philosophers.267 The corollary of Aristotle’s definition of knowledge implies that all forms of knowledge must have universal reach as well as absolute certainty.However, according tomodern opinion enumerative induction cannot serve as the foundation for the establishment of absolute truths.Any universal cognitive aspirations of this kind are now reserved for formal deductive reasoning, here represented by mathematical or recursive induction, which is formal and as such not hampered by empirical demands of either, or both, verification and validation.268 Consequently, the question that must be asked is this: How could classical metaphysical philosophy consider it possible to establish absolute formal truths by means of enumerative induction, which is a method that collects its arguments from a relative material? The answer is that the old view allowed the laws of logic to synthesize (factual) knowledge instead of functioning analytically, merely analyzing propositions, judgments, and concepts formally.269 The difference between synthesizing and analyzing knowledge and propositions is that when we synthesize knowledge we extend it beyond the trivial and thereby create and synthesize new knowledge.270 On the other hand, when we analyze propositions, we restrict our knowledge to the self-evident and trivial.271 In other words, if we use induction as an example, it can be said that it allows us to “proceed from individual cases to the universal and from the known to the unknown”272 thus induction “gives new knowledge, which deduction does not.”273 a ca l l f o r s c i e n t i f i c p u r i t y 123 267 See Schüling, Axiomatischen Methode, passim. 268 A Companion to Epistemology, Dancy and Sosa, eds., Induction: enumerative and hypothetical. 269 See, e.g., ChristianWolff (1679-1754) et al., but then one must ask if Hägerström really critcized the natural law of the 17th and 18th Centuries. However, Franz Wieacker holds that the roots of the so-called Begriffsjurisprudenz originate in the philosophy of Wolff. Wieacker, A History of Private Law in Europe: With Particular Reference to Germany, pp. 255 and 317-318. 270 Cf.Aristotle, TheWorks of Aristotle,Topica viii. 1 (156a 4). 271 Russell, History, p. 209. 272 Aristotle, TheWorks of Aristotle,Topica viii. 1 (156a 4). 273 Russell, History, p. 209.
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