John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...) argument, a particularly difficult task in Venn diagrams for more than four sets. Carroll diagrams can represent existential propositions easily, so they are capable of clearly representing more complex problems than Venn's system can. Finally, both Carroll and Venn diagrams are maximal, in the sense that no additional logic information like inclusive disjunctions is able to be represented by them. Carroll's logic diagrams and logic trees constitute his visual logic system. (shrink)

Lewis Carroll: Logic Charles L. Dodgson, 1832-1898, was a British mathematician, logician, and the author of the ‘Alice’ books, Alice’s Adventures in Wonderland and Through the Looking Glass and What Alice Found There. His fame derives principally from his literary works, but in the twentieth century some of his mathematical … Continue reading Lewis Carroll: Logic →.

Lewis Carroll: Logic Charles L. Dodgson, 1832-1898, was a British mathematician, logician, and the author of the ‘Alice’ books, Alice’s Adventures in Wonderland and Through the Looking Glass and What Alice Found There. His fame derives principally from his literary works, but in the twentieth century some of his mathematical … Continue reading Lewis Carroll: Logic →.

Dans une lettre adressée à Bertrand Russell, le 17 mai 1905, Hugh MacColl raconte avoir abandonné l’étude de la logique après 1884, pendant près de treize ans, et explique que ce fut la lecture de l’ouvrage de Lewis Carroll, Symbolic Logic (1896), qui ralluma le vieux feu qu’il croyait éteint. Dès lors, il publie de nombreux articles contenant certaines de ses innovations majeures en logique. L’objet de cet article est de discuter la familiarité de MacColl et son appréciation du travail (...) de Carroll, et de comprendre comment cela l’amena à réinvestir le domaine de la logique. Rien n’indique que les deux hommes se soient jamais rencontrés ou aient échangé une correspondance personnelle. Cependant, MacColl recensa dans le journal The Athenaeum plusieurs ouvrages de Carroll, essentiellement en géométrie et en logique. Souvent, Carroll répondait aux critiques de MacColl dans les éditions suivantes de ses ouvrages. Une discussion de ces sources fournit des éclaircissements intéressants sur les investigations mathématiques et logiques de MacColl et Carroll. (shrink)

Dans une lettre adressée à Bertrand Russell, le 17 mai 1905, Hugh MacColl raconte avoir abandonné l’étude de la logique après 1884, pendant près de treize ans, et explique que ce fut la lecture de l’ouvrage de Lewis Carroll, Symbolic Logic (1896), qui ralluma le vieux feu qu’il croyait éteint. Dès lors, il publie de nombreux articles contenant certaines de ses innovations majeures en logique. L’objet de cet article est de discuter la familiarité de MacColl et son appréciation du travail (...) de Carroll, et de comprendre comment cela l’amena à réinvestir le domaine de la logique. Rien n’indique que les deux hommes se soient jamais rencontrés ou aient échangé une correspondance personnelle. Cependant, MacColl recensa dans le journal The Athenaeum plusieurs ouvrages de Carroll, essentiellement en géométrie et en logique. Souvent, Carroll répondait aux critiques de MacColl dans les éditions suivantes de ses ouvrages. Une discussion de ces sources fournit des éclaircissements intéressants sur les investigations mathématiques et logiques de MacColl et Carroll. (shrink)

In the period 1893–1897 Charles Dodgson, writing as Lewis Carroll, published two books and two articles on logic topics. Manuscript material first published in 1977 together with letters and diary entries provide evidence that he was working toward a visual proof system for complex syllogistic propositional logic based on a mechanical tree method that he devised.

Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the (...) first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown nineteenth century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on ‘implication as inference’ where we explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas related to the subjects of this paper. (shrink)

Charles L. Dodgson's reputation as a significant figure in nineteenth-century logic was firmly established when the philosopher and historian of philosophy William Warren Bartley, III published Dodgson's ?lost? book of logic, Part II of Symbolic Logic, in 1977. Bartley's commentary and annotations confirm that Dodgson was a superb technical innovator. In this paper, I closely examine Dodgson's methods and their evolution in the two parts of Symbolic Logic to clarify and justify Bartley's claims. Then, using more recent publications and unpublished (...) letters, I argue that Dodgson approached the elimination problem in class logic differently than his contemporaries, and in doing so, anticipated several important concepts and techniques in automated deductive reasoning. These materials also provide additional insight into his reasons for writing this book. (shrink)

The question of Theodicy demands a reasonable justification of the nature, structures and goals of evil and suffering in the world. The paper attempts to explain the reasons for its presence in our lives and seeks to unveil its principles. If God is all knowing, almighty and also merciful, we must face the problem of the presence of evil and suffering in this world. The main goal of the paper is to show the way the New Testament deals with this (...) question, and further to show to what extent it has influenced the life of Christians from the point of view of teleology. (shrink)

In matters of governance, is believing subject to ethical standards? If so, what are the criteria how relevant are they in our personal and political culture today? The really important matters in politics and governance necessitate a confidence that our beliefs will lead dependably to predictable and verifiable outcomes. Accordingly, it is unethical to hold a belief that is founded on insufficient evidence or based on hearsay or blind acceptance. In this paper, we demonstrate that the pragmatist concept of truth (...) best meets this standard for ethically held belief in matters of politics and governance. Currently, these standards are abused by the gaslighting and distortion characteristics of the often social media driven ‘misinformation society’. The legitimacy and trust in our institutions and leadership that is requisite for good governance is challenged thereby, threatening the viability of our republic. (shrink)

Si prescindiéramos de la composición acto-potencial entre «essentia» y «esse» en la línea del ente creado, necesariamente nos veríamos arrojados al monismo spinozista, esto es, a admitir que solamente hay una substancia (a) única, (b) infinita, (c) increada, (d) necesariamente existente, (e) acto puro, (f) identificada, en último término, con la misma substancia de Dios. En el capítulo LII del segundo libro de la Summa contra gentiles, Santo Tomás obtiene esos atributos divinos a partir de siete argumentos que tienen como (...) objetivo probar que, en el caso que no se aceptara la diferencia real entre essentia y esse en el ente finito —tanto material como inmaterial—, necesariamente deberíamos reconocer que sólo hay una substancia con los seis atributos anteriormente mencionados (cada argumento da lugar a un atributo distinto, exceptuando los dos primeros que desembocan en el mismo, a saber, el de la unicidad). En el artículo presente, siguiendo la interpretación de Norberto del Prado, nos proponemos exponer cómo puede refutarse el monismo spinozista desde la doctrina de Santo Tomás en dos etapas: la primera viene representada por el ya citado capítulo de la Summa contra gentes; la segunda, por la cuarta vía (Summa Theologiae, I, q.2, a.3). (shrink)

An anthology of substantive selections on human nature from fifteen authors: Plato, Aristotle, Mencius, Seneca, Augustine, Aquinas, Descartes, Hume, Marx, Nietzsche, Freud, Sartre, Beauvoir, B. F. Skinner, and E. O. Wilson. Reprinted in 2015 by Biblio Publishing, ISBN 978-1-62249-267-1.

Epikurs Lehre erfreut sich wachsender Aufmerksamkeit. Doch verdient auch die Geschichte des Epikureismus, insbesondere der Kaiserzeit, Interesse. Keineswegs verschwindet die diesseits orientierte Lehre Epikurs trotz wachsendem Streben der Philosophie nach Transzendenz in der Spatantike. Eine Analyse paganer wie auch christlicher Autoren zeigt, dass insbesondere Epikurs Ethik und ihr Angebot praktischer Lebenshilfe als Teil einer "praeparatio philosophica" uberlebt, ins Mittelalter vermittelt wurde und in der Renaissance Auferstehung feierte. Die Vortrage dieses Bandes begeben sich deshalb auf Spurensuche. Unter verschiedenen Gesichtspunkten gehen sie (...) der Tradition des Epikureismus in der spaten Republik und der Kaiserzeit nach und folgen ihnen bis zur Renaissance. Inhalt: Einleitung Graziano Arrighetti: Filodemo fra poesia, mito e storia Marcello Gigante: Seneca, ein Nachfolger Philodems? Dieter Timpe: Der Epikureismus in der romischen Gesellschaft der Kaiserzeit Martin F. Smith: Digging up Diogenes: New Epicurean texts from Oinoanda in Lycia Diskin Clay: Diogenes and his gods Matthias Baltes: Epikureische Theologie Mauro Tulli: L'epitome die Epicuro e la trasmissione del sapere nel Medioplatonismo Carlos Levy: Philon d'Alexandrie et l'epicurisme Tiziano Dorandi: Plotina, Adriano e gli Epicurei di Atene Franco Ferrari: La falsita delle asserzioni relative al futuro: un argomento epicureo contro la mantica in Plut. Pyth. orac. 10 Keimpe A. Algra: The Treatise of Cleomedes and its Critique of Epicurean Cosmology Christoph Markschies: Epikureismus bei Origenes und in der origenistischen Tradition Jose Kany-Turpin: Lactance, un critique mesestime de l'epicurisme Therese Fuhrer: Zwischen Skeptizismus und Platonismus: Augustins Auseinandersetzung mit der epikureischen Lehre in conf. 6 Dominic O'Meara: Epikur bei Simplikios Clemens Zintzen: Epikur in der Renaissance Michael Erler: Epikur in Raffaels "Schule von Athen"? Register. (shrink)