Often assumptions are made which lead to equations in x which cannot be solved "rationally," i.e.
These assumptions marked a definite rejection of all allegiance to Rome.
When the assumptions on which it rests are proved to be baseless, the particular scepticism is also overcome.
He also gives us " natural law " 2 - a Stoic inheritance, preserving the form of an idealist appeal to systematic requirements of reason, while practically limiting its assumptions to those of intuitionalism.
It rested on a mass of legal assumptions and subtleties, fallacious indeed, but ingenious, and, as the result proved, effective.
There is no subject of human study which may not be at some time or other of economic significance, and anything which affects the character, the ideals or the environment of man may make it necessary to modify our assumptions and our reasoning with regard to his conduct in economic affairs.
His assumptions are based upon ordinary observation and experience, and are usually accurate in proportion to his practical shrewdness and sagacity, so that he is not interested in the speculative flights of philosophy, except in so far as they influence or have influenced conduct.
But the modern conception of society or the state owes more to biology than philosophy, and actual research has destroyed more frequently than it has justified the assumptions of the older philosophical school.
As a matter of fact, discussions of method and the criticism of hypotheses and assumptions are very rarely found in early economic works.
All the assumptions we require are furnished by observation of people in the mass and the larger generalizations of statistics.
The assumptions, the definitions, the reasoning, the conclusions of the classical writers have been ruthlessly overhauled.
We may talk of the assumptions implicitly involved in Ricardo's works.
Although Kekule founded his famous benzene formula in 1865 on the assumptions that the six hydrogen atoms in benzene are equivalent and that the molecule is symmetrical, i.e.
That two pairs of hydrogen atoms are symmetrically situated with reference to any specified hydrogen atom, the absolute demonstration of the validity of OH these assumptions was first given by A.
Regarding it as important that all reasoning with reference to magnetism should be conducted without any uncertain assumptions, he worked out a mathematical theory upon the sole foundation of a few wellknown facts and principles.
Morphology becomes a farce when such assumptions are made.
That it formed the starting-point, and largely prescribed the course of thought on the subject of planetary origin is due to the simplicity of its assumptions, and the clearness of the mechanical principles involved, rather than to any cogent evidence of its truth.
They are repelled by the dryness of much of the matter, the unsuitableness of many of the topics discussed for poetic treatment, the arbitrary assumption of premises, the entire failure to establish the connexion between the concrete phenomena which the author professes to explain and these assumptions, and the erroneousness of many of the doctrines which are stated with dogmatic confidence.
This theory, however, depended upon unverified assumptions, such as the supposed silence of theologians about the creed at the beginning of the 9th century; the suggestion that the completed creed would have been useful to them if they had known it as a weapon against the heresy of Adoptianism; the assertion that no MS. containing the complete text was of earlier date than c. 813.
Since the volume at constant pressure is exactly proportional to the absolute temperature, it follows that the coefficients of expansion of all gases ought, to within the limits of error introduced by the assumptions on which we are working, to have the same value 1/273.
But in Servetus, whose execution he approved, we find an isolated, feeble revolt against assumptions which both Catholics and Protestants of all shades accepted without question.
From the standpoint of the history of enlightenment, as Harnack has observed, " Socinianism with its systematic criticism (tentative and imperfect as it may now seem) and its rejection of all the assumptions based upon mere ecclesiastical tradition, can scarcely be rated too highly.
The struggle with the Crown, which ended in independence, began at the foundation of the colony, with assumptions of power under the charter which the colonial government was always trying to maintain, and the crown was as assiduously endeavouring to counteract.
Over against these sweeping assumptions and deductions, the Roman Catholic Church had to build up its own statement of the basis of belief.
That world of the learned offers us non-dogmatic definitions, drawn up from the outside; definitions which do not share the root assumptions either of Catholicism or of post-Reformation Protestant orthodoxy.
(a) The nature of the bounding curve or surface may not be exactly known, so that certain assumptions have to be made, a formula being then used which is adapted to these assumptions.
The application of Simpson's rule, for instance, to a plane figure implies certain assumptions as to the nature of the bounding curve.
In finding the line of pressure some principle such as the principle of least action must be used in determining the reactions at the crown and springings, and some assumptions must be made of not certain validity.
In finding the abutment reactions some principle such as the principle of least action must be used, and some assumptions of doubtful validity made.
Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load.
Such a distinction involves the assumptions that bodily pleasures are generically different from mental ones, and that there is in practice a clearly marked dividing line, - both of which hypotheses are frequently denied.
These assumptions, however, were fanciful.
But there is another species of deduction which, as Cliffe Leslie has shown, seriously tainted the philosophy of Smith - in which the premises are not facts ascertained by observation, but the a priori assumptions which we found in the physiocrats.
In his speculations as to the physical cause of the celestial motions, his mind, though not wholly emancipated from the tyranny of gratuitous assumptions, was working steadily towards the light.
On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.
While it is evident that some such conclusion must follow from the attempt to regard the cognitive consciousness as made up of disconnected feelings, it is equally clear, not only that the result is selfcontradictory, but that it involves certain assumptions not in any way deducible from the fundamental view with which Hume starts.
There can, on these assumptions, be no doubt that, from the early years of the 5th century B.C., the archonship was of practically no importance.
- The theory of conduction of heat by diffusion in gases has a particular interest, since it is possible to predict the value on certain assumptions, if the viscosity is known.
I buy something because I have certain assumptions about how much happiness it will bring me.
We compute the maximum amount of food the world can produce by beginning with total acres of land considered arable, but that is based on assumptions about the future of technology and agriculture.
I know that sounds preposterous—but only based on our assumptions that the future will be like the past.
In areas of uncertainty, we form our opinions on the basis of assumptions in other parts of our life.
Since thermochemical measurements of this type may be frequently performed with an error due to other causes of much less than i per cent., the error introduced by either of these assumptions is the chief cause of uncertainty in the method.
With one symbol for an unknown, it will easily be understood what scope there is foradroit assumptions, for the required numbers, of expressions in the one unknown which are at once seen to satisfy some of the conditions, leaving only one or two to be satisfied by the particular value of x to be determined.
Would give negative, surd or imaginary values; Diophantus then traces how each element of the equation has arisen, and formulates the auxiliary problem of determining how the assumptions must be corrected so as to lead to an equation (in place of the "impossible" one) which can be solved rationally.
= tions were; we only know what assumptions we should make in order to reach the same conclusions, and they may be very different from " the mind of Ricardo."
The conclusions of such a work are of wider significance than the assumptions we attribute to the author would warrant.
But, as applied to lower and more obscure forms of life, teleology presented alfnost insurmountable difficulties; and consequently, in place of exact experiment and demonstration, the most reckless though ingenious assumptions were made as to the utility of the parts and organs of lower animals.
Many zoologists - prominent among them in Great Britain being Huxley - had been repelled by the airy fancies and assumptions of the " philosophical " morphologists.
His methods, however, were not free from tentative assumptions, and were considerably improved by Edmund Halley (Phil.
The Calendar Is Constructed On The Assumptions That The Mean Lunation Is 29 Days 12 Hours 44 Min.
The point is that neither Buchner nor Haeckel could on their assumptions recognize any force but force of body, or any mind but mind of body, or any distinct thing or substance except body.
Schelling was right; but he had too much affinity with Hegelian assumptions, e.g.
Having, however, made a deduction, which is at all events consistent, that on Kantian assumptions all we know is mental phenomena, Lange proceeded to reduce the rest of Kantism to consistency.
In Part II., ch i., he makes three assumptions about the senses, and, without stopping to prove them, or even to make them consistent, deduces from them his thesis that the evidence of the senses is not a foundation of belief in Nature.
Balfour, however, having from unproved assumptions denied the evidence of the senses, and the rational power of using them to infer things beyond oneself, has to look out for other, and non-rational, foundations of belief.
This theory was adopted by Edme Mariotte, Sir Isaac Newton and Thomas Young; and, although certain of their assumptions were somewhat arbitrary, yet the general validity of the theory has been demonstrated by the researches of J.
These assumptions are often wrong.
If the answers to those questions are affirmative, then making assumptions about increasing rates of technological progress is very reasonable.
To the specialists in sciences which were advancing rapidly and in divergent directions to results which often reacted on and transformed their initial assumptions, Spencer has often appeared too much of a philosopher and defective in specialist knowledge.