Philosophy of science

"Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury."

"Man, being the servant and interpreter of Nature, can do and understand so much and so much only as he has observed in fact or in thought of the course of nature. Beyond this he neither knows anything nor can do anything."

"The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search for truth. So it does more harm than good."

"There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immoveable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried."

"Both ways set out from the senses and particulars, and rest in the highest generalities; but the difference between them is infinite. For the one just glances at experiment and particulars in passing, the other dwells duly and orderly among them. The one, again, begins at once by establishing certain abstract and useless generalities, the other rises by gradual steps to that which is prior and better known in the order of nature."

"There is a great difference between the Idols of the human mind and the Ideas of the divine. That is to say, between certain empty dogmas, and the true signatures and marks set upon the works of creation as they are found in nature."

"There can be no doubt that light consists of the motion of a certain substance. For if we examine its production we find that... when light is accumulated, say by concave mirrors, it has the property of combustion just as fire has, that is to say, it disunites the parts of bodies, which is assuredly a proof of motion, at least in the true philosophy, in which the causes of all natural effects are conceived as mechanical causes. Which in my judgment must be accomplished or all hope of ever understanding physics is renounced."

"[W]e offer this work as mathematical principles of philosophy. For all the difficulty of philosophy seems to consist in this, from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena."

"The only immediate utility of all sciences, is to teach us, how to control and regulate future events by their causes... And yet so imperfect are the ideas which we form concerning it, that it is impossible to give any just definition of cause, except what is drawn from something extraneous and foreign to it. Similar events are always conjoined with similar. Of this we have experience. Suitably to this experience, therefore, we may define a cause to be an object, followed by another, and where all the objects, similar to the first, are followed by objects similar to the second. Or in other words, where, if the first object had not been, the second never had existed. The appearance of the cause always conveys the mind, by a customary transition, to the idea of the effect. Of this also we have experience. We may, therefore, suitably to this experience, form another definition of cause; and call it, an object followed by another, and whose appearance always conveys the thought to that other. But though both these definitions be drawn from circumstances foreign to the cause, we cannot remedy this inconvenience, or attain any more perfect definition, which may point out that circumstance in the cause, which gives it a connexion with its effect. We have no idea of this connexion; nor even any distinct notion what it is we desire to know, when we endeavour at a conception of it."

"A judgment of observation can never rank as experience, without the law, that "whenever an event is observed, it is always referred to some antecedent, which it follows according to a universal rule." ...We cannot therefore study the nature of things a priori otherwise than by investigating the conditions and the universal (thought subjective) laws, under which alone such a cognition as experience (as to mere form) is possible..."

"Chemistry... Without this new order of phenomena the most important operations of terrestrial nature would be incomprehensible to us; and there is no other class of phenomena so intimate and so complex. Inert bodies can never appear so nearly like vital ones as when they produce in each other those rapid and profound perturbations which characterize chemical effects. ...the spirit of all theological and metaphysical philosophy consists in conceiving of all phenomena as analogous to the only one which is known by immediate consciousness—Life: and we can easily understand that the primitive method of philosophizing must have exerted a more powerful and obstinate dominion over chemical phenomena than any other, in the inorganic world.—We must consider, too, that direct and spontaneous observation must have been applied in the first place only to very complicated phenomena, such as vegetable combustions, fermentations, etc., the analysis of which now requires all the resources of our science: and that the most important chemical phenomena are produced only in artificial circumstances, which were long in being devised, and very difficult at first to institute. ...we can hardly imagine the difficulty there must have been, in the infancy of chemistry, in creating suitable subjects for observation: and we can not suppose that the ancient investigators of nature could have had energy and perseverance to discover the principal phenomena of the science if they had not been constantly stimulated by the unbounded hopes arising from their chimerical notions of the constitution of matter."

"Natural scientists believe that they free themselves from philosophy by ignoring or abusing it. They cannot, however, make any headway without thought, and for thought they need thought determinations. But they take these categories unreflectively from the common consciousness of so-called educated persons, which is dominated by relics of long obsolete philosophies, or from the little bit of philosophy compulsorily listened to at the university (which is not only fragmentary, but also a medley of views of people belonging to the most varied and mostly the worst schools) or from uncritical and unsystematic reading of philosophical writings of all kinds. Hence they are no less in bondage philosophy but unfortunately in most cases to the worst philosophy, and those who abuse philosophy most are slaves to precisely the worst vulgarized relics of the worst philosophies."

"Comte's work is the strongest embodied rebuke ever given to that form of theological intolerance which censures Positive Philosophy for pride of reason and lowness of morals. The imputation will not be dropped, and the enmity of the religious world to the book will not slacken... The theological world can not but hate a book which treats of theological belief as a transient state of the human mind. And again, the preachers and teachers, of all sects and schools, who keep to the ancient practice, once inevitable, of contemplating and judging of the universe from the point of view of their own minds, instead of having learned to take their stand out of themselves, investigating from the universe inward, and not from within outward, must necessarily think ill of a work which exposes the futility of their method, and the worthlessness of the results to which it leads. As M. Comte treats of theology and metaphysics as destined to pass away, theologians and metaphysicians must necessarily abhor, dread, and despise his work. ...We find ourselves suddenly living and moving in the midst of the universe,—as a part of it, and not as its aim and object. We find ourselves living, not under capricious and arbitrary conditions, unconnected with the constitution and movements of the whole, but under great, general, invariable laws, which operate on us as a part of the whole. ...We find here indications in passing of the evils we suffer from our low aims, our selfish passions, and our proud ignorance; and in contrast with them, animating displays of the beauty and glory of the everlasting laws, and of the sweet serenity, lofty courage, and noble resignation, that are the natural consequence of pursuits so pure, and aims so true, as those of Positive Philosophy. ...The law of progress is conspicuously at work throughout human history. The only field of progress is now that of Positive Philosophy, under whatever name it may be known to the real students of every sect; and therefore must that philosophy be favorable to those virtues whose repression would be incompatible with progress."

"The first process... in the effectual study of science must be one of simplification and reduction of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis."

"Mathematicians may flatter themselves that they possess new ideas which mere human language is yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations of their minds."

"[T]he only thing that I believe that I am really fit for is the investigation of abstract truth, and the more abstract the better. If there is any science that I am capable of promoting, I think it is the science of science itself, the science of investigation, of method."

"I cannot perceive that the part which conceptions have in the operation of studying facts, has ever been overlooked or undervalued as Mr. Whewell supposes it has. No one ever disputed that in order to reason about anything we must have a conception of it; or that when we include a multitude of things under a general expression, there is implied in the expression a conception of something common to those things. But it by no means follows that the conception is necessarily pre-existent, or constructed by the mind out of its own materials. If the facts are rightly classed under the conception, it is because there is in the facts themselves something of which the conception is itself a copy; and which if we cannot directly perceive, it is because of the limited power of our organs, and not because the thing itself is not there. The conception itself is often obtained by abstraction from the very facts which, in Mr. Whewell's language, it is afterwards called in to connect. This Mr. Whewell himself admits, when he observes... how great a service would be rendered to the science of physiology by the philosopher "who should establish a precise, tenable, and consistent conception of life." Such a conception can only be abstracted from the phenomena of life itself; from the very facts which it is put in requisition to connect. In other cases... instead of collecting the conception from the very phenomena which we are attempting to colligate, we select it from among those which have been previously collected by abstraction from other facts. In the instance of Kepler's laws the latter was the case."

"It is such a case as this which gives color to the doctrine that the mind, in framing the descriptions, adds something of its own which it does not find in the facts. Yet it is a fact, surely, that the planet does describe an ellipse... knowing what an ellipse was, Kepler tried whether the observed places of the planet were consistent with such a path. He found they were so... But this fact, which Kepler did not add to, but found in the motions of the planet, namely, that it occupied in succession the various points in the circumference of a given ellipse, was the very fact, the separate parts of which had been separately observed; it was the sum of the different observations. It superadded nothing to the particular facts which it served to bind together: except... the knowledge that a resemblance existed between the planetary orbit and other ellipses..."

"When our conceptions are clear and distinct, when our facts are certain and sufficiently numerous, and when the conceptions, being suited to the nature of the facts, are applied to them so as to produce an exact and universal accordance, we attain knowledge of a precise and comprehensive kind, which we may term Science. And we apply this term... still more decidedly when, facts being thus included in exact and general propositions, such propositions are... included with equal rigour in propositions of a higher degree of generality; and these again in others of a still wider nature, so as to form a large and systematic whole."

"Ideas and Conceptions are... distinct elements of the scientific truths... [this is] proved beyond doubt, not only by considering that the discoveries never were made, nor could be made, till the right Conception was obtained, and by seeing how difficult it often was to obtain this element; but also, by seeing that the Idea and the Conception itself, as distinct from the Facts, was, in almost every science, the subject of long and obstinate controversies;—controversies which turned upon the possible relations of Ideas, much more than upon the actual relations of Facts. ...These controversies make up a large portion of the history of each science; a portion quite as important as the study of the facts; and a portion, at every stage of the science, quite as essential to the progress of truth."

"[T]he elliptical motion was not merely the sum of the different observations... other persons, and Kepler himself before his discovery, did not find it by adding together the observations. ...it was the sum of the observations, seen under a new point of view, which point of view Kepler's mind supplied. Kepler found it in the facts, because it was there... but also... because he had in his mind those relations of thought which enabled him to find it. ...We too find the law in Kepler's book; but if we did not understand Latin, we should not find it there. ...In like manner, a discoverer must know the language of science, as well as look at the book of nature, in order to find scientific truth. All the discussions and controversies respecting Ideas and Conceptions of which I have spoken, may be looked upon as discussions and controversies respecting the grammar of the language in which nature speaks to the scientific mind. Man is the Interpreter of Nature; not the Spectator merely, but the Interpreter. The study of the language, as well as the mere sight of the characters, is requisite in order that we may read the inscriptions which are written on the face of the world."

"Upon these methods, the obvious thing to remark is, that they take for granted, the very thing which is most difficult to discover, the reduction of the phenomena to formulae... When we have any set of complex facts offered to us; for instance... the facts of the planetary paths, of falling bodies, of refracted rays, of cosmical motions, of chemical analysis; and when, in any of these cases, we would discover the law of nature which governs them, or, if any one chooses so to term it, the feature in which all the cases agree, where are we to look... ? Nature does not present to us the cases in this form... Who will tell us which of the methods of inquiry those historically real and successful inquiries exemplify? Who will carry these formulae through the history of the sciences, as they have really grown up; and shew us that these... methods have been operative in their formation; or that any light is thrown upon the steps of their progress by reference to these formulae?"

"Lagrange... was the first to draw sharply the line of demarcation between physics and metaphysics. The mechanical ideas of Descartes, Leibnitz, Maupertius, and even of Euler, had proved to be more or less hazy and unfruitful from a failure to separate those two distinct regions of thought. Lagrange put an end to this confusion, for no serious attempt has since been made to derive the laws of mechanics from a metaphysical basis."

"However far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is that simply by the word "experiment" we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics."

"It is my task to inquire how it has come about that a generation so amazingly proficient in the practice of science can be so amazingly impotent in the understanding of it... the state of unconscious automatism in which science finds itself today is due to the lack throughout history of a critical school working within the scientific movement itself and performing... at least one of the functions, which criticism has performed for literature from the earliest times."

"The conception... of the purely fictitious character of the basic principles of theory was in the eighteenth and nineteenth centuries still far from being the prevailing one. But it continues to gain more and more ground because of the everwidening logical gap between the basic concepts and laws on the one side and the consequences to be correlated with our experiences on the other—a gap which widens progressively with the developing unification of the logical structure, that is with the reduction in the number of the logically independent conceptual elements required for the basis of the whole system."

"It has often been said... that the man of science is a poor philosopher. Why then should it not be the right thing to let the philosopher do the philosophizing? ...it can not be right at a time when the very foundations of physics itself have become as problematic as they are now. ...the physicist cannot simply surrender to the philosopher the critical contemplation of theoretical foundations; for he... knows best and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear in his own mind just how far the concepts which he uses are justified, and are necessities."

"I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. ...A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is... the mark of distinction between a mere artisan or specialist and a real seeker after truth."

"[I]n textbooks and classrooms... an attempt is made to "purge science of philosophy"... Actually, great advances in sciences have consisted rather in breaking down the dividing walls, and a disregard for meaning and foundation is only prevalent in periods of stagnation. If the scientists, who play an immense social role in our present world, are not to become a class of learned ignoramuses, the education of these men must not restrict itself to the purely technical approach but must give full attention to the philosophical aspect and place of science within the general domain of human thought."

"The interest in science that is not due to its technical application but to its impact upon our common-sense picture of the world we may briefly call the "philosophical" interest. Science teaching in our schools... has for the most part ignored this philosophical interest, and has even proclaimed it a duty of the teacher to present science as completely isolated from its philosophical implications. ...It may seem paradoxical, but the dodging of philosophical issues has very frequently made science graduates captives of obsolete philosophies."

"Very frequently science has served by means of its metaphysical interpretations as a direct guide to human conduct. ...by its metaphysical interpretations it has served what has been called, occasionally, "human engineering." ..."philosophy of science" leads eventually to a research in the "pragmatics of science," which envisages a coherent system containing the physical and biological as well as the sciences of human behavior."

"In actual practice science has always made use of both induction and deduction... The contemporaries of Plato and Aristotle certainly knew from observation that the celestial bodies performed orbits in the heavens that could be identified vaguely as being circular. ...However ...the principle ...was "believed in" much more firmly than this "inductive inference" from observation would warrant. Men believed in it as "intelligible principle"; it seemed very plausible that perfect divine beings like the celestial bodies should also move in "perfect orbits," and the perfect curve is the circle. ...The difference between ancient and modern science was not the use of induction... but the criteria by which a discovered principle was recognized to be valid. The method of "verification" is different now; more weight is given to the agreement... with observed facts than to the agreement... with a world picture that has been accepted for what we called... "philosophical" reasons."

"The Philosopher, in his reflections on spatial and temporal relations, on number and quantity, on matter and motion, is in a region of thought in which the boundary between his own domain and that of the Mathematician is almost non-existent. The Epistemologist has always to take Mathematical knowledge as a kind of touchstone on which to test his theories of the nature of knowledge. The dominant views in various departments of philosophical thinking have been modified in important points by the results of recent Mathematical research, and will, I think, in the future, be further modified from the same quarter."

"In an ideal university the student would not proceed from the most recent observations back to the first principles, but from the first principles to whatever recent observations we claim significant in understanding them. ...The natural sciences derive their principles from the philosophy of nature which, in turn, depends on metaphysics. ...Metaphysics, the study of the first principles, pervades the whole. Dependent on it and subordinate to it are the social and natural sciences."

"Another frame which we impose on the world is space. Whence come the first principles of geometry? Are they imposed on us by logic? Lobachevski has proved not, by creating non-Euclidean geometry. Is space revealed to us by our senses? Still no, for the space our senses could show us differs absolutely from that of the geometer. Is experience the source of geometry? A deeper discussion will show us it is not. We therefore conclude that the first principles of geometry are only conventions; but these conventions are not arbitrary and if transported into another world (that I call the non-Euclidean world and seek to imagine), then we should have been led to adopt others."

"In mechanics we... should see that the principles of this science, though more directly based on experiment, still partake of the conventional character of the geometric postulates. Thus far triumphs; but now we arrive at the physical sciences, properly so called. Here the scene changes; we meet another sort of hypotheses and we see their fertility. Without doubt, at first blush, the theories seem to us fragile, and the history of science proves to us how ephemeral they are; yet they do not entirely perish, and of each of them something remains. It is this something we must seek to disentangle, since there and there alone is the veritable reality."

"The scientist who discovers a theory is usually guided to his discovery by guesses; he cannot name a method by means of which he found the theory and can only say that it appeared plausible to him, that he had the right hunch, or that he saw intuitively which assumptions would fit the facts. Some philosophers have misunderstood this psychological description of discovery as proving that there exists no logical relation leading from the facts to the theory... These philosophers do not see that the same scientist who discovered his theory through guessing presents it to others only after he sees that his guess is justified by the facts. ...The inductive inference is employed not for finding a theory but for justifying it in terms of observational data."

"Rather than treating the content of a natural science as a tight and coherent logical system, we shall... have to consider it as a conceptual aggregate, or 'population', within which there are—at most—localized pockets of logical systematicity. Seen in this light, the problem of scientific rationality can be restated in new terms. ...The extreme 'revolutionary' view of conceptual change remains attractive... only if we make the twin mistakes of equating 'rationality' and 'logicality', and supposing that an entire science has the same logical coherence as (say) Euclid's geometry of Newton's mechanics. ...Those who assume that an entire science necessarily forms a single, coherent intellectual system will correctly infer that 'radical' changes in its intellectual content must also be 'revolutionary'. In this respect, the problems arising over Kuhn's account of scientific change have significant parallels in sociology and elsewhere. The belief that society as a whole forms a single coherent and functional 'social system'... is a direct counterpart to the belief that physics as a whole forms a coherent 'logical system'. An oversytematic analysis of social structure has, in fact, dominated a great part of sociological theory for almost as long as its logical counterpart has dominated the philosophy of science; and, in each case, the revolutionary view is an understandable over-reaction to that domination. ...We can view an entire society as forming a single functional 'system', only if we fail to distinguish the looser social and political relations between the different institutions of a society ...[A]n entire science comprises an 'historical population' of logically independent concepts and theories, each with its own separate history, structure, and implications."

"Nothing... compels us either to treat 'representations' as being inner mental entities, or to regard 'things-in-themselves' as external objects hidden from direct perception, beyond the sensory 'representations' formed within our cerebral mechanisms. Yet this is the sense in which Kant's position was widely understood... by physiologists and psychologists like Müller, Helmholtz and Fechner, and... philosophers like Schopenhuaer. ...The term Vorstellung came to refer simply to the 'ideas' brought into existence as an effect of repeated sensory 'impressions' (Empfindungen); the critical philosophy lost the transcendental character... and... Mach... confuse[d] the theories of Kant's Critiques with those of Berkeley and Hume, which Kant himself had been trying to supercede. ...[W]e can equally well state Kant's epistemic point... using... Darstellung—as used by Hertz, Bühler, and Boltzmann, and Kant himself... a 'representation', in the sense in which a theatrical representation... exhibition or recital provides a public... representation of works of art or music. To darstellen a phenomenon is then to 'demonstrate' or 'display' it... in an entirely public manner what it comprises, or how it operates: as when an hydraulic system... is used to provide a simplified... explanatory model, of a complex electrical circuit. (By contrast... Vorstellung suggests a 'representation' as private or personal... 'in the mind' of an individual. ...[It] carries the same burden as words like 'idea' and 'imagination': it is, in fact, the standard German translation for the Lockean term 'idea'...) ...When Hertz spoke of a dynamical theory as providing a Darstellung of the motions that it explains, and when Wittgenstein declared... propositions of a language darstellen the facts of the world, their assertions had nothing specifically 'mental' or 'inner' about them. ...[C]ollective intellectual functions of concepts and representation techniques in the explanatory activities of science... in terms of Darstellungen can sidetrack... Cartesian and Humean puzzles about the relationship between the 'inner' concepts and 'external' phenomena. At the same time it concedes to Frege all that his anti-psychologism legitimately claimed... that 'explaining' a phenomenon requires us not just to imagine inwardly... but to demonstrate publicly the nature of the relationships..."

"To expect to reorganise our ideas of Time, Space, and Measurement without some discussion which must be ranked as philosophical is to neglect the teaching of history... it is well to understand the limitations to the meaning of philosophy in this connection. It has nothing to do with ethics or theology or the theory of aesthetics. It is solely engaged in determining the most general conceptions which apply to things observed by the senses. Accordingly it is not even metaphysics: it should be called pan-physics. Its task is to formulate those principles of science which are employed equally in every branch of natural science. ...The philosophy of science is the endeavour to formulate the most general characters of things observed. ...in human thought the particular precedes the general. Accordingly the philosophy will not advance until the branches of science have made independent progress. Philosophy then appears as a criticism and a corrective, and what is now to the purpose as an additional source of evidence in times of fundamental reorganisation."

"This assignment of the role of philosophy is borne out by history. It is not true that science has advanced in disregard of any general discussion of the character of the universe. The scientists of the Renaissance and their immediate successors of the seventeenth century, to whom we owe our traditional concepts, inherited from Plato, Aristotle and the medieval scholastics. It is true that the New Learning reacted violently against the schoolmen who were their immediate predecessors; but... they borrowed... certain root-presuppositions respecting space, time, matter, predicate and subject, and logic in general. It is legitimate (as a practical counsel in the management of a short life) to abstain from the criticism of scientific foundations so long as the superstructure works. But to neglect philosophy when engaged in the re-formation of ideas is to assume the absolute correctness of the chance philosophic prejudices imbibed from a nurse or a schoolmaster or current modes of expression. It is to enact the part of those who thank Providence that they have been saved from the perplexities of religious enquiry by the happiness of birth in the true faith. The truth is that your available concepts depend upon your philosophy."

"All the world over and at all times there have been practical men, absorbed in 'irreducible and stubborn facts': all the world over and at all times there have been men of philosophic temperament who have been absorbed in the weaving of general principles. It is the union of passionate interest in the detailed facts with equal devotion to abstract generalisation which forms the novelty in our present society. Previously it had appeared sporadically and as if by chance. This balance of mind has now become part of the tradition which infects cultivated thought. It is the salt which keeps life sweet. The main business of universities is to transmit this tradition as a widespread inheritance from generation to generation."

"Nowadays, explicit engagement with the philosophy of science plays almost no role in the training of physicists or physics research. What little the student learns about philosophical issues is typically learned casually, by a kind of intellectual osmosis. ...Careful reflection on philosophical ideas is rare. Even rarer is systematic instruction. Worse still, publicly indulging an interest in philosophy of science is often treated as a social blunder. ...explicitly philosophical approaches to physics are the exception. Things were not always so."

"[C]hallenges to positivism were born out of the context of , which has historically set the first main point of the opposition to positivism (or rather, to reductionism). The basic epistemological tenet of conventionalism holds that the laws of science (such as Newtonian mechanics) and the axioms of mathematics (like Euclidean geometry) are not experimental generalizations, neither a priori knowledge, but conventions or linguistic definitions. ...Henri Poincaré is considered the main proponent of conventionalism."

"Of course, it is well known from the philosophy of science that any evidence whatsoever can be made consistent with any theory whatsoever by introducing enough auxiliary hypotheses."