Passages about science and method

Nature is a source or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not in virtue of a concomitant attribute.

Motion is the fulfilment of what exists potentially, in so far as it exists potentially.

Human knowledge and human power meet in one, for where the cause is not known the effect cannot be produced.

Nature to be commanded must be obeyed.

Good sense is, of all things among men, the most equally distributed; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.

I think, therefore I am, was so certain and of such evidence, that no ground of doubt, however extravagant, could be alleged by the sceptics capable of shaking it.

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.

Custom, then, is the great guide of human life.

All men by nature desire to know.

There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature.

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses.

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

I cannot but conclude the bulk of your natives to be the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth.

And he gave it for his opinion, that whoever could make two ears of corn or two blades of grass to grow upon a spot of ground where only one grew before, would deserve better of mankind, and do more essential service to his country, than the whole race of politicians put together.

Thoughts without content are empty, intuitions without concepts are blind.

Hitherto it has been assumed that all our knowledge must conform to objects. We must therefore make trial whether we may not have more success if we suppose that objects must conform to our knowledge.

It is not the strongest of the species that survives, nor the most intelligent, but the one most responsive to change.

Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, will tend to the preservation of that individual, and will generally be inherited by its offspring.

What is that which always is and has no becoming, and what is that which becomes and never is?

The father and maker of all this universe is past finding out; and even if we found him, to tell of him to all men would be impossible.

A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so.

We think we understand a thing without qualification when we think we know the cause on account of which it is so, and that it cannot be otherwise.

A point is that which has no part.

Let the following be postulated: to draw a straight line from any point to any point.

I began to think whether there might not be a motion, as it were, in a circle.

The heart of creatures is the foundation of life, the prince of all, the sun of their microcosm, on which all vegetation does depend, from whence all vigour and strength does flow.

Life is short, the art long, opportunity fleeting, experiment perilous, and judgement difficult.

It is not, in my opinion, any more divine or more sacred than other diseases, but has a natural cause, and its supposed divine origin is due to men's inexperience and to their wonder at its peculiar character.

I know that I am mortal and the creature of a day; but when I search out the massed wheeling circles of the stars, my feet no longer touch the earth, but side by side with Zeus himself I take my fill of ambrosia.

It is our purpose to demonstrate for the five planets, as we did for the sun and moon, that all their apparent irregularities can be represented by uniform circular motions, since these alone are proper to the divine.

Nature does nothing in vain.

Each of the organs attracts the juice which is proper to it, as the lodestone attracts iron.

In the middle of all sits the sun enthroned. In this most beautiful temple could we place this luminary in any better position from which he can illuminate the whole at once?

Mathematics is written for mathematicians.

The orbit of a planet is an ellipse, with the sun at one of the two foci.

A line joining a planet to the sun sweeps out equal areas in equal times.

The End of our Foundation is the knowledge of Causes, and secret motions of things; and the enlarging of the bounds of Human Empire, to the effecting of all things possible.

We have consultations, which of the inventions and experiences which we have discovered shall be published, and which not.

All the sciences are nothing other than human wisdom, which always remains one and the same, however different the subjects to which it is applied.

By a method I mean reliable rules which are easy to apply, such that whoever follows them exactly will never take what is false to be true, and will arrive at a true understanding of everything within his capacity.

Any problem in geometry can easily be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction.

Taking one line which I shall call unity in order to relate it as closely as possible to numbers, the product of two lines may be taken as a line.

The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time intervals employed in traversing these distances.

If two stones of different weight are tied together, the slower should retard the faster and the faster hurry the slower, so that the pair moves more slowly than the heavier alone, and yet the pair is heavier than either.

My design in this book is not to explain the properties of light by hypotheses, but to propose and prove them by reason and experiments.

The light of the sun consists of rays differently refrangible.

Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.

Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger.

Nothing is created, either in the operations of art or in those of nature, and it may be laid down as a principle that in every operation there is an equal quantity of matter before and after.

We cannot improve the language of any science without at the same time improving the science itself; neither can we, on the other hand, improve a science without improving the language which belongs to it.

I have at last succeeded in illuminating a magnetic curve or line of force, and in magnetising a ray of light.

Nothing is too wonderful to be true, if it be consistent with the laws of nature.

We must acknowledge, as it seems to me, that man with all his noble qualities still bears in his bodily frame the indelible stamp of his lowly origin.

The difference in mind between man and the higher animals, great as it is, certainly is one of degree and not of kind.

The pragmatic method is primarily a method of settling metaphysical disputes that otherwise might be interminable. What difference would it practically make to anyone if this notion rather than that notion were true?

Theories thus become instruments, not answers to enigmas, in which we can rest.

The ego is not master in its own house.

A dream is a disguised fulfilment of a suppressed or repressed wish.

The things that are perish into the things out of which they come to be, according to necessity, for they pay penalty and retribution to each other for their injustice according to the ordering of time.

You cannot step twice into the same river, for other waters are ever flowing on.

Since we have to distinguish the causes and definitions of coming to be and passing away alike in all cases, and in the same way, we must treat also of growth and alteration.

The elements come to be out of one another reciprocally, and each has a pair of the qualities: fire is hot and dry, air hot and moist, water cold and moist, earth cold and dry.

We must not recoil with childish aversion from the examination of the humbler animals. Every realm of nature is marvellous.

If a man had been a work of art, we should not ask what he is made of but what he is for; and the same holds of the works of nature.

Give me a place to stand and I will move the earth.

The surface of any sphere is four times its greatest circle, and any cylinder having its base equal to the greatest circle of a sphere and height equal to the diameter is half as large again as the sphere.

Of the eight books, the first four form an elementary introduction. The first contains the modes of producing the three sections and the opposite branches, and their fundamental properties, worked out more fully and generally than in the writings of others.

The third book contains many remarkable theorems useful for the synthesis of solid loci, of which the most part and the most beautiful are new; and it was the discovery of these that made me aware that Euclid had not worked out the locus with respect to three and four lines.

All that has by nature with systematic method been arranged in the universe seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things.

Perfect numbers are equal to the sum of their own parts: six, twenty-eight, four hundred and ninety-six, eight thousand one hundred and twenty-eight.

In the discovery of hidden things and in the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators.

The terrella is a stone of magnetic substance ground into a sphere, and on it may be shown all the motions which the earth's own magnetic power produces in bodies placed upon it.

I have taken all knowledge to be my province.

They are ill discoverers that think there is no land, when they can see nothing but sea.

The square of the periodic time of any planet is to the square of the periodic time of another as the cube of its mean distance is to the cube of the other's.

I am stealing the golden vessels of the Egyptians to build a tabernacle to my God from them, far from the borders of Egypt. If you forgive me, I shall rejoice; if you reproach me, I shall endure.

Each little region of a luminous body, such as the Sun, a candle, or a burning coal, generates its own waves of which that region is the centre.

There is the further consideration that each particle of matter in which a wave spreads ought to communicate its movement not only to the next particle in the straight line drawn from the luminous point, but also to all the others which touch it, so that around each particle there arises a wave of which that particle is the centre.

Go into the Royal Exchange in London, a place more venerable than many a court, and you will see representatives of every nation assembled for the profit of mankind. There the Jew, the Mohammedan and the Christian deal with one another as if they were of the same religion, and reserve the name of infidel for those who go bankrupt.

If there were only one religion in England there would be danger of despotism, if there were two they would cut each other's throats; but there are thirty, and they live in peace and happiness.

Beautiful is that which pleases universally without a concept.

Taste is the faculty for judging an object or a kind of representation through a satisfaction or dissatisfaction without any interest. The object of such a satisfaction is called beautiful.

I had worked hard for nearly two years, for the sole purpose of infusing life into an inanimate body. For this I had deprived myself of rest and health. I had desired it with an ardour that far exceeded moderation; but now that I had finished, the beauty of the dream vanished, and breathless horror and disgust filled my heart.

I ought to be thy Adam, but I am rather the fallen angel, whom thou drivest from joy for no misdeed.

There is no better, there is no more open door by which you can enter into the study of natural philosophy than by considering the physical phenomena of a candle.

You must not take it as a discourtesy if I speak plainly. I claim the privilege of speaking to juveniles as a juvenile myself.

Habit is thus the enormous fly-wheel of society, its most precious conservative agent. It alone is what keeps us all within the bounds of ordinance, and saves the children of fortune from the envious uprisings of the poor.

Consciousness, then, does not appear to itself chopped up in bits. Such words as chain or train do not describe it fitly as it presents itself in the first instance. It is nothing jointed; it flows. A river or a stream are the metaphors by which it is most naturally described.

The axioms of geometry are neither synthetic a priori judgments nor experimental facts. They are conventions. Our choice among all possible conventions is guided by experimental facts, but it remains free.

One geometry cannot be more true than another; it can only be more convenient.

Hysterics suffer mainly from reminiscences.

The patient herself, who at this period of her illness strangely enough spoke and understood only English, gave this procedure the name of the talking cure.

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods, all generate the expectation of a speedy introduction to processes of interest.

It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilisation advances by extending the number of important operations which we can perform without thinking about them.

Is there any knowledge in the world which is so certain that no reasonable man could doubt it? This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked.

The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.

Every reference-body has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

The laws of physics are the same for all observers in uniform motion relative to one another, and light in empty space always travels at the same speed regardless of the motion of its source.

The pure conservative is fighting against the essence of the universe.

I will name this the Fallacy of Misplaced Concreteness. It consists in neglecting the degree of abstraction involved when an actual entity is considered merely so far as it exemplifies certain categories of thought.

Where id was, there ego shall be. It is a work of culture, not unlike the draining of the Zuider Zee.

In its relation to the id the ego is like a man on horseback, who has to hold in check the superior strength of the horse; with this difference, that the rider tries to do so with his own strength while the ego uses borrowed forces.

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.

It was an act of desperation. For six years I had struggled with the theory of black-body radiation. I knew the problem was fundamental and I knew the answer. I had to find a theoretical explanation at any price, however high.

We have already discussed the first and most fundamental element, and the ordered and eternal bodies that are carried in a circle, and next to these the number and nature of the bodies that move naturally between the heavens and the region nearest the earth.

There are two kinds of exhalation, one vaporous and moist, the other dry and smoky, and the sun draws both from the earth and from moisture on its surface, the moist producing clouds and rain, the dry producing wind and, when confined below the surface, earthquakes.

The body which moves in a circle must be without weight or lightness, for neither by nature nor contrary to nature could it move either towards or away from the center.

It is plain from what has been said that there is neither place nor void nor time outside the heaven, since it is not the nature of every body to be in a place.

Of fishes, the so-called selachians, and among them the dogfish, are seen to produce their young alive, and to nourish the embryo by means of a structure resembling, in position and function, the umbilical cord and placenta of viviparous quadrupeds.

The octopus uses its arms both as feet and as hands, drawing in food with them, and it has the remarkable habit of changing color to match the rocks near which it lives, doing this both from fear and for the purpose of concealment when hunting.

The male provides the form and the principle of movement, the female provides the body and the material; it is like the coagulation of milk, where the rennet acts on the milk to give it form.

The female is as it were a deformed male, and the menstrual discharge is semen, though not pure semen, for it lacks one thing only, the principle of soul.

Let it be granted that a fluid is of such a nature that, its parts lying evenly and being continuous, that part which is thrust the least is driven along by that which is thrust the more, and that each of its parts is thrust by the fluid which is above it in a perpendicular direction, if the fluid is sunk in anything and compressed by anything else.

Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.

If the situation is as I have described, then not much would be left of the sciences, and we should still be as ignorant as the ancients, without any small addition.

Galen himself, more than anyone, points out the errors of Hippocrates, and yet he loves and reveres him above all physicians; this did not prevent him from opposing him whenever the truth required it.

Speculative science is divided into three parts: natural science, mathematics, and divine science, which is also called metaphysics.

Some things depend on matter both for their being and for being understood, as do all natural things which cannot be defined without including matter in their definition. Others depend on matter for their being but not for being understood, as mathematical objects. Still others depend on matter neither for their being nor for being understood, and these belong to metaphysics.

As the Philosopher says in the Metaphysics, the office of the wise man is to order things. The reason for this is that wisdom is the most powerful perfection of reason, whose characteristic is to know order.

Certain knowledge, which is called science, is had when we know a thing through its cause, and know that this cause cannot be otherwise, and know that the conclusion necessarily follows from it.

Leonardo's notes on painting and perspective develop a systematic account of how light, distance and the human eye actually interact, treating rigorous observational and mathematical method as inseparable from painting's practical artistic technique.

Leonardo's anatomical studies record detailed observations of the human body's proportions and internal structure, drawn from his own direct dissection work, connecting his artistic interest in rendering the body accurately to genuine, systematic medical and biological investigation.

Paré discovers that boiling oil in gunshot wounds did more harm than a simple dressing, a finding that emerged from a specific practical emergency, running out of oil during battle, rather than from theoretical medical argument alone.

Paré finds that ligating arteries after amputation beat cauterising them, replacing a brutal, painful standard technique with a more humane and effective alternative grounded in accumulated clinical observation across decades of military surgical service.

Galileo describes observing the moon's surface through his telescope and finding it not smooth as ancient philosophy held but rough and uneven, covered with mountains and cavities that cast shadows exactly as terrestrial mountains do when struck by sunlight at an angle.

He reports that the Milky Way, when examined through the telescope, resolves into a multitude of stars packed so closely together that their combined faint light produces the hazy band visible to the naked eye, a finding that revealed the sky to contain vastly more stars than anyone had previously suspected.

Descartes states that the nature of matter, or body considered in general, consists not in its being something hard, or heavy, or coloured, but simply in its being something extended in length, breadth and depth.

He argues that since extension and matter are identical, there can be no vacuum anywhere in the universe, since any space, however apparently empty, is by definition extended and therefore is itself a body.

Harvey addresses Jean Riolan directly, noting that Riolan has accepted a limited circulation of the blood while still denying that it actually runs through the whole body, and argues that this partial acceptance is itself a serious error rather than a reasonable middle position.

He restates the original experiments from twenty years earlier and adds new observations specifically on the pulse, on how blood actually moves through the veins, and on what happens physically when an artery is deliberately cut, building his case through repeatable demonstration.

Harvey describes the development of the chick embryo day by day across the full period of incubation, documenting through repeated dissection exactly when and how each bodily structure actually appears and takes shape rather than assuming the embryo exists preformed from the start.

Against both Aristotle and Galen, Harvey argues that the embryo forms gradually through a process he calls epigenesis, its structures appearing and developing progressively over time, rather than existing complete in miniature from the moment of conception and simply increasing in size.

Pascal's account of the experiments on the vacuum, and his preface on the authority of the ancients in science, directly challenge the Aristotelian consensus that nature abhors a vacuum, arguing scientific progress requires testing inherited authority against actual experiment.

The treatises on the equilibrium of liquids and the weight of the mass of the air establish hydrostatics as a systematic mathematical science, giving Pascal's law its rigorous foundation and shaping subsequent physics and engineering well beyond his own century.

Argan is a healthy man convinced he is dying, surrounded by doctors and apothecaries who profit from his fear, a hypochondriac whose imaginary illness sustains an entire household economy built around treating a sickness that does not actually exist.

Argan wants to marry his daughter Angélique to a young physician so that he can have medical care in the family, while his second wife waits for him to die and leave her everything, two competing mercenary interests converging on his household.

The Discourse on Metaphysics, addressed initially to Arnauld and developed further through their subsequent correspondence, works through Leibniz's central concept of substance, establishing the philosophical groundwork that his mature theory of monads would later build upon and extend.

Leibniz describes the monad as simple, indivisible and windowless, containing no parts through which anything could genuinely enter or leave, yet argues that each monad nonetheless represents the entire universe from its own unique perspective, a striking combination of total isolation and total representation.

Kant credits Hume directly with waking him from his dogmatic slumber, a candid acknowledgment that frames his entire Critical philosophical project as an extended response to Hume's skeptical challenge about causation and whether necessary connection between events can ever be genuinely known.

Kant works backward analytically from the observed fact that pure mathematics and pure natural science exist as genuine, certain knowledge, asking what conditions must already hold true of the mind for this specific kind of a priori knowledge to actually be possible at all.

Jenner's 1798 Inquiry reports his 1796 experiment inoculating eight-year-old James Phipps with matter taken from a cowpox sore on milkmaid Sarah Nelmes's hand, and describes his subsequent confirmation that the boy had become immune to smallpox itself, the experiment's central and most audacious claim.

The 1798 Inquiry reports twenty-three total cases beyond the initial Phipps experiment, building a broader evidentiary base for Jenner's proposal that cowpox infection protects against the considerably deadlier disease of smallpox.

Fourier states his foundational physical law directly, that the flow of heat across any surface within a body is proportional to the temperature gradient at that surface, a simple proportional relationship from which the entire subsequent mathematical treatment of heat conduction is systematically derived.

He derives from this law the partial differential equation governing how temperature actually changes over time at every point within a conducting body, and then proceeds to solve this equation for a series of specific physical shapes, rings, bars, spheres and cubes, under various prescribed boundary conditions.

Lyell argues that the earth's surface has been shaped over immense stretches of time by the same causes now in operation, rivers, volcanoes, earthquakes, erosion and deposition, acting at roughly their present intensity, rather than by ancient catastrophes no longer occurring in the observable present.

The first volume reviews the history of geology as a discipline and surveys present-day geological processes in detail, establishing the observational foundation for the uniformitarian method the subsequent volumes will apply more extensively to the rock record.

The extracts survey the progress of geology from the ancient Greeks through the eighteenth-century theories of Hutton and Werner, tracing how earlier thinkers had attempted to account for the earth's visible transformations before Lyell's own uniformitarian synthesis.

The extracts set out Lyell's central principle directly, that the causes now acting on the earth's surface, given enough time, account for all its past changes, presenting this claim in compact, essential form rather than surrounded by the extensive supporting evidence of the complete work.

Comte states that in the theological stage the mind explains phenomena by the direct and continuous action of supernatural beings, in the metaphysical stage by abstract forces or entities substituted for those beings, and in the positive stage by observed laws of succession and resemblance among facts, without appeal to either cause.

He arranges the sciences, mathematics, astronomy, physics, chemistry and biology, in an order of decreasing generality and increasing complexity, arguing that each depends on the principles of the ones before it while adding genuinely new laws the earlier sciences cannot supply.

Darwin describes the extraordinary diversity of finches he collects on the Galápagos Islands, noting differences in beak size and shape between islands, an observation he records with real interest but without yet drawing from it the theoretical conclusions it would eventually help support decades later.

Witnessing a major earthquake in Chile, Darwin describes the ground itself as behaving like a thin crust over a fluid, and connects the sudden uplift of the coastline he observes afterward directly to the slow geological processes he had been tracking across the whole voyage.

Mill argues that all real inference is from particulars to particulars, and that the syllogism, rather than producing new knowledge through deduction, merely registers an inference already made, relocating genuine logical work away from formal deductive reasoning.

Mill grounds all inductive inference in the uniformity of nature, the assumption that what has been observed to hold in examined cases will hold in unexamined cases as well, giving induction itself a foundation earlier writers on method had largely left assumed rather than argued.

Holmes assembles reported cases in which a single doctor or midwife attended a run of women who died of childbed fever while other colleagues practicing in the same town during the same period saw no such pattern among their own patients, establishing a clear correlation between specific attendants and disease clusters.

He argues directly that childbed fever is carried from patient to patient on the hands and clothes of the physicians and midwives attending them, identifying the very people meant to be helping these women as the actual, unwitting vector transmitting a fatal disease between them.

Faraday demonstrates gravitation through simple falling-body experiments before moving to cohesion, showing through direct manipulation how the same underlying attractive forces that hold planets in orbit also hold the smallest particles of ordinary matter together in solid form.

He shows through experiments on combustion and chemical reaction how chemical affinity, the force by which different substances combine to form new compounds, operates by the same basic principles of attraction organizing the other forces he discusses, rather than as an entirely separate category of physical phenomenon.

Helmholtz begins from the long, unbroken history of failed attempts across many decades to build a perpetual motion machine, arguing that this consistent failure is not mere accident or engineering incompetence but expresses a genuine underlying physical law governing all such mechanical systems.

He traces the conversion of force through numerous everyday examples, falling weights, compressed springs, heat, electricity and chemical action, demonstrating that force changes form continuously without the total quantity ever actually increasing or being destroyed within an isolated system.