By Jaakko Hinitikka, Unto Remes (auth.)
As legitimate sponsors of the 1st foreign convention within the heritage and Philosophy of technology, the 2 Divisions of the foreign Union of the heritage and Philosophy of technology owe greatly to the college of Jyvliskyla and the 1973 Jyvliskylli summer season pageant for the additional regularly beneficiant hospitality they supplied. yet there's an extra debt owed, now not easily for the locale yet for the very substance of the convention, to the 2 Finnish students who've together authored the current quantity. For this quantity represents not just the 1st a part of the printed lawsuits of this primary foreign convention within the background and Philosophy of technology, but in addition, such a lot fittingly, the paper that opened the convention itself. but the appropriateness of the paper from which this ebook has resulted beginning the convention lies a ways much less within the indisputable fact that it used to be a contribution via Finnish authors to a gathering hosted in Finland than it does to the truth that this paper, and now the current ebook, involves grips in an severe ly direct manner with the very challenge the total convention used to be from the outset designed to regard. as a rule placed, this challenge was once to convey to gether a few historians and philosophers of technological know-how whose contrib uted papers could undergo witness to the ways that the 2 disciplines may be, and are, of price to every other.
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Extra info for The Method of Analysis: Its Geometrical Origin and Its General Significance
Sample text
But this tentative character of analysis is not essential to it objectively speaking. It is made heuristically natural only by the inconvenience of bringing part of one's information to bear on one's task in one way and part of it in another way. ) Thus we reach the important conclusion that from a strictly objective viewpoint neither of the two features which are often thought of as hallmarks of the analytical method touches the gist of its usefulness. These features are (a) its direction (starting from the desired conclusion) and (b) its tentative character which necessitates the use of synthesis as a complement to analysis.
This is again shown by the fact that analysis and synthesis were consistently conceived of by the Greeks as the two halves of one single method, not as two separate methods. Apart from these few problems, and certain others that will be taken up in the sequel, we seem to have made reasonably good sense of the problem of the direction of analysis in Pappus' general description of analysis. It is in order here to point out also that the whole problem of the direction of analysis has no bearing on the question of the objective sources of the heuristic value of the analytical method.
An interpretation of the passage that makes good sense is to understand 'to U1COAou90v to be the 'concomitant' or 'what goes together with' the theorem in the axioms, in the sense of justifying it. This is neither an unnatural nor (for an ancient mathematician) an unfamiliar way of looking at mathematical proofs. Aristotle already discussed on more than one occasion what the 'cause' of this or that geometrical figure's having certain geometrical properties is, finding them in the premisses of the argument that established these properties.