Astronomers From England

"Natural Groups are best described, not by any definition which marks their boundaries, but by a 'Type' which marks their centre. The Type of any natural group is an example which possesses in a marked degree all the leading characters of the class."

"A 'Natural System' is one which attempts to make 'all' the divisions natural, the widest as well as the narrowest; and therefore applies 'no' characters 'peremptorily'."

"An 'Artificial System' is one in which the 'smaller' groups (the Genera) are 'natural'; and in which the 'wider' divisions (Classes, Orders) are constructed by the 'peremptory' application of selected Characters"

"The Plan of the System, may aim at a Natural or an Artificial System. But no classes can be absolutely artificial, for if they were, no assertions could be made concerning them."

"The " Five Words," 'genus', 'species', 'difference', 'property', 'accident', were used by the Aristotelians, in order to express the subordination of kinds, and to describe the nature of definitions and propositions. In modern times, these technical expressions have been more referred to by Natural Historians than by Metaphysicians."

"A whale is not a fish in natural history, but it is a fish in commerce and law. A plea that human laws which mention fish do not apply to whales, would be rejected at once by an intelligent judge."

"We collect individuals into 'kinds' by applying to them the Idea of Likeness."

"All hypotheses respecting the manner in which the elements of inorganic bodies are arranged in space, must be constructed with regard to the general facts of crystallization."

"The governing principles of chemical affinity are, that it is elective ; that it is definite ; that it determines the properties of the compound; and that analysis is possible."

"Attractions take place between bodies, affinities between the particles of a body. The former may be compared to the alliances of states, the latter to the ties of family."

"Coexistent polarities are fundamentally identical."

"The solution is, that we do not see the image on the retina at all, we only see by means of it."

"The Sight cannot decompose a compound colour into simple colours, or distinguish a compound from a simple colour"

"We perceive by 'means' of a medium and 'by means' of impressions on the nerves: but we do not (by our senses,) perceive either the medium or the impressions on the nerves."

"Secondary Qualities are not 'extended' but 'intensive'; their effects are not augmented by addition of parts, but by increased operation of the medium. Hence they are not measured directly, but by 'scales'; not by 'units', but by 'degrees'."

"We necessarily perceive bodies as 'without' us: the Idea of 'Externality' is one of the conditions of perception."

"The Science of Hydrostatics depends upon the Fundamental Principle that 'fluids press equally in all directions'. This Principle necessarily results from the conception of a Fluid, as a body of which the parts are perfectly moveable in all directions. For since the Fluid is a body, it can transmit pressure; and the transmitted pressure is equal to the original pressure, in virtue of the Axiom that Reaction is equal to Action. That the Fundamental Principle is not derived from experience, is plain both from its evidence and from its history."

"'When two equal weights are supported on the middle point between them, the pressure on the fulcrum is equal to the sum of the weights.'"

"Mechanical Science depends on the Conception of Force; and is divided into 'Statics', the doctrine of Force preventing motion, and 'Dynamics', the doctrine of Force producing motion."

"The Idea of Cause is expressed for purposes of science by these three Axioms:—'Every Event must have a Cause':—'Causes are measured by their Effects':—'Reaction is equal and opposite to Action'."

"Among the foundations of the Higher Mathematics is also the 'Idea of a Limit'. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses."

"'Intuitive' is opposed to 'discursive' reason. In intuition, we obtain our conclusions by dwelling upon 'one' aspect of the fundamental Idea; in discursive reasoning, we combine several aspects of the Idea"

"The Perception of Time involves a constant and latent kind of memory, which may be termed a 'Sense of Succession'. The Perception of Number also involves this Sense of Succession, although in small numbers we appear to apprehend the units simultaneously and not successively."

"'Form' or 'figure' is space limited by boundaries. Space has necessarily 'three' dimensions, length, breadth, depth; and no ethers which cannot be resolved into these."

"In order to acquire any exact and solid knowledge, the student must possess with perfect precision the ideas appropriate to that part of knowledge: and this precision is tested by the student's 'perceiving' the axiomatic evidence of the 'axioms' belonging to each 'Fundamental Idea'."

"In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises."

"Truths obtained by Induction are made compact and permanent by being expressed in 'Technical Terms'."

"Truths once obtained by legitimate Induction are Facts: these Facts may be again connected, so as to produce higher truths: and thus we advance to 'Successive Generalizations'."

"The Sensations are the 'Objective', the Ideas the 'Subjective' part of every act of perception or knowledge."

"The antithesis of 'Sense' & 'Ideas' is the foundation of the Philosophy of Science. No knowledge can exist without the union, no philosophy without the separation, of these two elements."

"Man, servant and interpreter of Nature, does and understands only as much as he has observed of the order of Nature, either in reality or in mind; he neither knows nor can do more."

"The system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case."

"Our assent to the hypothesis implies that it is held to be true of all particular instances. That these cases belong to past or to future times, that they have or have not already occurred, makes no difference in the applicability of the rule to them. Because the rule prevails, it includes all cases."

"A scientific writer of modern times appears to wonder that men did not at once divine the weight of the air from which the phenomena formerly ascribed to the 'fuga vacui' really result. “Loaded, compressed by the atmosphere,” he says, “they did not recognize its action. In vain all Nature testified that air was elastic and heavy; they shut their eyes to her testimony. The water rose in pumps and flowed in siphons at that time as it does at this day. They could not separate the boards of a pair of bellows of which the holes were stopped; and they could not bring together the same boards without difficulty if they were at first separated. Infants sucked the milk of their mothers; air entered rapidly into the lungs of animals at every inspiration; cupping-glasses 'produced tumours on the skin; and in spite of all these striking proofs of the weight and elasticity of the air, the ancient philosophers maintained resolutely that air was light, and explained all these phenomena by the horror which they said Nature had for a vacuum.” It is curious that it should not have occurred to the author while writing this, that if these facts, so numerous and various, can all be accounted for by one principle, there is a strong presumption that the principle is not altogether baseless. And in reality is it not true that Nature does abhor a vacuum, and do all she can to avoid it? No doubt this power is not unlimited; and we can trace it to a mechanical cause, the pressure of the circumambient air. But the tendency, arising from this pressure, which the bodies surrounding a space void of air have to rush into it, may be expressed, in no extravagant or unintelligible manner, by saying that Nature has a repugnance to a vacuum."

"By speaking of space as an Idea, I intend to imply the apprehension of objects as existing in space, and of the relations of position prevailing among them, is not a consequence of experience but a result of a peculiar constitution and activity of the mind which is independent of all experience in its origin, though constantly combined with experience in its exercise."

"We unfold out of the Idea of Space the propositions of geometry, which are plainly truths of the most rigorous necessity and universality. But if the idea of space were merely collected from observation of the external world, it could never enable or entitle us to assert such propositions: it could never authorize us to say that not merely some lines, but all lines, not only have, but must have, those properties which geometry teaches. Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but half comprehends the meaning."

"According to the technical language of old writers, a thing and its qualities are described as subject and attributes; and thus a man’s faculties and acts are attributes of which he is the subject. The mind is the subject in which ideas inhere. Moreover, the man’s faculties and acts are employed upon external objects; and from objects all his sensations arise. Hence the part of a man’s knowledge which belongs to his own mind, is subjective: that which flows in upon him from the world external to him, is objective."

"Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error. Not only so; but scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of Error is without some latent charm derived from Truth."

"We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed."

"Although the semicircle of the Moon is placed above the circle of the Sun and would appear to be superior, nevertheless we know that the Sun is ruler and King. We see that the Moon in her shape and her proximity rivals the Sun with her grandeur, which is apparent to ordinary men, yet the face, or a semi-sphere of the Moon, always reflects the light of the Sun."

"Dee goes so far as to assert that, although he called the work hieroglyphic, it is endowed with a clarity and rigour almost mathematical; yet at the same time he leaves it to the reader even to guess that the subject of the elaborate display, which he is asked to view in such dim light, is the hermetic quest. The semblance of clarity is achieved by discussing the dark subject under the guise of a symbolic sign invented by Dee, which is his monad. This symbol indeed lends itself easily to digressive secondary interpretations of a numerological, cabbalistic, astrological, cosmological, or mathematical nature, all which, however, are without any doubt given so as to establish significant connexions with the all-embracing central theme, alchemy, which is barely mentioned."

"Such people, the real pioneers of the seaborne empire, were practical men: Captains Ralph Lane, John Smith and other soldiers of early Virginia, the merchant-commanders of the East Indiamen, the Arctic explorers from the Borough brothers to Baffin and the sea-captains of the Atlantic. Yet for success the movement needed also the moving power of ideas propagated by such men as Dee, Hakluyt, Ralegh and Drake. For who can doubt the inspiring force of Dee's Faustian genius, which cast a spell on the minds of mariners and intellectuals alike?"

"[T]he idea of a maritime empire did not immediately seize the imagination of the English people, nor did it arise spontaneously. It had to be propagated. John Dee, who invented the phrase "British Impire", was the most diligent and influential of the first generation of imperialists. He it was who sketched out the English claim to an empire of the North Atlantic, embracing the Arctic to the east and the west, the northern islands, including mythical Frisland, conquered allegedly by King Arthur and King Malgo, and Atlantis (the continent of North America), first discovered by the Welsh prince Owen Madoc in the twelfth century. All this Dee set down in 1578 in a statement for the queen of "Her Majesty's Title Royal" to the lands in question, depicted in his 1580 map of Atlantis. Thus the necessary underpinning of myth was provided, to be duly repeated by Peckham, Hakluyt and many more."

"A mervaylous newtrality have these thinges Mathematicall, and also a straunge participatió betwene thynges supernaturall, immortall, intellectual, simple and indivisible: and thynges naturall, mortall, sensible, compounded and divisible."

"O comfortable allurement, O ravishing persuasion to deal with a science whose subject is so ancient, so pure, so excellent, so surrounding all creatures, so used of the almighty and incomprehensible wisdom of the Creator, in distinct creation of all creatures: in all their distinct parts, properties, natures, and virtues, by order, and most absolute number, brought from nothing to the formality of their being and state."

"There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. Many arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry."

"We finish the brief hieroglyphic consideration of our Monad, which we would sum up in one only hieroglyphic context: The Sun and the Moon of this Monad desire that the Elements in which the tenth proportion will flower, shall be separated, and this is done by the application of Fire."

"Therefore, the central point which we see in the centre of the hieroglyphic Monad produces the Earth, round which the Sun, the Moon, and the other planets follow their respective paths. The Sun has the supreme dignity, and we represent him by a circle having a visible centre."

"Neither the circle without the line, nor the line without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that all things commence to emerge in principle. That which is affected at the periphery, however large it may be, cannot in any way lack the support of the central point."

"It is by the straight line and the circle that the first and most simple example and representation of all things may be demonstrated, whether such things be either non-existent or merely hidden under Nature's veils."