Hans Vaihinger - Collected Quotes

"It must be remembered that the object of the world of ideas as a whole [the map or model] is not the portrayal of reality - this would be an utterly impossible task - but rather to provide us with an instrument for finding our way about more easily in the world." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"[...] operations of an almost mysterious character, which run counter to ordinary procedure in a more or less paradoxical way. They are methods which give an onlooker the impression of magic if he be not himself initiated or equally skilled in the mechanism.  (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"Scientific thought is a function of the psyche [...]. Psychical actions and reactions are, like every event known to us, necessary occurrences; that is to say, they result with compulsory regularity from their conditions and causes." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"The opponents of the atom are generally content to point to its contradictions and reject it as unfruitful for science. A rash form of caution, for without the atom science falls." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"[...] the organic function of thought is carried on for the most part unconsciously. Should the product finally enter consciousness also, or should consciousness momentarily accompany the processes of logical thought, this light only penetrates to the shallows, an the actual fundamental processes are carried on in the darkness of the unconscious. The specifically purposeful operations are chiefly, and in any case at the beginning, wholly instinctive and unconscious, even if they later press forward into the luminous circle of consciousness [...]" (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"The organized activity of the logical function draws into itself all the sensations and constructs an inner world of its own, which progressively departs from reality but yet at certain points still retains so intimate a connection with it that transitions from one to the other continually take place and we hardly notice that we are acting on a double stage - our own inner world (which, of course, we objectify as the world of sense-perception) and also an entirely different and external world." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"The psyche works over the material presented to it by the sensations, i.e. elaborates the only available foundation with the help of the logical forms; it sifts the sensations, on the one hand cutting away definite portions of the given sensory material, in conformity with the logical functions, and on the other making subjective additions to what is immediately give. And it is in these very operations that the process of acquiring knowledge consists, and it is all the while departing from reality as given to it." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"We have repeatedly insisted [...] that the boundary between truth and error is not a rigid one, and we were able ultimately to demonstrate that what we generally call truth, namely a conceptual world coinciding with the external world, is merely the most expedient error." (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

"Where the logical function actively intervenes, it alters what is given and causes it to depart from reality. We cannot even describe the elementary processes of the psyche without at every step meeting this disturbing -or shall we say helpful? - factor. As soon as sensation has entered the sphere of the psyche, it is drawn into the whirlpool of the logical processes. The psyche quite of i t s own accord alters both what is given and presented. Two things are to be distinguished in this process: First, the actual forms in which this change takes place; and secondly, the products obtained from the original material by this change. " (Hans Vaihinger, "The Philosophy of 'As if': A System of the Theoretical, Practical and Religious Fictions of Mankind", 1911)

George Adams - Collected Quotes

"Conjectures in philosophy are termed hypotheses or theories; and the investigation of an hypothesis founded on some slight probability, which accounts for many appearances in nature, has too often been considered as the highest attainment of a philosopher. If the hypothesis (sic) hangs well together, is embellished with a lively imagination, and serves to account for common appearances - it is considered by many, as having all the qualities that should recommend it to our belief, and all that ought to be required in a philosophical system." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"It is of the utmost importance to your real advancement in science, to avoid every source of error, or whatever may lead you to form an erroneous judgment. Now a true judgment can only be obtained by a profound view of nature, and a strict examination into the mutual connections and dependencies of things; you will hence see the necessity of strict and accurate examination, of time to acquire the requisite knowledge, and of attention to comprehend it: for among the various sources of error, we may reckon the precipitation of our judgment and a presumptuous ignorance as the principal." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Most of our philosophical instruments are measures of effects. The progress made in natural philosophy increases every day by the number of these measures; by these it still continues to be improved." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Nothing can be more shocking to reason than eternal time; infinite divisibility is not less absurd." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 3, 1794

"The end of natural philosophy is to increase either the knowledge or power of man, and enable him to understand the ways and procedure of nature. By discovering the laws of nature, he acquires knowledge, and obtains power; for when these laws are discovered, he can use them as rules of practice, to equal, subdue, or even excel nature by art." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 2, 1794)

"The human mind, like a mirror, must be smoothed and polished, freed from false imaginations and perverted notions, before it is fi t to receive and reflect the light of truth, and just information." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 2, 1794)

"The knowledge of mechanics is one of those things that contribute to distinguish civilized nations from barbarians. From it the works of art derive much of their beauty and value; without it we can make very little progress in the knowledge of the works of nature. By this science we are enabled to improve every power and force in nature, and render the motions of the elements water, air, and fi re, subservient to the purposes of life." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 3, 1794)

"The natural propensity of the human mind to know the cause of every effect often leads men into errors, and makes them satisfied with a word which does not remove their ignorance." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"The principles of all knowledge are founded in mind; the mind of man, either animated by desire or pressed by necessity, puts in action it’s various energies, and unfolds the seeds of knowledge." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 3, 1794)

"The study of nature is as much distinguished from other subjects by the importance of its matter, as by the variety of its topics." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 2, 1794)

"The two kingdoms of nature and grace, as two parallel lines, correspond to each other, follow a like course, but can never be made to touch. An adequate understanding of this distinction in all its branches, would be the consummation of human knowledge." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Truth, though destined to be the guide of man, is not bestowed with an unconditional profusion; but is hidden in darkness, and involved in difficulties; intended, like all the other gifts of heaven, to be fought and cultivated by all the different powers and exertions of human reason." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

Gerald J Whitrow - Collected Quotes

"In classical physics, most of the fundamental laws of nature were concerned either with the stability of certain configurations of bodies, e.g. the solar system, or else with the conservation of certain properties of matter, e.g. mass, energy, angular momentum or spin. The outstanding exception was the famous Second Law of Thermodynamics, discovered by Clausius in 1850. This law, as usually stated, refers to an abstract concept called entropy, which for any enclosed or thermally isolated system tends to increase continually with lapse of time. In practice, the most familiar example of this law occurs when two bodies are in contact: in general, heat tends to flow from the hotter body to the cooler. Thus, while the First Law of Thermodynamics, viz. the conservation of energy, is concerned only with time as mere duration, the Second Law involves the idea of trend." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"Space-time is curved in the neighborhood of material masses, but it is not clear whether the presence of matter causes the curvature of space-time or whether this curvature is itself responsible for the existence of matter." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"The basic objection to attempts to deduce the unidirectional nature of time from concepts such as entropy is that they are attempts to reduce a more fundamental concept to a less fundamental one." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"[Time is not] a mysterious illusion of the intellect. [...] It is an essential feature of the universe." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"Our conscious appreciation of the fact that one event follows another is of a different kind from our awareness of either event separately. If two events are to be represented as occurring in succession, then - paradoxically - they must also be thought of simultaneously." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"Language itself inevitably introduced an element of permanence into the world. For, although speech itself is transitory, the conventionalized sound symbols of language transcended time." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

"Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

"The development of rational thought actually seems to have impeded man's appreciation for the significance of time. [...] Belief that the ultimate reality is timeless is deeply rooted in human thinking, and the origin of rational investigation of the world was the search for permanent factors that lie behind the ever-changing pattern of events." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

Jacques Monod - Collected Quotes

"There are living systems; there is no living 'matter'. No substance, no single molecule, extracted and isolated from a living being possess, of its own, the aforementioned paradoxical properties. They are present in living systems only; that is to say, nowhere below the level of the cell." (Jacques Monod, "From Biology to Ethics", 1969)

"A totally blind process can by definition lead to anything; it can even lead to vision itself." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Among all the occurrences possible in the universe the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. At the present time we have no legitimate grounds for either asserting or denying that life got off to but a single start on earth, and that, as a consequence, before it appeared its chances of occurring were next to nil. [...] Destiny is written concurrently with the event, not prior to it." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Even today a good many distinguished minds seem unable to accept or even to understand that from a source of noise natural selection alone and unaided could have drawn all the music of the biosphere. In effect natural selection operates upon the products of chance and can feed nowhere else; but it operates in a domain of very demanding conditions, and from this domain chance is barred. It is not to chance but to these conditions that evolution owes its generally progressive course, its successive conquests, and the impression it gives of a smooth and steady unfolding." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Every living being is also a fossil. Within it, all the way down to the microscopic structure of its proteins, it bears the traces if not the stigmata of its ancestry." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Evolution in the biosphere is therefore a necessarily irreversible process defining a direction in time; a direction which is the same as that enjoined by the law of increasing entropy, that is to say, the second law of thermodynamics. This is far more than a mere comparison: the second law is founded upon considerations identical to those which establish the irreversibility of evolution. Indeed, it is legitimate to view the irreversibility of evolution as an expression of the second law in the biosphere." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"A curious aspect of the theory of evolution is that everybody thinks he understands it." (Jacques Monod, "On the Molecular Theory of Evolution", 1974)

"One of the great problems of philosophy, is the relationship between the realm of knowledge and the realm of values. Knowledge is what is; values are what ought to be. I would say that all traditional philosophies up to and including Marxism have tried to derive the “ought” from the “is.” My point of view is that this is impossible, this is a farce." (Jacques Monod)

"The scientific attitude implies the postulate of objectivity - that is to say, the fundamental postulate that there is no plan; that there is no intention in the universe." (Jacques Monod)

Roger J Boscovich - Collected Quotes

"Especially when we investigate the general laws of Nature, induction has very great power; & there is scarcely any other method beside it for the discovery of these laws. By its assistance, even the ancient philosophers attributed to all bodies extension, figurability, mobility, & impenetrability; & to these properties, by the use of the same method of reasoning, most of the later philosophers add inertia & universal gravitation. Now, induction should take account of every single case that can possibly happen, before it can have the force of demonstration; such induction as this has no place in establishing the laws of Nature. But use is made of an induction of a less rigorous type ; in order that this kind of induction may be employed, it must be of such a nature that in all those cases particularly, which can be examined in a manner that is bound to lead to a definite conclusion as to whether or no the law in question is followed, in all of them the same result is arrived at; & that these cases are not merely a few. Moreover, in the other cases, if those which at first sight appeared to be contradictory, on further & more accurate investigation, can all of them be made to agree with the law; although, whether they can be made to agree in this way better than in any Other whatever, it is impossible to know directly anyhow. If such conditions obtain, then it must be considered that the induction is adapted to establishing the law." (Roger J Boscovich, "De Lege Continuitatis" ["On the law of continuity"], 1754)

"Any point has a real mode of existence, through which it is where it is; & another, due to which it exists at the time when it does exist. These real modes of existence are to me real time & space ; the possibility of these modes, hazily apprehended by us, is, to my mind, empty space & again empty time, so to speak ; in other words, space & imaginary time." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"Further we believe that GOD Himself is present everywhere throughout the whole of the undoubtedly divisible space that all bodies occupy; & yet He is onefold in the highest degree & admits not of any composite nature whatever. Moreover, the same idea seems to depend on an analogy between space & time. For, just as rest is a conjunction with a continuous series of all the instants In the interval of time during which the rest endures; so also this virtual extension is a conjunction of one instant of time with a continuous series of all the points of space throughout which this one-fold entity extends virtually. Hence, just as rest is believed to exist in Nature, so also are we bound to admit virtual extension; & if this is admitted, then it will be possible for the primary elements of matter to be simple, & yet not absolutely non-extended." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"Hence I acknowledge continuity in motion only, which is something successive and not co-existent ; & also in it alone, or because of it alone, in corporeal entities at any rate, lies my reason for admitting the Law of Continuity. From this it will be all the more clear that, as I remarked above, Nature accurately observes the Law of Continuity, or at least tries to do so. Nature observes it in motions & in distance, & tries to in many other cases, with which continuity, as we have defined it above, is in no wise in agreement; also in certain other cases, in which continuity cannot be completely obtained. This continuity does not present itself to us at first sight, unless we consider the subjects somewhat more deeply & study them closely." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"Hence the whole of geometry is imaginary; but the hypothetical propositions that are deduced from it are true, if the conditions assumed by it exist, & also the conditional things deduced from them, in every case; & the relations between the imaginary distances of points, derived by the help of geometry from certain conditions, will always be real, & such as they are found to be by geometry, when those conditions exist for real distances of points." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"If matter is continuous, it may & must be subject to infinite divisibility; but actual division carried on indefinitely brings in its train difficulties that are truly inextricable; however, this infinite division is required by those who do not admit that there are any particles, no matter how small, in bodies that are perfectly free from, & incapable of, compression." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"In the same way, this should also happen with regard to time, namely, that between a preceding continuous time & the next following there should be a single instant, which is the indivisible boundary of either. There cannot be two instants, as we intimated above, contiguous to one another; but between one instant & another there must always intervene some interval of continuous time divisible indefinitely. In the same way, in any quantity which lasts for a continuous interval of time, there must be obtained a series of magnitudes of such a kind that to each instant of time there is its corresponding magnitude; & this magnitude connects the one that precedes with the one that follows it, & differs from the former by some definite magnitude. Nay even in that class of quantities, in which we cannot have two magnitudes at the same time, this very point can be deduced far more clearly, namely, that there cannot be any sudden change from one to another. For at that instant, when the sudden change should take place, & the series be broken by some momentary definite addition, two -magnitudes would necessarily be obtained, namely, the last of the first series & the first of the next. Now this very point is still more clearly seen in those states of things, in which on the one hand there must be at any instant some state so that at no time can the thing be without some state of the kind, whilst on the other hand it can never have two states of the kind simultaneously." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"The Law of Continuity, as we here deal with it, consists in the idea that [...] any quantity, in passing from one magnitude to another, must pass through all intermediate magnitudes of the same class. The same notion is also commonly expressed by saying that the passage is made by intermediate stages or steps; [...] the idea should be interpreted as follows: single states correspond to single instants of time, but increments or decrements only to small areas of continuous time." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"The theory of non-extension is also convenient for eliminating from Nature all idea of a coexistent continuum — to explain which philosophers have up till now laboured so very hard & generally in vain. Assuming non-extension, no division of a real entity can be carried on indefinitely ; we shall not be brought to a standstill when we seek to find out whether the number of parts that are actually distinct & separable is finite or infinite ; nor with it will there come in any of those other truly innumerable difficulties that, with the idea of continuous composition, have given so much trouble- to philosophers. For if the primary elements of matter are perfectly non-extended & indivisible points separated from one another by some definite interval, then the number of points in any given mass must bc finite ; because all the distances are finite." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"(1) There is absolutely no argument that can be brought forward to prove that matter has continuous extension, that it is not rather made up of perfectly indivisible points separated from one another by a definite interval ; nor is there any reason apart from prejudice in favour of continuous extension in preference to composition from points that are perfectly indivisible, non-extended, forming no extended continuum of any sort. (2) There are arguments, & fairly strong ones too, which will prove that this composition from indivisible points is preferable to continuous extension." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

"There really must be, in the commencement of contact, in that indivisible instant of time which is an indivisible limit between the continuous time that preceded the contact & that subsequent to it (just in the same way as a point in geometry is an indivisible limit between two segments of a continuous line), a change of velocity taking place suddenly, without any passage through intermediate stages; & this violates the Law of Continuity, which absolutely denies the possibility of a passage from one magnitude to another without passing through intermediate stages." (Roger J Boscovich, "Philosophiae Naturalis Theoria Redacta Ad Unicam Legera Virium in Natura Existentium, 1758)

Ludwig Wittgenstein - Collected Quotes

"If a fact is to be a picture, it must have something in common with what it depicts. […] What a picture must have in common with reality, in order to be able to depict it correctly or incorrectly - in the way it does, is its pictorial form. […] What any picture, of whatever form, must have in common with reality, in order to be able to depict it - correctly or incorrectly in any way at all, is logical form, i.e., the form of reality. […] Logical pictures can depict the world." (Ludwig Wittgenstein, "Tractatus Logico-Philosophicus", 1922)

"The logical picture of the facts is the thought. […] A picture is a model of reality. In a picture objects have the elements of the picture corresponding to them. The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way." (Ludwig Wittgenstein, "Tractatus Logico-Philosophicus", 1922)

"The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience. This process, however, has no logical foundation but only a psychological one. It is clear that there are no grounds for believing that the  simplest course of events will really happen." (Ludwig Wittgenstein, "Tractatus Logico-Philosophicus", 1922)

"The so-called law of induction cannot possibly be a law of logic, since it is obviously a proposition with a sense. - Nor, therefore, can it be an a priori law." (Ludwig Wittgenstein, "Tractatus Logico Philosophicus", 1922)

"For a large class of cases - though not for all - in which we employ the word 'meaning' it can be defined thus: the meaning of a word is its use in language." (Ludwig Wittgenstein, "Philosophical investigations", 1953)

"Like everything metaphysical the harmony between thought and reality is to be found in the grammar of the language." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)

"The problems are solved, not by giving new information, but by arranging what we have known since long." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)

"To convince someone of the truth, it is not enough to state it, but rather one must find the path from error to truth." (Ludwig Wittgenstein, "Philosophical Occasions", 1953)

"Our craving for generality has [as one] source […] our preoccupation with the method of science. I mean the method the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization. Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer in the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness. I want to say here that it can never be our job to reduce anything to anything, or to explain anything. Philosophy really is ‘purely descriptive’." (Ludwig Wittgenstein, "The Blue and Brown Books", 1958)

"Images tell us nothing, either right or wrong, about the external world. […] It is just because forming images is a voluntary activity that it does not instruct us about the external world. […] When we form an image of something we are not observing. The coming and going of the pictures is not something that happens to us. We are not surprised by these pictures, saying ‘Look!’"  (Ludwig Wittgenstein, "Zettel", 1967)

"All testing, all confirmation and disconfirmation of a hypothesis takes place already within a system. And this system is not a more or less arbitrary and doubtful point of departure for all our arguments; no it belongs to the essence of what we call an argument. The system is not so much the point of departure, as the element in which our arguments have their life." (Ludwig Wittgenstein, "On Certainty", 1969)

"People are deeply imbedded in philosophical, i.e., grammatical confusions. And to free them presupposes pulling them out of the immensely manifold connections they are caught up in." (Ludwig Wittgenstein, "Philosophical Occasions 1912-1951", 1993)

Out of Context: Philosophy is... (Definitions)

"Philosophy is certainly the medicine of the soul." (Marcus Tullius Cicero, "Tusculan Disputations", 45 BC)

"Philosophy is written in this grand book, the universe, which stands continually open to our gaze." (Galileo Galilei, "The Assayer", 1623)

"Philosophy is such an impertinently litigious lady that a man had as good be engaged in law suits as have to do with her." (Isaac Newton, [letter to Edmond Halley] 1686)

"Each of the parts of philosophy is a philosophical whole, a circle rounded and complete in itself." (Georg W F Hegel, "Encyclopedia of the Philosophical Sciences", 1816)

"Philosophy is its own time comprehended in thoughts." (Georg W F Hegel, "Philosophy of Right", 1821)

"Philosophy is properly Home-sickness; the wish to be everywhere at home." (Georg von Hardenberg [Novalis], 1829)

"Philosophy and the arts are but a manifestation of the intelligible ideas that move the public mind; and thus they become visible images of the nations whence they emanate." (Lydia M Child, "Philothea", 1836)

"Philosophy [...] is a science, and as such has no articles of faith [...]" (Arthur Schopenhauer, Parerga and Paralipomena, 1851)

"Philosophy is the microscope of thought." (Victor Hugo, "Les Misérables", 1862)

"A system of philosophy, or metaphysics, is a union of a world view and a life view in one harmonious, complete, integral conception." (Joseph Alexander Leighton, "Man and the Cosmos - An introduction to Metaphysics", 1922)

"Every philosophy is tinged with the coloring of some secret imaginative, which never emerges explicitly into its trains of reasoning." (Alfred N Whitehead, "Science and the Modern World", 1925)

"Philosophy is the attempt to formulate principles or categories which the philosopher already possesses, in common with everyone else, but in an unformulated state." (Otis H Lee, "Philosophy of Science", Philosophy of Science 7 (1), 1940)

"Philosophy is in history, and is never independent of historical discourse." (Maurice Merleau-Ponty, "Éloge de la philosophie" ["In Praise of Philosophy"], 1953)

"Philosophy is metaphysics." (Martin Heidegger, "The End of Philosophy and the Task of Thinking", 1964)

"Philosophy is concerned with two matters: soluble questions that are trivial and critical questions that are insoluble." (Stefan Kanfer, Time magazine, 1982)

"I believe that philosophy is part of literature, and not the reverse." (Paul Virilio, [interview with Louise Wilson] 1994)

"[...] a philosophy is a scholarly discipline divided into special fields, every one of which is usually cultivated independently of the others." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)

"One view is that philosophy is a kind of halfway house for questions that have not yet yielded to the scientific method." (Ray Kurzweil, "How to Create a Mind", 2012)

"All philosophy is like a tree, the roots are metaphysics, the trunk is physics, and the branches are all the other sciences." (René Descartes)

"Philosophy is, in all, the problem of knowing. It is an undefined Science of the Sciences, a mysticism of the desire for knowledge; it is the very Spirit of the Sciences, and consequently unrepresentable, either in form or application, in the perfect representation of a special science." (Georg von Hardenberg [Novalis])

"Philosophy is empty if it isn't based on science. Science discovers, philosophy interprets." (Albert Einstein) 

"Philosophy is more often the systematization of the prejudices of philosophers than the systematization of nature." (Epifanio de los Santos)

H Rom Harré - Collected Quotes

"A theory describes a hypothetical mechanism or hypothetical structure which stands for the unknown real structure of things and materials. The hypothetical structure is modeled on some real structure known to the scientist and his colleagues. We can speak of the hypothetical mechanism as a model of the real mechanism of nature, and as modeled on some real mechanism we know." (H Rom Harré, "Philosophical Issues and Conceptual Change", Theory Into Practice Vol. 10 (2), 1971)

"Science is the combined effort to find out what sort of behavior ensues when various conditions are fulfilled. Chemistry is the study of reactions, that is, of the behavior of different substances, combined with the effort to discover their natures in virtue of which they behave as they do." (H Rom Harré, "Philosophical Issues and Conceptual Change", Theory Into Practice Vol. 10 (2), 1971)

"An analogy is a relationship between two entities, processes, or what you will, which allows inferences to be made about one of the things, usually that about which we know least, on the basis of what we know about the other. […] The art of using analogy is to balance up what we know of the likenesses against the unlikenesses between two things, and then on the basis of this balance make an inference as to what is called the neutral analogy, that about which we do not know." (Rom Harré," The Philosophies of Science" , 1972) 

"Metaphor and simile are the characteristic tropes of scientific thought, not formal validity of argument." (Rom Harré, "Varieties of Realism", 1986)

"A model can become a symbol when its source of projection is lost or forgotten as, for instance, the bull's head became alpha, but a symbol cannot become a model." (H Rom Harré, "Modeling: Gateway to the Unknown", 2004)

"An object, real or imagined, is not a model in itself. But it functions as a model when it is viewed as being in certain relationships to other things. So the classification of models is ultimately a classification of the ways things and processes can function as models." (H Rom Harré, "Modeling: Gateway to the Unknown", 2004)

"Models, analogies and metaphors are closely related, though not identical tools for rational thought. […] A model for something, be it thing or process, can be described in the language of simile as a thing or process analogous to that of which it is a model. […] The model offers us nothing by way of explanation, and no existential hypotheses, but it does provide, in the system of metaphors, a picturesque terminology. Many metaphors are indeed just this, the terminological debris of a dead model." (H Rom Harré, "Modeling: Gateway to the Unknown", 2004)

"The word that has survived throughout, enlarging its meaning and in some circles losing meaning altogether, is the word 'model'. Thinking with models is likewise called 'modeling'. We make and use 'models', concrete representations of the central material entities, structures and processes of a domain into which a scientist might be enquiring. The focus shifts from discourse, talking and writing about nature, the most general theory of which is logic, to modeling, reproducing and representing nature materially, the most general theory of which is analogy." (H Rom Harré, "Modeling: Gateway to the Unknown", 2004)

On Knowledge (1775-1799)

"Cultivate that kind of knowledge which enables us to discover for ourselves in case of need that which others have to read or be told of." (Georg C Lichtenberg, Notebook D, 1773-1775)

"Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it." (Samuel Johnson, 1775)

"Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of knowing an object through these representations (spontaneity [in the production] of concepts)." (Immanuel Kant, "Critique of Pure Reason", 1781)

"Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts." (Immanuel Kant, "Critique of Pure Reason", 1781)

"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (Immanuel Kant, "Critique of Pure Reason", 1781)

"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge." (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"On completing one discovery we never fail to get an imperfect knowledge of others of which you could have no idea before […]" (Joseph Priestley, 1786)

"As there is no study which may be so advantageously entered upon with a less stock of preparatory knowledge than mathematics, so there is none in which a greater number of uneducated men have raised themselves, by their own exertions, to distinction and eminence. […] Many of the intellectual defects which, in such cases, are commonly placed to the account of mathematical studies, ought to be ascribed to the want of a liberal education in early youth." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"The power of Reason […] is unquestionably the most important by far of those which are comprehended under the general title of Intellectual. It is on the right use of this power that our success in the pursuit of both knowledge and of  happiness depends; and it is by the exclusive possession of it that man is distinguished, in the most essential respects, from the lower animals. It is, indeed, from their subserviency to its operations, that the other faculties […] derive their chief value." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

On Concepts IX

"The symbols organized by knowledge, or concepts, themselves belong to social nature as its ideological elements. Therefore, by operating upon them, knowledge is able to expand its organizing function much more broadly than labour in its technological operation of real things; and as we have already seen that many things, which are not organized in practice, can be organized by knowledge, i.e. in symbols: where the ingression of things is absent, the ingression of their concepts is still possible." (Alexander A Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects." (Max Born physicist, "The Statistical Interpretations of Quantum Mechanics", [Nobel lecture] 1954)

"It is one of the consolations of philosophy that the benefit of showing how to dispense with a concept does not hinge on dispensing with it." (Willard v O Quine, "Word and Object", 1960)

"The idea that one can 'introduce' a kind of objects simply by laying down an identity criterion for them really inverts the proper order of explanation. As Locke clearly understood, one must first have a clear conception of what kind of objects one is dealing with in order to extract a criterion of identity for them from that conception. […] So, rather than 'abstract' a kind of object from a criterion of identity, one must in general 'extract' a criterion of identity from a metaphysically defensible conception of a given kind of objects." (Edward J Lowe," The metaphysics of abstract objects", Journal of Philosophy 92(10), 1995)

"The realm of the particularity of each experienced item differs from the formal realm of concepts. [...] The power of paradigmatic thought is to bring order to experience by seeing individual things as belonging to a category." (Donald E Polkinghorne, “Narrative configuration in qualitative analysis", International Journal of Qualitative Studies in Education Vol. 8 (1), 1995)

"In the new systems thinking, the metaphor of knowledge as a building is being replaced by that of the network. As we perceive reality as a network of relationships, our descriptions, too, form an interconnected network of concepts and models in which there are no foundations. For most scientists such a view of knowledge as a network with no firm foundations is extremely unsettling, and today it is by no means generally accepted. But as the network approach expands throughout the scientific community, the idea of knowledge as a network will undoubtedly find increasing acceptance." (Fritjof Capra, "The Web of Life: a new scientific understanding of living systems", 1996)

"Abstraction is an essential knowledge process, the process (or, to some, the alleged process) by which we form concepts. It consists in recognizing one or several common features or attributes (properties, predicates) in individ­uals, and on that basis stating a concept subsuming those common features or attributes. Concept is an idea, associated with a word expressing a prop­erty or a collection of properties inferred or derived from different samples. Subsumption is the logical technique to get generality from particulars." (Hourya B Sinaceur," Facets and Levels of Mathematical Abstraction", Standards of Rigor in Mathematical Practice 18-1, 2014)

Herbert Dingle - Collected Quotes

"A great idea invariably creates as many problems as it solves: that is a sign of its greatness." (Herbert Dingle, "Relativity for All", 1922)

"The aim of the scientist is to express, in as simple a statement as possible, the principles underlying the order and arrangement of phenomena." (Herbert Dingle, "Relativity for All", 1922) 

"The numerical side of the theory of relativity is derived from the failure of all attempts to detect the relative motion of matter and ether." (Herbert Dingle, "Relativity for All", 1922) 

"A science in its infancy is the least satisfactory, and, at the same time, the most profitable theme for a general description. It is the leas satisfactory because its conclusions - if we can call them conclusions are, at the best, little more than tentative summaries of observed facts, liable at any moment to be superseded by wider generalisations: the inconsequential playfulness of childhood has not given place to the graver consistency of mature age. It is the most profitable theme because it has not yet lost the quickening inspiration that alone can produce great things. It is in touch with the poetry and romance that go side by side with all true science. In its eyes still shines 'the light that never was on sea or land'." (Herbert Dingle, "Modern Astrophysics", 1924) 

"It is as though a star throws the whole secret history of its being into its spectrum, and we have only to learn how to read it aright in order to solve the most abstruse problems of the physical Universe." (Herbert Dingle, "Modern Astrophysics", 1924)

"Modem physics is, indeed, not unlike a ship, drawing nearer to a goal not yet in sight, but so tossed about by the buffetings of experiment and working hypothesis that the passenger scarcely knows whether he is progressing or drifting." (Herbert Dingle, "Through Science to Philosophy", 1937)

"Success in scientific theory is won, not by rigid adherence to the rules of logic, but by bold speculation which dares even to break those rules if by that means new regions of interest may be opened up." (Herbert Dingle, "Through Science to Philosophy", 1937)

"The older physicist believed in Nature and thought of himself as making experiments to see what She was like. She was there whether he could observe her or not. But the modern physicist thinks first of all of what he observes in his experiments and is not interested in anything that he cannot possibly observe. He looks for relations between his observations and ignores everything else. But he still expresses his results as though they were discoveries of the essence of Nature, because he is so used to this way of speaking that he does not realise that his discoveries no longer conform to it. When they are expressed as the characteristics of a world existing outside us and independently of us, which causes our experience by its impact on our sense organs, these discoveries require such a world to have contradictory properties. Hence, by retaining this form of expression, the physicist finds himself presenting his perfectly rational achievements as though they were nonsensical." (Herbert Dingle, "The Scientific Adventure", British Journal for the Philosophy of Science, 1952)

"Mathematics in itself, as I say, is independent of experience. It begins with the free choice of symbols, to which are freely assigned properties, and it then proceeds to deduce the necessary rational implications of those properties." (Herbert Dingle, "Science at the Crossroads", 1972)

On Conjecture (1750-1799)

"One of the most intimate of all associations in the human mind is that of cause and effect. They suggest one another with the utmost readiness upon all occasions; so that it is almost impossible to contemplate the one, without having some idea of, or forming some conjecture about the other." (Joseph Priestley, "The History and Present State of Electricity", 1767)

"It falls into this difficulty without any fault of its own. It begins with principles, which cannot be dispensed with in the field of experience, and the truth and sufficiency of which are, at the same time, insured by experience. With these principles it rises, in obedience to the laws of its own nature, to ever higher and more remote conditions. But it quickly discovers that, in this way, its labours must remain ever incomplete, because new questions never cease to present themselves; and thus it finds itself compelled to have recourse to principles which transcend the region of experience, while they are regarded by common sense without distrust. It thus falls into confusion and contradictions, from which it conjectures the presence of latent errors, which, however, it is unable to discover, because the principles it employs, transcending the limits of experience, cannot be tested by that criterion. The arena of these endless contests is called Metaphysic." (Immanuel Kant, "The Critique of Pure Reason", 1781)

"[...] the lofty aspirations of humanity and not delusions; they are realities. They link us to a purer order of existence, which makes us heirs of immortality. We repose order a confident and unwavering assurance that, in God’s own time, these earth-mists will be dispersed, and the dim twilight of conjecture will yield to the glorious, unclouded noonday of knowledge." (John LeConte, "The Nebular Hypothesis", The Popular Science Monthly Vol. 2, 1873)

"On the other hand, if we add observation to observation, without attempting to draw no only certain conclusions, but also conjectural views from them, we offend against the very end for which only observations ought to be made." (Friedrich W Herschel, "On the Construction of the Heavens", Philosophical Transactions of the Royal Society of London Vol. LXXV, 1785)

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Conjectures in philosophy are termed hypotheses or theories; and the investigation of an hypothesis founded on some slight probability, which accounts for many appearances in nature, has too often been considered as the highest attainment of a philosopher. If the hypothesis (sic) hangs well together, is embellished with a lively imagination, and serves to account for common appearances - it is considered by many, as having all the qualities that should recommend it to our belief, and all that ought to be required in a philosophical system." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

Clifford Truesdell - Collected Quotes

"Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use of knowledge gathered in a few observations, to predict by logical processes the outcomes in many other circumstances. Any logically sound theory satisfying this condition is a good theory, whether or not it be derived from 'ultimate' or 'fundamental' truth. It is as ridiculous to deride continuum physics because it is not obtained from nuclear physics as it would be to reproach it with lack of foundation in the Bible." (Clifford Truesdell & Walter Noll, "The Non-Linear Field Theories of Mechanics", 1965)

"The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply." (Clifford Truesdell & Walter Noll, "The Non-Linear Field Theories of Mechanics", 1965)

"A mathematical theorem cannot be escaped by denying its truth or by forgetting it for vague, intuitive reasons that blur the edges of all rational processes. The way to escape an unpleasant theorem is to prove another one." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"As mechanics is the science of motions and forces, so thermodynamics is the science of forces and entropy. What is entropy? Heads have split for a century trying to define entropy in terms of other things. Entropy, like force, is an undefined object, and if you try to define it, you will suffer the same fate as the force definers of the seventeenth and eighteenth centuries: Either you will get something too special or you will run around in a circle." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Despite two centuries of study, the integrals of general dynamical systems remain covered with darkness. To save the classical thermostatics, the practical success of which is shown by the wide use to which it has been put, we must find a way out. That is, we must find some mathematical connection between time averages of the functions of physical interest and the corresponding simple canonical averages." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Formerly, the beginner was taught to crawl through the underbrush, never lifting his eyes to the trees; today he is often made to focus on the curvature of the universe, missing even the earth." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"In all of natural philosophy, the most deeply and repeatedly studied part, next to pure geometry, is mechanics. […] The picture of nature as a whole given us by mechanics may be compared to a black-and-white photograph: It neglects a great deal, but within its limitations, it can be highly precise. Developing sharper and more flexible black-and-white photography has not attained pictures in color or three-dimensional casts, but it serves in cases where color and thickness are irrelevant, presently impossible to get in the required precision, or distractive from the true content." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Mathematicians, on the other hand, often regard all of physics as a kind of divine revelation or trickery, where mathematical morals are irrelevant, so that if they enter this red-light district at all, it is only to get what they want as cheaply as possible before returning to the respectability of problems purely mathematical in the older sense: analysis, probability, differential geometry, etc." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Mechanics seeks to connect these three elements -body, motion, and force -in such a way as to yield good models for the behavior of the materials in nature." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Nature does not seem full of circles and triangles to the ungeometrical; rather, mastery of the theory of triangles and circles, and later of conic sections, has taught the theorist, the experimenter, the carpenter, and even the artist to find them everywhere, from the heavenly motions to the pose of a Venus." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"[..] principle of equipresence: A quantity present as an independent variable in one constitutive equation is so present in all, to the extent that its appearance is not forbidden by the general laws of Physics or rules of invariance. […] The principle of equipresence states, in effect, that no division of phenomena is to be laid down by constitutive equations." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Rational mechanics is mathematics, just as geometry is mathematics. […] Mechanics cannot, any more than geometry, exhaust the properties of the physical universe. […] Mechanics presumes geometry and hence is more special; since it attributes to a sphere additional properties beyond its purely geometric ones, the mechanics of spheres is not only more complicated and detailed but also, on the grounds of pure logic, necessarily less widely applicable than geometry. This, again, is no reproach; geometry is not despised because it is less widely applicable than topology. A more complicated theory, such as mechanics, is less likely to apply to any given case; when it does apply, it predicts more than any broader, less specific theory." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"The purpose of statistical mechanics, for phenomena of equilibrium, is to calculate time averages, and the ensemble theory is useful only as a tool enabling us to calculate time averages without knowing how to integrate the equations of motion. The ensemble theory is a mathematical device; we are wasting our time if we try to explain it by itself." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense." (Clifford A Truesdell, "Six Lectures on Modern Natural Philosophy", 1966) 

"Thermostatics, which even now is usually called thermodynamics, has an unfortunate history and a cancerous tradition. It arose in a chaos of metaphysical and indeed irrational controversy, the traces of which drip their poison even today. As compared with the older science of mechanics and the younger science of electromagnetism, its mathematical structure is meager. Though claims for its breadth of application are often extravagant, the examples from which its principles usually are inferred are most special, and extensive mathematical developments based on fundamental equations, such as typify mechanics and electromagnetism, are wanting. The logical standards acceptable in thermostatics fail to meet the criteria of other exact sciences [...]." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Nothing is harder to surmount than a corpus of true but too special knowledge; to reforge the tradition of his forebears is the greatest originality a man can have." (Clifford Truesdell, The Creation and Unfolding of the Concept of Stress'' [in "Essays in the History of Mechanics"] , 1968) 

"Now a mathematician has a matchless advantage over general scientists, historians, politicians, and exponents of other professions: He can be wrong. A fortiori, he can also be right. [...] A mistake made by a mathematician, even a great one, is not a 'difference of a point of view' or 'another interpretation of the data' or a 'dictate of a conflicting ideology', it is a mistake. The greatest of all mathematicians, those who have discovered the greatest quantities of mathematical truths, are also those who have published the greatest numbers of lacunary proofs, insufficiently qualified assertions, and flat mistakes." (Clifford Truesdell, "Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia" [in "Essays in the History of Mechanics"], 1968)

"The mistakes made by a great mathematician are of two kinds: first, trivial slips that anyone can correct, and, second, titanic failures reflecting the scale of the struggle which the great mathematician waged. Failures of this latter kind are often as important as successes, for they give rise to major discoveries by other mathematicians. One error of a great mathematician has often done more for science than a hundred impeccable little theorems proved by lesser men." (Clifford Truesdell, "Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia" [in "Essays in the History of Mechanics"], 1968)

"Every physicist knows exactly what the first and the second law mean, but [...] no two physicists agree about them." (Clifford Truesdell)

On Induction (-1849)

"The only possible way to conceive universal is by induction, since we come to know abstractions by induction. But unless we have sense experience, we cannot make inductions. Even though sense perception relates to particular things, scientific knowledge concerning such can only be constructed by the successive steps of sense perception, induction, and formulation of universals." (Aristotle, "Posterior Analytics", cca. 350 BC)

"The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction." (Francis Bacon, "The New Organon", 1620)

"In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions." (Isaac Newton, "The Principia: Mathematical Principles of Natural Philosophy", 1687)

"As in Mathematics, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions but such as are taken from Experiments, or other certain Truths." (Sir Isaac Newton, "Opticks", 1704)

"It is often in our Power to obtain an Analogy where we cannot have an Induction." (David Hartley, "Observations on Man, His Frame, His Duty, and His Expectations", 1749)

"Especially when we investigate the general laws of Nature, induction has very great power; & there is scarcely any other method beside it for the discovery of these laws. By its assistance, even the ancient philosophers attributed to all bodies extension, figurability, mobility, & impenetrability; & to these properties, by the use of the same method of reasoning, most of the later philosophers add inertia & universal gravitation. Now, induction should take account of every single case that can possibly happen, before it can have the force of demonstration; such induction as this has no place in establishing the laws of Nature. But use is made of an induction of a less rigorous type ; in order that this kind of induction may be employed, it must be of such a nature that in all those cases particularly, which can be examined in a manner that is bound to lead to a definite conclusion as to whether or no the law in question is followed, in all of them the same result is arrived at; & that these cases are not merely a few. Moreover, in the other cases, if those which at first sight appeared to be contradictory, on further & more accurate investigation, can all of them be made to agree with the law; although, whether they can be made to agree in this way better than in any Other whatever, it is impossible to know directly anyhow. If such conditions obtain, then it must be considered that the induction is adapted to establishing the law." (Roger J Boscovich, "De Lege Continuitatis" ["On the law of continuity"], 1754)

"A discovery in mathematics, or a successful induction of facts, when once completed, cannot be too soon given to the world. But […] an hypothesis is a work of fancy, useless in science, and fit only for the amusement of a vacant hour." (Henry Brougham, Edinburgh Review 1, 1803)

"The most important questions of life are, for the most part, really only problems of probability. Strictly speaking one may even say that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, induction and analogy, the principal means for discovering truth, are based on probabilities, so that the entire system of human knowledge is connected with this theory." (Pierre-Simon Laplace, "Theorie Analytique des Probabilités", 1812)

"Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities”, 1814)

"Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth." (Pierre-Simon Laplace, "A Philosophical Essay on Probabilities", 1814)

"One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814)

"It is characteristic of higher arithmetic that many of its most beautiful theorems can be discovered by induction with the greatest of ease but have proofs that lie anywhere but near at hand and are often found only after many fruitless investigations with the aid of deep analysis and lucky combinations." (Carl Friedrich Gauss, 1817)

"Such is the tendency of the human mind to speculation, that on the least idea of an analogy between a few phenomena, it leaps forward, as it were, to a cause or law, to the temporary neglect of all the rest; so that, in fact, almost all our principal inductions must be regarded as a series of ascents and descents, and of conclusions from a few cases, verified by trial on many." (Sir John Herschel, "A Preliminary Discourse on the Study of Natural Philosophy" , 1830)

"We have here spoken of the prediction of facts of the same kind as those from which our rule was collected. But the evidence in favour of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such an extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena, so exactly represent a different class, when the agreement was unforeseen and contemplated. That rules springing from remote and unconnected quarters should thus leap to the same point, can only arise from that being where truth resides." (William Whewell, "The Philosophy of the Inductive Sciences" Vol. 2, 1840)

"There is in every step of an arithmetical or algebraical calculation a real induction, a real inference from facts to facts, and what disguises the induction is simply its comprehensive nature, and the consequent extreme generality of its language." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"The Higher Arithmetic presents us with an inexhaustible storehouse of interesting truths - of truths, too, which are not isolated but stand in the closest relation to one another, and between which, with each successive advance of the science, we continually discover new and sometimes wholly unexpected points of contact. A great part of the theories of Arithmetic derive an additional charm from the peculiarity that we easily arrive by induction at important propositions which have the stamp of simplicity upon them but the demonstration of which lies so deep as not to be discovered until after many fruitless efforts; and even then it is obtained by some tedious and artificial process while the simpler methods of proof long remain hidden from us." (Carl F Gauss, [introduction to Gotthold Eisenstein’s "Mathematische Abhandlungen"] 1847)

On Gravity II

"The weight of any heavy body of known weight at a particular distance from the center of the world varies according to the variation of its distance therefrom: so that as often as it is removed from the center, it becomes heavier, and when brought near to it, is lighter. On this account, the relation of gravity to gravity is as the relation of distance to distance from the center." (Al Khazini, "Book of the Balance of Wisdom", cca. 12th century)

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." (Sir Isaac Newton, "Philosophiæ Naturalis Principia Mathematica" ["The Mathematical Principles of Natural Philosophy"], 1687)

"It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact [...]That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers." (Sir Isaac Newton, [letter to Bentley] 1693)

"And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion." (Sir Isaac Newton, "Opticks", 1704)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe." (Thomas Carlyle, "Sartor Resartus", 1836)

"Gravity. Surely this force must be capable of an experimental relation to electricity, magnetism, and the other forces, so as to bind it up with them in reciprocal action and equivalent effect." (Michael Faraday, [Notebook entry] 1849) 

"It is no valid objection that science as yet throws no light on the far higher problem of the essence or origin of life. Who can explain gravity? No one now objects to following out the results consequent on this unknown element of attraction" (Charles Darwin, "The Origin of Species", 1859)

"Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance." (James C Maxwell, [Letter to William Huggins] 1868)

On Generalization (1920-1929)

"If we are not content with the dull accumulation of experimental facts, if we make any deductions or generalizations, if we seek for any theory to guide us, some degree of speculation cannot be avoided. Some will prefer to take the interpretation which seems to be most immediately indicated and at once adopted as an hypothesis; others will rather seek to explore and classify the widest possibilities which are not definitely inconsistent with the facts. Either choice has its dangers: the first may be too narrow a view and lead progress into a cul-de-sac; the second may be so broad that it is useless as a guide and diverge indefinitely from experimental knowledge." (Sir Arthur S Eddington, "The Internal Constitution of the Stars Observatory", Vol. 43, 1920)

"It is well to be explicit when a positive generalization is made from negative experimental evidence." (Arthur Eddington, "Space, Time and Gravitation: An Outline of the General Relativity", 1920)

"Generalization is the golden thread which binds many facts into one simple description." (Joseph W Mellor, "A Comprehensive Treatise on Inorganic and Theoretical Chemistry", 1922)

"[…] a history of mathematics is largely a history of discoveries which no longer exist as separate items, but are merged into some more modern generalization, these discoveries have not been forgotten or made valueless. They are not dead, but transmuted." (John W N Sullivan, "The History of Mathematics in Europe", 1925)

"Number knows no limitations, either from the side of the infinitely great or from the side of the infinitely small, and the facility it offers for generalization is too great for us not to be tempted by it." (Émile Borel, "Space and Time", 1926)

"[…] the statistical prediction of the future from the past cannot be generally valid, because whatever is future to any given past, is in tum past for some future. That is, whoever continually revises his judgment of the probability of a statistical generalization by its successively observed verifications and failures, cannot fail to make more successful predictions than if he should disregard the past in his anticipation of the future. This might be called the ‘Principle of statistical accumulation’." (Clarence I Lewis, "Mind and the World-Order: Outline of a Theory of Knowledge", 1929)

"The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation." (Alfred N Whitehead, "Process and Reality", 1929)

"Without doubt, if we are to go back to that ultimate, integral experience, unwarped by the sophistications of theory, that experience whose elucidation is the final aim of philosophy, the flux of things is one ultimate generalization around which we must weave our philosophical system." (Alfred N Whitehead, "Process and Reality: An Essay in Cosmology", 1929)

On Generalization (Unsourced)

"Facts are facts and it is from facts that we make our generalizations, from the little to the great, and it is wrong for a stranger to the facts he handles to generalize from them to other generalizations." (Charles Schuchert)

"Generalization is necessary to the advancement of knowledge; but particularity is indispensable to the creations of the imagination." (Thomas B Macaulay)

"Generalizations would be excellent things if we could be persuaded to part with them as easily as we formed them. They might then be used like the shifting hypotheses in certain operations of exact science, by help of which we may gradually approximate nearer and nearer to the truth." (Henry De la Beche)

"In these days of rapid scientific progress there is a tendency to accept the facts of nature, as at present known, without glancing back at the slow and difficult stages by which the knowledge of these facts has been arrived at. Yet such a retrospect is by no means unprofitable, since it warns us that hasty generalizations upon insufficient data retard rather than advance the progress of knowledge, and that the theories of the day must not be accepted as necessarily expressing absolute truths." (Archibald Garrod)

"Men are more apt to be mistaken in their generalizations than in their particular observations." (Niccolo Machiavelli)

"No one sees further into a generalization than his own knowledge of detail extends." (William James)

"Once we learn to expect theories to collapse and to be supplanted by more useful generalizations, the collapsing theory becomes not the gray remnant of a broken today, but the herald of a new and brighter tomorrow." (Isaac Asimov)

"Philosophy is more often the systematization of the prejudices of philosophers than the systematization of nature. Distrust all generalizations: stick to the concrete." (Epifanio de los Santos)

"So far as a theory is formed in the generalization of natural appearances, that theory must be just, although it may not be perfect, as having comprehended every appearance; that is to say, a theory is not perfect until it be founded upon every natural appearance; in which case, those appearances will be explained by the theory." (William Huggins)

On Generalization (1930-1949)

"The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. […] it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-Euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation." (Paul A M Dirac, "Quantities singularities in the electromagnetic field", Proceedings of the Royal Society of London, 1931)

"It is time, therefore, to abandon the superstition that natural science cannot be regarded as logically respectable until philosophers have solved the problem of induction. The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future." (Alfred J Ayer, "Language, Truth and Logic", 1936)

"The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future. There are only two ways of approaching this problem on the assumption that it is a genuine problem, and it is easy to see that neither of them can lead to its solution." (Alfred J Ayer, "Language, Truth, and Logic", 1936)

"The ethos of science involves the functionally necessary demand that theories or generalizations be evaluated in [terms of] their logical consistency and consonance with facts." (Robert K Merton, "Science and the Social Order", Philosophy of Science Vol 5 (3), 1938)

"The former distrust of specialization has been supplanted by its opposite, a distrust of generalization. Not only has man become a specialist in practice, he is being taught that special facts represent the highest form of knowledge." (Richard Weaver, "Ideas have Consequences", 1948)

Georg W F Hegel - Collected Quotes

"Knowledge is only real and can only be set forth fully in the form of science, in the form of system." (Georg W F Hegel, "The Phenomenology of Mind", 1807)

"The evident character of this defective cognition of which mathematics is proud, and on which it plumes itself before philosophy, rests solely on the poverty of its purpose and the defectiveness of its stuff, and is therefore of a kind that philosophy must spurn." (Georg W F Hegel, "The Phenomenology of Spirit", 1807)

"Each of the parts of philosophy is a philosophical whole, a circle rounded and complete in itself. In each of these parts, however, the philosophical Idea is found in a particular specificality or medium. The single circle, because it is a real totality, bursts through the limits imposed by its special medium, and gives rise to a wider circle. The whole of philosophy in this way resembles a circle of circles. The Idea appears in each single circle, but, at the same time, the whole Idea is constituted by the system of these peculiar phases, and each is a necessary member of the organisation." (Georg W F Hegel, "Encyclopedia of the Philosophical Sciences", 1816)

"It is because the method of physics does not satisfy the comprehension that we have to go on further." (Georg W F Hegel, "Encyclopedia of the Philosophical Sciences", 1816)

"Generally speaking, symbol is some form of external existence immediately present to the senses, which, however, is not accepted for its own worth, as it lies before us in its immediacy, but for the wider and more general significance which it offers to our reflection. We may consequently distinguish between two points of view equally applicable to the term: first, the significance, and, second, the mode in which such a significance is expressed. The first is a conception of the mind, or an object which stands wholly indifferent to any particular content; the latter is a form of sensuous existence or a representation of some kind or other" (Georg W F Hegel, "Ästhetik" Vol. 2, 1817)

"An idea is always a generalization, and generalization is a property of thinking. To generalize means to think." (Georg W F Hegel, "The Philosophy of Right", 1820)

"History in general is therefore the development of Spirit in Time, as Nature is the development of the Idea is Space." (Georg W F Hegel, "Lectures on the Philosophy of History", 1837)

"Poetry is the universal art of the spirit which has become free in itself and which is not tied down for its realization to external sensuous material; instead, it launches out exclusively in the inner space and the inner time of ideas and feelings." (G W Friedrich Hegel, "Introduction to Aesthetics", 1842)

"Education is the art of making man ethical." (Georg W F Hegel)

"Motion is the process, the transition of Time into Space and of Space into Time: Matter, on the other hand, is the relation of Space and Time as a peaceful identity." (Georg W F Hegel)

"Music is architecture translated or transposed from space into time; for in music, besides the deepest feeling, there reigns also a rigorous mathematical intelligence." (Georg W F Hegel)

"People who are too fastidious towards the finite never reach actuality, but linger in abstraction, and their light dies away." (Georg W F Hegel)

"Philosophy is by its nature something esoteric, neither made for the mob nor capable of being prepared for the mob." (Georg W F Hegel)

"Truth in philosophy means that concept and external reality correspond." (Georg W F Hegel)

On Imagination (1800-1849)

"The philosopher who is really useful to the cause of science, is he who, uniting to a fertile imagination, a rigid severity in investigation and observation, is at once tormented by the desire of ascertaining the cause of the phenomena, and by the fear of deceiving himself in that which he assigns." (Pierre-Simon Laplace, "System of the World" Vol. 2, 1809)

"When the eye or the imagination is struck with an uncommon work, the next transition of an active mind is to the means by which it was performed." (Samuel Johnson, 1810)

"The imagination […] that reconciling and mediatory power, which incorporating the reason in images of the sense and organizing (as it were) the flux of the senses by the permanence and self-circling energies of the reason, gives birth to a system of symbols, harmonious in themselves, and consubstantial with the truths of which they are the conductors." (Samuel T Coleridge, "The Statesman's Manual", 1816)

"It seems to be like taking the pieces of a dissected map out of its box. We first look at one part, and then at another, then join and dove-tail them; and when the successive acts of attention have been completed, there is a retrogressive effort of mind to behold it as a whole. The poet should paint to the imagination, not to the fancy; and I know no happier case to exemplify the distinction between these two faculties." (Samuel T Coleridge," Biographia Literaria", 1817)

"Whilst chemical pursuits exalt the understanding, they do not depress the imagination or weaken genuine feeling; whilst they give the mind habits of accuracy, by obliging it to attend to facts, they likewise extend its analogies; and, though conversant with the minute forms of things, they have for their ultimate end the great and magnificent objects of nature." (Sir Humphry Davy, "Consolations in Travel, or the Last Days of a Philosopher", 1830)

"No occupation is more worthy of an intelligent and enlightened mind, than the study of Nature and natural objects; and whether we labour to investigate the structure and function of the human system, whether we direct our attention to the classification and habits of the animal kingdom, or prosecute our researches in the more pleasing and varied field of vegetable life, we shall constantly find some new object to attract our attention, some fresh beauties to excite our imagination, and some previously undiscovered source of gratification and delight." (Sir Joseph Paxton, "A Practical Treatise on the Cultivation of the Dahlia", 1838)

"But a thousand unconnected observations have no more value, as a demonstrative proof, than a single one. If we do not succeed in discovering causes by our researches, we have no right to create them by the imagination; we must not allow mere fancy to proceed beyond the bounds of our knowledge."(Justus von Liebig, "The Lancet", 1844)

"The nose of a mob is its imagination. By this, at any time, it can be quietly led." (Edgar A Poe, "The Works of Edgar Allan Poe", 1849)

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