On the Pythagoreans
 

SALV.: To tell you true, I do not think myself bound by all these reasons to grant any more than this--that that which has beginning, middle, and end may be, and possibly ought to be, called perfect. But I cannot grant that, because beginning, middle, and end are three, the number three is a perfect number and has a faculty of conferring perfection on those things that have it. Neither do I understand nor believe that, for example, of feet, the number three is more perfect than four or two; nor do I conceive their number of four to be any imperfection in the elements; nor that they would be more perfect if they were three. Better therefore if he had left these sub tleties to the rhetoricians and had proved his intent by necessary demonstration; for so it be hooves to do in demonstrative sciences.
 

SIMP.: You seem to scorn these reasons, and yet it is all the doctrine of the Pythagoreans, who attribute so much to numbers; and you who are a mathematician, and believe many opinions in the Pythagorean philosophy, seem now to despise their mysteries.
 

SALV.: That the Pythagoreans had the science of numbers in high esteem, and that Plato himself admired human understanding and thought that it partook of divinity, in that it understood the nature of numbers, I know very well, nor should I be far from being of the same opinion. But that the mysteries for which Pythagoras and his sect held the science of numbers in such veneration are those follies that abound in the sayings and writings of the vulgar, I cannot believe. Rather, I know that, to the end that admirable things might not be exposed to the contempt and scorn of the vulgar, they censured as sacrilegious the publishing of the abstruse properties of numbers and incommensurable and irrational quantities by them investigated and also proclaimed that he who divulged them would be tormented in the other world.
 
 

Can human knowledge equal God's?
 

SALV. Now consider what effect the Sun would have in the torrid zone should it continually for fifteen days beam down its rays upon it: without all question it would destroy plants, herbs, and living creatures; and, if it should happen that there were any production, it would be of herbs, plants, and creatures very different from those which are now there. Secondly, I verily believe that in the Moon there are no rains, for if clouds should gather in any part thereof, as they do about the Earth, they would hide from our sight some of those things, which we behold with the Telescope. In a word, they would alter their appearance in some way or other, an effect which I could never by long and diligent observations discover, but always an even and pure serenity.
 

SAGR.: To this may be answered either that there might be great dewfalls or that it might rain in the time of their night, that is, when the Sun does not illuminate it.
 

SALV.: If other signs but hinted to us that there were generation in it as here, and that there was only wanting the concourse of rains, we might might think of this, or some other temperament to serve instead of it, as it happens in Egypt by the inundation of the Nile. But not meeting with any accidents which correspond with ours, of many that have been sought out for the production of the like effect, we need not trouble ourselves to introduce one alone; and that, too, not from certain observation of it but from a bare nonrepugnance of our imagination. Moreover, if I were demanded what my first apprehension and pure natural reason suggested to me concerning the production of things like or unlike there above, I would always reply that they ought to be most different, and to us altogether unimaginable, for so, I think, the richness of Nature and the omnipotence of our Creator and Ruler do require.
 

SAGR.: I always accounted as extraordinary foolish those who would make human comprehension the measure of what Nature has a power or knowledge to effect, whereas on the contrary there is not any least effect in Nature which can be fully understood by the most speculative minds in the world. Their vain presumption of knowing all can take beginning solely from their never having known anything; for if one has but once experienced the perfect knowledge of one thing, and truly tasted what it is to know, he shall perceive that of infinite other conclusions he understands not so much as one.
 

SALV.: Your discourse is very concluding; for confirmation we have the example of those who know, or have known, something; the wiser they are, the more they know and freely confess that they know little; nay, the wisest man in all Greece, and pronounced as such by the Oracle, openly professed to know that he knew nothing.
 

SIMP.: It must be confessed therefore that either Socrates or the Oracle itself was a liar, the latter declaring him to be most wise, and he confessing that he knew himself to be most ignorant.
 

SALV.: Neither one nor the other does follow, for both the assertions may be true. The Oracle adjuges Socrates the wisest among men, whose knowledge is limited; Socrates acknowledges that he knows nothing in relation to absolute wisdom, which is infinite; and, because of the infinite, much is the same part as is little and as is nothing (for to arrive, e.g., to the infinite number, it is all one to accumulate thousands, tens, or zeros); therefore, Socrates well perceived his wisdom to be nothing in comparison with the infinite knowledge that he lacked. But yet, because there is some knowledge found among men, and this not equally shared by all, Socrates might have a greater share thereof than others and therefore verified the answer of the Oracle.
 

SAGR.: I think I very well understand this particular. Amongst men, Simplicius, there is the power of influence, but not equally dispensed to all; it is without question that the power of an emperor is far greater than that of a private person, but both the former and the latter are nothing in comparison with the Divine Omnipotence. Amongst men there are some who better understand agriculture than many others; but what has the knowledge of planting a vine in a trench to do with the knowledge that it takes to make it sprout forth, to attract nourishment, select this good part from that other to make of it leaves, another part to make sprouts, another to make grapes, another to make seeds, another to make the husks of them, for such are the works of most wise Nature? This is only one particular operation of the innumerable ones which Nature carries out, and it alone is enough to reveal an infinite wisdom, so that Divine Wisdom may be concluded to be infinitely infinite.
 

SALV.: Take thereof another example. Do we not say that the skillful revealing of a most lovely statue in a piece of marble has sublimated the wit of Michelangelo Buonarroti far above the vulgar wits of other men? And yet this work is only the imitation of a mere aptitude and disposition of exterior and superficial members of an immovable man; but what is it in comparison of a man made by Nature, composed of so many exterior and interior members, of so many muscles, tendons, nerves, bones, which serve to so many and sundry motions? But what shall we say of the senses, and of the powers of the soul, and, lastly, of the understanding? May we not say, and with reason, that the structure of a statue falls far short of the formation of a living man, yea, more, of a contemptible worm?
 

SAGR: And what difference do you think was there between the dove of Archytas and one made by Nature?
 

SIMP: Either I am not one of the men who understand, or else there is a manifest contradiction in this your discourse. You account understanding the chief distinction ascribed to man, who is made by Nature, and a little earlier you said, with Socrates, that he had no knowledge at all; therefore you must say that neither did Nature understand how to make an understanding that understands.
 

SALV.: You argue very cunningly, but, to reply to your objection, we should have recourse to a philosophical distinction and say that the understanding is to be taken two ways, that is, intensively or extensively. Extensively, that is, as to the multitude of intelligibles, which are infinite, the understanding of man is as nothing, though he should understand a thousand propositions; for a thousand in respect of infinity is but as zero. But as for the understanding intensively, inasmuch as that term imports perfectly some propositions, I say that human wisdom understands some propositions as perfectly and is as absolutely certain thereof, as Nature herself; and such are the pure mathematical sciences, to wit, Geometry and Arithmetic. In these Divine Wisdom knows infinitely more propositions, because it knows them all; but I believe that the knowledge of those few comprehended by human understanding equals the Divine, as to objective certainty, for it arrives to comprehend the necessity of it, than which there can be no greater certainty.
 

SIMP.: This seems to me a very bold and rash expression.
 

SALV. These are common notions far from all umbrage of temerity, or boldness and detract not in the least from the majesty of Divine Wisdom, as it in no ways diminishes its omnipotence to say that God cannot make what once happened not to have happened. I believe, Simplicius, that your scruple arises from your having possibly misunderstood my words somewhat; therefore, the better to express myself, I say that as concerns the truth, of which mathematical demonstrations give us the knowledge, it is the same as that which the Divine Wisdom knows. But this I must grant you, that the manner whereby God knows the infinite propositions of which we understand some few is much more excellent than ours, which proceeds by ratiocinations and passes from conclusion to conclusion, whereas His is done at one single thought or intuition. For example, we, to attain the knowledge of some property of the circle, which has infinitely many, begin from one of the most simple and, taking that for its definition, do proceed with argumentation to another, and from that to a third, and then to a fourth, and so on. The Divine Wisdom by the simple apprehension of its essence comprehends, without temporal ratiocination, all these infinite properties which are also, in effect, virtually comprised in the definitions of all things, and, to conclude, being infinite, are perhaps but one alone in their nature and in the Divine Mind. Neither is this wholly unknown to human understanding, but only beclouded with deep and dense mists which in part come to be dissipated and clarified when we are made masters of any conclusions firmly demonstrated and made so perfectly ours that we can speedily run through them. For, in sum, what else is that proposition, that the square of the side subtending the right angle in any triangle is equal to the squares of the other two which include it, but that parallelograms built on common bases, and between parallels, are equal amongst themselves? And this, lastly, is it not the same as to say that those two areas are equal when superposed they coincide? Now these inferences, which our intellect apprehends with time and gradual motion, the Divine Wisdom, like light, penetrates in an instant, which is the same as to say has them always all present. I conclude therefore that our understanding, as to both the manner and the multitude of the things comprehended by us, is infinitely surpassed by the Divine Wisdom; but yet I do not so vilify it as to consider it absolutely nothing; rather, when I consider how many and how great mysteries men have understood, discovered, and contrived, I very plainly know and understand the mind of man to be one of the works of God, yea, one of the most excellent.
 

SAGR.: I have often considered with myself how great the wit of man is; and while I run through such and so many admirable inventions found out by him, in the arts as well as in the sciences, and again reflecting upon my own wit, which is so far from promising me the discovery of anything new that I despair of comprehending what is already discovered, I stand here confounded with wonder and surprised with desperation and account myself little less than miserable. If I behold a statue of some excellent master, I say with myself: "When will you know how to chisel away the refuse of a piece of marble and discover so lovely a figure as lies hidden within? When will you mix and spread so many different colours upon a cloth, or a wall, and represent there with all visible objects, like a Michelangelo, a Raphael, or a Titian?" If I behold what invention men have had in parting musical intervals and in establishing precepts and rules for their management with admirable delight to the ear, when shall I cease my astonishment? What shall I say of such and so various instruments of that art? The reading of excellent poets, with what admiration does it not fill anyone who attentively considers the invention of ideas and their arrangement? What shall we say of architecture? What of navigation? But, above all other stupendous inventions, what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very far distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand, or ten thousand years? And with no greater difficulty than the various collocation of twenty-four little characters upon a paper? Let this be the seal of all the admirable inventions of man and the close of our discourse for this day. The warmer hours being past, I suppose that Salviatus desires to go and enjoy the cool of our evenings in his gondola, but tomorrow we will both wait upon you to continue the discourse we have begun.
 

On nature and the human brain
 

SAGR.: I shall also, as being induced by natural reason, say something to this antagonist. He will condemn Copernicus unless I am able to answer him to all objections and to satisfy him in all questions he shall ask, as if my ignorance were a necessary argument of the falsehood of his doctrine. But if this way of condemning writers be in his judgment legal, he ought not to think it unreasonable if I should not approve of Aristotle and Ptolemy when he cannot resolve better than I myself those doubts which I propound to him touching their doctrine. He asks me what the principles are by which the terrestrial globe is moved with I the annual motion through the zodiac, and with the diurnal through the equinoctial about its own axis. I answer that they are like those by which Saturn is moved about the zodiac in thirty years, and about its own centre in a much shorter time along the equinoctial, as the apparition and occultation of its collateral globes evinces. They are principles like to those whereby he is willing to grant that the Sun runs through the ecliptic in a year and revolves about its own centre parallel to the equinoctial in less than a month, as its spots sensibly demonstrate. They are things like to those whereby the satellites of Jupiter run through the zodiac in twelve years and all the while revolve in small circles and short periods of time about Jupiter.

SIMP.: The Author will deny all these things as delusions of the sight caused by the crystals of the Telescope.
 

SAGR.: Oh, but this would be wanting everything his own way, in that he holds that the bare eye cannot be deceived in judging the right motion of descending bodies and yet holds that it is deceived in beholding these other motions at such time as its visual vertue is perfected and augmented thirty times as much as it was before. We tell him, therefore, that the Earth in a like manner partakes of the plurality of motions, and it is perhaps the same, whereby the lodestone has its motion downwards, as the heavy body that it is, and two circular motions, one horizontal, and the other vertical, under the meridian. But what more? Tell me, Simplicius, between which do you think this Author would put a greater difference, 'twixt straight and circular mot lion or twixt motion and rest?
 

SIMP.: 'Twixt motion and rest, certainly. And this is manifest, for circular motion is not contrary to the straight, according to Aristotle; nay, he grants that they may mix with each other, which it is impossible for motion and rest to do.
 

SAGR.: Therefore it is a proposition less improbable to place in one natural body two internal principles, one for straight motion and the other for circular, than two such internal principles, one for motion and the other for rest. Now both positions agree to the natural inclination that resides in the parts of the Earth to return to their whole, when by violence they are divided from it; and they only dissent in the operation of the whole, for the latter of them will have it by an internal principle to stand still, and the former ascribes to it the circular motion. But by your concession, and the confession of this philosopher, two principles, one of motion and the other of rest, are incompatible together, as their effects are incompatible. While this is not the case for the two motions, straight and circular, which have no repugnance to each other.
 

SALV.: Add this more: that in all probability it may be that the motion that the disjoined part of the Earth makes while it returns towards its whole is also circular, as has been already suggested; so that in all respects, as far as concerns the present case, mobility seems more likely than rest. Now proceed, Simplicius, to what remains.
 

SIMP.: The Author backs his argument with producing another absurdity, namely, that the same motions would have to agree to extremely different natures; but experience shows that the operations and motions of different natures are different; and reason confirms the same, for otherwise we should have no way left to know and distinguish natures, if they should not have their particular motions and operations that might guide us to the knowledge of their substances.
 

SAGR.: I have more than once observed in the discourses of this Author that, to prove that a thing is thus and thus, he resorts to the argument that in that manner it is conformable with our understanding, or that otherwise we should never be able to conceive of it, or that the criterium of philosophy would be overthrown. As if Nature had first made men's brains and then disposed all things in conformity to the capacity of their intellects. But I rather incline to think that Nature first made the things themselves, as she best liked, and afterwards framed the reason of men capable of conceiving ( though not without great pains) some part of her secrets.
 
 

On Christopher Scheiner's objections to Copernicus from the Bible
 

SIMP.: Having explained the universal system, he [Scheiner] begins to propound his objections against this annual motion. And the first are these, which he cites ironically and in derision of Copernicus and of his followers, writing that in this fantastic hypothesis of the world one must necessarily maintain very gross absurdities, namely: That the Sun, Venus, and Mercury are below the Earth; and that heavy bodies go naturally upwards, and the light downwards; and that Christ, our Lord and Redeemer, ascended into Hell and descended into Heaven when he approached towards the Sun; and that, when Joshua commanded the Sun to stand still, the Earth stood still, or the Sun moved a contrary way to that of the Earth; and that, when the Sun is in Cancer, the Earth runs through Capricorn; and that hiemal (or winter) signs make the summer, and the estival, winter; and that the stars do not rise and set to the Earth, but the Earth to the stars; and that the east begins in the west, and the west in the east; and, in a word, that almost the whole course of the world is inverted.
 

SALV.: Everything pleases me, except his having intermixed places out of the Sacred Scriptures, ever awesome and to be revered, among these too scurrilous fooleries, and attempting to wound with holy weapons those who, philosophizing in sport and for diversion, neither affirm nor deny but argue familiarly, starting from certain presupposals and positions.
 

SIMP.: Truth is, he has displeased me also, and not a little; especially by adding presently after that, even if the Copernicists were able to answer, although impertinently, to these and such like other reasons, yet they cannot reconcile or answer those things that follow.
 

SALV.: This is worse than all the rest, for he pretends to have things more efficacious and conclusive than the authority of the Holy Writ. But, I pray you, let us reverence it, and pass on to natural and human reasons. And yet, if he give us among his natural arguments things of no more solidity than those hitherto alleged, we may wholly decline this undertaking; for I, as to my own particular, do not think it fit to spend words in answering such trifling impertinencies. And as to what he pretends the Copernicans answer to these objections, it is most false; nor may it be thought that any man should set himself to waste his time so unprofitably.
 

STMP.: I concur with you in the same judgment.
 
 

Was the cosmos made solely for humans?
 

SALV.: I could wish, Simplicius, that, suspending for a time the affection that you bear to the followers of your opinion, you would sincerely tell me whether you think that they do in their minds comprehend that magnitude which they reject afterwards as impossible for its immensity to be ascribed to the Universe. For I, as to my own part, think that they do not. But I believe that, as, in the apprehension of members, when once a man begins to pass those millions of millions, the imagination is confounded and can no longer form a concept of them, so it happens also in trying to comprehend immense magnitudes and distances; so that there intervenes to the comprehension an effect like to that which befalls the sense. For when in a serene night I look towards the stars, I judge, according to sense, that their distance is but a few miles and that the fixed stars are not a jot more remote than Jupiter or Saturn or than the Moon. But, without more ado, consider the controversies that have passed between the astronomers and the Peripatetic philosophers, upon occasion of the new stars of Cassiopeia and of Sagittarius, the astronomers placing them amongst the fixed stars, and the philosophers believing them to be below the Moon, so unable is our sense to distinguish great distances from the greatest, though these be in reality many thousand times greater than those. In a word, I ask of you, oh, foolish men, does your imagination comprehend that vast magnitude of the Universe, which you afterwards judge to be too immense? If you comprehend it, will you hold that your apprehension extends itself further than the Divine Power? Will you say that you can imagine greater things than those which God can bring to pass? But if you apprehend it not, why will you pass verdict upon things beyond your comprehension?
 

SIMP.: All this is very well, nor can it be denied but that Heaven may in greatness surpass our imagination, as also that God might have created it thousands of times vaster than now it is; but we ought not to grant anything to have been made in vain and to be idle in the Universe. Now, since we see this admirable order of the planets, disposed about the Earth in distances proportionate for producing their effects for our advantage, to what purpose is to interpose afterwards between the highest sphere of Saturn and the starry sphere a vast vacancy, without any star, that is superfluous and to no purpose? To what end? For whose profit and advantage?
 

SALV.: I think we arrogate too much to ourselves, Simplicius, when we take it for granted that only the care of us is the adequate reason and limit, beyond which Divine Wisdom and Power does or disposes nothing. I will not consent that we should so much shorten its hand but desire that we may content ourselves with an assurance that God and Nature are so employed in the governing of human affairs that they could not apply themselves more thereto if they truly had no other care than only that of mankind. And this, I think, I am able to make out by a most pertinent and most noble example, taken from the operation of the Sun's light, which, while it attracts these vapours, or heats that plant, attracts and heats them as if it had no more to do; yea, in ripening that bunch of grapes, nay, that one single grape, it does apply itself so that it could not be more intense, if the sum of all its business had been the maturation of that one grape. Now if this grape receives, all that it is possible for it to receive from the Sun, not suffering the least injury by the Sun's production of a thousand other effects at the same time, well might we accuse that grape of envy or folly if it should think or wish that the Sun would appropriate all of its rays to its advantage. I am confident that nothing is omitted by the Divine Providence of what concerns the government of human affairs; but that there may not be other things in the Universe that depend upon the same infinite wisdom, I cannot, of myself, by what my reason holds forth to me, bring myself to believe. Surely, I should not forbear to believe any reasons to the contrary laid before me by some higher intellect. But, as I stand, if one should tell me that an immense space interposed between the orbs of the planets and the starry sphere, deprived of stars and idle, would be vain and useless, as likewise that so great an immensity for receipt of the fixed stars as exceeds our utmost comprehension would be superfluous, I would reply that it is rashness to go about to make our shallow reason judge of the works of God, and to call vain and superfluous whatever thing in the Universe is not of use to us.
 

SAGR.: Say rather, and I believe you would say better, that we know not what may be its use to us; and I hold it one of the greatest vanities, yea, follies, that can be in the world, to say, "Because I know not of what use Jupiter or Saturn are to me, therefore these planets are superfluous, yea, more, there are no such things in Nature"; whenas, oh, most foolish men, I do not know so much as to what purpose the arteries, the gristles, the spleen, the gall serve; nay, I should not know that I have a gall, spleen, or kidneys, if in many dissected corpses they were not shown to me; and only then shall I be able to know what the spleen works in me when it comes to be taken from me. To be able to know what this or that celestial body works in me ( since you will have it that all their influences direct themselves to us), it would be requisite to remove that body for some time; and then, whatever effect I should find wanting in me, I would say that it depended on that star. Moreover, who will presume to say that the space which they call too vast and useless between Saturn and the fixed stars is void of other mundane bodies? Must it be so, because we do not see them? Then the four Medicean Planets and the companions of Saturn came first into heaven, when we began to see them, and not before? And by this rule the innumerable other fixed stars had no existence before men did look on them? Those cloudy constellations called Nebulae were at first only white flakes, but afterwards with the Telescope we made them to become constellations of many lucid and bright stars. Oh, presumptuous, rather, oh, rash ignorance of man!
 

SALV.: It is to no purpose, Sagredus, to sally out any more into these unprofitable excursions.
 
 

The Pope's argument against Copernicus
 

SALV.: Now, since it is time to put an end to our discourses, it remains that I entreat you that, if, going over again at leisure the things that have been alleged, you meet with any doubts or scruples not well resolved, you will excuse my oversight, as well for the novelty of the notion as for the weakness of my intellect as also for the greatness of the subject, as also, finally, because I do not nor have pretended to that assent from others which I myself do not give to this theory, which I could very easily grant to be a vain chimera and a most huge paradox. And you, Sagredus, although in the discourses past you have many times, with great applause, declared that you were pleased with some of my conjectures, yet I believe that that was in part more occasioned by the novelty than by the certainty of them, but much more by your courtesy, which did think and desire, by its assent, to procure me that content which we naturally use to take in the approbation and applause of our own matters. And, as your civility has obliged me to you, so am I also pleased with the candour of Simplicius. Nay, his constancy in maintaining the doctrine of his master, with so much strength and undauntedness, has made me much to love him. And, as I am to give you thanks, Sagredus, for your courteous affection, so of Simplicius I ask pardon, if I have sometimes moved him with my too bold and resolute speaking, and let him be assured that I have not done it out of any inducement of sinister affection but only to give him occasion to set before us more lofty thoughts that might make me the more knowing.
 

SIMP.: There is no reason why you should make all these excuses that are needless, and especially to me, who, being accustomed to be at conferences and public disputes, have a hundred times seen the disputants not only grow hot and angry at one another but break forth into injurious words and sometimes come very near to blows. As for the past discourses, and particularly this last, of the reason of the ebbing and flowing of the sea, I do not, to speak the truth, very well comprehend it. But by that slight idea, whatever it be, that I have formed thereof to myself, I confess that your hypothesis seems to me far more ingenious than any of all those that I ever heard besides; still, I esteem it neither true nor conclusive, but, keeping always before the eyes of my mind a solid doctrine that I once received from a most learned and eminent person, and to which there can be no answer, I know that both of you, being asked whether God, by his infinite power and wisdom, might confer upon the element of water the reciprocal motion in any other way than by making the containing vessel to move, I know, I say, that you will answer that he could, and also knew how to bring it about in many ways, and some of them above the reach of our intellect.  Upon which I forthwith conclude that, this being granted, it would be an extravagant boldness for anyone to go about to limit and confine the Divine power and wisdom to some one particular conjecture of his own.
 

SALV.: An admirable and truly angelical doctrine, which is answered with perfect agreement by that other one, in like manner divine, which gives us leave to dispute touching the constitution of the Universe, but adds, withal (perhaps to the end that the exercise of the minds of men might not cease or become remiss), that we are not to find out the works made by His hands. Let, therefore, the disquisition permitted and ordained us by God assist us in the knowing, and so much more admiring, His greatness by how much less we find ourselves capable of penetrating the profound abysses of His infinite wisdom.
 

SAGR.: And this may serve for a final close of our four days' disputations, after which, if it seem good to Salviatus to take some time to rest himself, our curiosity must, of necessity, grant it to him, yet upon condition that, when it is less inconvenient for him, he will return and satisfy my desire concerning the problems that remain to be discuss and that I have set down to be propounded at one or two other conferences, according to our agreement. And, above all, I shall very impatiently wait to hear the elements of the new science of our Academic about the natural and violent local motions. In the meantime, we may, according to our custom, spend an hour in taking the air in the gondola that waits for us.