The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

A system S has the “converse Ackermann property” if -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has the (...) C.A.P. Thus, we think the problem proposed in Anderson & Belnap § 8.12 has been solved. (shrink)

LCo with the Converse Ackermann Property is defined as the result of restricting Contraction in LC. Intuitionistic and Superintuitionistic Negation is shown to be compatible with the CAP.

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was (...) right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation). (shrink)

Context: The idea to write this paper sprang up in a casual conversation that led to the question of how the word “experience” would be translated into German. Distinctions between the German “Erleben” and “Erfahren,” and their intricacies with “Erkennen” and “Anerkennen,” soon led to the conviction that this was a thread worth pursuing. Problem: Much has been written about the nature of experience, but there is little consensus, to this day, regarding the role of consciousness in the process of (...) experiencing. Although RC acknowledges the significance of tacit or sensorimotor knowledge in the individual’s practical operating, it cannot admit it as a basis to the formation of conceptual structures that, by definition, are conscious. Method: Drawing from our backgrounds in epistemology and psychology, and a shared interest in Piaget’s psychogenetic approach, we investigate the origins and development of human experience, in this case the mastery of space, time, causation, and object-permanency. We focus on how “noticeable encounters” are gauged, reflected upon, and ultimately worked through, consciously or unconsciously, by the “experiencer.” Results: A child’s abilities to enact a certain action pattern in a given situation no more demonstrates a re-presentation of the pattern than does recognition in the case of objects. In his studies with children, Piaget has shown that the Kantian categories of space, time object, and “causality” are co-constitutive of the child’s own motion – and its felt impact – as a means to make the world cohere. Of importance here are the concepts of “effective causality,” felicitous encounters, and agency. Implications: Understanding the circumstances under which some “lived” events, whether self-initiated or striking as if out of nowhere, become noticeable and able affect a person’s life is a daunting task. This joint essay is no more than a conversation-starter and an invitation to further explore the intricacies between agency and causation, sensation and cognition, and, yes, motions and emotions in the making of consciousness itself. (shrink)

Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People generally (...) respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit! (shrink)

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework is (...) cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse. (shrink)

Many philosophers have written in the past as though it were nearly obvious to rational reflection that the existence of evil in this world is incompatible with the presumed properties of the Christian God, and they have assumed a proof of incompatibility to be easy to construct. An informal underpinning for this line of thought is easy to develop. Surely God in his benevolence finds evil to be evil, and hence has both the desire and the means, provided by his (...) omnipotence and omniscience, to eradicate it. But it remains a brute fact that evil exists. While this seems plausible enough at first glance, and seems damaging to the rationality of Christian belief, attempts to pin down a definite proof of incompatibility have encountered difficulties. The root difficulty is perhaps that the surface plausibility of incompatibility is ultimately mistaken. In what he calls a Free Will Defence against natural atheology, Alvin Plantinga has presented what seems a definitive proof, on rather modest assumptions, of the logical compatibility of God's nature and the existence of evil. Logic alone can neither prove nor disprove God's existence, since the defence rests on the empirical assumption that evil exists in this world. What Plantinga shows, put very simply, is that God may have created a world as good as any that an omnipotent, omniscient, and benevolent being might have created given that human beings must exist in that world. Whether Christianity ought to court logical rationality may seem highly dubious, but on the supposition that it does, Plantinga's proof that the existence of God is logically compatible with the existence of evil seems to me to settle the issue of whether Christianity is a possible object of rational belief, at least insofar as the problem of evil is considered the major obstacle to rationality of belief. Perhaps it is now clear that I do not intend here to attack the validity or the significance of Plantinga's proof. At the same time, I think it possible to argue for Plantinga's conclusion on other grounds, grounds that seem to me philosophically more appealing, and grounds that are manifestly compatible with the Biblical record. After briefly summarizing Plantinga's argument, I shall propose an alternative free will defence that circumvents some of the presuppositions of his arguments, an alternative that may be attractive to philosophers who are not interested in an ontology involving Plantinga's conception of possible worlds. (shrink)

My purpose in this paper is to examine a pitfall in empiricistic analysis which has not been widely discussed, perhaps because it lies implicit in what may seem a harmless facet of such analysis. The kind of analysis I have in mind is analysis of any variety which seeks to reduce understanding of any object, concept event, institution, or whatever, and its appropriate properties, to understanding of discrete elements and their properties out of which the analytically reduced can be constructed. (...) Let us call the entity analysed into elements the molar object, and restrict elements hereafter to some set of discrete elements of some molar object which have been obtained by an analysis of the kind to be discussed. What I will have to say will apply most directly to the reductionist analyses of an older logical empiricism, but I hope to make it clear that more recent linguistic analyses encounter the same difficulty. (shrink)

La "Conversa de la Propiedad Ackermann" (CAP) es la no demostrabilidad de proposiciones puramente no-necesitivas a partir de proposiciones necesitivas. En nuestro trabajo definimos las dos restricciones básicas de la lógica intuicionista mínima con la CAP.

S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S40 that can be formulated with a modification of Anderson and Belnap's list of valid entailments.

S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S4o that can be formulated with a modification of Anderson and Belnap's list of valid entailments.

This article presents material from my ethnographic study in Śringēri, south India, the site of a powerful 1200yearold Advaitic monastery that has been historically an interpreter of ancient Hindu moral treatises. A vibrant diverse local culture that provides plural sources of moral authority makes Sringeri a rich site for studying moral discourse. Through a study of two conversational narratives, this essay illustrates how the moral self is not an ossified product of written texts and codes, but is dynamic, gen dered, (...) and emergent, endowed with historical and political agency and an aesthetic capacity that mediates many normative sources to articulate "appropriate" conduct. In so doing, the essay shows the value of including oral narrative in ethical inquiry, especially in narrative ethics, which, for most part, has focused on written sources. (shrink)

This article seeks to understand contractual rights through an examination of the possible ‘property’ content in contracts in the context of the inducement tort and conversion. It argues that, contrary to popular perception, contracts and property are different shades of a similar phenomenon. Not being a reified ‘thing’ with stable features and structure, property is a relative rather than an absolute concept. To determine whether the holder of an intangible resource ought to be conferred with ‘property’ (...) or exclusive control of access to such resource, one has to evaluate the relevant practical, legal and moral considerations. Applied to the context of inducing breach of contract and conversion, this analysis demonstrates that a contractual right is in fact a composite collection of distinct interests and each tort may be protective of one or more of such interests. Thus, liability is imposed for inducing breach of contract because tort law recognizes the promisee's exclusive right to the peremptory status of the promisor's promise. On the other hand, the wrongfulness of converting a contract lies in the usurpation of a contracting party's control, or the exclusive entitlement to decide whether and how to exercise her rights under the contract. (shrink)

It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties.

Following a suggestion of Feys, we use “rigorous implication” as a translation of Ackermann's strenge Implikation ([1]). Interest in Ackermann's system stems in part from the fact that it formalizes the properties of a strong, natural sort of implication which provably avoids standard implicational paradoxes, and which is consequently a good candidate for a formalization of entailment (considered as a narrower relation than that of strict implication). Our present purpose will not be to defend this suggestion, but rather (...) to present some information about rigorous implication. In particular, we show first that the structure of modalities (in the sense of Parry [4]) in Ackermann's system is identical with the structure of modalities in Lewis's S4, and secondly that (Ackermann's apparent conjecture to the contrary notwithstanding) it is possible to define modalities with the help of rigorous implication. (shrink)

McGowan argues that everyday verbal bigotry makes a key contribution to the harms of discriminatory inequality, via a mechanism that she calls sneaky norm enactment. Part of her account involves showing that the characteristic of conversational interaction that facilitates sneaky norm enactment is in fact a generic one, which obtains in a wide range of activities, namely, the property of having conventions of appropriateness. I argue that her account will be better-able to show that everyday verbal bigotry is a (...) key factor in social inequality if it tries to isolate a more specific property of conversation as the thing that facilitates sneaky norm enactment. (shrink)

A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.

Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the (...) redex and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions. (shrink)

I argue that the best scientific package is anti-Humean in its ontology, but Humean in its laws. This is because potencies and the best system account of laws complement each other surprisingly well. If there are potencies, then the BSA is the most plausible account of the laws of nature. Conversely, if the BSA is the correct theory of laws, then formulating the laws in terms of potencies rather than categorical properties avoids three serious objections: the mismatch objection, the impoverished (...) worlds objection, and the metaphysical 'oomph' objection. I argue that combining anti-Humean properties with Humean laws into a Potency-Best System Account of Laws is a powerful and science-friendly account---something that people on both sides should be able to appreciate. (shrink)

Robert John Ackermann deals decisively with the problem of relativism that has plagued post-empiricist philosophy of science. Recognizing that theory and data are mediated by data domains (bordered data sets produced by scientific instruments), he argues that the use of instruments breaks the dependency of observation on theory and thus creates a reasoned basis for scientific objectivity. Originally published in 1985. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished (...) backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Is it true that all conversational implicatures are cancellable? In some recent works (Weiner Analysis 66(2):127–130, 2004, followed by Blome-Tillmann Analysis 68(2):156–160, 2008 and, most recently, by Hazlett 2012), the property of cancellability that, according to Grice (1989), conversational implicatures must possess has been called into question. The aim of this article is to show that the cases on which Weiner builds his argument—the Train Case and the Sex Pistols Case— do not really suffice to endanger Grice’s Cancellability Hypothesis. (...) What Weiner has shown with his examples is that a conversational implicature cannot be cancelled if the speaker, whose utterance gives rise to the implicature, does not intend to cancel it. To implicate is an intentional speech act and, therefore, cancelling an implicature must also be intentional and must be performed by the same speaker whose utterance gives rise to the putative implicature. (shrink)

It is sometimes argued that contextualism cannot explain (dis)agreements concerning matters of personal taste because it treats sentences involving predicates of taste as indexical. I aim to weaken this charge. Given the idea that people sometimes use indexical sentences to express (dis)agreements about taste, two kinds of (dis)agreement are distinguished, namely doxastic and non-doxastic. Taste (dis)agreements are better explained in terms of the later kind, in which case they become amenable to contextualist treatment. It is argued that if something instantiates (...) a taste property (like being tasty for A), it has to instantiate a corresponding attitudinal property (like being liked by A). Based on this, utterances of taste sentences express propositions that concern tastiness of something (e.g., that X is tasty for A) and these propositions entail other propositions that concern non-doxastic attitudes the speakers bear toward something (e.g., that X is liked by A). One speaker is claimed to (dis)agree with another speaker provided their respective entailed propositions feature (in)compatible non-doxastic attitudes. Although this explanation is similar to hybrid accounts that are currently growing in popularity, it departs from them in some notable respects. (shrink)

We experience resistance when we are engaging with fictional works which present certain (for example, morally objectionable) claims. But in virtue of what properties do sentences trigger this ‘imaginative resistance’? I argue that while most accounts of imaginative resistance have looked for semantic properties in virtue of which sentences trigger it, this is unlikely to give us a coherent account, because imaginative resistance is a pragmatic phenomenon. It works in a way very similar to Paul Grice's widely analysed ‘conversational implicature’.

This book introduces concepts in philosophy of mind and neurophilosophy. Inside, three scholars offer approaches to the problems of identity, consciousness, and the mind. In the process, they open new vistas for thought and raise fresh controversies to some of the oldest problems in philosophy. The first chapter focuses on the identity problem. The author employs an explanatory model he christened sense-phenomenalism to defend the thesis that personal identity is something or a phenomenon that pertains to the observable/perceptible aspect of (...) the human person. The next chapter explores the problem of consciousness. It deploys the new concept equiphenomenalism as a model to show that mental properties are not by-products but necessary products of consciousness. Herein, the notion of qualia is a fundamental and necessary product that must be experienced simultaneously with neural activities for consciousness to be possible. The last chapter addresses the mind/body problem. It adopts the new concept proto-phenomenalism as an alternative explanatory model. This model eliminates the idea of a mind. As such, it approaches the mind-body problem from a materialistic point of view with many implications such as, the meaning of our existence, the possibility of thought engineering as well as religious implications. (shrink)

This essay explores claims made frequently by artists, critics, and philosophers that artworks bear personifying traits. Rejecting the notion that artists possess the Pygmalion-like power to bring works of art to life, the article looks seriously at how parallels may exist between the ontological structures of the artwork and human personhood. The discussion focuses on Arthur Danto’s claim that the “artworld” itself manifests properties that are an imprint of the historical representation of the “world.” These “world” representations are implicitly embodied (...) in the artist’s style. The “world” that is stamped on the people of a historical period entails a point of view that influences how they might act, something like the logic that guides a conversation. This “conversational” logic is also extant in the artworks that artists of a given period create. This analysis of Danto’s account of how people are connected to their world clarifies Danto’s assertions that a parallel structure of personification in the artwork and the human exists. It also explains his claims that artworks themselves appear to be in a kind of dialogue. (shrink)

This paper outlines a first attempt to model the special constraints that arise in language processing in conversation, and to explore the implications such functional considerations may have on language typology and language change. In particular, we focus on processing pressures imposed by conversational turn-taking and their consequences for the cultural evolution of the structural properties of language. We present an agent-based model of cultural evolution where agents take turns at talk in conversation. When the start of planning for the (...) next turn is constrained by the position of the verb, the stable distribution of dominant word orders across languages evolves to match the actual distribution reasonably well. We suggest that the interface of cognition and interaction should be a more central part of the story of language evolution. (shrink)

We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and super-lowness for sets of natural numbers. A computable non-decreasing unbounded function h is called an order function. Informally, a set A is strongly jump-traceable if for each order function h, for each input e one may effectively enumerate a set Te of possible values for the jump JA, and the number of values enumerated is at most h. A′ (...) is well-approximable if can be effectively approximated with less than h changes at input x, for each order function h. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and strong jump-traceability in terms of Kolmogorov complexity. We also investigate other properties of these lowness properties. (shrink)

Typed λ-calculus uses two abstraction symbols which are usually treated in different ways: λx:*.x has as type the abstraction Πx:*.*, yet Πx:*.* has type □ rather than an abstraction; moreover, C is allowed and β-reduction evaluates it, but C is rarely allowed. Furthermore, there is a general consensus that λ and Π are different abstraction operators. While we agree with this general consensus, we find it nonetheless important to allow Π to act as an abstraction operator. Moreover, experience with AUTOMATH (...) and the recent revivals of Π-reduction as in [11, 14], illustrate the elegance of giving Π-redexes a status similar to λ-redexes. However, Π-reduction in the λ-cube faces serious problems as shown in [11, 14]: it is not safe as regards subject reduction, it does not satisfy type correctness, it loses the property that the type of an expression is well-formed and it fails to make any expression that contains a Π-redex well-formed. In this paper, we propose a solution to all those problems. The solution is to use a concept that is heavily present in most implementations of programming languages and theorem provers: abbreviations or let-expressions. We will show that the λ-cube extended with Π-conversion and abbreviations satisfies all the desirable properties of the cube and does not face any of the serious problems of Π-reduction. We believe that this extension of the λ-cube is very useful: it gives a full formal study of two concepts that are useful for theorem proving and programming languages. (shrink)

The Pythagorean Life is the most extensive surviving source on Pythagoreanism, and has wider interest as an account of the religious aspirations of late antiquity. "...admirably clear translation and sensible introduction"--The Classical...

In lieu of an abstract, here is a brief excerpt of the content:diacritics 30.2 (2000) 113-126 [Access article in PDF] Dissenting Words:A Conversation with Jacques Rancière 1 Davide Panagia:In your writings you highlight the political efficacy of words. In The Names of History, for instance, this emphasis is discussed most vividly in terms of what you refer to as an "excess of words" that marks the rise of democratic movements in the seventeenth century. Similarly, in On The Shores of Politics, (...) you begin your discussion with an excursus on the end of politics as the end of the promise. Finally, in Dis-agreement you speak of "the part of those who have no-part" as voicing a "wrong" for the sake of equality.In each of these instances, however, your treatment of words (and language more generally) is very different from those thinkers of the "linguistic turn" in political philosophy who expound on an ethics of deliberation as the first virtue of modern democracies. For that matter, your approach is quite different from those thinkers who focus on the aporias of language as such.Could you discuss this thematic of the proliferation of words in your thinking about democratic politics?Would it be fair to characterize your research on and exposition of democratic thinking as a "poetics of politics"?Rancière's Reply:In order to address your question adequately, it would be wise to enlarge the sense of "linguistic turn" you invoke. In its most generally accepted sense, the linguistic turn in philosophy consists in ascribing to linguistic processes certain phenomena and specifiable modes of relating objects attributed, in a previous instance, either to factual processes or lines of thought. This approach is not limited to the two figures you invoke in your question. The linguistic turn also has two stages of development that, from my experience, have been more noticeable in France than in the United States. The first phase, then, emerged with Lévi-Strauss and his structural approach to social relations founded on a linguistic model of relationality, subsequently reprised in Lacan's psychoanalytic notion that "the unconscious is structured like a language" that, in its turn, conjoins the energetic mental processes Freud discusses to linguistic practices. The primacy of "the linguistic" thus granted language all the properties of the Freudian unconscious [End Page 113] along with those of a Marxist notion of infrastructure. The Saussurian opposition between langue and parole provided a privileged status to a linguistic model whose role was that of a general law that unconsciously structures the behavior of individuals and societies. It is on the basis of these parameters that the structuralist moment of the linguistic turn was constituted. At one and the same time, the analysis of speech acts became first and foremost a "symptomatic" analysis of those procedures of misrecognition that linguistically structured both the behavior of individuals and social relations. When we "read" Le Capital with Althusser, the interpretive and methodological schema for linguistic phenomena operated like a kind of "policing of the enunciated": that is, a search for those unsuccessful (i.e., inadequate) modes of expression that exemplify such symptomatic procedures of misrecognition.The second phase of the linguistic turn constituted itself more ambiguously. For those who shared intellectual experiences similar to my own, this version involved a critique of the langue/infrastructure model; that is, a further and more favorable consideration of the value of the political and the linguistic games therein that, according to the Althusserian/Marxist model (and, indeed, with structuralism more generally), were to be treated as ideological artifacts. In a very real sense, it all began with the May '68 assertion that "we are all German Jews"--an entirely ideological statement, the validity of which, if analyzed at the level of its content, one finds to rest entirely on the capacity to overturn the political relationship between the order of designations and that of events by emphasizing the gap that separates subject and predicate. From there, an entire field of understanding speech acts as political gestures opened up: a field that reconfigured the division between words and things while rearranging the distinction between legitimate... (shrink)

Large exchange markets, big money, interest-bearing credit, big landholdings, proletarian masses, imperial expansion and even ‘capital’ or ‘salaried workers’, are not in themselves specific, unique institutional features of Modern Capitalism. This article argues that the features that characterize Modern Capitalism are a massive emergence of ‘free’, monetized wage labour, a self-propelled rush to unbounded world expansion and the progressive conversion of expropriated and privatized land into a monetized commodity, as well as a radically new use of the ancestral social institutions (...) of money and credit as an instrument for financing the production of commodities to obtain a surplus in the form of monetary profit, but also to generate expropriatory social debt relations. This article explains these dynamic historical forces and their importance for political philosophy and for legal and economic history and economics and sheds some light on the relationship between ‘capitalism’ and ‘modernity’. (shrink)

As I have read the scholium, it divides into three main parts, not including the introductory paragraph. The first consists of paragraphs one to four in which Newton sets out his characterizations of absolute and relative time, space, place, and motion. Although some justificatory material is included here, notably in paragraph three, the second part is reserved for the business of justifying the characterizations he has presented. The main object is to adduce grounds for believing that the absolute quantities are (...) indeed distinct from their relative measures and are not reducible to them. Paragraph five takes this up for the case of time. Paragraphs eight to twelve endeavor to do this for rest and motion by appealing to their properties, causes and effects. In arguing that absolute motion is not reducible to any particular form of the relative motion of bodies with respect to one another, and thus, as is directly argued in the third argument, must be understood in terms of motionless places, Newton thereby constructs an indirect case that absolute space is indeed something distinct from any relative space. Paragraph thirteen functions as conclusion to this line of inquiry and comments on how, in the light of this, the names of these quantities are to be interpreted in the scriptures. The third and final part consists of paragraph fourteen alone, and addresses the question: given that true motion is motion with respect to absolute space, but the parts of the latter are not perceivable, is it possible for us to know the true motions of individual bodies? Newton illustrates how this may be done from the evidence provided by their apparent motions and the forces which are the causes and effects of true motion. This forms a bridge to the body of the work insofar as the purpose of the Principia, according to Newton, is to show how this, and the converse problem, of inferring true and apparent motions from the forces, can be dealt with.Part II of this paper will appear in the next issue of Studies in History and Philosophy of Science. (shrink)