Question I am a new comer to philosophy and metaphysics in particular. I would like to know about the method of analysing and proving statements in metaphysics.Being a student of mathematics I am familiar with the axiomatic method. Are there any systematic methods for proving statements in metaphysics?

Accepted:
July 24, 2010

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The following story is recounted in John Aubry's Life of Thomas Hobbes:

"He was forty years old before he looked on geometry; which happened accidentally. Being in a gentleman's library Euclid's Elements lay open, and 'twas the forty-seventh proposition in the first book. He read the proposition. 'By G ,' said he, 'this is impossible!' So he reads the demonstration of it, which referred him back to such a proof; which referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry. I have heard Sir Jonas Moore (and others) say that it was a great pity he had not begun the study of the mathematics sooner, for such a working head would have made great advancement in it. So had he done he would not have lain so open to his learned mathematical antagonists. But one may say of him, as one says of Jos. Scaliger, that where he errs, he errs so ingeniously, that one had rather err with him than hit the mark with Clavius. I have heard Mr Hobbes say that he was wont to draw lines on his thigh and on the sheets, abed, and also multiply and divide. He would often complain that algebra (though of great use) was too much admired, and so followed after, that it made men not contemplate and consider so much the nature and power of lines, which was a great hindrance to the growth of geometry; for that though algebra did rarely well and quickly in right lines, yet it would not bite in solid geometry."

Now Hobbes himself, in his own philosophical works, such as Leviathan, did not quite aspire to axiomatization, but he did seek proofs of the sort that can be found in geometry; his near-contemporary, Spinoza (whose views, if not his method, influenced Hobbes's own work--Hobbes even said of Spinoza, "He hath overshot me by a bar's length, for I durst not write so boldly,"--self-consciously modeled his Ethics on Euclid's Elements, following the "geometrical method," beginning each part of the Ethics with Definitions and Axioms, on which the Propositions 'proven' in each section were to be based: in the Preface to the Third Part of the Ethics, "Of the Origin and Nature of the Affects [in comtemporary language, emotions]," Spinoza claims to "treat the nature and powers of the affects...just as if it were a question of lines, planes, and bodies." However, if one opens the Ethics to any given proposition, while one will find rigorous argumentation, and 'proofs' that make reference only to the definitions, axioms, and prior propositions 'proved' in the relevant part of the Ethics, one will hardly be convinced by those proofs in the same way that Hobbes--or we--might be convinced by the proofs in Euclid's Elements. This reflects a frustrating, fascinating, feature of philosophy: the propositions it treats are not amenable to proof in the same way as propositions in mathematics. While philosophers over the centuries have sought to make philosophy into a 'rigorous science', more akin to mathematics, the propositions it treats do not seem to admit of proof like the propositions of mathematics. Indeed, it is reported that the philosopher Moritz Schlick once said, "Making lists of propositions proven by philosophers is a pastime heartily to be recommended," knowing full well that the list that one ended up with would be quite short indeed.

What's distinctive, it seems to me, of the claims in various branches of philosophy--such as ethics, epistemology, and metaphysics--is that they treat questions that do not admit of proof. One must, instead, seek to give arguments for the claims in which one is interested--just as Hobbes and Spinoza did--and those arguments will rest on reasons that may well be open to challenge by other philosophers. Consequently, there is no one method for analyzing and proving statements in metaphysics--or any other branch of philosophy, for that matter: instead, one must seek to give reasons for the claims that one seeks to advance, and to develop arguments in their support. This is what sets philosophy apart from other branches of knowledge, such as physics and mathematics.