(First paragraphs.) — The notion of “mental time” refers to the experience and awareness of time, including that of past, present, and future, and that of the passing of time. This experience and awareness of time raises a number of puzzling questions. How do we experience time? What exactly do we experience when we experience time? Do we actually experience time? Or do we infer time from something in, or some aspect of (...) our experience? And so forth. These and many related questions in the “philosophy of mental time”, the topic of this special issue of the Annals of the Japan Association for Philosophy of Science, are not purely philosophical questions. Or at least, they are not likely to be satisfactorily answered by philosophers alone. Rather, they also need the input of neuroscientists, psychologists, physicists, linguists, and others. And conversely, answers to these questions may have implications outside the scope of philosophy. The papers in this special issue illustrate this inherent multi- or interdisciplinarity of the philosophy and science of mental time. In this theme introduction, we want to give a few more examples to illustrate this interdisciplinarity, but also to point out that much of the field is still wide open—that is, these illustrations raise more questions than answers. (shrink)

While many aspects of cognition have been shown to be shared between humans and non-human animals, there remains controversy regarding whether the capacity to mentally time travel is a uniquely human one. In this paper, we argue that there are four ways of representing when some event happened: four kinds of temporal representation. Distinguishing these four kinds of temporal representation has five benefits. First, it puts us in a position to determine the particular benefits these distinct temporal representations (...) afford an organism. Second, it provides the conceptual resources to foster a discussion about which of these representations is necessary for an organism to count as having the capacity to mentally time travel. Third, it enables us to distinguish stricter from more liberal views of mental time travel that differ regarding which kind(s) of temporal representation is taken to be necessary for mental time travel. Fourth, it allows us to determine the benefits of taking a stricter or more liberal view of mental time travel. Finally, it ensures that disagreement about whether some species can mentally time travel is not merely the product of unrecognised disagreement about which temporal representation is necessary for mental time travel. We argue for a more liberal view, on the grounds that it allows us to view mental time travel as an evolutionarily continuous phenomenon, and to recognise that differences in the ways that organisms mentally time travel might reflect different temporal representations, or combinations thereof, that they employ. Our ultimate aim, however, is to create the conceptual framework for further discussion regarding what sorts of temporal representations are required for mental time travel. (shrink)

In these discussions between Mircea Eliade and Thomas Altizer we can recognise two important things: there are some points of contact between these two thinkers and some differences. The problem lies in determining whether or not these points of contact are simply two different ways of understanding the same concepts. On the one hand,“Death of God” theology was in vogue in the United States in the 1960s, but today has few adherents. However, a new evaluation of this theological movement is (...) necessary because we need to understand its possible impact on the renewal of Christianity. On the other hand, Eliade was considered an important scholar in the field of history of religions. In our time, many critics contest his influence in this field and criticize him for the fact that he relativizes Christianity. This new interpretation of both scholars was an opportunity to link the research in the theology with that in the history of religions, an important motive for our time. In ecumenical discussions, the link between research in both these fields is so important. The concept of coincidentia oppositorum, the understanding of the sacrality of our time, in different religions, and the new language for discussing with people of different faiths are the main preoccupations of the ecumenical movement. (shrink)

An Editorial for issue 128.1 of the Expository Times.

Worlds, Lewis says this: Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time. Perdurance corresponds to the way a road persists through space; part (...) of it is here, and part of it is there, and no part is wholly present at two different places. Endurance corresponds to the way a universal, if there are such things, would be wholly present wherever and whenever it is instantiated. Endurance involves overlap: the content of two different times has the enduring thing as a common part. Perdurance does not.1 Lewis's remarks suggest the following formulations of the two views in the 3D/4D controversy.2.. (shrink)

Time is one of the most enigmatic notions philosophers have ever dealt with. Once subjected to close examination, almost any feature usually ascribed to time, leads to a plethora of fundamental and hard to resolve questions. Just as philosophers of the eighteenth-century attempted to take account of revolutionary developments in the physical sciences in understanding space, life, and a host of other fundamental aspects of nature (see Jones, Gaukroger, and Smith in this volume) they also engaged in fundamental (...) and fruitful controversies about the nature of time spurred by Newton and others (see Schliesser and Schabas in this volume). In this article, I will attempt to trace the general outlines of these controversies. Special attention will be given to a question that was central for many eighteenth century philosophers and is somewhat less prominent in contemporary, twenty-first century, debates on the nature of time, i.e., whether time can be reduced to, grounded by, or explained through other more basic elements. The concept of time is commonly discussed – both in eighteenth and twenty first century philosophy – in analogy to space. Here I will attempt to focus on time and address the analogies to space only when relevant. This attitude is motivated both by the need to provide as detailed an account as possible of time in the allocated textual space, and by the various dissimilarities between space and time. While space and time can be fruitfully compared and contrasted, the use of metaphors taken from one domain to clarify features belonging to the other domain has the real potential of leading us astray by unconsciously and seamlessly taking metaphorical language in a literal sense. In the first part of this essay, I will discuss the famous debate between Newton, Leibniz and Clarke on the nature of space and time. The second part will address Hume’s understanding of time and the relation between time and causation. In the third and final part, I will discuss Kant’s views on the relation between time and causality, place them in the context of his predecessors, and then examine Salomon Maimon’s attempt to revive the Leibnizian program of reducing time to concepts, within the framework of Kantian philosophy, broadly conceived. (shrink)

The Controversy over the Existence of the World (henceforth Controversy) is the magnum opus of Polish philosopher Roman Ingarden. Despite the renewed interest for Ingarden’s pioneering ontological work whithin analytic philosophy, little attention has been dedicated to Controversy's main goal, clearly indicated by the very title of the book: finding a solution to the centuries-old philosophical controversy about the ontological status of the external world. -/- There are at least three reasons for this relative indifference. First, (...) even at the time when the book was published, the Controversy was no longer seen as a serious polemical topic, whether it was disqualified as an archaic metaphysical pseudo-problem, or taken to be the last remnant of an antiscientific approach to philosophy culminating in idealism and relativism. Second, Ingarden’s reasoning on the matter is highly complex, at times misleading, and even occasionally faulty. Finally, his analysis is not only incomplete – Controversy being unachieved – but also arguably aporetic. -/- One may wonder, then, why it is still worth excavating this mammoth treatise to study an issue apparently no longer relevant to contemporary philosophy. Aside from historical and exegetical purposes, which are of course very interesting in their own right, Ingarden’s treatment of the Controversy remains one of the most detailed and ambitious ontological undertakings of the twentieth century. Not only does it lay out an incredibly detailed map of possible solutions to the Controversy, but it also tries to show why the latter is a genuine and fundamental problem that owes its hasty disqualification to various oversimplifications over the course of the history of philosophy. -/- In this chapter, I first give an overview of Ingarden’s method, which relies mainly on a combinatorial analysis. Then, I summarize his examination of possible solutions to the Controversy, and determine which ones can be ruled out on ontological grounds. Finally, I explain why this ambitious project ultimately leads to a theoretical impasse, leaving Ingarden unable to come up with a definitive solution to the Controversy – regardless of the fact that the book is unachieved. I argue that his analysis of the problem yields a more modest but nonetheless valuable result. (shrink)

This paper is concerned with the senses in which paintings do and do not depict various temporal phenomena, such as motion, stasis and duration. I begin by explaining the popular – though not uncontroversial – assumption that depiction, as a pictorial form of representation, is a matter of an experiential resemblance between the pictorial representation and that which it is a depiction of. Given this assumption, I illustrate a tension between two plausible claims: that paintings do not depict motion in (...) the sense that video recordings do, and that paintings do not merely depict objects but may depict those objects as engaged in various activities, such as moving. To resolve the tension, I demonstrate that we need to recognise an ambiguity in talk of the appearance of motion, and distinguish between the depiction of motion and the depiction of an object as an object that is moving. Armed with this distinction, I argue that there is an important sense in which paintings depict neither motion, duration, nor – perhaps more controversially – stasis. (shrink)

Fermat’s Least Time Principle has a long history. World’s foremost academies of the day championed by their most prestigious philosophers competed for the glory and prestige that went with the solution of the refraction problem of light. The controversy, known as Descartes - Fermat controversy was due to the contradictory views held by Descartes and Fermat regarding the relative speeds of light in different media. Descartes with his mechanical philosophy insisted that every natural phenomenon must be explained (...) by mechanical principles. Fermat on the other hand insisted an end purpose for every motion. For example, least time of travel and not the least distance of travel is the end purpose for motion of light. This implied a thinking nature, which was rejected by Descartes. Surprisingly, with contradictory assumptions regarding the relative speeds of light in different media, both Descartes and Fermat came to the same result that the ratio of sines of angles of incidence and refraction is a constant. Fermat’s result came to be known as the ‘Fermat’s least time principle’. We show in this article that Fermat’s least time principle violates a fundamental theorem in geometry – the Ptolemy’s theorem. That leads to the invalidity of Fermat’s principle. -/- . (shrink)

There are many things that can be done to educate young people about controversial topics - including historical monuments - in schools. At the same time, however, we argue that there is little warrant for optimism concerning the educational potential of classroom instruction given the interpretative frame of the state-approved history curriculum; the onerous institutional constraints under which school teachers must labour; the unusual constellation of talents history teachers must possess; the frequent absence of marginalized voices in these conversations; (...) and finally, the not unlikely indifference - if not outright hostility - expressed by far too many members of the dominant group. For these reasons, we think it best to expand the scope of educational possibilities one is willing to consider. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental / intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction (...) of time in the universe. In this paper, we propose a minimal primitivism about laws of nature (MinP) according to which there is no such requirement. On our view, laws govern by constraining the physical possibilities. Our view captures the essence of the governing view without taking on extraneous commitments about the direction of time or dynamic production. Moreover, as a version of primitivism, our view requires no reduction / analysis of laws in terms of universals, powers, or dispositions. Our view accommodates several potential candidates for fundamental laws, including the principle of least action, the Past Hypothesis, the Einstein equation of general relativity, and even controversial examples found in the Wheeler-Feynman theory of electrodynamics and retrocausal theories of quantum mechanics. By understanding governing as constraining, non-Humeans who accept MinP have the same freedom to contemplate a wide variety of candidate fundamental laws as Humeans do. (shrink)

Some philosophers defend the possibility of synchronic multilocation, and have even used it to defend other substantive metaphysical theses. But just how strong is the case for the possibility of synchronic multilocation? The answer to this question depends in part on whether synchronic multilocation is wedded to other controversial metaphysical notions. In this paper, I consider whether the possibility of synchronic multilocation depends on the possibility of time travel, and I conclude that the answer hinges on the nature of (...) time and persistence. (shrink)

In early modern times it was not uncommon for thinkers to tease out from the nature of God various doctrines of substantial physical and metaphysical import. This approach was particularly fruitful in the so-called beast-machine controversy, which erupted following Descartes’ claim that animals are automata, that is, pure machines, without a spiritual, incorporeal soul. Over the course of this controversy, thinkers on both sides attempted to draw out important truths about the status of animals simply from the notion (...) or attributes of God. Automatists – led by Nicolas Malebranche and Antoine Dilly – developed six such arguments, appealing to divine justice, providence, economy, glory (twice) and wisdom, while opponents to animal automatism developed two arguments, appealing to divine wisdom and goodness. In this article I shall examine the substance of all eight of these arguments, along with their origins, patronage, and variations, and the objections they elicited from opponents, with the aim of determining their suitability for use in contemporary debates about animal sentience and consciousness, and hence their relevance for contemporary philosophers. (shrink)

This research was carried out in order to verify by simulation Mendel’s laws and seek for the clarification, from the author’s point of view, the Mendel-Fisher controversy. It was demonstrated from: the experimental procedure and the first two steps of the Hardy-Weinberg law, that the null hypothesis in such experiments is absolutely and undeniably true. Consequently, repeating hybridizing experiments as those showed by Mendel, it makes sense to expect a highly coincidence between the observed and the expected cell frequencies. (...) By simulation, 30 random samples were generated with size equal to the number of observations reported by Mendel for his single trait trial, in this case, seed shape; assuming complete dominance, with genes A and a; likewise, it was simulated the results for the experiment with two traits, segregating in separate chromosomes, in this case seed shape, as before, and albumen color, with genes B and b, both loci with complete dominance. In the case of a single trait, the data only showed evidence for rejecting the null hypothesis (Ho ) in 1/30 samples, with (P<0.05). In the case of the 30 samples of the two traits experiment, (Ho ) was rejected only on 3/30 times, when it was set a = 0.05. In both simulations there was a high correspondence between the observed and expected cell frequencies, which is simply due to the fact that (Ho ) is true, and under these conditions, that is what would to expect. It was concluded, that Mendel had no reason to manipulate his data in order to make them to coincide with his beliefs. Therefore, in experiment with a single trait, and in experiments with two traits assuming complete dominance, segregation ratios are 3:1; and 9:3:3:1, respectively. Consequently, Mendel’s laws, under the conditions as were described are absolutely valid and universal. (shrink)

Time in electromagnetism shares many features with time in other physical theories. But there is one aspect of electromagnetism's relationship with time that has always been controversial, yet has not always attracted the limelight it deserves: the electromagnetic arrow of time. Beginning with a re-analysis of a famous argument between Ritz and Einstein over the origins of the radiation arrow, this chapter frames the debate between modern Einsteinians and neo-Ritzians. It tries to find a clean statement (...) of what the arrow is and then explains how it relates to the cosmological and thermodynamic arrows, representing the most developed and sophisticated attack yet, in either the physics or philosophy literature, on the electromagnetic arrow of time. (shrink)

When Newton articulated the concept of absolute time in his treatise, Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), along with its correlate, absolute space, he did not present it as anything controversial. Whereas his references to attraction are accompanied by the self- protective caveats that typically signal an expectation of censure, the Scholium following Principia’s definitions is free of such remarks, instead elaborating his ideas as clarifications of concepts that, in some manner, we already possess. This is (...) not surprising. The germ of the concept emerged naturally from astronomers’ findings, and variants of it had already been formulated by other seventeenth century thinkers. Thus the novelty of Newton’s absolute time lay mainly in the use to which he put it. (shrink)

Excerpt: 1. Introduction This chapter provides insight into the diverse ethical debates on genetics and epigenetics. Much controversy surrounds debates about intervening into the germline genome of human embryos, with catchwords such as genome editing, designer baby, and CRISPR/Cas. The idea that it is possible to design a child according to one’s personal preferences is, however, a quite distorted view of what is actually possible with new gene technologies and gene therapies. These are much more limited than the editing (...) and design metaphors suggest. Such metaphors are therefore highly problematic phrases in the context of new gene technologies, for two reasons. On one hand, to design a child of choice by modifying the genome would require modifying any gene of choice, which is more than can be done with current gene technologies, such as CRISPR/Cas. On the other hand, a modification of genes would need to be enough to create any characteristic of choice in the future child. The latter presupposes the assumption of genetic determinism. Moreover, the CRISPR/Cas technology can not only be used in a potentially therapeutic manner at the germline level. In addition, there is the (more likely) scenario of a future clinical therapeutic use of these new gene technologies for modifying the DNA sequence of other cells of the body (somatic genome editing). There is also the option of modifying the epigenome, that is, the spatial configuration of DNA (epigenome editing) (see table 1). Like genetics and genome editing, epigenetics has been at the center of recent popular scientific and ethical discourse as well as scientific debates. The concept of epigenetics has given rise to very different notions of inheritability and responsibility for health, which, however, are oftentimes based on scientifically controversial basic assumptions. That there continues to be covert genetic determinism in the form of epigenetic determinism (see table 2) in debates about epigenetics has been pointed out in ethical analyses of epigenetics. Neither genetic determinism nor epigenetic determinism has been confirmed scientifically. It is therefore important to recognize the concepts that are discussed (and sometimes harshly criticized) in debates about genome editing and epigenetics—for example, concepts about the causal role of DNA for our own life course. This importance is based on the fact that if we understand such controversial concepts, we will be able to remain critical when evaluating scientific knowledge and ethical arguments about genome editing and epigenetics. This chapter, therefore, explains some of these concepts. For an ethical analysis of epigenetics as well as of genome editing, it is necessary to understand and critically reflect upon the underlying concepts of genetic determinism and other, related -isms. The following section offers a detailed introduction to these -isms (section 2; see also table 2). Section 3 provides an ethical analysis of genome editing and epigenetics based on the explanations in section 2. Section 3 focuses on inheritability and responsibility, justice, safety, the problem of consent, and the effects of genome editing and epigenetics on embryos and future generations. This section does not discuss in detail further points that can be found in ethical debates about epigenetics as well as in ethical debates about genome editing. These points include (among others): • fear that the findings of epigenetics and that the methods of genome editing are misused—this also with respect to eugenics and enhancement; • naturalness—an issue we mention in passing a few times in the following analysis; • a possible connection between the genome/epigenome and the concept of human dignity, and the derived danger of instrumentalization and infringement of autonomy when intervening in the genome or epigenome. Since current discourse about ethical issues associated with genome editing focuses mainly on germline interventions, which are, for instance, interventions into a human embryo’s genome, we mainly focus on germline interventions when comparing the debates on genome editing and on epigenetics in section 3. (shrink)

This paper argues that ordinary object languages for fundamental physics are incomplete, essentially because they are extensional, and consequently lack any adequate formal representation of contingency. It is shown that it is impossible to formulate adequate deduction systems for general transformations in such languages. This is argued in detail for the time reversal transformation. Two important controversies about the application of time reversal in quantum mechanics are summarized at the start, to provide the context of this problem, and (...) show its serious implications, but the aim here is not to solve these problems. The flaw is not special to quantum mechanics: it is a general feature traced to extensionality, and demonstrated through a simple example in classical physics. It is proposed that this defect can be overcome by extending to an intensional semantics, but this involves extending the usual formalism of physics. A detailed proposal for such an extension is given in Part 2. (shrink)

Both Franz Brentano and Edmund Husserl addressed sound while trying to explain the inner consciousness of time and gave to it the status of a supporting example. Although their inquiries were not aimed at clarifying in detail the nature of the auditory experience or sounds themselves, they made some interesting observations that can contribute to the current philosophical discussion on sounds. On the other hand, in analytic philosophy, while inquiring the nature of sounds, their location, auditory experience or the (...) audible qualities and so on, the representatives of that trend of thought have remained silent about the depiction of sound and the auditory phenomena in the phenomenological tradition. The paper’s intention is to relate both endeavours, yet the perspective carried out is that of analytic philosophy and, thus, I pay special attention to conceptual analysis as a methodological framework. In this sense, I first explain what sound ontology is in the context of analytic philosophy and the views that it encompasses— namely, the Property View (PV), the Wave View (WV) and the Event View (EV)—. Secondly, I address the problems it entails, emphasising that of sound individuation. In a third section, I propose the possibly controversial conjunction of a “Brentano-Husserl Analysis of the Consciousness of Time” (for short “Brentano-Husserl analysis”) and outline the commonalities of both authors, without ignoring its discrepancies. My main focus is Husserl’s 1905 Vorlesungen zur Phänomenologie des Inneren Zeitbewusstseins. While addressing the Brentano-Husserl analysis, I elaborate on the problem of temporal and spatial extension (Raumlichkeit and Zeitlichkeit, respectively) of both consciousness and sound. Such comparison is a key one, since after these two developments, one can notice some theoretical movements concerning the shift of attention from sounds to the unity of consciousness, and how they mirror each other. After examining the controversial claims concerning the temporal and spatial extension of both consciousness and sound, I argue in the concluding paragraphs that while considering the accounts of sound ontology, the Brentano-Husserl analysis would probably endorse a Property View and that this could have interesting consequences for the issue of Sound Individuation. (shrink)

Dirac’s relativistic theory of electron generally results in two possible solutions, one with positive energy and other with negative energy. Although positive energy solutions accurately represented particles such as electrons, interpretation of negative energy solution became very much controversial in the last century. By assuming the vacuum to be completely filled with a sea of negative energy electrons, Dirac tried to avoid natural transition of electron from positive to negative energy state using Pauli’s exclusion principle. However, many scientists like Bohr (...) objected to the idea of sea of electrons as it indicates infinite density of charge and electric field and consequently infinite energy. In addition, till date, there is no experimental evidence of a particle whose total energy (kinetic plus rest) is negative. In an alternative approach, Feynman, in quantum field theory, proposed that particles with negative energy are actually positive energy particles running backwards in time. This was mathematically consistent since quantum mechanical energy operator contains time in denominator and the negative sign of energy can be absorbed in it. However, concept of negative time is logically inconsistent since in this case, effect happens before the cause. To avoid above contradictions, in this paper, we try to reformulate the Dirac’s theory of electron so that neither energy needs to be negative nor the time is required to be negative. Still, in this new formulation, two different possible solutions exist for particles and antiparticles (electrons and positrons). (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely (...) that the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. (...) We demonstrate in this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

The history of the science of the stars (astronomy and astrology) in fourteenth-century Byzantium is significantly intertwined with the implications of theological and philosophical controversies. A less-explored astronomical text authored by the fourteenth-century Byzantine scholar Theorodos Meliteniotes (ca. 1320–1393 CE) provides new historical factors toward a historiography of the differences between scientific and theological discourses, their development in the transition to early modern times, and the different historical developments of science in the worlds of the Eastern and Western Churches.

This is not your typical book about the A-theory/B-theory controversy in metaphysics. Peter Ludlow attempts something that few philosophers have tried in the last thirty years: he actually argues from linguistic premises for metaphysical conclusions. The relevant linguistic premises have to do with the nature of language, a general theory of semantics, the proper analysis of tense, and various technical theses involving the treatment of temporal indexicals and temporal anaphora. The metaphysical conclusions that Ludlow argues for from these linguistic (...) premises are some of the main claims normally associated with the A-theory in the philosophy of time, namely, that tense is a genuine feature of the world – and that the instantiation of these properties does not somehow reduce to the instantiation of two-place, temporal relations like earlier than, simultaneous with, later than, etc.), that temporal becoming is intrinsic to all events, and that only the present is real. The overall plan of the book is as follows. First Ludlow spends four chapters defending a cluster of related claims about language and semantics in general and, in particular, the semantics for temporal indexicals and temporal anaphora. (Ludlow says that none of this material is original – he attributes most of it to Davidson, Chomsky, Evans, and Higginbotham – but it seems to me that a fair portion of what goes into this part of the book (including, especially. (shrink)

Two hundred years after Darwin’s birth, the evolution of living systems is an accepted fact but there is scope for controversy on the mechanisms involved in such a process. Mainstream neo-Darwinism champions the role of natural selection (NS) as the fundamental cause of the evolutionary process as well as of random, contingent events at the genetic level as the main source of variation upon which NS performs its causal role. Thus, according to neo-Darwinism the course of biological evolution is (...) quite unpredictable and the past can only be partially reconstructed by means of a historical narrative.This second-class status for biology within the natural sciences as a merely descriptive, historical science results from the chronic neglect of biological form in the neo-Darwinian discourse. Hereunder I discuss the need for reintroducing form as the central object of biology, aiming at the identification of the general and fundamental principles of biological form. Such a formal biology may go beyond simple historical description achieving a complete, rational explanation of how previous and current morphologies corresponding to identifiable species were established, and so providing a rational foundation for predicting the possible outcomes of future biological evolution on earth and perhaps elsewhere in the universe. (shrink)

Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis (...) would not have liked. The explanation is an obvious one but controversial, so it is defended against all the objections that can be mustered. (shrink)

The chemical characterization of the substance responsible for the phenomenon of “transformation” of pneumococci was presented in the now famous 1944 paper by Avery, MacLeod, and McCarty. Reception of this work was mixed. Although interpreting their results as evidence that deoxyribonucleic acid (DNA) is the molecule responsible for genetic changes was, at the time, controversial, this paper has been retrospectively celebrated as providing such evidence. The mixed and changing assessment of the evidence presented in the paper was due to (...) the work’s interpretive flexibility – the evidence was interpreted in various ways, and such interpretations were justified given the neophytic state of molecular biology and methodological limitations of Avery’s transformation studies. I argue that the changing context in which the evidence presented by Avery’s group was interpreted partly explains the vicissitudes of the assessments of the evidence. Two less compelling explanations of the reception are a myth-making account and an appeal to the wartime historical context of its publication. (shrink)

Waiting time is widely used in health and social policy to make resource allocation decisions, yet no general account of the moral significance of waiting time exists. We provide such an account. We argue that waiting time is not intrinsically morally significant, and that the first person in a queue for a resource does not ipso facto have a right to receive that resource first. However, waiting time can and sometimes should play a role in justifying (...) allocation decisions. First, there is a duty of fairness prohibiting line-cutting where a sufficiently just queue exists. Second, waiting time has several morally attractive features that can justify its incorporation into allocation schemes. Where candidates are in relevantly similar circumstances, allocating by waiting time is relatively efficient, maximizes distribution equality relative to other Pareto efficient distributions, and treats candidates fairly. The claim that allocation using waiting time is fair is controversial. Some have claimed that formal lotteries are a fairer way to select among equal beneficiaries. We argue that lotteries are no fairer than allocation based on waiting time when it is equiprobable how a prospective queue will be ordered. In practice, lotteries share many of the disadvantages of queues; which is fairer will depend on contingent features of the allocation scenario. The upshot is that first-come, first-served is in fact a just way to allocate resources in many of the cases where it seems pre-theoretically compelling, and waiting time has unique normative properties which frequently justify its incorporation into resource allocation schemes. (shrink)

ABSTRACT: Titu Maiorescu had a special relationship with psychology under the influence of both Kant and Herbart. The following study presents Maiorescu’s answers to the main issues raised by the materialism controversy that broke out in Germany in the mid-1850s century, at a time when he was writing and defending his doctoral thesis in Giessen. Most of these issues were related to the mind–body liaison and the capability of science to explain the mind. KEYWORDS: materialism controversy; mind–body (...) relationship; psychology and metaphysics; materialism vs, spiritualism; transcendental idealism. (shrink)

JOURNAL OF THE HISTORY OF PHILOSOPHY PRIZE for the best published book in the history of philosophy [Awarded in 2010] _______________ -/- Although it is widely recognized that David Hume's A Treatise of Human Nature (1739-40) belongs among the greatest works of philosophy, there is little agreement about the correct way to interpret his fundamental intentions. It is an established orthodoxy among almost all commentators that skepticism and naturalism are the two dominant themes in this work. The difficulty has been, (...) however, that Hume's skeptical arguments and commitments appear to undermine and discredit his naturalistic ambition to contribute to "the science of man". This schism appears to leave his entire project broken-backed. The solution to this riddle depends on challenging another, closely related, point of orthodoxy: namely, that before Hume published the Treatise he removed almost all material concerned with problems of religion. Russell argues, contrary to this view, that irreligious aims and objectives are fundamental to the Treatise and account for its underlying unity and coherence. It is Hume's basic anti-Christian aims and objectives that serve to shape and direct both his skeptical and naturalistic commitments. When Hume's arguments are viewed from this perspective we can solve, not only puzzles arising from his discussion of various specific issues, we can also explain the intimate and intricate connections that hold his entire project together. This "irreligious" interpretation provides a comprehensive fresh account of the nature of Hume's fundamental aims and ambitions in the Treatise. It also presents a radically different picture of the way in which Hume's project was rooted in the debates and controversies of his own time, placing the Treatise in an irreligious or anti-Chrisitan philosophical tradition that includes Hobbes, Spinoza and freethinking followers. Considered in these terms, Hume's Treatise constitutes the crowning achievement of the Radical Enlightenment. (shrink)

This paper defends Priorianism, a theory in the philosophy of time which combines three theses: first, that there is a metaphysical distinction between the present time and non-present times; second, that there are temporary propositions, that is, propositions that change in truth-value simpliciter over time; and third, that there is change over time only if there are temporary propositions. Priorianism is accepted by many Presentists, Growing Block Theorists, and Moving Spotlight Theorists. However, it is difficult to (...) defend the view without appealing to premises that those who reject the view find controversial. My aim in this paper is to defend Priorianism in a way that largely avoids appealing to such premises. I do three things: first (Section 1), I describe the component theses of Priorianism and the relations between them. Next (Section 2), I show how Priorians can respond to the argument that the B-theory implies that there are temporary propositions, and therefore satisfies the Priorian condition for there being change over time. Finally (Section 3), I defend the Priorian thesis that there is change over time only if there are temporary propositions against an alternative principle of change defended by Ross Cameron (The Moving Spotlight, 2015). (shrink)

In both scientific and popular circles it is often said that we are in the midst of a sixth mass extinction. Although the urgency of our present environmental crises is not in doubt, such claims of a present mass extinction are highly controversial scientifically. Our aims are, first, to get to the bottom of this scientific debate by shedding philosophical light on the many conceptual and methodological challenges involved in answering this scientific question, and, second, to offer new philosophical perspectives (...) on what the value of asking this question has been — and whether that value persists today. We show that the conceptual challenges in defining ‘mass extinction’, uncertainties in past and present diversity assessments, and data incommensurabilities undermine a straightforward answer to the question of whether we are in, or entering, a sixth mass extinction today. More broadly we argue that an excessive focus on the mass extinction framing can be misleading for present conservation efforts and may lead us to miss out on the many other valuable insights that Earth’s deep time can offer in guiding our future. (shrink)

This thesis consists of several independent papers in population ethics. I begin in Chapter 1 by critiquing some well-known 'impossibility theorems', which purport to show there can be no intuitively satisfactory population axiology. I identify axiological vagueness as a promising way to escape or at least mitigate the effects of these theorems. In particular, in Chapter 2, I argue that certain of the impossibility theorems have little more dialectical force than sorites arguments do. From these negative arguments I move to (...) positive ones. In Chapter 3, I justify the use of a 'veil of ignorance', starting from three more basic normative principles. This leads to positive arguments for various kinds of utilitarianism - the best such arguments I know. But in general the implications of the veil depend on how one answers what I call 'the risky existential question': what is the value to an individual of a chance of non-existence? I chart out the main options, and raise some puzzles for non-comparativism, the view that life is incomparable to non-existence. Finally, in Chapter 4, I consider the consequences for population ethics of the idea that what is normatively relevant is not personal identity, but a degreed relation of psychological connectedness. In particular, I pursue a strategy based in population ethics for understanding the controversial 'time-relative interests' account of the badness of death. (shrink)

The aim of this doctoral dissertation is to closely explore the nature of Einstein’s block universe and to tease out its implications for the nature of time and human freedom. Four questions, in particular, are central to this dissertation, and set out the four dimensions of this philosophical investigation: (1) Does the block universe view of time follow inevitably from the theory of special relativity? (2) Is there room for the passage of time in the block universe? (...) (3) Can we distinguish past from future in the block universe? (4) Is there room for human freedom in the block universe? Although the answer of most philosophers would be yes, triple no, my own answer, controversially, is no, triple yes. -/- I thereby challenge the status quo with respect to each of these metaphysical questions, and argue that none of these questions can be answered from looking at physics alone. Physics may constrain our metaphysics, but it certainly does not settle it. What is needed in order to answer these questions, are additional metaphysical assumptions that fall outside the scope of modern physics. My primary goal in this dissertation, therefore, is not to settle the debates on the nature of time and human freedom, but to clarify them by expliciting the metaphysical assumptions that are otherwise left implicit. (shrink)

Causal finitism, the view that the causal history of any event must be finite, has garnered much philosophical interest recently—especially because of its applicability to the Kalām cosmological argument. The most prominent argument for causal finitism is the Grim Reaper argument, which attempts to show that, if infinite causal histories are possible, then other paradoxical states of affairs must also be possible. However, this style of argument has been criticized on the grounds of (i) relying on controversial modal principles, and (...) (ii) providing a false diagnosis of the paradoxes involved. In this paper, I develop a new kind of Grim Reaper argument immune to these criticisms. I show that, by using insights from the literature on time travel, causal finitists should instead argue that infinite causal histories are problematically inexplicable, as they entail the possibility of unexplained foiling mechanisms. The fruits of this paper are that (i) a novel supporting argument for the Kalām is developed, and (ii) along the way of building this argument, it is shown that the literatures on time travel and causal finitism are deeply and intimately connected. (shrink)

Thomas Aquinas embraces a controversial claim about the way in which parts of a substance depend on the substance’s substantial form. On his metaphysics, a ‘substantial form’ is not merely a relation among already existing things, in virtue of which (for example) the arrangement or configuration of those things would count as a substance. The substantial form is rather responsible for the identity or nature of the parts of the substance such a form constitutes. Aquinas’ controversial claim can be roughly (...) put as the view that things are members of their kind in virtue of their substantial form. To put it simply, Aquinas’ claim results in the implication that, every time the xs come to compose a y, those xs have to undergo a change in kind membership. -/- This has been called the “homonymy principle,” and it follows from Aquinas’ view of substantial forms, and specifically from the position that substantial forms inform prime matter, rather than substance-parts. The aim of this paper will be to defend that the Thomistic claim that substantial forms account for the determinate actuality of every part of a substance is plausible and coherent. After defending the Thomistic account, I propose that approaching problems of material composition as a Thomist has a significant, oft-overlooked advantage of involving a thorough-going naturalistic methodology that resolves such problems by appeal to empirical considerations. (shrink)

The philosophical investigation of perceptual illusions can generate fruitful insights in the study of subjective time consciousness. However, the way illusions are interpreted is often controversial. Recently, proponents of the so-called dynamic snapshot theory have appealed to the Waterfall Illusion, a kind of motion aftereffect, to support a particular view of temporal consciousness according to which experience is structured as a series of instantaneous snapshots with dynamic qualities. This dynamism is meant to account for familiar features of the phenomenology (...) of time, such as succession, continuity, and change. Previous theories have typically appealed to a subjective present occupying an interval of time; that is, a “specious present.” I argue, through analysis of motion aftereffect illusions and the rare condition of akinetopsia, i.e. motion-blindness, that the Waterfall Illusion fails to support the dynamic snapshot theory as intended. Furthermore, I suggest that future theories of subjective time should see temporal phenomenology as the result of non-localised processes closely tied to the mechanism underlying consciousness generally. (shrink)

The article examines the so-called slippery slope argument (SSA) against the legalization of active voluntary euthanasia (AVE). According to the SSA, by legalizing AVE, the least morally controversial type of euthanasia, we will take the first step onto a slippery slope and inevitably end up in the moral abyss of widespread abuse and violations of the rights of the weakest and most vulnerable patients. In the first part of the paper, empirical evidence to the contrary is presented and analyzed: None (...) of the forecasted regrettable trends can be elicited from the body of existing statistical data. Accordingly, we have no good reason to believe either that we already are, or are sooner or later going to be, sliding into a moral abyss. A related question is then considered: Would it not be wiser and safer to stick to the status quo and preserve the existing legal ban on AVE even if the risk of its abuse is uncertain and may well turn out to be relatively low? It is argued that such an appeal to precautionary reasoning fails to justify an outright legal ban on AVE for at least two reasons: (i) it grossly underestimates the hidden moral costs of current legal arrangements (competent terminal patients suffer both disrespect for their autonomous will and deprivation of the good of a timely death) and (ii) the ban is both too inefficient and disproportionate to qualify as a reasonable measure of precaution. (shrink)

The article examines the so-called slippery slope argument (SSA) against the legalization of active voluntary euthanasia (AVE). According to the SSA, by legalizing AVE, the least morally controversial type of euthanasia, we will take the first step onto a slippery slope and inevitably end up in the moral abyss of widespread abuse and violations of the rights of the weakest and most vulnerable patients. In the first part of the paper, empirical evidence to the contrary is presented and analyzed: None (...) of the forecast regrettable trends can be elicited from the body of existing statistical data. Accordingly, we have no good reason to believe either that we already are, or are sooner or later going to be, sliding into a moral abyss. A related question is then considered: Would it not be wiser and safer to stick to the status quo and preserve the existing legal ban on AVE even if the risk of its abuse is uncertain and may well turn out to be relatively low? It is argued that such an appeal to precautionary reasoning fails to justify an outright legal ban on AVE for at least two reasons: (i) it grossly underestimates the hidden moral costs of current legal arrangements (competent terminal patients suffer both disrespect for their autonomous will and deprivation of the good of a timely death) and (ii) the ban is both too inefficient and disproportionate to qualify as a reasonable measure of precaution. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of (...) rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

Physicalism, the thesis that everything is physical, is one of the most controversial problems in philosophy. Its adherents argue that there is no more important doctrine in philosophy, whilst its opponents claim that its role is greatly exaggerated. In this superb introduction to the problem Daniel Stoljar focuses on three fundamental questions: the interpretation, truth and philosophical significance of physicalism. In answering these questions he covers the following key topics: -/- (i)A brief history of physicalism and its definitions, (ii)what a (...) physical property is and how physicalism meets challenges from empirical sciences, (iii)'Hempel’s dilemma’ and the relationship between physicalism and physics, (iv)physicalism and key debates in metaphysics and philosophy of mind, such as supervenience, identity and conceivability, and (v)physicalism and causality. -/- Additional features include chapter summaries, annotated further reading and a glossary of technical terms, making Physicalism ideal for those coming to the problem for the first time. (shrink)

Samuel Lebens and Tyron Goldschmidt provided original theodicies, which suggest that at one time God will change the past, either by erasing/substituting the sins of humans or erasing the whole entirety of evils. Both theodicies imply the idea that God can completely change the past without leaving any traces. In this paper, I argue that Lebens’ and Goldschmidt’s preferred model, which they call the scene-changing theory, is problematic. First, its complex metaphysical foundation could be replaced with presentism (roughly, the (...) view in the ontology of time that only present things exist) without losing any substantial heuristics. Second, their theory either implies a controversial theory of truthmaking under presentistic and hyper-presentistic ontology or implies controversial views on the counting of events under presentistic and hyper-presentistic ontology. Thirdly, I will argue that any theory of elimination/substitution of evils of the past implies that there are unnecessary evils, which is inconsistent with God’s goodness. (shrink)

In Latin Europe, the controversy over spontaneous generation of perfect animals – namely those whose breeding occurs through sexual reproduction – is received in different ways, varying from positions very close to Avicenna’s, as in the case of Pietro Pomponazzi, to interpretations that rather refer to Averroes’ perspective. To this ‘Averroist front’ undoubtedly belongs the figure of Urbano da Bologna, author of the Expositio commenti Averrois in VIII libros Physicorum – a work that can be defined a supercommentary to (...) Averroes’ Physica – composed in Bologna around 1334. The present study aims to provide the complete transcription of a quaestio that is present in the work – but which was disputed according to its author also in public – as an example of the elaboration of the theme of spontaneous generation in the early 14th century. The text deals with many aspects of the problem, especially elaborating on the correspondence between each specific form and its appropriate matter, in the light of the lively debates of the time, and reveals a mature understanding of Aristotle’s natural philosophy and its Averroist interpretation. (shrink)

Is well-being the kind of thing that can be summed across individuals? This paper takes a measurement-theoretic approach to answering this question. To make sense of adding well-being, we would need to identify some natural "concatenation" operation on the bearers of well-being that satisfies the axioms of extensive measurement and can therefore be represented by the arithmetic operation of addition. I explore various proposals along these lines, involving the concatenation of segments within lives over time, of entire lives led (...) alongside one another or in sequence, and of evaluatively basic propositions via conjunction. All of these proposals turn out to carry highly controversial commitments about the good. I do not claim that these commitments are unacceptable. But they suggest that we cannot simply take for granted, as many philosophers do, that there is any such thing as the sum of well-being. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

The thesis of this article is that there has never been any ground for the controversy between the doctrine of free will and determinism, that it is based upon a misapprehension, that the two assertions are entirely consistent, that one of them strictly implies the other, that they have been opposed only because of our natural want of the analytical imagination. In so saying I do not tamper with the meaning of either phrase. That would be unpardonable. I mean (...) free will in the natural and usual sense, in the fullest, the most absolute sense in which for the purposes of the personal and moral life the term is ever employed. I mean it as implying responsibility, merit and demerit, guilt and desert. I mean it as implying, after an act has been performed, that one " could have done otherwise " than one did. I mean it as conveying these things also, not in any subtly modified sense but in exactly the sense in which we conceive them in life and in law and in ethics. These two doctrines have been opposed because we have not realised that free will can be analysed without being destroyed, and that determinism is merely a feature of the analysis of it. And if we are tempted to take refuge in the thought of an "ultimate ", an "innermost" liberty that eludes the analysis, then we have implied a deterministic basis and constitution for this liberty as well. For such a basis and constitution lie in the idea of liberty. -/- The thesis is not, like that of Green or Bradley, that the contending opinions are reconciled if we adopt a certain metaphysic of the ego, as that it is timeless, and identifies itself with a desire by a " timeless act". This is to say that the two are irreconcilable, as they are popularly supposed to be, except by a theory that delivers us from the conflict by taking us out of time. Our view on the contrary is that from the natural and temporal point of view itself there never was any need of a reconciliation but only of a comprehension of the meaning of terms. (The metaphysical nature of the self and its identity through time is a problem for all who confront memory, anticipation, etc.; it has no peculiar difficulties arising from the present problem.) -/- I am not maintaining that determinism is true; only that it is true insofar as we have free will. That we are free in willing is, broadly speaking, a fact of experience. That broad fact is more assured than any philosophical analysis. It is therefore surer than the deterministic analysis of it, entirely adequate as that in the end appears to be. But it is not here affirmed that there are no small exceptions, no slight undetermined swervings, no ingredient of absolute chance. All that is here said is that such absence of determination, if and so far as it exists, is no gain to freedom, but sheer loss of it; no advantage to the moral life, but blank subtraction from it. -- When I speak below of "the indeterminist" I mean the libertarian indeterminist, that is, him who believes in free will and holds that it involves indetermination. (shrink)

Journal impact factor is a value calculated annually based on the number of times articles published in a journal are cited in two, or more, of the preceding years. At the time of its inception in 1955 , the inventor of the impact factor did not imagine that 1 day his tool would become a controversial and abusive measure, as he confessed 44 years later . The impact factor became a major detrimental factor of quality, creating huge pressures on (...) authors, editors, stakeholders and funders. More tragically, in some countries the number of publications in journals with “high impact factors” condition the allocation of government funding for entire institutions . Based on the assumption that IF reflects scientific quality, the impact factor produces a widespread impression of prestige and reputation, though no experimental data support this hypothesis .The impact factor was originally conceived as a bibliome .. (shrink)

Former NAACP chapter head Rachel Dolezal's attempted transition from the white to the black race occasioned heated controversy. Her story gained notoriety at the same time that Caitlyn Jenner graced the cover of Vanity Fair, signaling a growing acceptance of transgender identity. Yet criticisms of Dolezal for misrepresenting her birth race indicate a widespread social perception that it is neither possible nor acceptable to change one's race in the way it might be to change one's sex. Considerations that (...) support transgenderism seem to apply equally to transracialism. Although Dolezal herself may or may not represent a genuine case of a transracial person, her story and the public reaction to it serve helpful illustrative purposes. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)