Abstract
Logic as a discipline has a long history, and this must be taken into account when attempting to reconstruct the logic that was functional in Galileo’s early writings. In the present day logic is generally divorced from natural philosophy or psychology and thought of as a formal system that can be used independently of the knowledge content to which it is applied. Not infrequently it is spoken of as a formal logic, or alternatively as a symbolic logic, since content can be replaced by symbols, or again as a mathematical logic, since symbols can be manipulated in much the same way as the numbers and figures of mathematics. While this way of viewing logic has elements in common with that implicit in Galileo’s MS 27, it leaves out of consideration much of what would be important for understanding the logical teaching contained in the lecture notes on which that manuscript is now known to be based.
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Notes
On this usage, see Henry Veatch, Intentional Logic: A Logic Based on Philosophical Realism, New Haven: Yale University Press, 1952; also his Two Logics: The Conflict Between Classical and Neo-Analytic Philosoph y, Evanston, Ill.: Northwestern University Press, 1969. The first of these acknowledges Veatch’s use of the Ars Logica of John of St. Thomas (ix), the name under which John Poinsot was known in the Dominican Order; see the following note.
The expression “mind-dependent” as a proper translation of ens ration is has been suggested by John N. Deely in his translation of Tractatus de signis: The Semiotic of John Poinsot, Berkeley, Cal.: University of California Press, 1985, 548–551. Poinsot’s logic is later than Vallius’s, but its general orientation is the same. The only work of this type now available in English, Poinsot’s treatise may be consulted with profit by those desiring a fuller understanding of late scholastic logic. Other portions of the Ars logica have been translated by Y.R. Simon, J.J. Glanville, and G.D. Hollenhorst, The Material Logic of John of St. Thomas, Chicago: University of Chicago Press, 1955.
To date the best systematic analysis of Galileo’s logic is that of Maurice A. Finocchiaro, Galileo and the Art of Reasoning: Rhetorical Foundations of Logic and Scientific Method, Dordrecht-Boston: D. Reidel Publishing Company, 1980. Most of the analysis bears on Galileo’s Dialogue on the Two Chief World Systems, some samples of which will be seen in Secs. 5.5 and 5.6 below. While the texts Finocchiaro analyzes are historical texts, and while he is aware that Galileo knew Aristotelian logic, he himself does not use Aristotelian logic in his analysis. The limitations this imposes on his work are discussed in the author’s review of it in the Journal of the History of Philosophy 20 (1982), 307–309.
The full title of this work is Ludovicus Carbone, Introductio in logicam sive totius logicae compendii absolutissimi libri sex, Venice: Apud Ioannem Baptistam et Ioannem Bernardum Sessam, 1597. For ease of citation references to it are inserted directly into the text, using the abbreviation CL followed by page number(s).
The titles of these works read as follows: Ludovico Carbone, Additamenta ad commentaria D. Francisci Toleti in Logicam Aristotelis: Praeludia in libros Priores Analyticos; Tractatio de Syllogismo; de Instrumentis sciendi; et de Praecognitionibus, atque Praecognitis, Venice: Apud Georgium Angellerium, 1597; references to it are likewise inserted directly into the text, using the abbreviation CA followed by folio number(s). Paulus Vallius, Logica Pauli Vallii Romani ex Societate Jesu, duobus tomis distincta, Lyons: Sumptibus Ludovici Prost haeredibus Rouille, 1622; each volume of this is referenced separately, using the abbreviations VL1 and VL2, followed by page number(s). Ludovicus Carbone, Introductio in dialecticam Aristotelis per Magistrum Franciscum Toletum Sacerdotem Societatis Iesu, Philosophiae in Romano Societatis Collegio Professorem. Additis in eandem introductionem praeludiis, eiusdem introductionis Tabulis, Venice: Apud Paulum Meiettum, 1588; this too is cited in the text, using the abbreviation CT followed by folio number(s).
The paraphrases are identified as such, so that the reader will not mistake them for translations. Generally they follow the text literally, except that some expressions are abbreviated or omitted (without indicating ellipses), and punctuation has been changed more liberally than it would be in a normal translation.
Those acquainted with scholastic psychology will recognize that Vallius-Carbone here do not enumerate the estimative or cogitative sense as a fourth internal sense distinct from the other three, as does Thomas Aquinas, but rather include its functions under that of the imagination or phantasia, thus staying closer to the text of Aristotle. Other variations from the Thomistic account, as will be seen below, are their teachings that the agent intellect and the receptive intellect in man are not two in number but only different activities of the one intellect, and that the intellective memory is a power distinct from the intellect itself. These teachings undoubtedly derive from Toletus’s Commentaria una cum questionibus in III libros de anima, first published at Cologne in 1575 and often thereafter. For a brief account of Toletus’s teachings on the soul and how it compares with those of other Renaissance commentators, see Eckhard Kessler, “The Intellective Soul,” The Cambridge History of Renaissance Philosophy, eds. C.B. Schmitt et al., Cambridge: Cambridge University Press, 1988, 511–512.
Thomas Aquinas, Summa theologiae, Prima pars, qq. 84–85; for an English translation, with notes and appendices, see St. Thomas Aquinas, Summa theologiae, 60 vols. ed. Thomas Gilby, New York: McGraw-Hill, 1964–1976. Vol. 12. Human Intelligence, tr. P.T. Durbin, 1968.
Meaning by this the natural light of reason, and poorly translated by Drake as “my good sense,” though this conveys the general idea — Galileo Galilei, Two New Sciences, tr. Stillman Drake, Madison, Wis.: The University of Wisconsin Press, 1974, 162.
It is at this point, of course, that empiricists and idealists would later part company with the type of realism being explained here. The empiricist became a skeptic: he takes the position — fatal from an Aristotelian viewpoint — that he knows sensations or concepts, not things, and so he has doubts about any natures to which these intentions might correspond. The Kantian would replace that skepticism by agnosticism: not wishing to deny that things have natures, he maintains that he cannot know them but only their sensible appearances, and this — an Aristotelian might critique — because of some quirk in his psychological makeup. Galileo was certainly not agnostic in the Kantian sense, and he did not subscribe to the empiricist brand of skepticism either. For the most part his was a natural realism; he trusted in his ability to know things as they are, to grasp their natures in some way and possibly to define them, and, if so, then to demonstrate properties flowing from those definitions in the accepted scientific fashion. See the comments in the Epilogue.
Note, in the second paragraph, the statements that the final cause of logic “is not demonstration alone” and that it is not “to distinguish the true from the false,” contrary to positions that were held by Zabarella, as will be made explicit below.
We say “less probably,” because at the time Vallius was preparing the logic lectures of 1588, on which Carbone’s Additamenta is based, Pappus’s work had just been published in Latin translation and in all probability was not available to Vallius.
Notably Jardine, “Galileo’s Road to Truth,” 306, 315, and, following him, Wisan, “Galileo’s Scientific Method,” 29; both cite the reading of Pappus provided by J. Hintikka and U. Remes, The Method of Analysis: Its Geometrical Origin and Its General Significance, Dordrecht-Boston: D. Reidel Publishing Company, 1974, 8–9.
This translation is a redaction based on that of T.L. Heath, cited by Jardine, 306, but incorporating emendations made by M.S. Mahoney, in his “Another Look at Greek Geometrical Analysis,” Archive for History of Exact Sciences 5(1968–1969), 322. We have here rendered analysis by resolution, synthesis by composition, in accord with the Renaissance Latin tradition.
Following Heath and Mahoney, replacing analysis by resolution.
Again following Heath and Mahoney, replacing analysis by resolution.
See his Apparatus ad mathematicarum studium,Bologna: Typis Sebastiani Bonomii, 1620, 411.
Blancanus, Apparatus,400.
Apparatus, 412.
Apparatus, 412.
Apparatus, 412.
Ghetaldus’s analyses will be found in his posthumous De resolutione et compositione mathematica,Rome: Ex Typographia Reverendae Camerae Apostolicae, 1630.
In this connection, see Jardine’s “Galileo’s Road to Truth” (295–303), where he references many of Zabarella’s texts but seems to have missed the text just cited.
His main textual support is Galileo’s discussion in the Dialogo to which reference has been made at the beginning of this section [GG7: 75–76]; to this he appends another text, a remark made by Salviati later in the Dialogo [GG7: 434–435], which is amenable to the same interpretation we have given the first (304–306). A subsidiary text, which Jardine imputes to Galileo (304–305), is actually taken from Benedetto Castelli’s critique of Ludovico delle Colombe’s treatise on floating bodies [GG4: 521]. Jardine admits that, while much of the manuscript for Castelli’s critique is in Galileo’s hand, this particular passage is not (305 n. 62). The fact that Castelli was a mathematician more than a philosopher could easily explain why his explanation of resolution would more resemble Pappus’s than the kind of regressus explained in Galileo’s D3.3.
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Wallace, W.A. (1992). The Understanding of Logic Implicit in MS 27. 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_2
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