General Quotes - page 94
The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with the general method of Frege, Whitehead and Russell. Following these authorities, I hold that mathematics is part of logic, and so belong to what may be called the logical school as opposed to the formalist and intuitionist schools. I have therefore taken Principia Mathematica as a basis for discussion and ammendment; and believe myself to have discovered how, by using the work of Mr Ludwig Wittgenstein, it can be rendered free from the serious objections which have caused its rejection by the majority of German authorities, who have deserted altogether its line of approach.
Frank P. Ramsey
[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are... two distinct categories of things of which an account must be given-the ideas or concepts of mathematics, and the propositions of mathematics. ...the great majority of writers on the subject have concentrated their attention on the explanation of one or the other... and erroneously supposed that a satisfactory explanation of the other would immediately follow.
Frank P. Ramsey
Our Lord's new doctrines were the new wine, while the Jewish sects were the old wine-skins. Suppose that our Lord had joined one of those sects and had begun a reform in it: what would have been the result? There can be no doubt that the new truths, if received, would have broken up that sect completely. The power of its organization, built largely upon sectarian pride, and cemented by errors, superstitions and human traditions, would forthwith have been destroyed, and the new doctrines would have been left stranded - hampered, too, by all the old errors and traditions of that sect, and held responsible for its past record by the world in general.
Charles Taze Russell
The feeling of uneasiness and insecurity, if not bound by the chains of some sect, is general. It is begotten of the false idea, first promulgated by Papacy, that membership in an earthly organization is essential, pleasing to the Lord and necessary to everlasting life. These earthly, humanly organized systems, so different from the simple, unfettered associations of the days of the apostles, are viewed involuntarily an almost unconsciously by Christian people as so many Heaven Insurance Companies, to some one of which money, time, respect, etc., must be paid regularly, to secure heavenly rest and peace after death. Acting on this false idea, people are almost as nervously anxious to be bound by another sect, if they step out of one, as they are if their policy of insurance has expired, to have it renewed in some respectable company.
Charles Taze Russell
After Indira Gandhi revoked the emergency and declared general elections, he contested for General Elections, won from the Nandyal Parliamentary Constituency and became Speaker in the Lok Sabha as the democracy had been restored after two years of emergency, which came about through democratic process of the ballot.
Neelam Sanjiva Reddy
An explanation of a phenomenon is regarded, apparently instinctively, as the most general possible when it is a mechanical explanation. The "mechanism" of the process is the ultimate goal of experiment. Now this mechanism in general lies beyond the range of the senses; either by reason of their limitations, as in the case of the atomic structure of matter, or by the very nature of the supposed mechanism, as in the theory of the ether. The only way to bridge the gap between the machinery of the physical process and the world of sense-impressions is to think out some consequence of that mechanism. This we will call the hypothesis. The hypothesis, resting still on the mechanical basis, is yet beyond the range of direct experimental investigation; but if, by mathematical reasoning, a consequence of the hypothesis can be deduced, this will often lie within the range of experimental inquiry, and thus a test of the soundness of the original mechanical conception may be instituted.
J. R. Partington
Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison with regard to quantity is accomplished in the case of discrete magnitudes by counting, in the case of continuous magnitudes by measuring. Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case also we can only determine the more or less and not the how much. The researches which can in this case be instituted about them form a general division of the science of magnitude in which magnitudes are regarded not as existing independently of position and not as expressible in terms of a unit, but as regions in a manifoldness.
Bernhard Riemann
Zend-Avesta, a truly life giving word creating new life in knowledge as in faith! ...As Fechner in his Nanna sought to show that plants have souls, so the point of departure of his contemplations in the Zend-Avesta is the doctrine that the stars have souls. The method he employs is not that of the abstraction of general laws by induction and the application and testing of these in the explanation of nature, it is analogy. He compares the earth with our own organism, which we know to be endowed with a soul. He searches out not merely in a one-sided way the similarities, but does equal justice to the dissimilarities, too, and so arrives at the conclusion that all the former show the earth to be a being with a soul, and that all the latter indicate that it is a being with a soul far higher than our own.
Bernhard Riemann
Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisations. According as there exists among these specialisations a continuous path from one to another or not, they form a continuous or discrete manifoldness; the individual specialisations are called in the first case points, in the second case elements, of the manifoldness.
Bernhard Riemann
That such comparisons with non-arithmetic notions have furnished the immediate occasion for the extension of the number-concept may, in a general way, be granted (though this was certainly not the case in the introduction of complex numbers); but this surely is no sufficient ground for introducing these foreign notions into arithmetic, the science of numbers.
Richard Dedekind
Because he did not care about his country, Lenin was prepared to promise everybody whatever they wanted without giving much thought to the future. The peasants wanted private land for their communes? Let them take it: eventually all the land will be confiscated and collectivized anyway. Until then, ‘looting the loot' will win over, or at least neutralize, the peasantry. The workers demand to run the factories? Even though ‘workers' control is a detestable syndico-anarchist slogan, there is no harm in granting their desires-for the time being. Once industries have been nationalized and subjected to general economic plan of production, ‘workers' control' will vanish of itself.
Richard Pipes
They have two distinguishing characteristics. The vast majority of them are laborers, and, as a rule, they expect the violent overthrow of existing institutions by revolution to precede the introduction of the socialistic state. I would not, by any means, say that they are all revolutionists, but the most of them undoubtedly are...
The most general demands of the social democrats are the following: The state should exist exclusively for the laborers; land and capital must become collective property, and production be carried on unitedly. Private competition, in the ordinary sense of the term, is to cease.
Richard T. Ely
There is always the danger that the use of traditional grammatical terms with reference to a wide variety of languages may be taken to imply a secret belief in universal grammar. Every analysis of a particular ‘language' must of necessity determine the values of the ad hoc categories to which traditional names are given. What is here being sketched is a general linguistic theory applicable to particular linguistic descriptions, not a theory of universals for general linguistic description.
John Rupert Firth
We form at La Faucille now a little colony where concord and happiness reign, and have not even for enemies the bears of the country... We are situated in a very movable manner, however, on one of the mountains of the Jura, where the inn is the most remarkable building. For I must tell you that we enjoy the company of an unaccountable old man of sixty, who resembles poor Father Colombert as if it were he himself. He is of the ancient nobility. He held the grade of General under the Restoration, having had possessions, which he has lost by the changes. He consoles himself now by carrying all his fortune. With him, a much rarer lot it consists in good humour and strength and philosophy. I have never seen a more excellent man. He is here to search for plants and stones.
Théodore Rousseau
Just as Mycenaean civilisation is a development of the Minoan, so too the Philistines who came to Palestine from Caphtor were an offshoot of the same general Aegean civilisation. ...until David's victories around 1000 B. C., the Philistines dominated the Hebrews, so that, militarily at least, the Davidic monarchy was the Hebrew response to the Philistine stimulus. ...the Achaeans, Trojans, Philistines and Hebrews during the closing centuries of the second millennium belonged to the same international complex of peoples, sharing many conventions and institutions, specifically in military matters.
Cyrus H. Gordon
Currency competition and free banking might increase the efficiency of the financial system, and bring some small triangle welfare gains. But the key question is whether their adoption would improve macroeconomic performance. Even though Salin argues (p. 281) that ‘the best system is that which produces the least inflation', fluctuations in output are also expensive.
Hayek states that the adoption of his proposal would end recessions. There is absolutely no reason to believe that. Nineteenth century history is evidence that free banking and currency issue, in the wrong legal and regulatory framework, can produce rather than reduce instability. The proponents of free banking and currency issue in this volume do not go much beyond a general belief in competition in justifying their views; they have certainly not explored the necessary legal and regulatory environment in any detail.
Stanley Fischer
Among the various subjects of the inquiry, however, which, inconsequence of the vague use of language, are comprehended under the general title of metaphysics, there are some, which are essentially distinguished from the rest, both by the degree of evidence which accompanies their principles, and by the relation which they bear to the useful sciences and arts: and it has unfortunately happened, that these have shared in that general discredit, into which the other branches of metaphysics have fallen. To this circumstance is probably to be ascribed, the little progress which has hitherto been made in the PHILOSOPHY OF THE HUMAN MIND; a science, so interesting in its nature, and so important in its applications, that it could scarcely have failed, in these inquisitive and enlightened times, to have excited a very general attention, if it had not accidentally been classed, in the public opinion with the vain and unprofitable disquisitions of the schoolmen.
Dugald Stewart
