Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

I analyze the meaning of mass in Newtonian mechanics. First, I explain the notion of primitive ontology, which was originally introduced in the philosophy of quantum mechanics. Then I examine the two common interpretations of mass: mass as a measure of the quantity of matter and mass as a dynamical property. I claim that the former is ill-defined, and the latter is only plausible with respect to a metaphysical interpretation of laws of nature. I explore the following options (...) for the status of laws: Humeanism, primitivism about laws, dispositionalism, and ontic structural realism. (shrink)

Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call ‘additivity’ the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze (...) and assess manuscript versions of Newton's initial argument within his initial deduction, dating from early 1685. Newton's strategy depends on distinguishing two quantities of matter, which I call ‘active’ and ‘passive’, by how they are measured. These measurement procedures frame conditions on the additivity of each quantity so measured. While Newton has direct evidence for the additivity of passive quantity of matter, he does not for that of the active quantity. Instead, he tries to infer the latter from the former via conceptual analyses of the third law of motion grounded largely on analogies to magnetic attractions. The conditions needed to establish passive additivity frustrate Newton's attempted inference to active additivity. (shrink)

It is common to assume that Descartes did not have a conception of an object's matter density independently of its size, but this is a rather incomplete assessment of the early modern natural philosopher's theory. Key to our understanding of Descartes's physics is a consideration of the ratios between the quantities of the different types of matter in which an object consists. As these ratios determine the degree of an object's porosity and elasticity, they also affect in Descartes's (...) theory the phenomena of gravity and weight. (shrink)

This paper deals with the interpretation of the Mechanics chapter of Kant’s Metaphysical Foundations of Natural Science. It is aimed at clarifying the procedure Kant invokes for the transcendental determination of the quantity of matter in mechanical respect. Kant’s intention is to ground mass measurement on the moving force that matter possesses by virtue of its motion, and that moving bodies display by setting other bodies in motion. An important issue in this context concerns the role of (...) gravitation as compared to mechanical processes in the narrow sense of “pressure and impact”. (shrink)

This paper deals with Suárez's theory of extension and continuous quantity, as it is discussed in the Metaphysical Disputations and as a possible source for Descartes's concept of res extensa. In a first part of the paper, I analyse Suárez' account of divisibility and extension in a comparison with the Dominicans', Scotus and Fonseca's, and Ockham's. In the light of this analysis, Suárez's most original contribution seems being the claim that material composites have integral parts 'entitatively' extended (partem extra (...) partem) independently from categorial quantity. Such a theory allows Suárez to merge the Dominicans', the Scotists' and the Ockhamists' account, as the integral parts fund the internal but pre-quantitative divisibility of body, which is the source of quantity. In a second part of the paper, I deal with the reception of Suárez’s theory (especially in Rubio, Arriaga, Araujo, Eustachius and Abra de Raçonis), as well as with Descartes’ concept of res extensa. I conclude that Suárez’s account has been mainly criticized by the seventeenth Century Aristotelianism, as well as by Descartes. Despite that, Suárez’s idea of non-quantitatively extended parts had an interesting reception and effect in the debate, and especially in the (dominant) Scotistic context. (shrink)

One way to rebut the standard evidential problem of evil is to develop a sceptical form of theism. The resulting position – sceptical theism – is a sophisticated philosophical elaboration on the traditional claim that God works in mysterious ways. Yet sceptical theism is contentious because it has a quite natural tendency to entail a degree of scepticism in other areas of discourse that is normally taken to be unacceptable. To curb this tendency a moderately sceptical theism can be developed (...) that nevertheless retains the benefit of rebutting the standard evidential problem of evil – the moderately sceptical theist attempts to steer a middle course between the Charybdis of mysticism and the Scylla of evil. However, a new evidential problem can be developed and reworked in a formal Bayesian framework. There are various ways to mitigate the new evidential problem and my reworked version, but none of these ways is open to the moderately sceptical theist – her particular ship, I argue, sails too close to Scylla. The moral is quite intuitive: if evil matters at all, then the sheer quantity of evil ensures that it matters a lot. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist (...) methodologies. Newton's thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

There are clear associations between the overall quantity of input children are exposed to and their vocabulary acquisition. However, by uncovering specific features of the input that matter, we can better understand the mechanisms involved in vocabulary learning. We examine whether exposure to wh-questions, a challenging quality of the communicative input, is associated with toddlers' vocabulary and later verbal reasoning skills in a sample of low-income, African-American fathers and their 24-month-old children. Dyads were videotaped in free play sessions (...) at home. Videotapes were transcribed and reliably coded for sheer quantity of fathers' input as well as the number of wh-questions fathers produce. Children's productive vocabulary was measured at 24 months using the McArthur Bates Communicative Development Inventory MCDI, and children's verbal reasoning skills were measured 1 year later using the Bayley Scales of Infant Development. Results indicate that the overall quantity of father talk did not relate to children's vocabulary or reasoning skills. However, fathers' use of wh-questions related to both vocabulary and reasoning outcomes. Children's responses to wh-questions were more frequent and more syntactically complex, measured using the mean length of utterance, than their responses to other questions. Thus, posing wh-questions to 2-year-olds is a challenging type of input, which elicits a verbal response from the child that likely helps build vocabulary and foster verbal reasoning abilities. (shrink)

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case (...) of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation. (shrink)

The equation for the fundamental field quantity ϱ is obtained. It is Div $\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } $ ,where h is an arbitrary function oft andr, and [,]− is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ϱ.(2) Relativistic covariance of the equations governing ϱ.(3) Principle of continguous action.(4) Conservation of total (...) amount of ϱ. The equation appears to be unique. It is suggested that the physical world corresponds to ϱ being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential Aμ is identified with ε ρμ dΩ. Conservation laws on various measures of ϱ are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ϱ to the metric is made via Einstein's gravitational equation Gμυ =KTμυ. (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)

In the Corpus Hippocraticum and in tragedy, γκος is difficult to translate, for it corresponds to a very primitive notion, intuitively implying a confusion between two aspects that were gradually distinguished: 1) a thing's bulk or extension, and 2) an appreciation, as a function of its bulk and its extension, of the load represented by this thing, or its weight. This explains why the term usually designates something that has a certain mass. As an indefinite quantity of formless (...) class='Hi'>matter, this is probably a notion which was used by medio-Platonists, strongly influenced by Stoicism, to understand matter the Timaeus . In Plotinus' polemic against the Stoics, γκος, which refers to a magnitude with resistance bereft of qualities, is thus situated at a level intermediate between matter (λη), bereft of all determination, and the body (σμα), which is endowed with magnitude and qualities. In the Sentences , Porphyry uses the term γκος 30 times in its technical sense, almost as often as Plotinus in the whole of the Enneads . This is probably because he felt uncomfortable with Plotinus' notion of matter bereft of all determination, including magnitude. (shrink)

I have argued that there is a philosophical problem posed by a need to determine the reference of expressions which seem to refer to kinds of stuff or matter and to make identity claims about it (e.g., ‘the gold’, ‘the same clay’). Ordinary sortal expressions such as ‘lump’, and ‘piece’ have been shown to be inadequate to the task of providing reference for the expressions in question. What is necessary is an expression which does not have an ordinary sortal (...) use and which meets certain other conditions which I have enumerated. There does not seem to be an expression in ordinary language which fits these conditions. The technical term, ‘quantity’, as defined by Helen Cartwright, meet the conditions. ‘Parcel’, suggested V. C. Chappell, fails to meet the conditions. Another technical term, ‘m-elements’, coined by Laycock, comes close to meeting the conditions, but has a number of difficulties. Mose of these difficulties stem from the fact that counting (rather than measuring, as with quantities) is behind the application of ‘m-elements’, and stuff is as a matter of fact measured, rather than counted, in most situations. I have also considered a possible difficulty with ‘quantity’ (that in most cases in which someone talks of ‘same stuff’ strictly speaking we don't have the same quantity of stuff) and shown it not to be a genuine difficulty. (shrink)

Peter Kosso discusses the weak gravitational lensing observations of the Bullet Cluster and argues that dark matter can be detected in this system solely through the equivalence principle without the need to specify a full theory of gravity. This paper argues that Kosso gets some of the details wrong in his analysis of the implications of the Bullet Cluster observations for the Dark Matter Double Bind and the possibility of constructing robust tests of theories of gravity at galactic (...) and greater scales. Even the Bullet Cluster evidence is not sufficiently detailed to allow precision tests of General Relativity that would distinguish it from its rivals at galactic and greater scales. Taking into account the total evidence available, we cannot rule out “ugly” solutions to the dynamical discrepancy in astrophysics that involve both a large quantity of dark matter and a theory of gravity whose predictions differ significantly from those of General Relativity for interactions taking place at galactic and greater scales. (shrink)

When does more data help and when does it not in the sciences? In the past decade, this question has become central because of the phenomenon of Big Data. While these discussions started as a result of somewhat naive ideas that have been closely analyzed and mostly rejected in the philosophy of data, the question about the epistemic difference that more or less data makes still matters, especially in light of the impressive performance of data science and machine learning tools, (...) which seem to improve their outcomes when they are trained on large volumes of data. In several areas of the sciences, having more data is also connected to methodological and epistemic benefits and more generally something that research should strive toward. More data is often equated to better science: this elicits crucial questions about the epistemic value of the quantity of data. In this chapter, we discuss this problem in light of current discussions in the life and health sciences and the philosophy of data. (shrink)

This book is about matter. It involves our ordinary concept of matter in so far as this deals with enduring continuants that stand in contrast to the occurrents or processes in which they are involved, and concerns the macroscopic realm of middle-sized objects of the kind familiar to us on the surface of the earth and their participation in medium term processes. The emphasis will be on what science rather than philosophical intuition tells us about the world, and (...) on chemistry rather than the physics that is more usually encountered in philosophical discussions. It is the everyday science of matter characterised by differences of chemical substance that constitutes individuated macroscopic bodies of geological and biological complexity—the continuous matter of macroscopic theory and described by mass terms. -/- The discussion might be characterised as descriptive metaphysics, being content, to paraphrase Strawson’s use of the term, to describe the structure of our scientific thought about the actual world. The method in the central chapters dealing with the nature of matter will be to pursue key steps in the historical development of scientific thought about chemical substance and related concepts with a view to tracing the emergence of a systematic ontological interpretation. Aristotle’s and the Stoics’ discussions of elements and mixtures, based on a continuous view of matter, bear some resemblance to modern, macroscopic conceptions and therefore have some interest as precursors to modern views as well as being of conceptual interest in their own right. Some of the issues they raised are still reflected in modern discussions, despite the considerable increase in complexity of the subject. Other ideas, such as the intimate connection between what modern science distinguishes as substance and phase, maintained their grip on the understanding of matter until the end of the eighteenth century. These are some of the important aspects of the properties of matter that have been neglected by linguistic concerns that have dominated the recent study of mass terms and which the present study seeks to redress. It will be of interest to see how the bounds of possibility are delimited by the laws governing the appropriate use of concepts refined for the purpose of describing the behaviour of matter. But the concern with modality will not stretch to venturing into the realms of metaphysical possibility governed by philosophical speculation about individual essences and underlying natures. -/- Like many contemporary discussions of material objects, this one relies heavily on mereology. Unlike several such discussions, this one adheres to the classical principles of mereology governing the usual dyadic relations of part, overlapping, etc. and the operations of sum, product and difference. These principles apply to the mereological structure of regions of space, intervals of time, processes and quantities of matter. Material objects that gain and lose matter are not understood to gain and lose parts and don’t call for a modification of the classic dyadic mereological relations to triadic relations with the introduction of a third term referring to time. Rather, a distinction is drawn between quantities of matter, which don’t gain or lose parts over time, and individuals, which are typically constituted of different quantities of matter at different times. The proper treatment of the temporal aspect of the features of material objects is a central issue in this book. The topics falling under this heading are addressed by investigating the conditions governing the application of predicates relating time and other entities. Of particular interest here are relations between quantities of matter and times expressing substance kind, phase and mixture. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices (...) by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

In this chapter, we offer a reconstruction of the evolution of Leibniz’s thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability, and syncategorematicity, and the closely related question of the possibility of infinitesimal quantities, both in physics and in mathematics.Some scholars have argued that syncategorematicity is a mature acquisition, to which Leibniz resorts to solve the question of his infinitesimals – namely the idea that infinitesimals are just signs for Archimedean exhaustions, and their unassignability (...) is a nominalist maneuver. On the contrary, we show that syncategorematicity, as a traditional idea of classical scholasticism, is a feature of young Leibniz’s thinking, from which he moves away in order to solve the same problem, as he gains mathematical knowledge.We have divided Leibniz’s path toward his mature view of infinitesimals into five phases, which are especially significant for reconstructing the entire evolution. In our reconstruction, an important role is played by Leibniz’s text De Quadratura Arithmetica. Based on this and other texts, we dispute the thesis that fictionality coincides with syncategorematicity, and that unassignability can be bypassed. (In this chapter, we employ “syncategorematic” as a shorthand for “eventually identifiable with a procedure of exhaustion” and, as a consequence, “involving only assignable quantities.” We also identify syncategorematicity with potentiality, as suggested by some part of the scholastics, and in Sect. 2.2, we show that the two characterizations are equivalent, provided that “potentiality” is intended in the correct way: namely as in the unending iterative procedures of Greek mathematics.) On the contrary, we maintain that unassignability, as incompatible with the principle of harmony, is the ultimate reason for the fictionality of infinitesimals. (shrink)

Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of (...) ordinary fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications. (shrink)

In this essay I propose a new measure of social welfare. It captures the intuitive idea that quantity, quality, and equality of individual welfare all matter for social welfare. More precisely, it satisfies six conditions: Equivalence, Dominance, Quality, Strict Monotonicity, Equality and Asymmetry. These state that i) populations equivalent in individual welfare are equal in social welfare; ii) a population that dominates another in individual welfare is better; iii) a population that has a higher average welfare than another (...) population is better, other things being equal; iv) the addition of a well-faring individual makes a population better, whereas the addition of an ill-faring individual makes a population worse; v) a population that has a higher degree of equality than another population is better, other things being equal; and vi) individual illfare matters more for social welfare than individual welfare. By satisfying the six conditions, the measure improves on previously proposed measures, such as the utilitarian Total and Average measures, as well as different kinds of Prioritarian measures. (shrink)

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to (...) have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)

This paper compares four techniques for measuring the masses of galaxies and larger astrophysical systems from their dynamics. The apparent agreement of these techniques is sometimes invoked as reason for hypothesizing the existence of huge quantities of “dark matter” as the best solution to “the dynamical discrepancy”, the 100-fold disparity between the amount of mass visible in large scale astrophysical systems and the amount calculated from dynamics. This paper argues that the agreement, though suggestive, is not definitive. The coincident (...) measurements remain the best reason for preferring dark matter over revisions to General Relativity for solving the dynamical discrepancy, but the resulting warrant for this preference is weak. (shrink)

This dissertation elucidates the notion of physical system which opens new conceptual pathways that connect the three realms of physical theory; spacetime, material bodies and their properties, and the laws of nature which govern their evolution. The notion of physical system includes two presuppositions regarding their structure. The first presupposition is a description of isolated systems and their evolution in time, which amounts to a Paradigm of Uniform Motion. The second presupposition describes how parts of a physical system are combined (...) into wholes. This presupposition amounts to a Rule of Composition. Once we make these presuppositions explicit we can derive the spacetime structures and the fundamental equations of motion. "Newtonian" and "relativistic" systems are shown to differ with respect to the paradigm of uniform motion, a difference that leads to the respective structures of Newtonian mechanics and the Special Theory of Relativity. ;The philosophical framework offered in this dissertation provides a new interpretation of the concept of mass, and a new elucidation of the relation between the conservations of mass and momentum. Previous analyses of the concept have claimed that "mass" cannot be defined and broken down to more primitive predicates. The framework offered here, on the other hand, enables the systematic reduction of the concept of mass to motions and the presuppositions we have regarding the nature of physical systems. The new interpretation of mass reveals a surprising connection between mass and inertial reference frames, as they are both shown to be derived, in a similar way, from our definition of physical systems. Mass is by necessity attributed to bodies in virtue of the frame we use to describe their motions. This account also enables us to understand the different conceptual roles of mass and their interconnections. In the context of Newtonian mechanics, the roles of mass as a Quantity of Matter, as the Inertial property of bodies, and as Gravitational mass are shown to be various aspects of a single role the concept has in the new framework offered here. In the context of the Special Theory of Relativity, rest mass and relativistic mass are similarly analyzed as consequences of our presuppositions regarding physical systems. (shrink)

This paper investigates Isaac Newton's rather unique account of God's relation to matter. According to this account, corpuscles depend on a substantially omnipresent God endowing quantities of objective space with the qualities of shape, solidity, the unfaltering tendency to move in accord with certain laws, and—significantly—the power to interact with created minds. I argue that there are important similarities and differences between Newton's account of matter and Berkeley's idealism. And while the role played by the divine will might (...) at first appear to be a species of occasionalism, I conclude that there are, for Newton, genuine causal relations between minds and bodies. Ultimately, to fully appreciate this account of the creation and persistence of matter, we must consider not only Newton's metaphysical writings, but also his sensorium theory of mind-body interaction, his heterodox theological commitments, and the influences of Descartes, More, and Locke. (shrink)

An examination of Plotinus’s treatise on matter, II 4[12], reveals interesting paradoxes. He seems to use Aristotle’s matter to explain Plato’s receptacle. Attention to the text reveals that both matter and the receptacle are, in fact, recast in terms of the otherness of Plato’s Sophist. By this, Plotinus articulates how matter and the receptacle function as the condition of possibility for the sensible cosmos. His analysis of related terms further supports this rapprochement: privation and substrate exclude (...) quality and quantity as attributes of matter; and the indefinite, the unlimited, size and mass echo the paradoxical language of the Timaeus. (shrink)

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

Emergent research in metagenomics has unveiled large quantities of previously unknown and unclassified prokaryotic DNA. As these prokaryotes constitute the vast majority of microbial life in environmental samples, some microbiologists and commentators in scientific media have referred to this expansive unknown as ‘biological dark matter’, translating the rhetorical power of dark matter from the physical to the life sciences. Engaging literatues and approaches from across the philosophy, history, and social studies of science, we explore the cultural significance of (...) the dark matter theory in the physical sciences and examine the implications of its conceptual reworking in biology, through critically engaging the political narratives folded within dark matter’s genealogies. ‘Dark matter’ designates both zones of importance and zones of turbulence, simultaneously emphasizing microbiologists’ creativity whilst constructing new ways of relating to microbiota. Such a situation, we propose, also invites theoretical analysis as it calls for a conceptual reconsideration of the gene and its fundamental role within the life sciences. (shrink)

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to (...) have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)

Many philosophers believe that identity through time cannot depend on features extrinsic to the relata and relations between them. This goes with the view that one must deny identity in cases for which there is a ‘duplication case’-a case just like the first, but for an additional, ‘external’ element which provides an equal or better ‘candidate’ for identity with one of the relata. Such friends of intrinsicness cannot remedy the failure of continuity of function/form to be one-one by non-branching or (...) closest competitor clauses. The obvious intrinsic approach-perhaps taken for granted-appeals to considerations of quantity of matter, requiring over 50% shared matter between identicals . But this rules out plausible cases of halving and doubling for which there are not duplication cases. After bringing out this problem, I ask what makes duplication cases possible, and use this to formulate an intrinsic condition which allows identity whenever there is continuity of function, but no threat to intrinsic ness via duplication cases. (shrink)

The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in the (...) traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half we show how to do all this in a proper differential-geometric fashion and on arbitrary space-time manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue's theorem, which is shown to generalise from Minkowski space to space-times with significantly less symmetries. This result, which seems to be new, not only generalises but also clarifies the geometric content and hypotheses of Laue's theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text. (shrink)

From late 1684 through mid-1685, Isaac Newton turned to developing and refining the conceptual foundations presupposed by his emerging physics. Analysis of his manuscripts from this period reveals that Newton’s understanding of the relativity of acceleration led him to seek a spatiotemporally invariant quantity of matter. He found two such quantities and then designed an experiment to discover their relationship. Interpreting the experiment, however, required distinguishing a new notion of force. Others have recognized the conceptual distinction between inertial (...) and gravitational mass. I show here that Newton clearly saw this distinction and that he provisionally established their equivalence. (shrink)

© 2013 The Editors of The Philosophical QuarterlyWhy did matter matter for Descartes and Leibniz? The answer, Kurt Smith argues in this thought‐provoking book, is that without it mathematics would be unintelligible. A world without matter is insufficient for mathematics because the immaterial cannot be divided into discrete quantities. Without a divisible material structure, the determinate unities necessary for the additive quantities in turn necessary for mathematics are unactualisable. God needs matter to institute mathematics. However, with (...) the creation of matter, mathematical intelligibility necessarily follows. Smith's main aim, therefore, is to show that Descartes and Leibniz believed the biconditional: ‘Mathematics is intelligible if, and only if, matter exists’.The bulk of the book is dedicated to ‘analysis’ and ‘synthesis’. For Smith, analysis is a kind of transcendental process by which one discovers the basic conceptual categories necessary for the possibility of any object under investigation. A triangle's... (shrink)

Cognition means different things to different psychologists depending on the position held on the mind-matter problem. Ecological psychologists reject the implied mind-matter dualism as an ill-posed theoretic problem because the assumed mind-matter incommensurability precludes a solution to the degrees of freedom problem. This fundamental problem was posed by both Nicolai Bernstein and James J. Gibson independently. It replaces mind-matter dualism with animal-environment duality -- a better posed scientific problem because commensurability is assured. Furthermore, when properly posed (...) this way, a conservation law is suggested that encompasses a psychology of transactional systems, a biology of self-actional systems, and a physics of interactional systems. For such a solution, a theory of cognition for goal-directed behaviour is needed. A sketch is supplied for how such a theory might be pursued in the spirit of the new physics of evolving complex systems. (shrink)

This is a preprinted excerpt from: Kochiras, “By ye Divine Arm: God and Substance in De gravitatione”, Religious Studies (Sept. 2013), 49(3): 327-356. In this preprinted excerpt, I explicate the concepts of matter and space that Newton develops in De gravitatione. As I interpret Newton’s account of created substances, bodies are constructed from qualities alone, as configured by God. Although regions of space and then “determined quantities of extension” appear to replace the Aristotelian substrate by functioning as property-bearers, they (...) actually serve only as logical subjects. An implication of the interpretation I develop is that only space is extended by having parts outside parts; material bodies are spatially extended only in a derivative sense, via the presence of their constitutive qualities or powers in space. (shrink)

The principles of Kant's pure physics (conservation of quantity of matter, inertia, equality of action and reaction) are a priori in the same sense as are the principles of the understanding. We account for the empirical content of physics by showing that the pure principles operate as rules for generating wellformed empirical descriptions, and as rules for analysis of motion. The relationship between the metaphysics of matter and empirical descriptions is neither deductive, nor as loose as Buchdahl (...) alleges. Belief that a priori principles will apply to empirical cases requires acceptance of methodological presuppositions, chief among which is the principle of affinity. (shrink)

The chemist Jeremias Benjamin Richter (1762–1807) coined the term “stoichiometry” and proposed the “law of definite proportions.” He is also commonly acknowledged as having been a student of Immanuel Kant (1724–1804). This paper demonstrates how Kant’s philosophy positively shaped Richter’s approach to chemistry in the _Anfangsgründe der Stöchiometrie_ (1792–1794) and outlines two ways in which Richter attempted to represent the chemical force in “pure intuition”: (1) “reductionistic forces,” in which qualitative features scale with the quantity of matter; and (...) (2) generalized “abstracted forces,” in which a plurality of dissolution- and bonding-properties are latent within the chemical in the manifold of space-time. (shrink)

Animal size is a relevant and unappreciated consideration in moral evaluations of killing animals for food, especially for utilitarians, who must weigh the gustatory satisfaction of eating meat-the quantity of which varies greatly throughout the animal kingdom-against animal suffering in utilitarian calculations. I argue that animal size can drastically alter not only the extent but even the valence of such calculations. Then I show how the business ethics literature on vegetarianism is deficient for not taking animal size into account. (...) Last, I argue that market conditions are also relevant in moral assessments of vegetarianism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:347 THE ROLE OF PART XII IN HUME'S DIALOGUES CONCERNING NATURAL RELIGION Anyone appreciative of Hume's greatness as a philosopher will want to suppose that the Dialogues both form a coherent whole and express Hume's own views on natural religion or religion based on reason (as opposed to religion based on revelation). In the last connection, given what we know of Hume's epistemology, life, and correspondence, one would be (...) inclined to suppose that he would reject out of hand the claims of revealed religion and contend that if there existed an acceptable religion it would have to be some form of natural religion. But insofar as natural religion claimed to establish scientifically the existence and nature of God one would envisage Hume dissenting. Now as long as we restrict our gaze to Parts I-XI of the Dialogues we seem to be able, easily enough, to satisfy all these suppositions. In Part IV, under the name of 'mysticism, ' revealed religion is summarily and facetiously dismissed as 2 indistinguishable from atheism. Demea's apparently permanent departure from the discussion at the conclusion of Part XI as much as says, symbolically, that revealed religion is not a serious contender for one's belief. Its a priori arguments -- the argument from sufficient reason and the ontological argument -- are almost as shortly attacked and dismissed (D 188-192). Also quite in keeping with Hume's philosophical view on knowledge of matters of fact is, on the other hand, the lengthy and detailed examination he bestows on the empiricist argument from design. That Philo, ostensibly his spokesman, is however able to uncover all kinds of logical short-comings in its claims to scientifically 348 establish the existence and nature of God does not surprise us; it coheres perfectly with our preconceived picture of Hume the skeptic, and his system as restricting science to numbers and quantities or, in the term's looser sense, to human nature and its more immediate surroundings. In short, Parts I-XI seem to be all of one Humean whole. But at first and even second glance Part XII notoriously seems to tear our hopes to find coherence and a plausible representation of Hume to tatters. There are, for one thing, those mocking sentences that seem to paint Hume in the colors of a devout, believing Christian, 'avid' for revelation. Thus, at the end of Part XII, apparently expressing Hume's deepest convictions, Philo says that "a person, seasoned with a just sense of the imperfections of natural reason, will fly to revealed truth with the greatest avidity" and immediately afterwards, "To be a philosophical sceptic is, in a man of letters, the first and most essential step towards being a sound, believing Christian" (D 227, 228). For another thing, in Part XII Hume seems to be completely reversing his refutations in Parts I-XI of the argument from design's claims to establish the existence and nature of God. Thus, where in Part II he had Philo reject the use of causal reasoning in the establishment of a Mind as the first cause of the universe on the relevantly Humean grounds that, to do so, "it were requisite, that we had experience of the origin of worlds" (D 150), in Part XII he has Philo, apparently speaking for himself (Hume), argue that "as there are also considerable differences, we have reason to suppose a proportional difference in the causes; and in particular ought to attribute a much higher degree of power and energy to the supreme cause than any we have ever observed in mankind. 349 Here then the existence of a DEITY is plainly ascertained by reason" (D 217). Indeed, all forms of the argument of design, purely analogical as well as causal, seem resurrected in Part XII, although they were one and all hanged and buried in Parts I-XI. Moreover, it seems that in Part XII Hume via Philo is saying that science itself leads us "to acknowledge a first intelligent Author" (D 214-215). Before proceeding to deal with certain other incoherencies with which Part XII seems to confront us let us address ourselves to the two that I have so far... (shrink)

Prime matter plays an indispensable role in Aristotle’s philosophy, enabling him to avoid the pitfalls of both naïve Platonism and nominalism. Prime matter is best thought of as a kind of infinitely divisible and atomless bare particularity, grounding the distinctness of distinct members of the same species. Such bare particularity is needed in symmetrical situations, like a world consisting of indistinguishable Max Black spheres. Bare particularity is especially important in modern physics, given the homogeneity and isotropy of space. (...) With the importance of fields in classical, relativistic, and quantum physics, we have good reason to prefer something like Aristotle’s continuous, infinitely divisible matter over indivisible particles. Mass and energy in relativistic physics also points in the direction of prime matter as the enduring substrate of these quantities. Recent work on Aristotelian interpretations of quantum mechanics, further underscores the contemporary relevance of prime matter. (shrink)

Hylomorphically complex objects are things that change their parts or matter or that might have, or have had, different parts or matter. Often ontologists analyze such objects in terms of sets (or functions, understood set-theoretically) or other extensional entities such as mereological fusions or quantities of matter. I urge two reasons for being wary of any such analyses. First, being extensional, such things as sets are ill-suited to capture the characteristic modal and temporal flexibility of hylomorphically complex (...) objects. Secondly, sets are often appealed to because they seem to contain their members. But the idea that sets do contain their members, in the ordinary sense of containment, is a substantive metaphysical position that makes analyses that rely on that idea for their plausibility much more metaphysically committing than is generally thought. (shrink)

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain (...) kinds of 'time observables' to find a representation within quantum theory, including clock operators and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack. (shrink)

This paper is about the relevance, to the definition of freedom, of values or goods other than freedom. In this respect,its subject matter is not at all new. However, I do believe that new light can be thrown on the nature of this relationship by paying more attention to another relationship – one which exists within the concept of freedom itself. There are two senses in which we can be said to possess freedom. Firstly, there is the sense in (...) which we can be said to be free to do a certain particular thing. Secondly,there is the sense in which we can be said to possess a certain ‘amount’,‘degree’ or ‘quantity’ of freedom, in some overall sense.1 I believe that most recent accounts of the relationship between freedom and other goods are inconsistent, because they see those other goods as affecting the truth value of claims about freedom in the second sense, but not in the first. (shrink)

The bases of tenets of the World came from the East; Pythagoras learnt all there up the 26 years. At a home, the east ideas where took in no; then he bound the mathematics with the elements of matter. This was the best way to a blood feud of the all Humanity. The 17th age gave the bases of mathematics and the Greek atomism; this had led to the paranoia in all sciences. The LCE was brought in 19th age (...) with bases no; really it was the box of Pandora in the form of wrong sciences of the Nature. The wise revenge of Pythagoras was in the form of riddle for the best thinkers in the World in all times; us solved one in the 50th years. A base of the World is of the material space (MS) with praatoms (PAs) Ao; they are of the affinity to matter. A density of the MS is of ~ 5.10‐6 kg/m3 close to the Ears. PA Ao is of quant of matter and antimatter; they are of rotate in the different sides. All matter takes up Ao and to grow. In the giant stars to go the bursts giving Ao, or caloric. The matter of being in the World on base of the key law of conservation of heat (caloric) and matter by loss of energy; it is main. Leibniz offered to the conservation of mv2 in the World. But Newton knew that any move is damped, and it need in filled up. This the author proved by tests over the 300 years just. D.Bernoulli given to the model of gas. I. Kant proved that mv2 is the quantity of heat by stop of the body; it is no the energy! A key leitmotiv of thought is blocked the grasp of facts if ones not leaded to an accepted concept. P. Mayer had the blunder in base of the LCE; a work of gas expansion in Torricelli tube is equal nil strong! This is the gross blunder of a sick paranoiac! The 21 age gave up a new philosophy and a way to endless engine. The super skills from ideal quartz with moving jaws to respond to the all new philosophy and sciences. (shrink)

What would Christianity be like without the soul? While most people would expect the Christian bible to reveal a highly traditional opposition of matter and spirit, the spirit forces of the Old and New Testaments are often surprisingly physical, dynamic, and practical, a matter of energy as much as ethics. The Secret History of the Soul examines the forgotten or suppressed models of body, soul, and human consciousness found in the literature, philosophy and scripture of the ancient and (...) classical worlds. It shows how the spirit forces of Homer, Plato, Aristotle, and the Old and New Testaments tended to be quantities not entities, and to be closely bound up with the dynamic physical flux of the human body, rather than cleanly abstracted in some absolute immaterial realm. Forces such as menos and thymos, nephesh, pneuma and dynamis not only blurred the line between body and soul, but were potent and transferable, being used, in New Testament culture, to effect magical cures or bestow magical power. Related to this surprising lack of body-soul dualism is a lack of dualistic afterlife in either Homer or Hebrew scripture, where Hades and Sheol are the sole post-mortem destinations. The Secret History of the Soul restores the living strangeness of a spirit world filled with potent energy and practical magic, in cultures which had not yet glimpsed the abstracted soul of later Christianity. (shrink)

Chemistry is concerned with all aspects of the changing of one kind of matter into another. It has many parts and all but one of these are so different from all the adjacent sciences that their distinctness is obvious; the exception is physical chemistry. The activities of its practitioners resemble prima facie those of physicists. These however deal with unchanging matter that retains its chemical identity, and virtually all their experimental information is numerical. The physical chemist's concerns are (...) the nature, extent, and rate of chemical changes, and on these much information may be gathered by the observer's unaided senses.A fundamental feature or chemistry with few parallels in other sciences is that the variables determining chemical behaviour include the purity of reaction vessels, reagents, and the gas-phase in contact with these, as well as the exact experimental procedures when bringing about the chemical changes. For this reason, when encountering ostensibly new chemical phenomena, it is even more important than in other areas to distinguish between repeatability (of phenomena, e.g. explosions) and reproducibility (of quantities, e.g. reduction potentials). The distinction is not always clear, as differences of degree may develop into differences of kind. Unrepeatability may be of great heuristic significance, but irreproducibility is often of trivial origin. Examples from the author's researches illustrate how chemical behaviour, e.g. electrochemical conductivity or the nature of a product, such as the shape of a polymer molecule, can be altered profoundly by very small changes of experimental conditions, which is uncommon in other sciences. (shrink)

This volume contains eighteen papers, three with new postscripts, that were written over the past 35 years. Five of the papers have not been previously published. Together they provide a comprehensive account of modal reality—the realm of possible worlds—from a Humean perspective, with excursions into neighboring topics in metaphysics. Part 1 sketches an account of reality as a whole, both the mathematical and the modal, defending a form of plenitudinous realism: every consistent proposition is true of some portion of reality. (...) Part 2 presents and defends a realist theory of concrete possible worlds with an absolute ontological distinction between the actual and the merely possible. Part 3 presents and defends a Humean account of modal plenitude, formulating and endorsing principles of recombination, of plenitude of possible structures, and of plenitude of alien contents. Part 4 applies the Humean account to truthmaking, mereology, spacetime, and quantities. I argue that holding fast to Humean strictures leads to views that differ in radical ways from those put forth by contemporary metaphysicians. (shrink)