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Hobbes on Demonstration and Construction DAVID GAUTHIER 1~ IN 1656 Hobbes published Six Lessons to the Professors of Mathematics, with an Epistle Dedicatory to the Marquis of Dorchester, Lord Pierrepont. In this Epistle, Hobbes distinguishes the demonstrable from the indemonstrable arts: "demonstrable are those the construction of the subject whereof is in the power of the artist himself, who, in his demonstration, does no more but deduce the consequences of his own operation" (VII. 183-84). Although this passage, with the explication Hobbes offers for it and the consequences he draws from it, and a similar discussion in De homine, published two years later, have not been unnoticed, their significance for Hobbes's account of science in general, and civil philosophy or politics in particular, has not, I think, been I am grateful to the University of East Anglia for appointing me a Visiting Research Fellow during the period in which the first draft of this paper was written. A second draft was presented at the Third Quadrennial International Fellows Conference of the Center for Philosophy of Science at the University of Pittsburgh, sponsored by the Florence Center for the History and Philosophy of Science. I am grateful for the remarks of my commentator, J. E. McGuire, and for the discussion. I am also grateful for the comments of the two referees who read this paper for the Journal of the History ofPhilosophy. References to Hobbes's works appear as follows: To De cive by DCv, with chapter and paragraph numbers; I have used the English translation attributed to Hobbes, and edited by Bernard Gert in Man and Citizen (Garden City, N.Y.: Doubleday , 197~) [that the attribution to Hobbes is mistaken is argued by Richard Tuck in "Warrender's De Cive," Political Studies 33 0985): 31o-12]; To De corporeby DCp, with chapter and paragraph numbers; I have used the English version in vol. I of the English Works, ed. Sir William Molesworth (London: 1839); To De homine by DH, with chapter and paragraph numbers; I have used the translation by T. S. K. Scott-Craig and Bernard Gert in Man and Citizen; To Leviathan by L, with chapter numbers, and paragraph numbers as given in the text edited by E. Curley (Indianapolis: Hackett, 1994); To writings in vol. VII of the English Works, by VII, with page numbers. [509] 51o JOURNAL OF THE HISTORY OF PHILOSOPHY 35:4 OCTOBER 3997 sufficiently understood and appreciated.' My aim, then, is to examine what Hobbes says about demonstration in the Six Lessons and the De homine, to show how what he says enables us to understand the status he gives to definitions in science and the emphasis he places on their role, and finally, to show how Hobbes employs his method of demonstration in treating the rights of sovereigns and the liberty of subjects in Leviathan. Although Hobbes speaks of the demonstrable arts in the passage I have quoted, he proceeds immediately to talk of science, which is his more usual term for the demonstrable. He says, explaining his claim that demonstration rests on construction: "The reason whereof is this, that the science of every subject is derived from a precognition of the causes, generation, and construction of the same; and consequently where the causes are known, there is place for demonstration, but not where the causes are to seek for" (VII. 384). Demonstration proceeds from cause to effect, where cause is understood as efficient . Demonstrable knowledge proceeds from prior knowledge of the cause to posterior knowledge of the effect. What is the basis of this prior knowledge? Prior demonstration will ultimately take us back to what must be known without demonstration, and this, Hobbes insists, can only be what the knower can do, what is within his power. In De homine Hobbes begins from "Science... as being concerned with theorems, that is, with the truth of general propositions, that is, with the truth of consequences.... Therefore it is science when we know a certain proposed theorem to be true, either by knowledge derived from the causes, or from the generation of the subject by right reasoning.... [S]cience is allowed to men through... [this] kind of a pr/or/demonstration...

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Additional Information

ISSN
1538-4586
Print ISSN
0022-5053
Pages
pp. 509-521
Launched on MUSE
2008-01-01
Open Access
No
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