Galileo on God, Mathematics, Certainty, and the Nature and Possibility of Human Knowledge
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In this chapter we examine Galileo’s arguments for the use of geometry and its role in his characterization of knowledge. Galileo’s own presentation takes the whole of Day 1 and much of Day 2 of the Dialogue to complete, although it appears as if most of the discussion is not spent explicitly arguing for his views in this area. The heart of his epistemology is presented at the close of Day 1, as the climax to the long and often convoluted discussion that precedes it. Here he offers an account of what man can know as against the capacity and scope of God’s knowledge. Although it is not clear to what extent he is addressing some of the issues that exercised the Neoplatonists, his comments here would certainly cause them some concern. For in making his case for the possibility of human knowledge, Galileo argues for a difference in kind between what God can know and what man can know. The distinction is essential to his characterization of nature as a book to be read in the language of geometry, but it also contains some theological suggestions.
KeywordsHuman Knowledge Mathematical Proof Geometric Proof Silver Coin Mathematical Demonstration
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- 22.My account of Galileo’s strategy differs from Carugo and Crom-bie’s  and from Wallace’s [ 1984 ], which derive from a close analysis of the forms of reasoning used by Jesuit Aristotelians (Wallace) and Aristotelians and Neoplatonists (Carugo and Crom-bie). I do not reject their analyses; I Substitute my own because, while accommodating theirs, it is also more flexible -allowing Galileo to grow methodologically.Google Scholar
- 23.This, by the way, does not make him a Piatonist. I do not think that the question of whether he is one or the other can be answered. Koyre  argued for Platonism, Wallace  for the in-fluence of the Jesuits, Clavelin  for the medievals, Jardin [ 1976 ] for Proclus, and the list goes on. I am sure that I cannot resolve the issue. Furthermore, I see nothing wrong with acknowl-edging that Galileo was probably influenced, directly or indirectly by all of the above. Tracing these issues out is difficult and fascinat-ing work, all of it worthwhile. But we should not lose sight of the fact that it is Galileo’s own methodology with which we are ulti-mately concerned. That being the case, I will leave the battles over ancestry to others.Google Scholar
- 24.For in-depth discussions of Galileo’s scientific achievements see Clavelin [ 1974 ], Drake , and Wisan .Google Scholar
- 25.Despite the fact that the structure of the Dialogue was altered by the Church censors, the changes they introduced did not affect my general argument here -even if it can be shown, as Drake would have it, that the structure of the Dialogue has the rational order we discuss in Chapter 4, that does not bear on my analysis of these issues. In fact, it strengthens it, as we will see.Google Scholar
- 26.Galileo also gets a little heavy-handed here in his literary style. There is little doubt that his use of the dialogue format is influenced by the popularity of Plato’s dialogues. Nevertheless, Galileo cannot resist taking a bit of a dig at Plato’s theory of “innate” knowledge (reminiscence) when he provides the proof that Simplicio Claims would have been produced by Aristotle if it existed. In response to Sagredo’s challenge to provide such a proof so that he can compre-hend it, Salviati obliges, noting that it can be understood “Not only by you, but by Simplicio too; and not merely comprehended, but already known -though perhaps without your realizing it.” (Drake [1967, p. 12]; Opere [VII, 36]) It is no wonder that Galileo assumes Simplicio would not realize what he knew since Simplicio often even denies that what he admits has been demonstrated before his very eyes! Unfortunately, what Galileo intended as wit has been misinterpreted as proof of his Platonistic leanings. This is a mistake. Just as Galileo’s choice of the dialogue form for this populär work does not make him a Piatonist, his jokes ought not to be taken as philosophical endorsements.Google Scholar
- 27.Of interest to those concerned with questions about the various in-fluences in Galileo’s thought, this argument establishes for Galileo a position which is incompatible with the Neoplatonic tradition because it constrains God’s freedom. On this view God has knowledge of the world through mathematics, which functions as a con-straint on his abilities. And yet, while this would indicate that Galileo is not at this point a Neoplatonist, it says nothing about in-fluences as such.Google Scholar
- 28.See Brehier  for a succinct discussion of some of these issues.Google Scholar
- 29.This is not to beg the issue and say that an object is only the sum of its properties, but it is sympathetic to that point of view.Google Scholar
- 30.I have explored the notion of justification as vindication in Pitt .Google Scholar
- 31.If, as Pietro Redondi Claims in his Galileo Heretic [ 1987 ], Galileo really was tried on trumped up charges to avoid his being tried for heresy because of the threat posed to the doctrine of transubstan-tiation by Galileo’s alleged theory of matter, what would Redondi make of Galileo’s talk about the immutability of matter here? Sure-ly, if there was serious worry about the threat of atomism to the doctrine of transubstantiation, Galileo would not be talking about the immutability of matter, as Redondi would have it, he just es-caped being tried for heresy for that very reason.Google Scholar