This book is written for middle and high school students, for teachers and for those with a passion for math, containing 150+1 problems (which are followed by solutions) to make it more accessible to the reader. The last problem (150+1), a very interesting one, leaves some space for comments and generalizations. The book is a collaboration between a multi-awarded student at Romania’s National Mathematics Olympiad (Carina Maria Viespescu, student in year 10 at Liceul International of Informatics Bucuresti), a teacher from (...) Colegiul National “Fratii Buzesti” din Cravoia and prof. Dr. Emeritus Florentin Smarandache from the University of New Mexico. A couple of problems are proposed by colleagues, and their names indicated in footnotes. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. -/- From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? -/- The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. -/- The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). -/- The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. -/- * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. -/- The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). -/- The other subheadings in this essay are – -/- NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) -/- BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) -/- WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) -/- DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) -/- PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) -/- INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). 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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)

Simple regression (regression analysis with a single explanatory variable), and multiple regression (regression models with multiple explanatory variables), typically correspond to very different biological questions. The former use regression lines to describe univariate associations. The latter describe the partial, or direct, effects of multiple variables, conditioned on one another. We suspect that the superficial similarity of simple and multiple regression leads to confusion in their interpretation. A clear understanding of these methods is essential, as they underlie a large range of (...) procedures in common use in biology. Beyond simple and multiple regression in their most basic forms, understanding the key principles of these procedures is critical to understanding, and properly applying, many methods, such as mixed models, generalised models, and causal inference using graphs (including path analysis and its extensions). A simple, but careful, look at the distinction between these two analyses is valuable in its own right, and can also be used to clarify widely-held misconceptions about collinearity (correlations among explanatory variables). There is no general sense in which collinearity is a problem. We suspect that the perception of collinearity as a hindrance to analysis stems from misconceptions about interpretation of multiple regression models, and so we pursue discussions about these misconceptions in this light. In particular, collinearity causes multiple regression coefficients to be less precisely estimated than corresponding simple regression coefficients. This should not be interpreted as a problem, as it is perfectly natural that direct effects should be harder to characterise than univariate associations. Purported solutions to the perceived problems of collinearity are detrimental to most biological analyses. (shrink)

In this paper, we propose the introduction of a neutrosophic chi-square-test for consistency, incorporating neutrosophic statistics. Our aim is to modify the existing chi-square -test for consistency in order to analyze imprecise data. We present a novel test statistic for the neutrosophic chi-square -test for consistency, which accounts for the uncertainties inherent in the data. To evaluate the performance of the proposed test, we compare it with the traditional chi-square -test for consistency based on classical statistics. (...) By conducting a comparative analysis, we assess the efficiency and effectiveness of our proposed neutrosophic chi-square-test for consistency. Furthermore, we illustrate the application of the proposed test through a numerical example, demonstrating how it can be utilized in practical scenarios. Through this implementation, we aim to provide empirical evidence of the improved performance of our proposed test when compared to the traditional chi-square-test for consistency based on classical statistics. We anticipate that the proposed neutrosophic chi-square-test for consistency will outperform its classical counterpart, offering enhanced accuracy and reliability when dealing with imprecise data. This advancement has the potential to contribute significantly to the field of statistical analysis, particularly in situations where data uncertainty and imprecision are prevalent. (shrink)

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. (...) I will conclude with some consideration on scope interactions between quantifiers. (shrink)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of (...) the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

Epicurean ethics has been subject to withering ancient and contemporary criticism for the supposed irreconcilability of Epicurus’s emphatic endorsement of friendship and his equally clear and striking ethical egoism. Recently, Matthew Evans (2004) has suggested that the key to a plausible Epicurean response to these criticisms must begin by understanding why friendship is valuable for Epicurus. In the first section of this paper I develop Evans’ suggestion further. I argue that a shared conception of the human telos and of what (...) is required to attain it structures the confidence that characterizes friendship. In the second part of the paper I return to two contemporary criticisms of Epicurean friendship. The first criticism focuses on the problem of free riders. The second criticism points to a seeming inconsistency in Epicurean doctrine. I suggest that both criticisms can be adequately addressed once we understand Epicurean friendship in greater depth. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.

According to Greimas, the semiotic square is far more than a heuristic for semantic and literary analysis. It represents the generative “deep structure” of human culture and cognition which “define the fundamental mode of existence of an individual or of a society, and subsequently the conditions of existence of semiotic objects” (Greimas & Rastier 1968: 48). The potential truth of this hypothesis, much less the conditions and implications of taking it seriously (as a truth claim), have received little attention (...) in the literature. In response, this paper traces the history and development of the logical square of opposition from Aristotle to Greimas and beyond, to propose that the relations modelled in these diagrams are embodied relations rooted in gestalt memories of kinesthesia and proprioception from which we derive basic structural awareness of opposition and contrast such as verticality, bilaterality, transversality, markedness and analogy. To make this argument, the paper draws on findings in the phenomenology of movement (Sheets-Johnstone 2011a, 2011b, 2012, Pelkey 2014), recent developments in the analysis of logical opposition (Beziau & Payette 2008), recent scholarship in (post)Greimasian semiotics (Corso 2014, Broden 2000) and prescient insights from Greimas himself (esp. 1968, 1984). The argument of the paper is further supported through a visual and textual content analysis of a popular music video, both to highlight relationships between the semiotic square and mundane cultural ideologies and to show how these relationships might be traced to the marked symmetries of bodily movement. In addition to illustrating the enduring relevance of Greimasean thought, the paper further illustrates the neglected relevance that embodied chiasmus holds for developments in anthropology, linguistics and the other cognitive sciences. (shrink)

Review of “The Mad Square: Modernity in German Art 1910-37”, National Gallery of Victoria, Melbourne, Australia, November 25, 2011-March 4, 2012. A version of this essay appeared in the Appendices of Gavin Keeney, Not-I/Thou: The Other Subject of Art and Architecture (CSP, 2014), pp. 153-57.

Conditional perfection is the phenomenon in which conditionals are strengthened to biconditionals. In some contexts, “If A, B” is understood as if it meant “A if and only if B.” We present and discuss a series of experiments designed to test one of the most promising pragmatic accounts of conditional perfection. This is the idea that conditional perfection is a form of exhaustification—that is a strengthening to an exhaustive reading, triggered by a question that the conditional answers. If a speaker (...) is asked how B comes about, then the answer “If A, B” is interpreted exhaustively to meaning that A is the only way to bring about B. Hence, “A if and only if B.” We uncover evidence that conditional perfection is a form of exhaustification, but not that it is triggered by a relationship to a salient question. (shrink)

It is often thought that traditional recidivism prediction tools used in criminal sentencing, though biased in many ways, can straightforwardly avoid one particularly pernicious type of bias: direct racial discrimination. They can avoid this by excluding race from the list of variables employed to predict recidivism. A similar approach could be taken to the design of newer, machine learning-based (ML) tools for predicting recidivism: information about race could be withheld from the ML tool during its training phase, ensuring that the (...) resulting predictive model does not use race as an explicit predictor. However, if race is correlated with measured recidivism in the training data, the ML tool may ‘learn’ a perfect proxy for race. If such a proxy is found, the exclusion of race would do nothing to weaken the correlation between risk (mis)classifications and race. Is this a problem? We argue that, on some explanations of the wrongness of discrimination, it is. On these explanations, the use of an ML tool that perfectly proxies race would (likely) be more wrong than the use of a traditional tool that imperfectly proxies race. Indeed, on some views, use of a perfect proxy for race is plausibly as wrong as explicit racial profiling. We end by drawing out four implications of our arguments. (shrink)

Anselmian theists claim (a) that there is a being than which none greater can be conceived; and (b) that it is knowable on purely—solely, entirely—a priori grounds that there is a being than which none greater can be conceived. In this paper, I argue that Anselmian Theism gains traction by conflating different interpretations of the key description ‘being than which no greater can be conceived’. In particular, I insist that it is very important to distinguish between ideal excellence and maximal (...) possible excellence. At the end of my paper, I illustrate the importance of this distinction by applying my discussion to the recent defence of Anselmian Theism in Nagasawa (Philos Q 58:577–591, 2008). (shrink)

This paper aims to analyze the square beyond an architectural element in the city, but weaves this blank slate, with its contemporary socio political atmosphere as a new paradigm. As a result, this research investigates the historical, social and political concept of Meydan – a term which has mostly applied for the Iranian and Islamic public squares. This interpretation, suggested the idea of Meydan as the core of the projects in the city, which historically exposed in formalization of power (...) relations and religious ideologies. In this sense, studying the spatial transformation of Iranian public squares introduces the framework, which is adaptable to contemporary urban context. (shrink)

Classic perfect being theologians take ‘being perfect’ to be conceptually necessary and sufficient for being God. I argue that this claim is false because being perfect is not conceptually necessary for being God. I rest my case on a simple thought experiment inspired by an alternative I developed to perfect being theology that I call “functional theology.” My findings, if correct, are a boon for theists since if it should turn out that there is no (...) class='Hi'>perfect being, there could still be a God. (shrink)

Locke's claims about the "inadequacy" of substance-ideas can only be understood once it is recognized that the "sort" represented by such an idea is not wholly determined by the idea's descriptive content. The key to his compromise between classificatory conventionalism and essentialism is his injunction to "perfect" the abstract ideas that serve as "nominal essences." This injunction promotes the pursuit of collections of perceptible qualities that approach ever closer to singling out things that possess some shared explanatory-level constitution. It (...) is in view of this norm regulating natural-historical inquiry that a substance-idea represents a sort for which some such constitution serves as the "real essence," i.e. as that on which all the sort's characteristic "properties" depend. (shrink)

Excellence in sport performance is normally taken to be a matter of superior performance of physical movements or quantitative outcomes of movements. This paper considers whether a wider conception can be afforded by certain kinds of nature based sport. The interplay between technical skill and aesthetic experience in nature based sports is explored, and the extent to which it contributes to a distinction between different sport-based approaches to natural environments. The potential for aesthetic appreciation of environmental engagement is found to (...) be strongly dependent on whether or not environmental engagement is exploited for the end of producing a quantifiable result or enhancing technical skill. It is also argued that an existential rather than spectatorial attitude to aesthetic experience is offered by specifically nature oriented sport. Aesthetic experience achieved in this way is therefore neither passive nor detached, but extends Berleant's concept of participatory environmental aesthetics and underpins both an alternate (wide) conception of excellence in sport activity and a richer experience of aesthetic engagement than more objectivised standpoints. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds (...) of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

My chapter deals with an important part of how Wolff pursued the normative ambitions of his ethics in giving practical guidance with regard to specific moral issues. I first consider how Wolff’s ethics tackles the duties to others, which traditionally represent a difficult issue for moral perfectionism. In this regard, I argue that Wolff’s strategy combines two aspects: (a) he includes in perfection non-active aspects and (b) operates with an agent-neutral notion of perfection, in spite of important passages that might (...) suggest differently. I then focus on Wolff’s treatment of the duties concerning veracity and lying, and show how it follows that general strategy. Combining its two aspects, Wolff examines specific moral issues by adopting a non-welfarist notion of benefit and harm as the standard that can give guidance about practical cases. (shrink)

In this paper, I will focus on the nature of the modernity from the perspective of a «logical» square. On the basis of its vectorial orientation, I will show the value of Guy Debord’s work, according to which, undeniably, there is a need to articulate two core issues of our time: «How does a multitude turn into a class?» (Benjamin’s question) and «How does the individual become a subject?» (Althusser’s question). It is precisely the nexus between these questions that (...) allows us to draw the line between the modernity and the postmodernity. (shrink)

Perfect being theism is the view that the perfect being exists and the property being-perfect is the property being-God. According to the strong analysis of perfection, a being is perfect just in case it exemplifies all perfections. On the other hand, the weak analysis of perfection claims that a being is perfect just in case it exemplifies the best possible combination of compatible perfections. Strong perfect being theism accepts the former analysis while weak (...) class='Hi'>perfect being theism accepts the latter. In this paper, I argue that there are good reasons to reject both versions of perfect being theism. On the one hand, strong perfect being theism is false if there are incompatible perfections; I argue that there are. On the other hand, if either no comparison can be made between sets of perfections, or they are equally good, then there is no best possible set of perfections. I argue for the antecedent of this conditional statement, concluding that weak perfect being theism is false. In the absence of other analyses of perfection, I conclude that we have reason to reject perfect being theism. (shrink)

In this paper, I ask whether there is a defensible philosophical view according to which everybody is beautiful. I review two purely aesthetical versions of this claim. The No Standards View claims that everybody is maximally and equally beautiful. The Multiple Standards View encourages us to widen our standards of beauty. I argue that both approaches are problematic. The former fails to be aspirational and empowering, while the latter fails to be sufficiently inclusive. I conclude by presenting a hybrid ethical–aesthetical (...) view according to which everybody is beautiful in the sense that everybody can be perceived through a loving gaze. I show that this view is inclusive, aspirational and empowering, and authentically aesthetical. (shrink)

My paper discusses the philosophical interrelationship between perfection, truth, and knowledge. The connection that exists between these three concepts underscores the argument of my paper that they are all one and the same thing. -/- The concepts of perfection, truth and knowledge are analysed in that order. I analyse perfection and demonstrate the practicalities of my arguments. Truth is then scrutinized and defined to illustrate its intimate relationship with perfection leading to the conclusion that knowledge being ‘truth that is (...) class='Hi'>perfect’. -/- In dealing with the theory of knowledge, I take into account the justification of knowledge and highlighted arguments that I found to be insufficient. I derive a premise to refute and replace both the traditional and contemporary views of knowledge. -/- In the paper presented, I consider views of some prominent philosophers including; Locke, Russell, Plato, Aristotle and Leibniz. (shrink)

God is typically conceived as perfectly good and necessarily so, in two senses: in terms of always performing the best possible act and in terms of having maximal moral worth. Yet any being that freely performs the best act she can must be accorded greater moral worth for any such action than a being that does so necessarily. I conclude that any being that performs the best possible act of necessity cannot also have maximal moral worth, making the concept of (...) God’s perfect goodness incoherent. (shrink)

It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern (...) of oppositions that proceeds with colored diagrams and an increasing set of bitstrings. (shrink)

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a (...) different status over the other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined as (...) the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

I consider a new, non-disjunctive strategy for ‘relational’ or ‘naïve realist’ theories to respond to arguments from ‘perfect’ (causally matching) hallucinations. The strategy, in a nutshell, is to treat such hypothetical cases as instances of perception rather than hallucination. After clarifying the form and dialectic of such arguments, I consider three objections to the strategy. I provide answers to the first two objections but concede that the third — based on the possibility of ‘chaotic’ (uncaused) perfect hallucinations — (...) cannot obviously be dealt with by the proposed strategy. However, such ‘chaotic’ scenarios are also problematic for standard representational accounts of experience. Thus I conclude that perfect hallucinations pose no more of a threat to the relational theory than to its main representational rival. (shrink)

Development has been themain strategy in addressing the problemof sustainability since at least the mid-1980s. The results of this strategy have been mixed, if not disappointing. In their objections to this approach, critics frequently invoke constraints imposed by physical reality of which the most important one is entropy production. They question the belief that technological innovations are capable of solving the problem of sustainability. Is development the right response to this problem and is the current course capable of attaining sustainability? (...) The article examines closely and critiques the principal theoretical objection to sustainable development that emphasizes physical constraints, and more specifically entropy production. It also offers a critique of the current approach to sustainable development. The article advocates a systems approach as a way to anchor a broad consensus in the ongoing sustainability debates. (shrink)

This paper examines how Plato’s rejection of the friends of the forms at 248a–249b in the Sophist is continuous with the arguments that he develops shortly after this part of the dialogue for the interrelatedness of the forms. I claim that the interrelatedness of the forms implies that they are changed, and that this explains Plato’s rejection of the friends of the forms. Much here turns on the kind of change that Plato wants to attribute to the forms. I distinguish (...) my view of the sort of change that the forms experience from other kinds of change—such as ‘Cambridge change’—that scholars have believed Plato has in mind in rejecting the friends of the forms. On the view that I advance, a form experiences a change (which I call ‘perfect change’) in its association with another form that distinguishes it as the distinctive being that it is—that is, through its possession of its distinctive properties. (shrink)

The growing power of communication and information technologies and their reliance on systems, poses great challenges to cultural and religious diversity, and even education. Will these technological systems continue to homogenize cultures and religions? Will this process lead to increasing strife? Or is there a possibility of maintaining both identity and diversity in a peaceful manner? This paper explores an early attempt to consider this problem. It will focus on the Ikhwān al-Ṣafā and their attempt to construct an encyclopedic system (...) to coordinate knowledge during the flowering of Islamic Civilization in the tenth century. It will primarily deal with Epistle or Rasā'il twenty-two – a fable concerning a debate between the humans, the animals and the Jinn. It will discuss their debate and show how the major concern for the Ikhwān al-Ṣafā was not only to embrace the diversity of knowledge but also the need to navigate through this diversity. I would like to suggest through this analysis that a culture gains its richness and identity by recognizing perfections outside of their own identity. This is analogous to the way that the individual human being gains meaning and dignity by reaching beyond its individuality. It also shows the importance of cultural and religious diversity and how the world cannot be unified by a single all-encompassing system. This approach is important because it shows the possibility of maintaining cultural and religious identity while participating in a technological world involving the flow of information on one hand, and global cultural diversities on the other. (shrink)

Ideas for integrating AI into politics are now emerging and advancing at accelerating pace. This chapter highlights a few different varieties and show how they reflect different assumptions about the value of democracy. We cannot make informed decisions about which, if any, proposals to pursue without further reflection on what makes democracy valuable and how current conditions fail to fully realize it. Recent advances in political philosophy provide some guidance but leave important questions open. If AI advances to a state (...) where it can secure superior political outcomes, leading perspectives in political philosophy suggest that democracy may become obsolete. If we find this suggestion troubling, we need to put the case for democracy on stronger foundations. (shrink)

It is commonly believed that intrinsically bad possible worlds are inconsistent with the perfect goodness of God. A perfectly good being could not exist in possible worlds that are intrinsically bad. Indeed it is widely believed that possible worlds that are insufficiently good are inconsistent with a perfectly good God. Modal atheological arguments aim to show that, since the pluriverse includes intrinsically bad worlds and insufficiently good worlds, there necessarily does not exist a perfectly good God. I show that (...) modal atheological arguments are in general invalid. Modal atheological arguments fail to show that there exists no perfectly good God even on the assumption that there are extremely bad worlds in the pluriverse. Modal atheological arguments depend entirely on the logic of modality in S5. But the logic of S5 ensures that a perfectly good God is consistent with extremely bad possible worlds and so guarantees that a perfectly good God is consistent with a plenitudinous pluriverse. (shrink)

In Squaring the Circle in Descartes’ Meditations, Stephen Wagner aims to show that Descartes’ project in the Meditations is best understood as a ‘strong validation of reason’ i.e., as proving in a non-circular way that human reason is a reliable, truth-conducive faculty. For such an enterprise to qualify as a ‘strong’ validation, Wagner contends, skeptical doubt must be given its strongest force. The most stringent doubt available in the Meditations is the deceiving God. To rule out the possibility that an (...) omnipotent God created humans so that their best functioning cognitive faculties provide misleading information about what the world is like, Descartes must prove that a non-deceiving God exists. Furthermore, only a non-circular proof will count as a ‘validation.’ Wagner spells out the requirements of non-circularity as involving a proof for God’s existence that is not deductive, does not simply achieve a clear and distinct perception of God’s existence, and proceeds on the basis of perceptions that remain true even when the reasons underlying them are not attended to any longer by the meditator. (shrink)

Modal dispositionalism is the view that possibilities are a matter of the dispositions of individual objects: it is possible that p if and only if something has a disposition for p to be the case. We raise a problem for modal dispositionalism: nothing within the theory rules out that there could be necessary, perfect masks, which make the manifestation of a disposition impossible. Unless such necessary perfect masks are ruled out, modal dispositionalism runs the risk of failing to (...) provide a sufficient condition for possibility, and indeed of engendering contradictions. But to rule them out, modal dispositionalism would have to revise a crucial tenet of the view, its localism. (shrink)

The heart of Aristotelian Logic is the square of opposition. This study engaged on further [re]investigation and meta-logical analysis of the validity of the square of opposition. Further, in this paper, it has been modestly established, with greater clarity, the exposition of the strengths, more than the presentation of the defects, loopholes and weaknesses, of the Aristotelian Logic in a descriptive and speculative manner. The unconcealment of the breakdown of the square of opposition marked a rupture and (...) the opening of avenues of alternative reasoning. The critical and analytical exposition of the loopholes of the square of opposition led to a realization that things around us could have been and still be different; and there could have been better alternative reasoning than what we have called, adopted, and worshipped [Greek] logic. Results show that the downfall of the oppositional relationships in the square of opposition provided a proof of the logical illusion of Aristotle or the loophole of Traditional Logic. The laws of opposition, that have been considered the measures of logically deductive inferences, are practically almost totally logical deceptions. By implication, if the laws of subcontrariety, contrariety, and subalternation [and may be contradiction] have collapsed, the square of opposition has also collapsed; hence, Aristotle‟s square of opposition is a fallacy. This means that the square of opposition has errors and in itself an error. (shrink)

Kant’s views about the nature and value of enlightenment have been discussed very much since 1784, and without ever losing any of their relevance and importance. I will discuss a topic that has not been discussed quite that extensively: Kant’s conception of enlightenment as it relates to the idea of perfection (Vollkommenheit) in particular. Is the project of enlightenment also a project of perfection (and vice versa), and if yes, in what sense and to what degree? My aim is twofold (...) here: not just to present a sketch of Kant’s views but also to do so in the light of contemporary, systematic questions and ideas concerning the idea of perfection. (shrink)

In this paper, we consider two different attempts to make an end run around the experimentalist challenge to the armchair use of intuitions: one due to Max Deutsch and Herman Cappelen, contending that philosophers do not appeal to intuitions, but rather to arguments, in canonical philosophical texts; the other due to Joshua Knobe, arguing that intuitions are so stable that there is in fact no empirical basis for the experimentalist challenge in the first place. We show that a closer attention (...) to philosophical practices reveal, in turn, that we cannot make sense of these philosophical texts as arguments all the way down; and that our methods are so sensitive to error that even a modest amount of instability is enough to raise deep methodological concerns. (shrink)

An imaginary report of Square’s plans for a journey aimed to find out whether the topology of Flatland is sphere-like or torus-like, intended as a trubute to Hans Herzberger’s uncompromising philosophical style, courage, and passion.

In this essay I will show that the incoherence many commentators have found in Kant’s Religion is due to Augustinian assumptions about human evil that they are implicitly reading into the text. Eliminate the assumptions, and the inconsistencies evaporate: both theses, those of universality and moral responsibility, can be held together without contradiction. The Augustinian view must be replaced with what John Hick has dubbed an “Irenaean” account of human evil, which portrays the human being and his or her task (...) in developmental terms. This developmental model is put forward by Kant in both the Lectures in the Philosophy of Religion and in his Conjectural Beginnings of Human History. In this essay I discuss both the Augustinian and Iranaean accounts of human evil, and argue for the advantages of the developmental (Iranaean) account in making philosophical sense of Kant’s texts. I show that Kant indeed held such a view in both the Lectures and in the Conjectural Beginnings, and that he never abandoned the developmental model in Religion. Reading Kant’s Religion through an “Iranaean” lens reframes the locus of the debate, illumines multiple elements of the text that previously remained obscure, and demonstrates why Kant had good reason to claim that we all begin in a condition of radical evil but must nevertheless assume responsibility for this. (shrink)

In “On Oppy’s Objections to the Modal Perfection Argument,” Philo 8, 2, 2005, 123–30, Robert Maydole argues that his modal perfection argument—set out in his “The Modal Perfection Argument for a Supreme Being,” Philo 6, 2, 2003, 299–313—“remains arguably sound” in the face of the criticisms that I made of this argument in my “Maydole’s 2QS5 Argument,” Philo 7, 2, 2004, 203–11. I reply that Maydole is wrong: his argument is fatally flawed, and his attempts to avoid the criticisms that (...) I have made of his argument are to no avail. (shrink)

In a previous issue of Philosophia Christi, Kirk MacGregor responded to an essay of mine in which I argued for a neo-Molinist account of open theism. The argument demonstrated how, given standard counterfactual semantics, one could derive an “open future square of opposition,” that is, a depiction of the logical relations that hold between future-tense statements from an open theistic standpoint. Conceding the validity of the argument, MacGregor nevertheless sought to deny its soundness by criticizing both its conclusion and (...) the Stalnaker-Lewis semantics on which the argument was based. In this paper, I argue that MacGregor’s reasons for rejecting the open future square, as well as his Molinist alternative to the Stalnaker-Lewis semantics, are uncompelling. (shrink)

Summary This paper examines contemporary virtue ethics and the claim that Christian ethics is a virtue ethic. Three central theses are identified as being central to virtue ethics: a priority thesis, a perfectionist thesis and a communitarian thesis. It is argued that defences of the priority thesis—it best addresses the moral crisis in our society, it does justice to historical consciousness and it remedies the incompleteness in deontic ethics—are unconvincing. It is argued that virtue and moral perfection are best understood (...) in terms of psychologically appropriate dispositions to act in accordance with moral principles. It is further argued that the communitarian thesis raises relativist difficulties and fails to do justice to the universal elements of morality. Each of these arguments is developed philosophically and the implications for Christian ethics are explored. In light of the theory of virtue sketched in the paper it is concluded that the independence thesis, upon which virtue ethics rests, is untenable and that an examination of the structure of the universal moral principles underlying the Christian faith remains the proper subject matter for Christian ethics. (shrink)

The claim that perfect hallucination is introspectively indistinguishable from perception has been a centrepiece of philosophical theorizing about sense experience. The most common interpretation of the indistinguishability claim is modal: that it is impossible to distinguish perfect hallucination from perception through introspection alone. I run through various models of introspection and show that none of them can accommodate the modal interpretation. Rejecting the modal interpretation opens up two alternative interpretations of the indistinguishability claim. According to the generic interpretation, (...) hallucination is indistinguishable from perception despite the existence of possible exceptions, while according to the actuality interpretation, the indistinguishability of hallucination from perception consists in the actual failure to distinguish hallucination from perception. These alternative understandings of the indistinguishability claim have a number of significant implications for the problem of perception, including the rejection of perfect hallucination and illusion in favour of our ordinary, non-philosophical concepts of these states. (shrink)