From Essential Selections in Early Modern Philosophy, by James Fieser


Copyright 2015, updated 3/1/2015



Nicholas Copernicus

Galileo Galilei

Isaac Newton


During the Scientific Revolution there were two distinct types of contributions. One concerns the methods of scientific investigation, which has already seen in the previous section on Francis Bacon. The other concerns particular discoveries, the most notable example of which occurred in astronomy. The first selection below is from Nicholas Copernicus (1473-1543) who rejected the ancient and medieval earth-centered system of the cosmos and proposed instead the sun-centered system. He was born in Torun, Poland, into a wealthy merchant family, attended the University of Bologna, Italy, and worked in the church as a cleric although never ordained as a priest. At age 30 he returned to Poland where he remained working in various capacities in the church and government. Beginning in his University days he developed an interest in astronomy, and by 1514 developed the idea of an sun-centered system. It was not until the end of his life, though, that he presented his full system in his book On the Revolutions of the Celestial Spheres (1543), from which the passages below are taken. In the Preface he explains his reluctance to write on the topic, his reasons for adopting the new theory, and he appeals to the Pope to accept the theory.

            The second selection is from Galileo Galilei (1564-1642). He was born near Florence, Italy, son to a musician, and he studied medicine and mathematics at the University of Pisa. For 18 years he taught at the University of Padua, where he did his most important work. The passages below are from several of his writings. The first ones describe his work with the telescope, how he made one and how he used it to discover the moon’s mountainous surface. Through his astronomical observations he accumulated evidence supporting Copernicus’s earth-centered system, and quickly came into conflict with the Catholic Church. In two published letters he argues that the domain of Scripture and religious authority does not cross over into areas of scientific study. He eventually laid out his full argument for the sun-centered system in Dialogues on the Two Chief Systems of the World (1632); the passages below from the Preface to that work reflect his belief that he received Church approval for its publication. However, for this the Church brought him before Inquisition, convicted him of heresy, and had him sign a statement of retraction, included below.

            Last are selections from Isaac Newton (1642-1727). He was born in the English county of Lincolnshire, three months after his father’s death, and was raised by his grandmother when his mother remarried. He attended the Trinity College at the University of Cambridge, later obtained a teaching position there which he held until 1701. During his early years, Newton made his three chief scientific discoveries which he refined and published later. The first was the development of calculus, published posthumously in Method of Fluxions (1736). The second was his experiments with prisms which showed how white light is composed of colored light, published in Opticks (1704). The third was the idea of universal gravitation which explained the orbits of the moon and planets, published in Principia Mathematica (1687). With the appearance of Principia he achieved international fame. He was briefly a member of parliament, appointed master of the British mint and elected president of the Royal Society, Great Britain’s oldest scientific society. In the passages below Newton he describes his inductive method of scientific investigation, the broad implications of his theory of gravity, and evidence of God in the creation and sustaining of the universe.


COPERNICUS (from On the Revolutions of the Celestial Spheres, 1543, Preface)


Initial Reluctance to Write on this Controversial Subject

In this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth. I can easily conceive, most Holy Father, that as soon as some people learn that, they will cry out at once that I and my theory should be rejected. For I am not so much in love with my conclusions that I will not weigh what others will think about them. I know that the meditations of a philosopher are far removed from the judgment of the laity, because his job is to seek out the truth in all things, so far as this is permitted by God to the human reason. Nevertheless, I still believe that one must avoid theories altogether foreign to orthodoxy. I consider in my own mind how absurd a performance it must seem to those who know that the judgment of many centuries has approved the view that the Earth remains fixed as center in the midst of the heavens. This has me consider if I should, to the contrary, assert that the Earth moves. I was for a long time at a loss to know whether I should publish the commentaries which I have written in proof of its motion. It may be better to follow the example of the Pythagoreans and of some others, who were accustomed to test the secrets of Philosophy not in writing but orally, and only to their relatives and friends, as the letter from Lysis to Hipparchus bears witness. They did this, it seems to me, not because of a certain selfish reluctance to give out their views to the world, as some think. Instead it was so that the noblest truths, worked out by the careful study of great people, should not be rejected by those who are disturbed at the idea of taking great pains with any forms of literature except such as would be profitable. Other people might also reject it who are driven to the study of philosophy for its own sake (by the admonitions and the example of others) but, on account of their stupidity, hold a place among philosophers similar to that of drones among bees. Therefore, when I considered this carefully, the contempt which I had to fear because of the novelty and apparent absurdity of my view, nearly induced me to abandon utterly the work I had began.

            My friends, however, in spite of long delay and even resistance on my part, withheld me from this decision. First among these was Nicolaus Schonberg, Cardinal of Capua, distinguished in all branches of learning. Next to him comes my very dear friend, Tidemann Giese, Bishop of Culm, a most earnest student, as he is, of sacred and, indeed, of all good learning. The latter has often urged me, at times even spurring me on with reproaches, to publish and at last bring to the light the book which had lain in my study not nine years merely, but already going on four times nine. Several other very eminent and scholarly people made the same request, urging that I should no longer through fear refuse to give out my work for the common benefit of students of mathematics. They said I should find that the more absurd most people currently thought this theory of mine concerning the motion of the earth [prior to publication], the more admiration and gratitude it would command after they saw in the publication of my commentaries the mist of absurdity cleared away by most transparent proofs. I was influenced by these advisors and this hope, and I have finally allowed my friends to publish the work, as they had long encouraged to do.


Problems with Traditional Theories of Celestial Motion

But perhaps Your Holiness will see better why I published these studies after seeing the pains I’ve taken in elaborating them, and have not hesitated to commit my views of the motion of the earth to writing. You may similarly be curious to hear how it occurred to me to form a conception of any terrestrial motion in the first place – contrary to both the accepted view of mathematicians and common sense. Therefore I will have it known to Your Holiness that the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigations of this subject. For, in the first place, they are so much in doubt concerning the motion of the sun and the moon, that they can not even demonstrate and prove by observation the constant length of a complete year. In the second place, in determining the motions both of these and of the five other planets, they fail to employ consistently one set of first principles and hypotheses; instead, they use methods of proof based only on the apparent revolutions and motions. For some employ concentric circles only [with many epicycles]. Others use eccentric circles and [a single] epicycles. Even by these means they do not completely attain the desired end. For, although those who have depended upon concentric circles [and many epicycles] have shown that certain diverse motions can be deduced from these. Yet they have not succeeded thereby in laying down any sure principle, corresponding indisputably to the phenomena.

            Those, on the other hand, who have devised systems of eccentric circles, seem in great part to have solved the apparent movements by calculations which by these eccentrics are made to fit. However, they have nevertheless introduced many things which seem to contradict the first principles of the uniformity of motion. Nor have they been able to discover or calculate from these the main points, which is the shape of the world and the fixed symmetry of its parts. Their procedure has been as if someone were to collect hands, feet, a head, and other members from various places, all very fine in themselves, but not proportionate to one body, and no single one corresponding in its turn to the others. From these, then, a monster rather than a man would be formed. Thus in their process of demonstration which they term a “method,” they are found to have omitted something essential, or to have included something foreign and not pertaining to the matter in hand. This certainly would never have happened to them if they had followed fixed principles. For if the hypotheses they assumed were not false, all that resulted therefrom would be verified indubitably. Those things which I am saying now may be obscure, yet they will be made clearer in their proper place.


Advantages of the Sun-Centered System

I turned over in my mind for a long time this uncertainty of the traditional mathematical methods of calculating the motions of the celestial bodies. I began to grow disgusted that no more consistent scheme of the movements of the mechanism of the universe (set up for our benefit by that best and most law abiding Architect of all things) was agreed upon by philosophers who otherwise investigate so carefully the minutest details of this world. Thus, I undertook the task of re-reading the books of all the philosophers I could get access to, to see whether anyone ever was of the opinion that the motions of the celestial bodies were other than those postulated by the people who taught mathematics in the schools. I found first, indeed, in Cicero, that Niceta perceived that the Earth moved. After that, in Plutarch, I found that some others were of this opinion, whose words I have seen fit to quote here, that they may be accessible to all:


Some maintain that the Earth is stationary, but Philolaus the Pythagorean says that it revolves in a circle about the fire of the ecliptic, like the sun and moon. Heraklides of Pontus and Ekphantus the Pythagorean make the Earth move, not changing its position, however, confined in its falling and rising around its own center in the manner of a wheel.


Taking this as a starting point, I began to consider the mobility of the Earth. Although the idea seemed absurd, yet because I knew that the liberty had been granted to others before me to postulate all sorts of little circles for explaining the phenomena of the stars, I thought I also might easily be permitted to try whether by postulating some motions of the Earth, more reliable conclusions could be reached regarding the revolution of the heavenly bodies, than those of my predecessors.

            So, I postulated movements which (further on in the book) I ascribe to the Earth, and though many and long observations I discovered the following. I assumed that the movements of the other planets are applied also to the circular motion of the Earth, and are also substituted for the revolution of each star. From this, not only do their phenomena follow logically, but the relative positions and magnitudes both of the stars and all their orbits, and of the heavens themselves, become closely related. So closely related are they that nothing can be changed in any of its parts without causing confusion in the other parts and in the whole universe. Therefore, in the course of the work I have followed this plan: I describe in the first book all the positions of the orbits together with the movements which I ascribe to the Earth, in order that this book might contain, as it were, the general scheme of the universe. In the remaining books, I establish the motions of the other stars and of all their orbits together with the movement of the Earth. This is done so that one may see from this to what extent the movements and appearances of the other stars and their orbits can be saved, if they are transferred to the movement of the Earth.


Appeal to the Pope to Support the Theory

I do not doubt that inventive and educated mathematicians will support me, so long as they are willing to recognize and weigh those matters which have been adduced by me in this work to demonstrate these theories. They must not do this superficially, though, but with that thoroughness which Philosophy demands above everything. In order, however, that both the learned and the unlearned equally may see that I do not avoid anyone’s judgment, I have preferred to dedicate these studies of mine to your Holiness rather than to any other, because, even in this remote corner of the world where I live, you are considered to be the most eminent man in dignity of rank and in love of all learning and even of mathematics. Thus, by your authority and judgment you can easily suppress the bites of slanderers, even though the proverb states that there is no remedy for the bite of a flatterer. I care not at all if there happen to be idle talkers, who, though they are ignorant of all mathematical sciences, nevertheless assume the right to pass judgment on these things, and if they should dare to criticize and attack this theory of mine because of some passage of scripture which they have falsely distorted for their own purpose. I will even despise their judgment as foolish. For it is not unknown that Lactantius, otherwise a famous writer but a poor mathematician, speaks most childishly of the shape of the Earth when he makes fun of those who said that the Earth has the form of a sphere.

            It should not seem strange then to zealous students, if some such people shall ridicule us also. Mathematics are written for mathematicians, to whom, if my opinion does not deceive me, our labors will seem to contribute something to the ecclesiastical state whose chief office Your Holiness now occupies; for when not so very long ago, under Leo X, in the Lateran Council the question of revising the ecclesiastical calendar was discussed, it then remained unsettled, simply because the length of the years and months, and the motions of the sun and moon were held to have been not yet sufficiently determined. Since that time, I have given my attention to observing these more accurately, urged on by a very distinguished man, Paul, Bishop of Fossombrone, who at that time had charge of the matter. But what I may have accomplished herein I leave to the judgment of Your Holiness in particular, and to that of all other learned mathematicians; and lest I seem to Your Holiness to promise more regarding the usefulness of the work than I can perform, I now pass to the work itself.




Reverse Engineering the Telescope (from The Assayer, 1623)

On the simple information of the effect obtained [of the telescope], I discovered the telescope, not by chance [as was the case with the original Dutch inventor], but by the way of pure reasoning. Here are the steps. The artifice of the instrument depends either on one glass or on several. It cannot depend on one, for that must be either convex, or concave, or plain. The last form neither augments nor diminishes visible objects. The concave diminishes them, and the convex increases them, but both show them blurred and indistinct. Passing then to the combination of two glasses, and knowing that glasses with plain surfaces change nothing, I concluded that the effect could not be produced by combining a plain glass with a convex or a concave one. I was thus left with the two other kinds of glasses, and after a few experiments I saw how the effect sought could be produced. Such was the march of my discovery, in which I was not assisted in any way by the knowledge that the conclusion at which I aimed was a fact.


The Moon has a Rough Surface but does Not contain Life (from Letter to Giacomo Muti, Feb. 28, 1616)

A few days ago, when paying my respects to the illustrious Cardinal Muti, a discussion arose on the inequalities of the moon’s surface. Signor Alessandro Capoano argued to disprove the fact [of its rough surfaces]. He argued that if the lunar surfaces be unequal and mountainous, and since nature has made our earth mountainous for the benefit of plants and animals beneficial to mankind, one may say as a consequence that on the moon there must be other plants and other animals beneficial to other intellectual creatures. Since such a consequence is most false, he said, then the fact from which it is drawn must also be false; therefore lunar mountains do not exist! To this I replied as follows. As to the inequalities of the moon’s surface we have only to look through a telescope to be convinced of their existence. As to the “consequences,” I said, they are not only unnecessary, but absolutely false and impossible. For I was in a position to prove that neither mankind, nor animals, nor plants as on this earth, nor anything at all like them can exist on the moon.

            I said then, and I say now, that I do not believe that the body of the moon is composed of earth and water, and lacking these two elements we must necessarily conclude that it lacks all the other things which without these elements cannot exist or subsist. I added further that even allowing that the matter of the moon may be like that of the earth (a most improbable supposition), still not one of those things which the earth produces can exist on the moon. For, to their production other things besides earth and water are necessary, namely, the sun – the greatest agent in Nature – and the resulting variance of heat and cold, and of day and night. Now, such variances are on the moon very different from those on the earth. In the latter case, to produce a diversity of seasons, the sun rises and falls more than 47 degrees (in passing from one tropic to the other). In the former case the variation is only 5 degrees on each side of the ecliptic. While, therefore, on the earth the sun in every 24 hours illuminates all parts of its surface, each half of the moon is alternately in sunshine and darkness for 15 continuous days of 24 hours. Now, if our plants and animals were exposed to ardent sunshine every month for 360 consecutive hours, and then for a similar time were plunged in cold and darkness, they could not possibly preserve themselves, much less produce and multiply. We must, therefore, conclude that what would be impossible on our earth under the circumstances we have supposed to exist, must be impossible on the moon where those conditions do exist.


Distinction between Primary and Secondary Qualities (from The Assayer, 1623)

I have now only to fulfil my promise of declaring my opinions on the proposition that motion is the cause of heat, and to explain in what manner it appears to me that it may be true. But I must first make some remarks on that which we call heat, since I strongly suspect that a notion of it prevails which is very remote from the truth. For it is believed that there is a true accident, affection, and quality, really inherent in the substance by which we feel ourselves heated. This much I have to say, that as soon as I conceive a material or corporeal substance, I simultaneously feel the necessity of conceiving that it has its boundaries, and is of some shape or other; that, relatively to others, it is great or small; that it is in this or that place, in this or that time; that it is in motion, or at rest; that it touches, or does not touch another body; that it is unique, rare, or common; nor can I, by any act of the imagination, disjoin it from these qualities. But I do not find myself absolutely compelled to apprehend it as necessarily accompanied by such conditions, as that it must be white or red, bitter or sweet, sonorous or silent, smelling sweetly or disagreeably. If the sense had not pointed out these qualities, it is probable that language and imagination alone could never have arrived at them. For, I am inclined to think that these tastes, smells, colors, etc., with regard to the subject in which they appear to reside, are nothing more than mere names, and exist only in the sensitive body. This is to the extent that, when the living creature is removed, all these qualities are carried off and annihilated, even though we have imposed particular names upon them, and different from those of the other first and real accidents, and would gladly persuade ourselves that they are truly and in fact distinct. But I do not believe that there exists anything in external bodies for exciting tastes, smells, and sounds, but size, shape, quantity, and motion, swift or slow; and if ears, tongues, and noses were removed, I am of opinion that shape, number, and motion would remain, but there would be an end of smells, tastes, and sounds, which, abstractedly from the living creature, I take to be mere words.


Reinterpret Scripture to Fit Science, Not the Reverse (from Letter to Castelli, December 21, 1613)

It seems to me that it was well said by her Most Serene Ladyship, and insisted on by your reverence, that the Holy Scriptures cannot err, and that the decrees therein contained are absolutely true and inviolable. But I should in your place have added that, though Scripture cannot err, its expounders and interpreters are liable to err in many ways. But one error in particular would be most grave and most frequent, if we always restricted ourselves to the literal signification of the words. By doing so not only many contradictions arise, but grave heresies and blasphemies. For then it would be necessary to give God hands and feet and ears, and human and bodily emotions, such as anger, repentance, hatred, and sometimes forgetfulness of past things, and ignorance of the future. In Scripture there are found many propositions which, taking the bare sense of the words, appear contrary to the truth. But they are placed there in such a way to accommodate themselves to the capacity of common people. For those few who deserve to be separated from the common crowd, it is necessary for wise expositors to produce the true meaning, and to explain the particular reasons for which they have been thus worded.

            It being laid down, therefore, that Scripture is not only capable of varied interpretations, but that in many places it requires an interpretation differing from the apparent meaning of the words, it seems to me that in mathematical disputes it must be interpreted according to the latter way. Holy Scripture and nature are both come from the Divine word; the former dictated by the Holy Spirit, the latter, the executor of God’s commands. Holy Scripture has to be accommodated to the common understanding in many things which differ in reality from the terms used in speaking of them. But Nature, on the contrary, is unchangeable and immutable, and it cares not one bit whether her secret reasons and methods of operation are above or below the capacity of men’s understanding. It appears that, as she never transgresses her own laws, those natural effects which the experience of the senses places before our eyes, or which we infer from adequate demonstration, are in no way to be revoked because of certain passages of Scripture, which may be turned and twisted into a thousand different meanings. For Scripture is not bound to such severe laws as those by which nature is ruled. For this reason alone, that is, to accommodate itself to the capacities of common and undisciplined people, Scripture has not abstained from veiling in shadow its principal dogmas, attributing to God himself conditions differing from and contrary to the Divine essence. Who can assert or sustain that, in speaking incidentally of the sun, or of the earth, or of other created bodies, Scripture should have elected to restrain itself rigorously to the strict signification of the words used? May it not be, that, had the truth been represented to us bare and naked, its intention would have been annulled, from the vulgar being thereby rendered more stubborn and difficult of persuasion in the articles concerning their salvation?

            This, then, being conceded, and it being clear that two truths cannot be contrary to each other, it becomes the duty of wise expounders to labor until they find how to make these passages of holy scripture consistent with those conclusions, of which either necessary demonstration or the evidence of our senses have made us sure and certain. The Bible, although dictated by the Holy Spirit, admits (for the reasons given above) in many passages of an interpretation other than the literal one; and, moreover, we cannot be certain that the interpreters are all divinely inspired. Therefore, I think it would be the part of wisdom to forbid anyone to apply passages of Scripture in such a way as to force them to support as true any conclusions concerning nature, the contrary of which may afterwards be revealed by the evidence of our senses, or by actual demonstration. Who will set bounds to human understanding? Who can assure us that everything that can be known in the world is known already? With the unchangeableness of articles concerning salvation and the stability of the faith, there is no danger of any valid and worthwhile innovation being introduced against them. But beyond these, it would perhaps be best to advise that none should be added unnecessarily. If it be so, how much greater the disorder to add to these articles at the demand of people who, though they may be divinely inspired, yet we see clearly that they are destitute of the intelligence necessary, not merely to disprove, but to understand, those demonstrations by which scientific conclusions are confirmed.

            I believe that holy scripture is intended to convince people of those truths which are necessary for their salvation, and which, being far above man’s understanding, cannot be made credible by science or any other learning, but only through the voice of the Holy Spirit. But I do not think it necessary to believe that the same God who gave us our senses, our speech, our intellect, would have us put aside the use of these, to teach us instead such things as with their help we could find out for ourselves, particularly in the case of these sciences, of which there is not the smallest mention in the Scripture; and, above all, in astronomy, of which so little notice is taken that the names of all the planets are not mentioned. Surely if the intention of the sacred writers had been to teach the people astronomy, they would not have passed the subject over so completely.


Cannot Order Scientists to Disbelieve what they Demonstrate (from “Letter to the Granduchess,” 1615)

I think that in discussing natural phenomena we should not to begin with texts from Scripture, but with experiment and demonstration. For, from the Divine Word, both Scripture and Nature do alike proceed. . . . I conceive that, concerning natural effects, that which experience sets before our eyes, or which demonstration proves to us, should not on any account to be called in question, much less condemned, upon the testimony of Scriptural texts, which may (under their mere words) have meanings of a contrary nature. . . .

            To command professors of astronomy that they must themselves see to disproving their own observations and demonstrations is to ask the impossible. For it is not only to command them not to see what they do see, and not to understand what they do understand, but to seek for and to find the contrary. . . . I would beg these wise and prudent Fathers to consider diligently the difference between opinionative and demonstrative doctrines, to the end that they may assure themselves that it is not in the power of professors of demonstrative sciences to change their opinions at pleasure, and adopt first one side and then the other. For, there is a great difference between ordering a mathematician, or a [natural] philosopher, as to what opinion to hold, and doing the same with a merchant, or a lawyer. For, demonstrated conclusions touching things of nature and of the heavens cannot be changed with the same facility as opinions touching what is lawful, or not, in a contract, bargain, or bill of exchange. . . .

            Therefore, let such people apply themselves to the study of the arguments of Copernicus and others, and leave the condemning of them as erroneous and heretical to whom it belongs. Yet, as to this latter, they must not hope to find such rash and hurried determinations in the vigilant Holy Fathers, or in the absolute wisdom of him who cannot err, as those into which they permit themselves to be hurried by some particular affection or interest of their own. In these, and such like opinions which are not directly articles of faith, certainly no one doubts that his Holiness has always an absolute power of admitting or condemning them. But it is not in the power of any creature to make them to be true or false, otherwise than as, in fact, they are.


Church Approval to Present the Copernican System as a Hypothesis (from Dialogues on the Two Chief Systems, 1635, Introduction)

Some years ago a beneficial edict was proclaimed at Rome, which, in order to hinder the dangerous scandals of the present age, commanded a fitting silence on the Pythagorean opinion of the earth’s motion. Some were uninhibited who rashly asserted that this decree originated, not from a judicious examination, but from an ill-informed passion. Complaints were heard that counselors totally inexperienced in astronomical observations ought not by hasty prohibitions to clip the wings of speculative minds. My zeal could not keep silence when I heard these rash lamentations, and I thought it proper, as being fully informed with regard to that most prudent edict, to appear publicly as a witness of the actual truth. At that time I happened to be in Rome. I was admitted to the audiences, and enjoyed the approval of the most distinguished prelates of that Court. Nor did the publication of the aforesaid decree occur without my receiving some prior indication of it. For that reason . . . collecting together all my own speculations on the Copernican system, it is my intention in this present work to show to foreign nations that the knowledge of this preceded the Roman censures. Thus, from this country proceeded not only dogmas for the salvation of the soul, but also inventive discoveries for the gratification of the understanding. With this object I have taken up in the dialogue the Copernican side of the question, treating it as a pure mathematical hypothesis. I try in every artificial manner to represent it as having the advantage, not over the opinion of the stability of the earth absolutely, but over it as taught and defended by some who profess to be peripatetics [that is, followers of Aristotle]. For they retain only the name [“peripatetic”], and are content, without improvement, to worship shadows, not philosophizing with their own reason, but only from the recollection of four principles imperfectly understood.


Galileo’s Recantation: The High Price of Doing Science (June 22, 1633)

I Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged 70 years, being brought personally to judgment, and kneeling before you, Most Eminent and Most Reverend Lords Cardinals, General Inquisitors of the universal Christian republic against heretical depravity, having before my eyes the Holy Gospels, which I touch with my own hands, swear, that I have always believed, and now believe, and with the help of God will in future believe, every article which the Holy Catholic and Apostolic Church of Rome holds, teaches, and preaches. But because I had been ordered by this Holy Office altogether to abandon the false opinion which maintains that the sun is the center and immovable, and forbidden to hold, defend, or teach, the said false doctrine in any manner, and after it had been signified to me that the said doctrine is repugnant with the Holy Scripture, I have written and printed a book, in which I treat of the same doctrine now condemned, and adduce reasons with great force in support of the same, without giving any solution, and therefore have been judged grievously suspected of heresy ; that is to say, that I held and believed that the sun is the center of the world and immovable and that the earth is not the center and movable:

            Willing, therefore, to remove from the minds of Your Eminences, and of every Catholic Christian, this vehement suspicion rightfully entertained towards me, with a sincere heart and unfeigned faith, I abjure, curse, and detect the said errors and heresies, and generally every other error and sect contrary to the said Holy Church; and I swear that I will never more in future say or assert anything verbally, or in writing, which may give rise to a similar suspicion of me: but if I shall know any heretic, or anyone suspected of heresy, that I will denounce him to this Holy Office, or to the Inquisitor and Ordinary of the place in which I may be. I swear, moreover, and promise, that I will fulfil, and observe fully, all the penances which have been, or shall be laid on me by this I Holy Office. But if it shall happen that I violate any of my said promises, oaths, and protestations, (which God, avert!) I subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons, and other general and particular constitutions, against delinquents of this description. So may God help me, and his Holy Gospels, which I touch with my own hands.




Implications of Universal Gravity (from Principia Mathematica, 1687, Preface)

Our design not respecting arts, but philosophy, and our subject not manual but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as the 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; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the system of the world. For, by the propositions mathematically demonstrated in the first book, we there derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles. For I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other and cohere in regular figures, or are repelled and recede from each other. Which forces being unknown, philosophers have hitherto attempted the search of nature in vain. But I hope the principles here laid down will afford some either to that or some truer method of philosophy.


Four Rules of Reasoning in Philosophy (from Principia Mathematica, 1687)

            Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

            To this purpose the philosophers say that nature does nothing in vain, and more is in vain when less will serve. For nature is pleased with simplicity and affects not the pomp of superfluous causes.

            Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

            As to respiration in a man and in a beast, the descent of stones in Europe and in America, the light of our culinary fire and of the sun, the reflection of light in the earth and in the planets.

            Rule 3. The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

            For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments, and such as are not liable to diminution can never be quite taken away. . . .

            Rule 4. In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur by which they may either be made more accurate or liable to exceptions.

            This rule we must follow, that the argument of induction may not be evaded by hypotheses.


God Needed to Create Luminous Bodies (Letter to Richard Bentley, December 10, 1692)

As to your first query, it seems to me that if the matter of our sun and planets and all the matter in the universe were evenly scattered throughout all the heavens, and every particle had an innate gravity toward all the rest, and the whole space throughout which this matter was scattered was but finite, the matter on the outside of the space would, by its gravity, tend toward all the matter on the inside, and by consequence, fall down into the middle of the whole space and there compose one great spherical mass. But if the matter [of the universe] was [initially] evenly disposed throughout an infinite space, it could never convene into one mass. But some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one to another throughout all that infinite space. And thus might the sun and fixed stars be formed, supposing the [original] matter were of a lucid nature. But how the matter should divide itself into two sorts, and the part of it which is fit to compose a shining body should fall down into one mass and make a sun and the rest which is fit to compose an opaque body should coalesce (not into one great body, like the shining matter, but into many little ones); or if the sun at first were an opaque body like the planets or the planets lucid bodies like the sun, how he alone should be changed into a shining body whilst all they continue opaque (or all they be changed into opaque ones whilst he remainst unchanged), I do not think explicable by mere natural causes, but am forced to ascribe it to the counsel and contrivance of a voluntary agent.


God Needed for Precise Motion of Planets (Letter to Richard Bentley, December 10, 1692)

To your second query, I answer that the motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent Agent. . . . Were all the planets as swift as Mercury or as slow as Saturn or his satellites [i.e. its moons]; or were the several velocities otherwise much greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the distances from the centers about which they move been greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the quantity of matter in the sun or in Saturn, Jupiter, and the earth (and by consequence their gravitating power) been greater or less than it is; [then, in any of these cases,] the primary planets could not have revolved about the sun nor the secondary ones about Saturn, Jupiter, and the earth, in concentric circles as they do, but would have moved in hyperbolas or parabolas or in ellipses very eccentric. To make this system, therefore, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets and the gravitating powers resulting from thence.... And to compare and adjust all these things together in so great a variety of bodies, [such a design] argues that cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry.


Possibility of Evenly Spaced Particles Not Converging, but Not Likely (Letter to Richard Bentley, January 17, 1693)

I agree with you that if matter evenly diffused through a finite space, not spherical, should fall into a solid mass, this mass would affect the figure of the whole space . . . The reason why matter evenly scattered through a finite space would convene in the midst you conceive the same with me, but that there should be a central particle so accurately placed in the middle as to be always equally attracted on all sides, and thereby continue without motion, seems to me a supposition as fully as hard as to make the sharpest needle stand upright on its point upon a looking glass. For if the very mathematical center of the central particle be not accurately in the very mathematical center of the attractive power of the whole mass, the particle will not be attracted equally on both sides. And much harder it is to suppose all the particles in an infinite space should be so accurately poised one among another as to stand still in a perfect equilibrium. For I reckon this as hard as to make, not one needle only, but an infinite number of them (so many as there are particles in an infinite space) stand accurately poised upon their points. Yet I grant it possible, at least by a divine power; and if they were once to be placed, I agree with you that they would continue in that posture without motion forever, unless put into new motion by the same power. When, therefore. I said that matter evenly spread through all space would convene by its gravity into one or more great masses, I understand it of matter not resting in an accurate poise. . . .

            And so a mathematician will tell you that if a body stood in equilibrio between any two equal and contrary attracting infinite forces, and if to either of these forces you add any new finite attracting force, that new force, howsoever little, will destroy their equilibrium and put the body into the same motion into which it would put it were those two contrary equal forces but finite or even none at all; so that in this case the two equal infinities, by the addition of a finite to either of them, become unequal in our ways of reckoning; and after these ways we must reckon, if from the considerations of infinities we would always draw true conclusions.


Scientific Method of Analysis (from Opticks, 1704, Bk. 3, Queries)

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. For, hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments and observations by induction be no demonstration of general conclusions, yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger by how much the induction is more general. And if no exception occurs from phenomena, the conclusion may be pronounced generally. But if at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them, and, in general, from effects to their causes, and from particular causes to more general ones, until the argument ends in the most general. This is the method of analysis, and the synthesis consists in assuming the causes discovered and established as principles, and by them explaining the phenomena proceeding from them and proving the explanations.


Questions for Review

1. According to Copernicus, why did the Pythagoreans not publish their discoveries in writing, but only communicate them orally?

2. According to Copernicus, what are some of the problems with traditional theories of celestial motion?

3. For Galileo, what are the similarities and differences between the surface of the earth and the surface of the moon?

4. According to Galileo, which qualities of external objects seem to be really part of them, and which qualities do not but exist only within our human physiology of perception?

5. According to Galileo, what was God’s intended purpose of scripture?

6. According to Galileo, what should be our source of knowledge about astronomy?

7. What is Galileo’s distinction between opinionative and demonstrative doctrines?

8. What, for Newton, are the four rules of reasoning in philosophy?

9. According to Newton, what kind of skills does God have which enable him to make the motion of the planets so perfect?

10. According to Newton, why is God needed to create luminous bodies, adjust planetary motion, and keep the universe from collapsing?


Questions for Analysis

1. The selections by Copernicus, Galileo and Newton raise issues about the boundaries between faith and reason, that is, religion and science. Is there a unified message that emerges from these three scientists on that subject?

2. In 1882 the Catholic Church lifted the ban on Galileo’s Dialogues and in 1992 Pope John Paul II gave a speech before the Pontifical Academy of Sciences in which he discussed the Church’s errors in their treatment of Galileo. He stated, “the new science [in Galileo’s time], with its methods and the freedom of research which they implied, obliged theologians to examine their own criteria of scriptural interpretation. Most of them did not know how to do so. Paradoxically, Galileo, a sincere believer, showed himself to be more perceptive in this regard than the theologians who opposed him. ‘If Scripture cannot err’, he wrote to Benedetto Castelli, ‘certain of its interpreters and commentators can and do so in many ways’. We also know of his letter to Christine de Lorraine (1615) which is like a short treatise on biblical hermeneutics.” Would Galileo agree with the Pope? Explain.

3. The Pope also stated that “Galileo made no distinction between the scientific approach to natural phenomena and a reflection on nature, of the philosophical order, which that approach generally calls for. That is why he rejected the suggestion made to him to present the Copernican system as a hypothesis, inasmuch as it had not been confirmed by irrefutable proof. Such therefore, was an exigency of the experimental method of which he was the inspired founder.” What is the distinction that the Pope is making here, and would Galileo agree?

4. The Pope also stated the following: “From the beginning of the Age of Enlightenment down to our own day, the Galileo case has been a sort of “myth”, in which the image fabricated out of the events was quite far removed from reality. In this perspective, the Galileo case was the symbol of the Church’s supposed rejection of scientific progress, or of “dogmatic” obscurantism opposed to the free search for truth. This myth has played a considerable cultural role. It has helped to anchor a number of scientists of good faith in the idea that there was an incompatibility between the spirit of science and its rules of research on the one hand and the Christian faith on the other. A tragic mutual incomprehension has been interpreted as the reflection of a fundamental opposition between science and faith. The clarifications furnished by recent historical studies enable us to state that this sad misunderstanding now belongs to the past.” What exactly is the myth that the Pope is describing, and would Galileo agree with him?

5. Newton proposes two separate accounts of scientific method, one from Principia Mathematica on “four rules of reasoning in philosophy” and the other from Opticks on the method of analysis. Contemporary philosopher Jaakko Hintikka summarizes Newton’s method of analysis as follows: (1) the analysis of a complex phenomenon into ingredients; (2) the experimental or observational discovery of dependencies between different ingredients; (3) the inductive generalization of these dependencies to all similar cases; and, (4) the deductive application of the generalization to other cases. Are Newton’s two accounts of scientific method different from each other or essentially the same? Explain.