complex tapestry of existence, we journey down the corridors of thought, proclaiming Descarte's famed words: "Cogito ergo sum." Yet, the journey does not conclude with merely affirming our existence but falls down the endless pit of the dimensions and complex corridors of free will and autonomy. Let us establish the terms that shall guide our thoughts for this voyage. First, a multi-faceted free will that transcends mere ownership of thoughts, extending to the profound responsibility for our actions within (...) the temporal plane we inhabit," an existence yet to be fully revealed. Second, the insistence on the necessity, or at least the belief in the potential, of self-control. Here, we differ from conventional definitions of free will to assert the capacity to govern the mind and ego, even when one perceives a lack of control. The mind, which exists somewhere, owns the authority over its thoughts, which is you. And thirdly, the elusive question: What is "I"? Not into the human "you" or the one that speaks and sees but into the core thinker, the intangible essence that animates. The "I" resides within, shaping the tangible reality and, paradoxically, depending on nothing while being the core of reality. Yet, the pivotal question still stands: Do others exist? Autonomy becomes the litmus test. If I, as an autonomous being, fail to wield dominion over external circumstances. Weakness in reshaping the external world confirms the separation, a stark admission of being powerless in the face of objective reality. While using ocoms razer, our answer is found. Thus, the conclusion is a solitary existence in the ability to affirm one's own being while recognizing others through autonomy. (shrink)

Through the philosophies of Bergson and Deleuze, my paper explores a different theory of time. I reconstitute Deleuze’s paradoxes of the past in Difference and Repetition and Bergsonism to reveal a theory of time in which the relation between past and present is one of coexistence rather than succession. The theory of memory implied here is a non-representational one. To elaborate this theory, I ask: what is the role of the “virtual image” in Bergson’s Matter and Memory? Far from representing (...) the simple afterimage of a present perception, the “virtual image” carries multiple senses. Contracting the immediate past for the present, or expanding virtually to hold the whole of memory (and even the whole of the universe), the virtual image can form a bridge between the present and the non-representational past. This non-representational account of memory sheds light not only on the structure of time for Bergson, but also on his concepts of pure memory and virtuality. The rereading of memory also opens the way for Bergsonian intuition to play an intersubjective role; intuition becomes a means for navigating the resonances and dissonances that can be felt between different rhythms of becoming or planes of memory, which constitute different subjects. (shrink)

As boundaries between domesticity and the undomesticated increasingly blur for cohabitants of Vancouver Island, home to North America’s densest cougar population, predatorial problems become more and more pressing. Rosemary-Claire Collard responds on a pragmatic plane, arguing that the encounter between human and cougar is only ever destructive, that contact results in death and almost always for the cougar. Advocating for vigilance in policing boundaries separating cougar from civilization, therefore, she looks to Foucault’s analysis of modern biopower in the first (...) volume of his History of Sexuality for support in favor of a more contemporary notion of biosecurity. In response to Collard’s arguments, concerned with ethical conclusions drawn on the basis of her policy-based proposal, I challenge the prohibition she places on encounter. In the first section, “Becoming Killable,” I address her use of Donna Haraway’s phraseology, and in the second section, “Biological Dangers,” I scrutinize her reading of Foucault, arguing that the appeals she makes distort the mode of argumentation at work for each thinker. The final section, “Facing Cougar, Facing Death,” advocates further ethical possibilities generated on the basis of Foucault’s correlation between overcoming the fear of death and resisting abuses of power with respect to others. My contention is that our transgressing boundaries constructed to separate humanity from the inhumane curtails tendencies toward the marginalization and subjugation of those animal others whose very existence brings us face to face with the fact of our own mortality. (shrink)

Throughout most of the 20th century, analytical and reductionist approaches have dominated in biological, social, and humanistic sciences, including linguistics and communication. We generally believed we could account for fundamental phenomena in invoking basic elemental units. Although the amount of knowledge generated was certainly impressive, we have also seen limitations of this approach. Discovering the sound formants of human languages, for example, has allowed us to know vital aspects of the ‘material’ plane of verbal codes, but it tells us (...) little about significant aspects of their social functions. I firmly believe, therefore, that alongside a linguistics that looks ‘inward’ there should also be a linguistics that looks ‘outward’, or one even that is constructed ‘from the outside’, a linguistics that I refer to elsewhere as ‘holistic’ though it could be identified by a different name. My current vision is to promote simultaneously the perspective that goes from the part to the whole and that which goes from the whole to the parts, i.e., both from the top down and from the bottom up. This goal is shared with other disciplines which recognize that many phenomena related to life are interwoven, self-organising, emergent and processual. Thus, we need to re-examine how we have conceived of reality, both the way we have looked at it and the images we have used to talk about it. Several approaches now grouped under the label of complexity have been elaborated towards this objective of finding new concepts and ways of thinking that better fit the complex organisation of facts and events. (shrink)

Alhazen problem of reflection at a concave spherical surface is one of the most discussed problems in optics. It was solved by Alhazen, The number of solution points vary from zero to a maximum of four. However, his solution is known to be prolix. Huygens solved the problem and identified the solution points to be points of intersection of the given circle and a hyperbola. Many other lines of attack were attempted with their solutions. New solutions are offered from time (...) to time. In this paper we offer a solution based on the criterion to be satisfied by reflection of a ray of light at a concave spherical surface. Based on that criterion we show that it is impossible for a circle containing both end points of the path of the ray inside it, to reflect rays from one point to the other. However, for every point on the given circle, we can construct two orthogonal circles (orthogonal conics in general) which reflect rays from one given point to the other, while the given circle is a non-reflector. (shrink)

Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of (...) the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”? (shrink)

Poorly saturated colors are closer to a pure grey than strongly saturated ones and, therefore, appear less “colorful”. Color saturation is effectively manipulated in the visual arts for balancing conflicting sensations and moods and for inducing the perception of relative distance in the pictorial plane. While perceptual science has proven quite clearly that the luminance contrast of any hue acts as a self-sufficient cue to relative depth in visual images, the role of color saturation in such figure-ground organization has (...) remained unclear. We presented configurations of colored inducers on grey ‘test’ backgrounds to human observers. Luminance and saturation of the inducers was uniform on each trial, but varied across trials. We ran two separate experimental tasks. In the relative background brightness task, perceptual judgments indicated whether the apparent brightness of the grey test background contrasted with, assimilated to, or appeared equal (no effect) to that of a comparison background with the same luminance contrast. Contrast polarity and its interaction with color saturation affected response proportions for contrast, assimilation and no effect. In the figure-ground task, perceptual judgments indicated whether the inducers appeared to lie in front of, behind, or in the same depth with the background. Strongly saturated inducers produced significantly larger proportions of foreground effects indicating that these inducers stand out as figure against the background. Weakly saturated inducers produced significantly larger proportions of background effects, indicating that these inducers are perceived as lying behind the backgrounds. We infer that color saturation modulates figure-ground organization, both directly by determining relative inducer depth, and indirectly, and in interaction with contrast polarity, by affecting apparent background brightness. The results point towards a hitherto undocumented functional role of color saturation in the genesis of form, and in particular figure-ground percepts in the absence of chromatostereopsis. (shrink)

We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.

In this reading of the Euthyphro, Socrates and Euthyphro are seen less in a primordial conflict between reason and devotion, than as sincere Hellenic polytheists engaged in an inquiry based upon a common intuition that, in addition to the irreducible agency of the Gods, there is also some irreducible intelligible content to holiness. This reading is supported by the fact that Euthyphro does not claim the authority of revelation for his decision to prosecute his father, but rather submits it to (...) elenchus, and that Euthyphro does not embrace the ‘solution’ of theological voluntarism when Socrates explicitly offers it. Since the goal of this inquiry is neither to eliminate the noetic content of the holy, nor to eliminate the Gods’ agency, the purpose of the elenchus becomes the effort to articulate the results of this productive tension between the Gods and the intelligible on the several planes of Being implied by each conception of the holy which is successively taken up and dialectically overturned to yield the conception appropriate to the next higher plane, a style of interpretation characteristic of the ancient Neoplatonists. (shrink)

Modeling is central to scientific inquiry. It also depends heavily upon the imagination. In modeling, scientists seem to turn their attention away from the complexity of the real world to imagine a realm of perfect spheres, frictionless planes and perfect rational agents. Modeling poses many questions. What are models? How do they relate to the real world? Recently, a number of philosophers have addressed these questions by focusing on the role of the imagination in modeling. Some have also drawn parallels (...) between models and fiction. This chapter examines these approaches to scientific modeling and considers the challenges they face. (shrink)

Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in (...) triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations. (shrink)

Ordinary people shudder at the thought that people in positions of power might do whatever they think they can get away with. But that is often the way it is in the real world, and the risks go even higher when opportunity is compounded with impatience. The ways of negotiation and diplomacy are not considered entirely outmoded. But more and more we are being duped by a dream of some ultimate technological fix: that one more fancy gadget is all it (...) will take to solve the vexing problems that less well-tooled folks have been stumbling over for centuries. Our success rate, this reasoning goes, has been limited so far only by the limits on our equipment. With the new super-missile, or the new super-plane, or the new superlaunching system in space, we will be able to leap tall buildings in a single bound-or, what is more to the point, just blow them away and walk across the crater. "Bombs can be clean." "Nuclearwar is winnable." The illusion of omnipotence that accompanies this megalomania is well nurtured by manufacturers who stand in line for contracts to help build some super-weapon. This should not be surprising. What at first glance is surprising is the almost total failure of our commercial media to call this myth into question. This criticism is meant to be sweeping, but I will here focus my remarks on film. (shrink)

There are striking parallels between current capability theories and the moral philosophy of Karl Christian Friedrich Krause. This article reconstructs central arguments of Krause’s ethics and correlates them with passages from the works of Martha Nussbaum, showing that such similarities extend not only to what, substantially, is being professed in either philosophy but also, procedurally, to the question of how the respective moral conclusions are reached. As Krause correlates responsibility with capability, the article begins with an examination of Krause’s idea (...) of human — as compared to animal — freedom and their respective normative implications. Next, the argument is extended to the social responsibilities of personal freedom, before widening the scope to the cosmopolitan plane. The paper then briefly examines historical links between Krause and current capability theorists, before concluding. (shrink)

Transdisciplinary analogies and metaphors are potential useful tools for thinking and creativity. The exploration of other conceptual philosophies and fields can be rewarding and can contribute to produce new useful ideas to be applied on different problems and parts of reality. The development of the so-called 'sustainability' approach allows us to explore the possibility of translate and adapt some of its main ideas to the organisation of human language diversity. The concept of 'sustainability' clearly comes from the tradition of thinking (...) that criticises the perspective of economic development that overlooks almost totally the natural environment -the precise context where this development takes place -and which thus leads it to a final end devoid of resources and clearly harmful for the life of human beings. Against this economicist view, which is blind to its very important side effects, some academic and activist enclaves have proposed the perspective of 'sustainable development' or 'lasting development'. In other words, they have theorised, constructed, and begun to practice an economic and urbanistic development respectful of, integrated into, and in keeping with the dynamics of nature. Such perspective provides a way of improving the material aspects of human life while at the same time not damaging other environmental aspects still more necessary and fundamental for the quality —and even for the simple possibility- of human existence. In fact, the view is a synthesis of possible opposed patterns. It does not renounce material and economic improvement, but nor does it exclude a fully healthy environment that is appropriate for the continuation of the species. If we now try to transfer and to apply this way of thinking to the linguodiversity reality, are there useful analogies and metaphors to be made? We believe there are, and ones that can be used to good advantage, and linked, moreover, to the traditions of thought that have always been present but perhaps even more so these last years with the drive to develop the thinking we are calling ‘eco-linguistic’. From the outset, we would underscore the will to connect apparent ‘opposites’ in an integrative conceptualisation, such as the very syntagm ‘sustainable development’. On the sociolinguistic plane, our debate should probably be about our ‘opposites’, which could be on the one hand the expansion of the dominant languages and, on the other hand, the maintenance and development of human linguistic diversity. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are (...) devoted. At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Who, over the age of 20, hasn’t experienced a serendipitous event: unexpected information that yields some unintended but potential value later on? Sitting next to a stranger on a plane who becomes a business partner? Stumbling onto an article in a journal or newspaper that helps tackle a nagging problem? Creating a new drug by accident?

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point (...) of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. -/- Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. -/- ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: -/- Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. -/- Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.] . (shrink)

The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one (...) is greater than the other or the one is greater than the other [sc. in appropriate correlated senses of ‘equals’, ‘is greater than’ and ‘is less than’]. In case there are two or more appropriate senses of ‘equals’, the one intended is often indicated by an adverb. For example, one plane figure may be said to be equal in area to another and, in certain cases, one plane figure may be said to be equal in length to another. Each sense of ‘equality’ is tied to a specific domain and is therefore non-logical. Notice that in every cases ‘equality’ is definable in terms of ‘is greater than’ and also in terms of ‘is less than’ both of which are routinely considered domain specific, non-logical. The word ‘identity’ in the logical sense does not require disambiguation. Moreover, it is not correlated ‘is greater than’ and ‘is less than’. If it is not the case that a certain designated triangle is [sc. is identical to] an otherwise designated triangle, it is not necessary for the one to be greater than or less than the other. Moreover, if two magnitudes are equal then a unit of measure can be chosen and, no matter what unit is chosen, each magnitude is the same multiple of the unit that the other is. But identity does not require units. In this regard, congruence is like identity and unlike equality. In arithmetic, the logical concept of identity is coextensive with the arithmetic concept of equality. The logical concept of identity admits of an analytically adequate definition in terms of logical concepts: given any number x and any number y, x is y iff x has every property that y has. The arithmetical concept of equality admits of an analytically adequate definition in terms of arithmetical concepts: given any number x and any number y, x equals y iff x is neither less than nor greater than y. As Aristotle told us and as Frege retold us, just because one relation is coextensive with another is no reason to conclude that they are one. (shrink)

I argue that Galileo regarded unaccelerated motion as requiring cause to sustain in. In an inclined plane experiment, the cause ceases when the incline ceases. When the incline ceases, what ceases is acceleration, not motion. Hence, unaccelerated motion requires no cause to sustain it.

We have a striking ability to alter our psychological access to past experiences. Consider the following case. Andrew “Nicky” Barr, OBE, MC, DFC, (1915 – 2006) was one of Australia’s most decorated World War II fighter pilots. He was the top ace of the Western Desert’s 3 Squadron, the pre-eminent fighter squadron in the Middle East, flying P-40 Kittyhawks over Africa. From October 1941, when Nicky Barr’s war began, he flew 22 missions and shot down eight enemy planes in his (...) first 35 operational hours. He was shot down three times, once 25 miles behind enemy lines while trying to rescue a downed pilot. He escaped from prisoner of war camps four times, once jumping out of a train as it travelled from Italy into Austria. His wife Dot, who he married only weeks before the war, waited for him at home. She was told on at least three occasions that he was missing in action or dead. For 50 years, Nicky Barr never spoke publicly, and rarely privately, of his war-time experiences. He was very much a forgotten and forgetting hero (for further details, see Dornan, 2002). In his first public interview in 2002 on the Australian documentary program “Australian Story”, Nicky explained his 50 year silence by saying. (shrink)

This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined (...) for this lecture. To repeat, a subregular polyhedron has congruent faces and congruent [polyhedral] angles. A subregular polyhedron whose faces are all regular polygons is regular—using standard terminology. -/- Geometers before Euclid showed that there are “essentially” only five regular polyhedra: every regular polyhedron is a tetrahedron (4 faces), a hexahedron or cube (6 faces), an octahedron (8 faces), a dodecahedron (12 faces), or an icosahedron (20 faces). -/- The first question is whether there are subregular polyhedra that are not regular. For example, are there tetrahedra having congruent angles and congruent triangular faces but whose faces are not equilateral triangles? -/- Another question is the classification of subregular polyhedra if they exist. For example, considering the fact that the regular tetrahedra all have equilateral triangles as faces, we ask which triangles other than equilaterals are faces of subregular tetrahedra. Similarly, considering the fact that the regular hexahedra all have squares as faces, we ask which quadrangles other than squares are faces of subregular hexahedra. -/- After introductory remarks that include historical and philosophical points, we concentrate on tetrahedra. A triangle that is congruent to each of the four faces of a tetrahedron is called a generator of the tetrahedron. The main result proved is that every acute triangle is a generator of a subregular tetrahedron. The proof includes an algorithm –implementable with scissors and paper –that constructs from any given acute triangle a subregular tetrahedron whose faces are congruent to the given triangle. -/- Algorithm: Given any acute triangle. Construct a similar triangle whose sides are double the sides of the given triangle. Draw the three lines connecting the three midpoints of the sides (making four triangles congruent to the given triangle—a central triangle surrounded by three peripheral triangles). Make three “hinges” along the lines connecting the midpoints. “Fold” the peripheral triangles together (into a tetrahedron). [LIGHTLY EDITED VERSION OF PRINTED ABSTRACT] Acknowledgements: William Lawvere, Colin McLarty, Irvin Miller, Frango Nabrasa, Lawrence Spector, Roberto Torretti, and Richard Vesley. -/- . (shrink)

The aim of this paper is to investigate Nishida Kitarō’s way of philosophizing in the light of the concept of “transition” in order to deepen our understanding of both Nishida’s philosophy and our thinking about and in transitions, using the concept of “boundary” or “border” (Grenze) as a catalyst. For that purpose, we focus on Nishida’s essay “Place” (「場所」), passing through different parts of the text as if through successive gates on a path of transition between one place and the (...) next, until we reach the final place of “absolute nothingness.” Dwelling on this place, we turn our attention to its internal structure and try to depict it along the outlines of a boundary, following the movements taking place in Nishida’s essay. The second part proposes an interpretation of the place of nothingness as an interminable practice of boundary-crossing that doesn’t come to a halt in a final, all-encompassing place, but dynamically situates itself on countless intersecting planes. After a more or less abstract analysis of the concept of “boundary,” we will apply and concretize this approach by using the example of the skin. To this end, we expose five main features of the skin as boundary: permeability, enclosure, excessiveness, interstitiality and reciprocal self-formation. (shrink)

What is the relationship between knowledge and ethics? Does what we know and the reason that secures knowledge determine ethical responsibility, or might ethical responsibility itself awaken and animate the enterprise of knowing? The dissertation affirms the priority of ethics by juxtaposing two accounts of the relationship between truth and goodness. It critiques Hegel's systematic conception of absolute knowing by showing that this knowing elides the anarchical ethical demand arising from the other person. Hegel's dialectic reconciles the problem of the (...) relation with the other by transposing it to the plane of cognition where it becomes spirit's self-knowing. However, Emmanuel Levinas's phenomenological reduction of the structures of knowing exposes an ethical level of experience that both inspires and interrupts this adventure of knowing. ;After the introduction of this problematic, Chapter 1 examines the challenge that Levinas poses to Hegel, discovering in experience and subjectivity a ground where real dialogue can take place. Chapter 2 traces the reconception of subjectivity by which Hegel brings all exteriority within the experience of self-consciousness and compares this with Levinas's notion of "lived experience." In Chapter 3, I show how Levinas's account of sensibility and enjoyment resists incorporation into Hegel's notion of self-consciousness. Chapter 4 examines the encounter with the other person and explicates why Hegel's and Levinas's accounts cannot be reconciled or made to complement one another, for the non-allergic responsibility incurred in the face to face relation is inassimilable to the antagonism of the same and the other experienced as self-consciousness. Then, in Chapter 5, I trace Hegel's pursuit of a more authentic recognition of otherness through the development of the concept of spirit, paying special attention to the role of language. The ultimate accomplishment of spiritual recognition in Hegel's account is again challenged by Levinas's notion of responsibility, which signifies as an ethical "saying" apart from the "said." Finally, I contest the absoluteness of knowing without denying the dialectic that animates it by suggesting that philosophy can be maintained as a human enterprise, a pursuit of knowing that is ever subject to and interrupted by the face of the other. (shrink)

The book, ‘The Crisis of World and Krishna Pure Monism: A Long Essay’, is more a cathartics of the crisis of world as viewed from the plane of Krishna pure monism than critique of hither to development of idea and philosophy. It sees a correlation of the crisis of world in praxis of objectification of subject, undermining of the knowledge and violation of Krishna pure monism-one has become all and inherence of knowledge. If objectification of subject is juxtaposed with (...) resultant objectification of women, nature, ‘other’, knowledge and idea or Reason or Dharma, it would certainly validate the hypothesis of the essay. The main hypothesis of the essay is as to how objectification of subject on the plane of sciencitization of philosophy and violation of Krishna pure monism-one has become all and inherent knowledge and , and its subversion by muses have led to the crisis of world. The objectification of subject or consciousness or spirit in sciences seems to be cause and effect of objectification of the Woman, Nature, Other, Knowledge and Reason or Idea or Dharma. When one has become all or creator has become creation, the plurality and difference is transitory which appear to have been assigned the permanent value. The transitory value has been given permanence, while the permanent has been dislodged from discourse, conveniently tucked to the abstract. This seems to be real narrative of the crisis of the world. -/- . (shrink)

In my dissertation (Rutgers, 2007) I developed the proposal that one can establish that material quantum objects behave classically just in case there is a “local plane wave” regime, which naturally corresponds to the suppression of all quantum interference.

Como dijo Ramón y Cajal, “mientras el cerebro continúe siendo un misterio, el universo también lo será”. El mejor ejemplo de esto son las emociones involucradas en la toma de decisiones, en donde aún no existe un consenso sobre cómo definirlas desde un punto de vista neurológico y teórico correlacionados. Se sabe que las emociones permiten dar significado a hechos y eventos; que son estados cerebrales desde donde la persona hace planes de acción y toma distintas decisiones, pero no todos (...) los autores están de acuerdo en que puedan ser explicadas únicamente como cambios físicos o marcadores somáticos: tensión muscular, frecuencia cardíaca o temperatura corporal. También ocurren cambios en el cerebro en términos de neurotransmisores, pero aún se desconocen los detalles de algunos de estos procesos emergentes. Por eso se consideró una revisión sistemática de los trabajos de los especialistas y una interpretación desde la neuroética fundamental como disciplina filosófica —como filosofía del cerebro— que hace posible la habilitación de un andamiaje teórico conceptual capaz de explicar y comprender algunos de los correlatos neurales asociados a la toma racional y no racional de las decisiones, y la aspiración de explicaciones teóricas subyacentes. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.

According to a widespread view, Thomas Kuhn’s model of scientific development would relegate rationality to a second plane, openly flirting with irrationalist positions. The intent of this article is to clarify this aspect of his thinking and refute this common interpretation. I begin by analysing the nature of values in Kuhn’s model and how they are connected to rationality. For Kuhn, a theory is chosen rationally when: i) the evaluation is based on values characteristic of science; ii) a theory (...) is considered better the more it manifests these values; and iii) the scientist chooses the best-evaluated theory. The second part of this article deals with the thesis of the variability of values. According to Kuhn, the examples through which epistemic values are presented vary for each person, and for this reason individuals interpret these criteria differently. Consequently, two scientists, using the same values, can come to a rational disagreement over which theory to choose. Finally, I point out the limitations of this notion of rationality for the explanation of consensus formation, and the corresponding demand for a sociological theory that reconnects individual rationality with convergence of opinions. (shrink)

In this paper I deal with Nietzsche's theory of knowledge in the context of 19th century epistemology. In particular, I argue that, even though Nietzsche shows the ontological lack of content of truths (both on the theoretic and on the moral plane), he nevertheless leaves the space for a practical use of them, in a way that can be compared with William James' pragmatism. I thus deal with Nietzsche's and James' concept of "truth", and show their relationship with some (...) outcomes of Ernst Mach's epistemology. (shrink)

In this article, Deleuze & Guattari (D+G)’s conception of democracy will be approached with regard to art’s envisagement of “becoming-democratic” as a mode of thinking through percepts and affects. For D+G, democracy is, by no means, a desirable political goal or the name of a type of governance appropriate for the world. On the contrary, as long as it is a representation mechanism, democracy has negative connotations since it promotes the dominance of majority. For this reason, the only way of (...) affirming democracy is to cleanse and subtract the governmental layers which fix it as a system of social measurement, and re-associate it with “multiplicity” & “becoming”. In this respect, democracy can only be affirmed if it is paired with the notions of becoming-democratic, becoming-revolutionary and becoming-minor. Nevertheless, it is not the case that mainstream political philosophy or professional politics are the only methods for formulating opinions on democracy. “Politics of art” would provide means of thinking upon becoming democratic since art—being a mode of thinking by itself—may place many issues about which one could talk only theoretically (or which would hardly become a part of daily life) on a living plane, even though that plane would solely exist in the world of the work of art. In brief, on the condition that it is not an apparatus of representation, art may turn into a medium of thinking upon becoming-democratic, in addition to all the other becomings that it is related to. (shrink)

Text classification is one of the most important task in natural language processing, In this research, we carried out several experimental research on three (3) of the most popular Text classification NLP classifier in Convolutional Neural Network (CNN), Multinomial Naive Bayes (MNB), and Support Vector Machine (SVN). In the presence of enough training data, Deep Learning CNN work best in all parameters for evaluation with 77% accuracy, followed by SVM with accuracy of 76%, and multinomial Bayes with least performance of (...) 69% accuracy. CNN has the best performance in the presence of large enough training dataset because of the presence of filter/ kernels which help to indentify patterns in text data regardless of their position in the sentence. We repeated the training again with just one-third of our data, at this point SVM comes with the best performance, the performance of CNN noticeably drops but still better than Multinomial Naive Bayes, the reason why SVM works best when we reduce the training data was because of its ability to look for a hyper-plane that creates a boundary between different classes of data so as to properly classify them, so we believed that getting the hyper-plane was more efficient when we reduce the dataset, hence reason for the good performance. Multinomial Naive Bayes have the least performance which we attributed to its assumption of independency between the features which sometimes does not hold true. We concluded that availability of data should be an important factor when choosing classifier for Natural Language Processing Text Classification task. CNN should be use in the presence of enough dataset, and SVM should be use when data is not enough. Multinomial Naive Bayes must not be trusted with state of the art NLP task due to its assumption of independency between the features . (shrink)

In the prospectus for his later work pronounced in 1952, Merleau-Ponty announced that his move beyond the phenomenological to the ontological level of analysis is motivated by issues of sociality, notably communication with others.' I propose to interrogate this priority attributed by the author to this interpersonal bond in his reflections on corporeality in general, marking a departure from The Structure of Behavior and The Phenomenology of Perception, which privileged the starting point of consciousness and the body proper. My interest (...) lies particularly in exposing the psychological sources of Merleau-Ponty's thinking about the primacy of sociality. Referring to his lectures on Child Psychology and Pedagogy, which he delivered as Professor at the Sorbonne in Paris in 1949-52,2 I will develop the contention that the developmental psychology of child sociality significantly informed his understanding of relations between self and other laid out in the later texts, and henceforth informed also his conception of the flesh. Specifically, the psychological hypotheses about the anonymous and fusional form initially taken by human sociality appears to play a determining role in his conception of interpersonal life formulated on the ontological plane. I will then point to the internal tensions involved in the theory of sociality based on the thesis of anonymity and disclose an alternative theoretical account, which has the merit of preserving the advantages of the anonymity thesis while avoiding its drawbacks; it also facilitates continued dialogue between Merleau-Ponty's philosophy and recent developmental psychology. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under (...) control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

The rapid increase of the old age people imposes the reconsideration of the rehabilitation techniques and procedures and/or the development of the existing ones, at least from two points of view: the limitation use of the pharmaceutical drugs because of their secondary effects in the debilitated organisms and their avoidance; the high risk of the induced anxiety states, depression or other symptoms as a consequence of the main disease, i.e. the neuro-degenerative or mobility dysfunctions, limiting again the use of such (...) excessive drug medication. Moreover, Alzheimer’s or Parknson’s diseases are otherwise incurable, so the application of rehabilitating procedures like music-based therapy becomes preferential. The advances both in the identification of the specific auditory musical-sensitive circuits and of the non- musical neuro-connections but activated indirectly by music, otherwise inaccessible by other techniques, and in the understanding of consciousness, which can be described by seven cognitive centers, allows to improve and develop the music based therapy. A multitask procedure based on the activation of these cognition centers is presented, allowing to increase the personal psychical engagement of the patient in the recommended music based therapeutic program, addressed both to the rehabilitation of the main degenerative disease and to the secondary induced dysfunctions. This procedure combines the evidence based medicine assisted by laboratory expertise for the determination of a correct diagnostic, and narrative based medicine allowing to quantify the personal engaging qualities of the patient with respect to the proposed music based program, reducing in this way the gap between these two basic procedures and bringing in a first plane the patient care, not only the disease, with beneficial consequence for the therapy efficiency and for the patient-medical care relations. (shrink)

The attempt to define meaning arouses numerous questions, such as whether life can be meaningful without actions devoted to a central purpose or whether the latter guarantee a meaningful life. Communities of inquiry are relevant in this context because they create relationships within and between people and the environment. The more they address relations—social, cognitive, emotional, etc.—that tie-in with the children’s world even if not in a concrete fashion, the more they enable young people to search for and find meaning. (...) Examining the way in which philosophical communities of inquiry serve as a dialogical space that enables a search for meaning on the personal and collective plane, this article seeks to expand the discussion of how/whether finding meaning on a private or communal level can promote recognition of the existential uniqueness of each individual and the development of a sense of responsibility for him or her. Grounded in the writings of Matthew Lipman, it links his ideas about finding meaning in philosophical communities of inquiry with those of Jean-Paul Sartre, Viktor Frankl, and Emmanuel Levinas, in particular with regard to the association between meaning and responsibility. (shrink)

This article focuses on the distinction between psychosocial types and conceptual personae advanced by Gilles Deleuze and Félix Guattari in What is Philosophy? The conceptual persona is the tool that a philosopher invents in order to create new concepts with which to bring forth new events. Although they present it as one of the three elements of philosophy, its nature and function and, above all, its conjunctions with psychosocial types have been overlooked by scholars. What is Philosophy? contains a list (...) of character traits of which each conceptual persona is composed. The central argument of this article is that this list can well be regarded as a table of categories that enable the exercise and experience of philosophy’s creative thinking. Since the character traits of a conceptual persona match the characteristics of the given psychosocial types, it is necessary to keep inventing new conceptual personae always starting from the historical presuppositions. The philosopher requires the conceptual persona to transfer his or her movements of thought to philosophy’s plane of immanence and thereby transform them in such a manner that philosophy can unfold as a creative power. It emerges as the subject of creative thinking at the same time as the concepts that subject creates, with which it coincides in the moment of creation. With the conceptual persona in What is Philosophy?, Deleuze and Guattari determine the one element of philosophy that makes the transcendental empiricism a method of creation that appears as a precise operation with all its convincing and transparent results. (shrink)