Abstract
Equipped now with a fairly extensive knowledge of the logica docens appropriated by Galileo at the beginning of his teaching career, we move to the more difficult part of our study, that relating to his actual use of the scientific methodology it implies, his logica utens.1 Before citing specific examples of such use we would stress a point made earlier, one on which Zabarella, Vallius, and Galileo all agree, namely, that there is a vast difference between logica docens and logica utens [Sec. 1.5]. The logic discussed thus far, the instrumental habit that directs the mind’s operations to the attainment of truth, is logica docens,logic pure and simple. As opposed to this the logica utens that is used by an astronomer or a physicist to reach conclusions about the heavens or motion is, strictly speaking, not logic at all. When applied to subject matters in the real world it ceases to be logic and becomes instead the science of astronomy or that of mechanics. That is what logica utens means in an Aristotelian context: the use of logic in a scientific discipline — a use so intrinsic to the discipline that it becomes identified with the discipline itself.
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Notes
Since this volume is in effect a sequel and further development of materials already presented in Galileo and His Sources, in this chapter and the next we now survey and summarize essentially the same texts as in the previous work. The difference between the two treatments is that in Galileo and His Sources we were intent on showing how Galileo’s scientific writings were in basic continuity with Jesuit teachings at the Collegio Romano, whereas here we have the much less demanding task of showing internal consistency in Galileo’s works themselves, and particularly how the logica docens of MS 27 manifests itself in the logica utens of his later treatises.
The expression closest to this in Aristotle’s text is kuklos (Lat. circulus), when he speaks of demonstration being circular in I.3, 72b25–73a6. Probably on this account Galileo refers to the regressus as a circulus imperfectus in D3.3.5.
Identified as I.12 in Zabarella’s division of the text.
This coheres precisely with the sentiment of Christopher Clavius when he wrote, at the conclusion of his commentary on the Sphere of Sacrobosco: Finally, we may conclude our project as follows: just as in natural philosophy we arrive at knowledge of causes through their effects, so too in astronomy, which treats of heavenly bodies very far distant from us, we can only attain to knowledge of the bodies themselves, of how they are arranged and constituted, through study of their effects, that is, through their movements as perceived by us through our senses [Rome: 1581, 450].
An analysis of this treatise in the context of the logical teaching contained in MS 27 will be found in Galileo and His Sources, 255–261.
For a clear modern explanation of these phenomena, with diagrams, see Otto Struve, Elementary Astronomy, rev. ed., New York: Oxford University Press, 1959, 74–80. We cite this edition because it is the last to demonstrate such properties of the moon on the basis of how it appears from earth and prior to its close observation by satellite. From Struve’s text one gains the impression that astronomers of his day regarded these arguments as apodictic and as providing certain knowledge of the causes of the moon’s appearance long before satellite data became available.
A denial that the demonstrative regress works in this simple case effectively rules out the possibility of astronomy ever being a science in Aristotle’s apodictic sense. As noted in Chap. 1, McMullin rejects on principle Aristotle’s teaching in Posterior Analytics I.13 [Sec. 1.2f] and so, along with that teaching, must deny the validity of the proof for the moon’s phases here elaborated, as well as the validity of Galileo’s proofs detailed in the next section. The simplest reply to such a rejection is the argument ad hominem. Is McMullin himself certain that the moon is a sphere, that it has mountains on its surface, that Jupiter has satellites, that Venus has phases, and so on? If not, then he is consistent with his critique of Aristotle, but he must hold as a consequence that planetary astronomy is not an apodictic science but only opinion, highly probable opinion, but opinion nonetheless. If he is certain of these conclusions, then his problem is that of identifying at what point in the history of thought, and by what reasoning process, he, or others before him, became convinced of their truth. Should he situate his discoveries prior to the age of satellite exploration (thus ruling out the radical empiricist alternative, that such conclusions were not reasoned to but grasped directly in sense experience), he will have arrived at a demonstrative regressus, whether he recognizes it under that name or not. See the previous note.
For the background to Galileo’s discoveries see Albert van Helden’s new annotated translation of Galileo’s Sidereus Nuncius, or The Sidereal Messenger (Chicago and London: The University of Chicago Press, 1989, 1–24. We generally use Van Helden’s analysis in what follows.
This expression is sometimes heard in philosophy of science circles with the connotation that being “dead” it is trivial or unimportant, the really interesting science being that done at the frontiers of knowledge. This is the reverse of the Aristotelian view: “live science” is probably opinion and not science at all, whereas any topic on which scientists have “closed the book,” as it were, probably constitutes valid science in the Aristotelian sense.
Van Helden, Sidereus Nuncius, 9–12, 39–57.
Sidereus Nuncius, 21–22.
Following Van Helden’s translation, 105–106.
For the geometrical details, see Struve, Elementary Astronomy, 98–101.
Again using Van Helden’s translation, 111.
See Stillman Drake, Galileo: Pioneer Scientist, Toronto: University of Toronto Press, 1990, 136.
Drake, Galileo: Pioneer Scientist, 142.
Called such because it was proposed by Tycho Brahe as a compromise between the Ptolemaic and the Copernican systems that could be reconciled more readily with Aristotelian and Scriptural teachings.
For further methodological observations about the letters on sunspots, see Galileo and His Sources, 289–291.
Cesalpino did so in his Peripateticae quaestiones, first published at Venice in 1571 and again in Geneva in 1588. According to Cesalpino the ebb and flow of the tides was caused not by the moon but by the movement of the earth; likewise he thought he could explain the motion of trepidation attributed by astronomers to the eighth sphere by a similar movement, seemingly one of slow oscillation. Some details relating to Cesalpino’s teaching will be found in Helbing, Buonamici, 57, 200.
This passage suggests that the argument occurred to Galileo on the basis of his experience with barges carrying fresh water to Venice from the mainland during his early years at Padua; see Stillman Drake, Galileo at Work: His Scientific Biography, Chicago: The University of Chicago Press, 1978, 37.
For details on Fantoni, see Essay 10 in C.B. Schmitt, Studies in Renaissance Philosophy and Science, London: Variorum Reprints, 1981.
Additional comments about the early discourse on tides and the context in which it was written will be found in Galileo and His Sources, 291–295.
Again, further details are given in Galileo and His Sources, 295–298.
Publication details are given in note 3 of Chap. 2 above; the work is cited hereafter as Art of Reasoning.
Our own review of the Dialogue in the context of the terminology of MS 27 will be found in Galileo and His Sources,299–311.
Finocchiaro, Art of Reasoning, 29.
Art of Reasoning, 33–35.
See her “Galileo’s Rhetorical Strategies in Defense of Copernicanism,” 99–103.
Art of Reasoning, 35–39.
Such assent is mentioned mainly to eliminate from consideration arguments about the earth’s motion deriving from Newtonian or relativistic mechanics that sometimes intrude themselves into discussions of Galileo’s proofs. However valid or interesting these arguments may be, they are irrelevant for understanding the logic Galileo himself used and thus are not dwelt on here.
Art of Reasoning, 39–42.
The equivalence of the Tychonian and Copernican systems in this regard is explained by Keith Hutchinson, “Sunspots, Galileo, and the Orbit of the Earth,” Isis 81 (1990), 68–74, replying to an earlier discussion by A. Mark Smith, “Galileo’s Proof for the Earth’s Motion from the Movement of Sunspots,” Isis 76 (1985), 543–551. Smith’s essay contains diagrams that are helpful for understanding the kinematical relationships involved.
This term, it may be recalled, was used by Antonio Riccobono, professor of rhetoric at Padua and Galileo’s friend there, to characterize the formal object of rhetoric and thus to differentiate it from dialectics; see Sec. 3.8.
Art of Reasoning, 42–44.
See his Galileo’s Intellectual Revolution: Middle Period, 1610–1632, New York: Science History Publications, 1972, 177.
More serious criticisms directed against the tidal argument include that of Ernst Mach, in effect one already lodged by Galileo’s contemporaries, namely, that the centripetal acceleration deriving from the earth’s rotation is constant over its entire surface and so cannot combine with a linear acceleration to cause a tidal variation. Another is Galileo’s contemptuous attitude toward Kepler and the lunar explanation of the tides, causing him to deny the dependence of their half-monthly period on the moon and to omit entirely the monthly period whereby the tides occur later each day by the same time as the moon’s transit. Antonio Rocco, who had read the Dialogue carefully shortly after it was published, called attention to Galileo’s many claims of relying on sense experience at the beginning of the work but his conspicuous omission at the end of the evidence such experience provides [GG7: 712].
The similarity becomes clear when examining arguments brought against the intermediate stage of the regressus by those, such as Ernan McMullin, who maintain on logical grounds that it is impossible ever to arrive at a unique causal explanation for any natural phenomenon. Logical possibility allows for any state of affairs that does not involve an explicit contradiction, and oddly enough, this squares with the only limitation theologians would place on God’s absolute power. This puts McMullin in Urban VIII’s corner: both reject the very possibility of Galilean science on a priori grounds, though they use a different language to do so.
In his commentary on the Sphaera of Sacrobosco (Rome: 1581), 451.
That is, his celebrated Regulae philosophandi with which he begins Book III, The System of the World, of the Principia.
The question naturally arises whether Galileo thought that he had demonstrated the earth’s motion in the Dialogue itself, without benefit of the principles he would later make explicit in the Two New Sciences. From the arguments analyzed above it seems clear that he did not, that he realized that the arguments he had advanced in the Dialogue were dialectical rather than scientific in the strict sense. An unexpected confirmation of this view is found in a notation he made in his own hand on the flyleaf of the first edition of the Dialogue; it has been transcribed by Favaro and translates as follows: Take note, theologians, that in your wish to make a matter of faith out of propositions relating to the motion and rest of the sun and the earth, you run the risk of having in time to condemn as heresy propositions that assert that the earth standsstill and the sun changes its place ¡ª at such time, I say, as it will have been demonstrated on the basis of sense experience and with necessity (sensatamente e necessariamente) that the earth moves and the sun stands still [GG7: 541].
This seems an implicit admission that, at least at the time of writing this, Galileo realized he had not yet achieved his goal of offering a “necessary demonstration” of the earth’s motion based on “sense experience,” although he remained convinced that one day such a demonstration would come within man’s grasp.
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Wallace, W.A. (1992). Galileo’s Search for a New Science of the Heavens. In: Galileo’s Logic of Discovery and Proof. Boston Studies in the Philosophy of Science, vol 137. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8040-3_5
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