Leonhard Euler (1707–1783) treated in his study „De motu vibratorio tympanorum [6], published in 1766, the theory of the vibrating rectangular and circular membrane mathematically in such a comprehensive way that little more had to be added, considering today's standards. However, he omitted to interprete his results physically. Therefore his uncomparable work found little recognition, especially in the field of musical accoustics.

. In logic, diagrams have been used for a very long time. Nevertheless philosophers and logicians are not quite clear about the logical status of diagrammatical representations. Fact is that there is a close relationship between particular visual (resp. graphical) properties of diagrams and logical properties. This is why the representation of the four categorical propositions by different diagram systems allows a deeper insight into the relations of the logical square. In this paper I want to give some examples.

This collection sheds new light on the nature, role and practice of philosophy and science in the renewed Berlin Academy from the mid-1740s to the 1790s, and in so doing provides a robust new instalment of materials for the broader task of constructing a historiography of philosophy at this important Enlightenment institution. The collection ranges from discussions of the roles of philosophy and natural philosophy in the formation of the reinvigorated Academy in the mid-1740s, to conceptions of the correct philosophical (...) methodology to be deployed by the Academy. It provides the first ever study of the nature and arrangement of the new classes of the Academy, and a fresh appraisal of the Academy's methodological eclecticism. One recurring theme is the status of metaphysics: there are studies of both special metaphysics, including the study of the soul; general metaphysics, that is, the study of being in general; and foundational metaphysical principles and concepts, such as Maupertuis's Principle of least action, Euler's concept of space and Lambert's notion of an experimental metaphysics. The collection also takes the study of the Academy in new directions through focused studies of important figures whose writings deserve to be better understood, such as Jean Bernard Merian, Louis de Beausobre, Jean Henri Samuel Formey and Johann Georg Sulzer. (shrink)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

Free rides and observational advantages occur in visualizations when they reveal facts that must be inferred from an alternative representation. Understanding whether these concepts correspond to cognitive advantages is important: do they facilitate information extraction, saving the ‘deductive cost’ of making inferences? This paper presents the first evaluations of free rides and observational advantages in visualizations of sets compared to text. We found that, for Euler and linear diagrams, free rides and observational advantages yielded significant improvements in task performance. (...) For Venn diagrams, whilst their observational advantages yielded significant performance benefits over text, this was not universally true for free rides. The consequences are two-fold: more research is needed to establish when free rides are beneficial, and the results suggest that observational advantages better explain the cognitive advantages of diagrams over text. A take-away message is that visualizations with observational advantages are likely to be cognitively advantageous over competing representations. (shrink)

This article provides a spatial analysis of the conceptual framework of fluid dynamics during the nineteenth century, focusing on the transition from the Euler equation to the Navier–Stokes equation. A dynamic version of Peter Gärdenfors's theory of conceptual spaces is applied which distinguishes changes of five types: addition and deletion of special laws; change of metric; change in importance; change in separability; addition and deletion of dimensions. The case instantiates all types but the deletion of dimensions. We also (...) provide a new view upon limiting case reduction at the conceptual level that clarifies the relation between the predecessor and successor conceptual framework. The nineteenth-century development of fluid dynamics is argued to be an instance of normal science development. (shrink)

This reissue of his collection of early essays, Logico-Linguistic Papers, is published with a brand new introduction by Professor Strawson but, apart from minor ...

Name der Zeitschrift: Das Mittelalter Jahrgang: 19 Heft: 1 Seiten: 72-85.

A complete system of classical Aristotelian logic intended for honors high school and college.

Ohne Rücksicht auf disziplinäre Schranken bringt dieses Buch verschiedene nicht-reduktionistische Lerntheorien miteinander ins Gespräch. In einem offenen Diskurs, der die Konzepte zueinander in Beziehung setzt, werden die unterschiedlichen Perspektiven kritisch abgewogen und hinsichtlich ihrer Stärken und Schwächen diskutiert.

Delo se loteva vprašanja aktualnosti pojma subjekta v filozofiji in politiki skozi analizo tistih avtorjev, ki so ga domnevno najbolj radikalno pokopali: pokaže, da vznik radikalno novega in problematika subjekta zavzema osrednje mesto v Deleuzovi filozofiji, kakor tudi v Lyotardovi pozni misli posvečeni praznini, v Foucaultovi obravnavi biopolitike in biooblasti, v delu Negrija in Hardta o Imperiju, ter nazadnje v Badioujevi predelavi temeljnih filozofskih kategorij biti, resnice in subjekta, na osnovi katerih je dandanes znova možna renesansa filozofije. Ta ima po (...) Badiouju štiri razsežnosti, ki se v delu Vznik subjekta nenehno prepletajo: »V osnovi želja filozofije implicira razsežnost upora: ni filozofije brez nezadovoljstva mišljenja v njegovem soočenju s svetom, kakršen je. Pa vendar želja filozofije vključuje tudi logiko: to je, prepričanje v moč argumenta in uma.«. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next (...) twenty or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

In this short but meaty book, Peter Unger questions the objective answers that have been given to central problems in philosophy. As Unger hypothesizes, many of these problems are unanswerable, including the problems of knowledge and scepticism, the problems of free will, and problems of causation and explanation. In each case, he argues, we arrive at one answer only relative to an assumption about the meaning of key terms, terms like "know" and like "cause," even while we arrive at (...) an opposite answer relative to quite different assumptions, but equally arbitrary assumptions, about what the key terms mean. (shrink)

Narrative thinking -- Narrative thinking about one's past -- Grief : a case study -- Narrative thinking about one's future -- Self-forgiveness : a case study -- The narrative sense of self -- Narrative, truth, life, and fiction.

While Hermann Levin Goldschmidt didn’t read Yiddish anarchists, there seems to have been a convergent evolution in their thinking. Goldschmidt’s looking up to Jewish lore as a source of liberating creativity is commonly encountered in Yiddish anarchist texts. His view of action as a constant response to internal and external challenges in the struggle for an open future is developed by Isaac Nachman Steinberg on the basis of nineteenth-century vitalism. Goldschmidt’s theory of anarchist individualism as willed self-limiting solidarity has a (...) compelling parallel in Hillel Solotaroff’s view of history. His use of impressionism and photography to eternalize the immediacy of human actuality is akin to Rudolf Rocker’s championing of decadent literature. In both cases, the goal of anarchism is not a dictatorship of the former downtrodden, but a continuous and contradictory evolution of freedom in ever-changing contexts. (shrink)

The norm of assertion, to be in force, is a social norm. What is the content of our social norm of assertion? Various linguistic arguments purport to show that to assert is to represent oneself as knowing. But to represent oneself as knowing does not entail that assertion is governed by a knowledge norm. At best these linguistic arguments provide indirect support for a knowledge norm. Furthermore, there are alternative, non-normative explanations for the linguistic data (as in recent work from (...) Van Elswyk). Direct arguments would rely on normative judgments about the permissibility or impermissibility of assertions with and without the speaker knowing the content asserted. John Turri's work experimental results purport to show that our norm of assertion is factive, and probably knowledge. But as a number of recent experimentalists (Kneer, Reuter and Broessel, Marsili and Wiegmann) have shown, Turri's results rely on the problemmatic use of 'should' as in 'Maria should assert that she owns a 1990 watch.' Correcting for this, these experimentalists provide strong evidence that our norm of assertion is not factive. The standard reply to evidence like this from the assertion of unlucky falsehoods is the excuse maneuver. But Marsili and Wiegmann, following Turri's protocol for testing for excuse validation, show that participants who judge that assertions unlucky falsehoods are permissible are not guilty of excuse validation. Given our current understanding of the experimental evidence, knowledge is not our norm of assertion. (shrink)

Metz holds that we can use African communal ethics to constitute global economic practices such as appropriation, production, distribution and consumption in such a way that promotes harmonious relations. In this article, I will show that Metz’s reformist approach to constituting the global economic practices is problematic as it fails to deal with the fundamental problem that pertains to a racialised world order that is structurally configured by coloniality of being. I will show that reformist approaches such as Metz’s use (...) of African communal ethics to constitute global economic practices in a way that promotes harmonious relations are undesirable attempts that are opposed and curtailed by a structural racialised logic/ontology of the world that governs and supervises the evolution of the world economic structures and practices in a way which undermines harmonious relations and in a way which causes economic marginalisation and impoverishment of historically disadvantaged indigenous Africans. (shrink)

Philosophy of music has flourished in the last thirty years, with great advances made in the understanding of the nature of music and its aesthetics. Peter Kivy has been at the center of this flourishing, and now offers his personal introduction to philosophy of music, a clear and lively explanation of how he sees the most important and interesting philosophical issues relating to music. Anyone interested in music will find this a stimulating introduction to some fascinating questions and ideas.

Abstractabstract:Karl Marx’s acerbic observation in the opening lines of The Eighteenth Brumaire that “all facts and personages of great importance in world history occur the first time as tragedy, the second as farce” may be profitably applied to a reconsideration of literary farce sui generis, a genre represented in this article by a long-neglected work of utopian fiction, Archibald Marshall’s Upsidonia (1915). Although Upsidonia’s current disregard is arguably undeserved, the article’s chief interest is not to reclaim the novel on aesthetic (...) grounds but to illuminate the mechanics of what Marx would call its “serious buffoonery.” In its persistent reversal of capitalist principles and relations, Upsidonia naturally invites readers to revisit Marx, whose mordant gambit may serve as a key to Marshall’s own farcical plot and praxis, rooted in return and repetition, the essential maneuvers of farce itself. (shrink)

This introduction by leading scholar Peter Trawny is the first to tackle the Black Notebooks, whose recent publication revealed the extent of Heidegger's anti-Semitism. Trawny directly confronts the most problematic aspects of Heidegger's thought, also fully surveying his work, from early writings to his magnum opus, Being and Time.

The so-called "Theology of Aristotle" is a translation of the Enneads of Plotinus, the most important representative of late ancient Platonism. It was produced in the 9th century CE within the circle of al-Kindī, one of the most important groups for the early reception of Greek thought in Arabic. In part because the "Theology" was erroneously transmitted under Aristotle's authorship, it became the single most important conduit by which Neoplatonism reached the Islamic world. It is referred to by such thinkers (...) as al-Fārābī, in an attempt to demonstrate the agreement between Platonism and Aristotelianism, Avicenna, who wrote a set of comments on the text, and later on thinkers of Safavid Persia including Mullā Ṣadrā. Yet the "Theology" is not just a translation. It may in fact more accurately be described as a creative paraphrase, which takes frequent liberties with the source text and even includes whole paragraphs' worth of new material. Adamson's book offers a philosophical interpretation of the changes introduced in the Arabic version. It is argued that these changes were in part intended to show the relevance of Plotinus' thought for contemporary Islamic culture, for instance by connecting the Neoplatonist theory of the First Principle to theological disputes within Islam over the status of God's attributes. At the same time the paraphrase reflects a tendency to harmonize the various strands of Greek thought, so that a critique by Plotinus of Aristotle's theory of the soul is subtly changed into a defense of Aristotle's theory against a possible misinterpretation. The upshot, or so Adamson argues, is that the "Theology" needs to be read as an original philosophical work in its own right, and understood within the context of the ʿAbbāsid era. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs (...) of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...) number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Morality and economic rationality: integrative economic ethics as the rational ethics of economic activity; Part II. Reflections on the Foundations of Economic ...

Confirmation bias is one of the most widely discussed epistemically problematic cognitions, challenging reliable belief formation and the correction of inaccurate views. Given its problematic nature, it remains unclear why the bias evolved and is still with us today. To offer an explanation, several philosophers and scientists have argued that the bias is in fact adaptive. I critically discuss three recent proposals of this kind before developing a novel alternative, what I call the ‘reality-matching account’. According to the account, confirmation (...) bias evolved because it helps us influence people and social structures so that they come to match our beliefs about them. This can result in significant developmental and epistemic benefits for us and other people, ensuring that over time we don’t become epistemically disconnected from social reality but can navigate it more easily. While that might not be the only evolved function of confirmation bias, it is an important one that has so far been neglected in the theorizing on the bias. (shrink)

Peter Anstey presents a thorough and innovative study of John Locke's views on the method and content of natural philosophy. Focusing on Locke's Essay concerning Human Understanding, but also drawing extensively from his other writings and manuscript remains, Anstey argues that Locke was an advocate of the Experimental Philosophy: the new approach to natural philosophy championed by Robert Boyle and the early Royal Society who were opposed to speculative philosophy. On the question of method, Anstey shows how Locke's pessimism (...) about the prospects for a demonstrative science of nature led him, in the Essay, to promote Francis Bacon's method of natural history, and to downplay the value of hypotheses and analogical reasoning in science. But, according to Anstey, Locke never abandoned the ideal of a demonstrative natural philosophy, for he believed that if we could discover the primary qualities of the tiny corpuscles that constitute material bodies, we could then establish a kind of corpuscular metric that would allow us a genuine science of nature. It was only after the publication of the Essay, however, that Locke came to realize that Newton's Principia provided a model for the role of demonstrative reasoning in science based on principles established upon observation, and this led him to make significant revisions to his views in the 1690s. On the content of Locke's natural philosophy, it is argued that even though Locke adhered to the Experimental Philosophy, he was not averse to speculation about the corpuscular nature of matter. Anstey takes us into new terrain and new interpretations of Locke's thought in his explorations of his mercurialist transmutational chymistry, his theory of generation by seminal principles, and his conventionalism about species. (shrink)

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

Paulo Freire : the educator, his oeuvre, and changing contexts -- Holistic interpretations of Freire's work : a critical review -- Critical literacy, praxis, and emancipatory politics -- "Remaining on the same side of the river" : neo-liberalism, party movements, and the struggle for greater coherence -- Reinventing Freire in a Southern context : the Mediterranean -- Engaging with practice : a Freirean reflection on different pedagogical sites.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

What is ethics? Where do moral standards come from? Are they based on emotions, reason, or some innate sense of right and wrong? For many scientists, the key lies entirely in biology---especially in Darwinian theories of evolution and self-preservation. But if evolution is a struggle for survival, why are we still capable of altruism? In his classic study The Expanding Circle, Peter Singer argues that altruism began as a genetically based drive to protect one's kin and community members but (...) has developed into a consciously chosen ethic with an expanding circle of moral concern. Drawing on philosophy and evolutionary psychology, he demonstrates that human ethics cannot be explained by biology alone. Rather, it is our capacity for reasoning that makes moral progress possible. In a new afterword, Singer takes stock of his argument in light or recent research on the evolution of morality.--Publisher's description. (shrink)

1,857 adults rated the grandparental solicitude they received in childhood. Through a simple model based on the evolutionary concepts of ontogenetically differentiated reproductive strategy and paternity confidence, an ordered discriminative pattern of grandparental caregiving was predicted and confirmed by solid main effects, based on 603 complete cases. The maternal grandmother was the most caring. Unlike prevalent gender stereotypes, she was followed by the maternal grandfather, the paternal grandmother, and the paternal grandfather. The preferential grandparental solicitude was not influenced by residential (...) distance, grandparent age, and availability of other grandparents. A predicted higher correlation for male than for female progenitors between solicitude and phenotypic resemblance could be confirmed. (shrink)

Children from various countries have been acknowledged and studied for their ability to philosophize, while, unfortunately, Filipino children have not received similar recognition. In this paper, I make a rather unpopular claim that Filipino children can and already are doing philosophy in their efforts to make sense of their existential conditions. “Doing philosophy” here refers to the act of being perplexed by one's own or other people's experiences and making an effort to comprehend them. Filipino children, are a vast and (...) diverse group, coming from various backgrounds, speaking different or even multiple languages, and representing rich cultures and unique circumstances. This diversity adds richness to the wide array of experiences from which existential questions can emerge. However, to truly comprehend the philosophical thinking of Filipino children, they need opportunities and guidance to explore their existential questions and solutions, regardless of how tentative or rudimentary these may seem to adults. Without such opportunities, it remains unclear to what extent their thinking engages with philosophical themes and issues. This not only offers Filipino adults a view of children’s inner worlds but also brings fresh perspectives to commonly held assumptions. (shrink)

"Divination and Human Nature" casts a new perspective on the rich tradition of ancient divination--the reading of divine signs in oracles, omens, and dreams. Popular attitudes during classical antiquity saw these readings as signs from the gods while modern scholars have treated such beliefs as primitive superstitions. In this book, Peter Struck reveals instead that such phenomena provoked an entirely different accounting from the ancient philosophers. These philosophers produced subtle studies into what was an odd but observable fact--that humans (...) could sometimes have uncanny insights--and their work signifies an early chapter in the cognitive history of intuition. Examining the writings of Plato, Aristotle, the Stoics, and the Neoplatonists, Struck demonstrates that they all observed how, setting aside the charlatans and swindlers, some people had premonitions defying the typical bounds of rationality. Given the wide differences among these ancient thinkers, Struck notes that they converged on seeing this surplus insight as an artifact of human nature, projections produced under specific conditions by our physiology. For the philosophers, such unexplained insights invited a speculative search for an alternative and more naturalistic system of cognition. Recovering a lost piece of an ancient tradition, "Divination and Human Nature" illustrates how philosophers of the classical era interpreted the phenomena of divination as a practice closer to intuition and instinct than magic. (shrink)

Von Peter Sloterdijk kann man zu Recht sagen, daß jeder seiner Aufsätze, jeder seiner Vorträge auch ein ungeschriebenes Buch ist.

The relationship of part to whole is one of the most fundamental there is, yet until now there has been no full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. This has far-reaching consequences for our understanding of such classical philosophical (...) concepts as identity, individual, class, substance and accident, matter, form, essence, dependence, and integral whole. It also enables the author to offer new solutions to long-standing problems surrounding these concepts, such as the Ship of Theseus Problem and the issue of mereological essentialism. The author shows by his use of formal techniques that classical philosophical problems are amenable to rigorous treatment, and the book represents a synthesis of issues and methods from the analytical tradition and from the older continental realist tradition of Brentano and the early Husserl. (shrink)