Humanities Core Course Spring 2011 Instructor: Bencivenga

LECTURE NOTES

Lecture 2.

The most basic methodological principle Galileo lays down is that science should be based on empirical evidence, and that most important in this regard is recalcitrant evidence: evidence one has a hard time accounting for. So, when one is inclined to believing a given theory, one should pay special attention to anything that can be offered against that theory—and here the Copernicans have fared much better than their opponents.

[Y]ou will hear the followers of the new system producing observations, experiments, and arguments against it more forcible than those adduced by Aristotle and Ptolemy and the other opponents of the same conclusions. Thus you will become assured that it is not through ignorance or inexperience that they have learned to adhere to such opinion. (p. 148)

[O]ne who forsakes an opinion which he imbibed with his milk and which is supported by multitudes, to take up another that has few followers and is rejected by all the schools and that truly seems to be a gigantic paradox, must of necessity be moved, not to say compelled, by the most effective arguments. (pp. 149-150)

One major way of avoiding contrary evidence, Galileo points out, consists in paying selective attention to facts and making them subservient to one’s own preconceived ideas: “Aristotle … [is] more intent upon arriving at a goal previously established in his mind than upon going wherever his steps directly lead him” (p. 19). “This fellow goes about thinking up, one by one, things that would be required to serve his purposes, instead of adjusting his purposes step by step to things as they are” (p. 108). By proceeding in this way, one ends up giving circular and ultimately inconclusive accounts; the starting point as well as the ultimate vindication of scientific knowledge must be found in unbiased, systematic, careful observation.

Once the facts are known, one must proceed to explain them, and that means: to provide a causal account of them—an account of, say, fact a that shows how a must have necessarily followed from a previous fact b (which may well be quite a complex one, with elements d, e, f). For example, the fact that a given billiard ball moved is explained by showing that it followed necessarily from its being hit (which implicitly includes being hit on the surface of the earth, in normal conditions of temperature, pressure, etc.). “In questions of natural science …, a knowledge of the effects is what leads to an investigation and discovery of the causes. Without this, ours would be a blind journey” (p. 484). “[I]f it is true that one effect can have only one basic cause, and if between the cause and the effect there is a fixed and constant connection, then whenever a fixed and constant alteration is seen in the effect, there must be a fixed and constant variation in the cause” (p. 517). And, as indeed the last passage suggests, a causal account is also a general account: one that leaves off all idiosyncratic aspects of individual situations and focuses on what is common to an indefinite number of situations: causal connections come in the form of causal laws, connecting facts (or phenomena, or data—all these expressions point to different aspects of the same reality: it takes place, it shows up, and it is given to us) of kind A with facts of kind B—not just a single fact a with a single fact b. When the necessity of the relation between causes and effects is combined with the generality of the laws, we obtain what is probably the most striking aspect of scientific work: the capacity that science appears to have to make absolutely certain predictions (say, of an eclipse). If facts of kind A always necessarily follow facts of kind B, then upon observing an event of the first kind we must become absolutely certain that an event of the second kind will follow.

Finally, a causal law should also let one calculate the effect starting from the cause; hence it should be formulated mathematically. The abstractions that matter to science, the ones from which true scientific knowledge is acquired, are mathematical abstractions. “[I]t must be admitted that trying to deal with physical problems without geometry is attempting the impossible” (p. 236). Galileo’s enthusiasm for mathematics is extreme: when humans attain mathematical knowledge humans reach a state on which not even God could improve—though of course God could reach that state infinitely more often than humans. (And this was indeed one of the theses the Inquisition condemned.)

[T]he human understanding can be taken in two modes, the intensive or the extensive. Extensively, that is, with regard to the multitude of intelligibles, which are infinite, the human understanding is as nothing even if it understands a thousand propositions; for a thousand in relation to infinity is zero. But taking man’s understanding intensively, in so far as this term denotes understanding some proposition perfectly, I say that the human intellect does understand some of them perfectly, and thus in these it has as much absolute certainty as Nature itself has. Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater success. (p. 118)

The claim made by supporters of this method, and certainly made by Galileo, is that by its means one can arrive at the truth; and, once one gets there, one cannot do any better. The truth needs no embellishments or rhetorical flourish: even mediocre minds endowed with no natural grace can discover it and, though it is likely that brilliant minds can discover more truths, they can also get lost in their own subtlety:

And if this is not enough, there are more brilliant intellects who will find better answers…. If what we are discussing were a point of law or of the humanities, in which neither true nor false exists, one might trust in subtlety of mind and readiness of tongue and in the greater experience of the writers, and expect him who excelled in those things to make his reasoning most plausible, and one might judge it to be the best. But in the natural sciences, whose conclusions are true and necessary and have nothing to do with human will, one must take care not to place oneself in the defense of error; for here a thousand Demotheneses and a thousand Aristotles would be left in the lurch by every mediocre wit who happened to hit upon the truth for himself. Therefore, Simplicio, give up this idea and this hope of yours that there may be men so much more learned, erudite, and well-read than the rest of us as to be able to make that which is false become true in defiance of nature. (p. 61)

I will now consider two applications of the method. First, a major topic of the first day is the following: contra what Aristotle believed, there are no substantial differences between the earth and the other celestial bodies. In particular, it is not the case that those other bodies are made of an incorruptible substance, and that no changes ever occur in them, nor are they ever generated or corrupted. The participants in the dialogue bring up phenomena that seem to prove Aristotle wrong in this regard: the sunspots and the appearance of what seemed to be two new stars (and, in fact, were two novas) in 1572 and 1604. Here I will focus on their discussion of the moon, and specifically of the Aristotelian view that the moon is “as polished and smooth as a mirror and, as such, fitted to reflect to sunlight, and the earth, on the other hand, because of its roughness, … [has] no power to make a similar reflection” (p. 81). As a matter of fact, Galileo argues, the earth makes as much of a reflection of the sunlight for the moon’s benefit as the moon itself does, as indeed can be seen from the moon’s secondary reflection: “a certain baffling light which is seen on the moon, especially when it is horned, comes from the reflection of the sun’s light from the surface of the earth and the sea; and this light is seen most clearly when the horns are the thinnest” (p. 77). Also, the moon is not at all smooth and polished as a mirror but as rough as the earth: “its material … [is] very dense and solid, no less than the earth’s, of which a sufficiently clear proof … is the unevenness of the major parts of its surface, evidenced by the many prominences and cavities revealed by the aid of the telescope. The prominences there are mainly very similar to our most rugged and steepest mountains, and some of them are seen to be drawn out in long tracts of hundreds of miles” (p. 72). Simplicio objects that a rough body could not reflect the sunlight as well as the moon does; that is why “the earth … is incapable of reflecting the sun’s rays by reason of its extreme roughness and darkness” (p. 79), whereas the moon is “suited to receive a polish and lustre superior to that of the smoothest mirror, as observed in the hardest stones on earth. For thus must be its surface in order to make such a vivid reflection of the sun’s rays” (p. 80). As for the irregularities observed on the moon, he explains them away as due to the moon’s composition: “such appearances belong merely to the unevenly dark and light parts of which the moon is composed inside and out” (p. 80). Finally, its secondary reflection Simplicio takes to be due to the moon’s own light: “that brightness which is observed on the balance of its disc outside of the thin horns lighted by the sun I take to be its own natural light” (p. 79).

Galileo’s strategy in answering this objection is twofold. On the one hand he brings up experiments to show that, contra what might appear if one just thinks about it, a mirror looks generally darker than a rough surface when the two reflect the same light. The three characters actually try out various things outside Sagredo’s house, and what they do confirms Galileo’s view: “Now please take that mirror which is hanging on the wall, and let us go out into that court…. Hang the mirror on that wall, there, where the sun strikes it. Now let us withdraw into the shade. Now, there you see two surfaces struck by the sun, the wall and the mirror. Which looks brighter to you; the wall, or the mirror?” (p. 82) If one is at the right angle with the mirror, Simplicio points out, the mirror’s reflection is stronger, but Salviati considers this observation additional evidence for the moon’s roughness:

You see how the reflection that comes from the wall diffuses itself over all the points opposite to it, while that from the mirror goes to a single place no larger than the mirror itself. You see likewise how the surface of the wall always looks equally light in itself, no matter from what place you observe it, and somewhat lighter than that of the mirror from every place except that small area where the reflection from the mirror strikes; from there, the mirror appears very much brighter than the wall. From this sensible and palpable experiment it seems to me that you can very readily decide whether the reflection which comes here from the moon comes like that from a mirror, or like that from a wall; that is, whether from a smooth or a rough surface. (pp. 83-84)

But observation is not enough: we still have to overcome the natural impression that a rough surface is not the best one to provide a strong reflection. Echoing a number of other similarly puzzled scientists in similar predicaments, Simplicio says, in essence, “I see it, but I cannot believe it”: “I am more perplexed than ever…. How can it be that the wall, being of so dark a material and so rough a surface, is able to reflect light more powerfully and vividly than a smooth and well-polished mirror?” (p. 88). Galileo must also provide a theoretical explanation that resolves this perplexity, which he does as follows:

Not more vividly, but more diffusely…. [C]onsider how the surface of this rough wall is composed of countless very small surfaces placed in an innumerable diversity of slopes, among which of necessity many happen to be arranged so as to send the rays they reflect to one place, and many others to another. In short, there is no place whatever which does not receive a multitude of rays reflected from very many little surfaces dispersed over the whole surface of the rough body upon which the luminous rays fall. From all this it necessarily follows that reflected rays fall upon every part of any surface opposite that which receives the primary incident rays, and it is accordingly illuminated. It also follows that the same body on which the illuminating rays fall shows itself lighted and bright all over when looked at from any place. Therefore the moon, by being a rough surface rather than smooth, sends the sun’s light in all directions, and looks equally light to all observers. If the surface, being spherical, were as smooth as a mirror, it would be entirely invisible, seeing that that very small part of it which can reflect the image of the sun to the eyes of any individual would remain invisible because of the great distance. (pp. 88-89)

Against this powerful combination of observation and theoretical ingenuity, the Aristotelian view appears as simple prejudice (that is, pre-judgment; or, in Salviati’s words, “an inveterate affection and a deeply rooted opinion,” p. 111) that trusts itself so much as never to look for proper confirmation.