In his prefatory epistle dedicating his Naturalis Historia to Vespasian, the elder Pliny takes great pains to plead that his magnum opus is unworthy of the emperor: ‘maiorem te sciebam, quam ut descensurum hue putarem’ . Continuing in this vein, Pliny goes on to say ‘praeterea est quaedam publica etiam eruditorum reiectio’, and appeals for support to the great Cicero: ‘utitur ilia et M. Tullius extra omnem ingenii aleam positus, et, quod miremur, per aduocatum defenditur’ . Cicero's aduocatus is the (...) satirist Lucilius, from whom a mangled fragment in trochaic septenarii is then quoted: ‘nec doctissimis. Manium Persium haec legere nolo, Iunium Congum uolo.’ The sense of this fragment, which Pliny very probably quoted from the now-lost beginning of Cicero's preface to his De Re Publica, can be restored from Cicero, De Oratore 2.25: ‘nam ut C. Lucilius…dicere solebat ea quae scriberet neque ab indoctissimis se neque a doctissimis legi uelle, quod alteri nihil intelligerent, alteri plus fortasse quam ipse; quo etiam scripsit “Persium non curo legere” , “Laelium Decimum uolo” : sic ego…’. This latter passage has allowed the former to be restored, to some extent exempli gratia, to the following form in Warmington's and Krenkel's editions of Lucilius. (shrink)

In his prefatory epistle dedicating his Naturalis Historia to Vespasian, the elder Pliny takes great pains to plead that his magnum opus is unworthy of the emperor: ‘maiorem te sciebam, quam ut descensurum hue putarem’. Continuing in this vein, Pliny goes on to say ‘praeterea est quaedam publica etiam eruditorum reiectio’, and appeals for support to the great Cicero: ‘utitur ilia et M. Tullius extra omnem ingenii aleam positus, et, quod miremur, per aduocatum defenditur’. Cicero's aduocatus is the satirist Lucilius, (...) from whom a mangled fragment in trochaic septenarii is then quoted: ‘nec doctissimis. Manium Persium haec legere nolo, Iunium Congum uolo.’ The sense of this fragment, which Pliny very probably quoted from the now-lost beginning of Cicero's preface to his De Re Publica, can be restored from Cicero, De Oratore 2.25: ‘nam ut C. Lucilius…dicere solebat ea quae scriberet neque ab indoctissimis se neque a doctissimis legi uelle, quod alteri nihil intelligerent, alteri plus fortasse quam ipse; quo etiam scripsit “Persium non curo legere”, “Laelium Decimum uolo” : sic ego…’. This latter passage has allowed the former to be restored, to some extent exempli gratia, to the following form in Warmington's and Krenkel's editions of Lucilius. (shrink)

This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan’s laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this (...) principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes. (shrink)

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De (...) class='Hi'>Morgan monoids may be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

The standard Brouwer–Zadeh poset Σ(H) is the poset of all effect operators on a Hilbert space H, naturally equipped with two types of orthocomplementation. In developing the theory, the question occured if (when) Σ(H) fulfils the de Morgan property with respect to both orthocomplementation operations. In Ref.3 the authors proved that it is the case provided dimH<∞, and they conjectured that if dimH=∞, then the answer is in the negative. In this note, we first give a somewhat simpler proof (...) of the known result for dimH<∞, and then we give a proof to the conjecture: We show that if dimH=∞, then the de Morgan property is not valid. (shrink)

A great deal is known about the technical issues surrounding the introduction of Hugo De Vries's mutation theory and the subsequent development of the modern genetical theory of natural selection. But so far little has been done to relate these events to the wider issues of the time. This article suggests that extra-scientific factors played a significant role, and substantiates this by comparing De Vries's respect for the original Darwinian spirit with Thomas Hunt Morgan's use of the mutation theory (...) as part of an attack on the whole philosophy of Darwinism. In particular, it is argued that Morgan's attitude was dictated by his moral objections to the picture of a world dominated by struggle. (shrink)

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 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. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of the (...) founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan's own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh. (shrink)

The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.

Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But (...) the 4-valued logic is deductive in nature, and its matrix is discrete: there are just four values. In this paper I investigate embedding the 4-valued logic into a context of probability. Jøsang's Subjective Logic introduced uncertainty to allow for degrees of belief, disbelief, and uncertainty. We extend this so as to allow for two kinds of uncertainty— that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflicted). Jøsang's "Opinion Triangle" becomes an "Opinion Tetrahedron" and the 4-values can be seen as its vertices. I make/prove various observations concerning the relation of non-classical "probability" to non-classical logic. (shrink)

Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorousFrom the introduction:"If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use such (...) arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others-I should feel quite at my ease. I should certainly say, My little friends, the case of each one of you is destroyed by the rest. I intend to show flies in the swarm, with a few larger animals, for reasons to be given.In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many.I have insisted on the isolated character of the dissentients, as an element of the a priori probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; but an organized opposition, supported by the efforts of many acting in concert, appealing to common arguments and experience, with perpetual succession and a common seal, as the Queen says in the charter, is, be the merit of the schism what it may, a thing wholly different from the case of the isolated opponent in the mode of opposition to it which reason points out.During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular.". (shrink)

This book is one of the series entitled "Rare Masterpieces of Philosophy and Science" and it is entitled to both distinctions. The papers collected here are virtually unobtainable except in the most complete libraries; and de Morgan's work is clearly that of a master-between Boole and Frege, he is the leading figure in formal logic. The papers found herein include the series of six on the syllogism published between 1846 and 1868, together with three shorter notes concerning logical phraseology, (...) a syllabus for a system of logic, and an encyclopaedia article whose topic is logic. The editor has added a useful introduction which, among other important services, allows us to see de Morgan, not, as we today see him, as a founder of symbolic logic, but as a rival of William Hamilton, engaged in controversy much of his life.—P. J. M. (shrink)

Simply put, charter schools have not lived up to their advocates’ promise of equity. Using examples of tangible civil rights gains of the twentieth century and extending feminist theories of invisible labor to include the labor of democracy, the authors argue that the charter movement renders invisible the labor that secured civil protections for historically marginalized groups. The charter movement hangs a quality public education—previously recognized as a universal guarantee—on the education consumer’s ability to navigate a marketplace. The authors conclude (...) that the neoliberal agenda of positioning choice as the best mechanism for securing an education rolls back the rights that were already secured through the labor of democracy. (shrink)