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عدد الرسائل : 1500
الموقع : center d enfer
تاريخ التسجيل : 26/10/2009
وســــــــــام النشــــــــــــــاط : 6
 | |  Probability in the Renaissance | |
The Renaissance is considered here as a cultural movement which bridged two historical epochs, the Middle Ages and early modernity. There is notorious disagreement on the temporal boundaries of the Renaissance. One familiar view is that it covers the period from the middle of the fourteenth century to the end of the sixteenth. The Renaissance is closely linked to the rise of humanism as a style of thought, and humanism is often conceived of as a rival and antagonist of scholasticism. Recent scholarship has found less clear-cut boundaries between humanism and scholasticism than were formerly assumed, and this is also true for humanist and scholastic uses of probability-related terms. The whole range of Latin probability-related words was used by Renaissance humanists and medieval scholastics alike, with roughly similar meanings based on ancient precedent. In the period from 1200–1500, there were no great debates on probability; and what Renaissance authors, like their contemporaries, had to say about the subject fills a few lines at most in their works. Nonetheless, the differences between humanist and scholastic uses of probability should be noted.Humanist concern with probability was largely stimulated by attempts to clarify the relationship between rhetoric and dialectic. A second, but related, field in which probability-terms became important for humanists was the translation, recovery, and interpretation of ancient texts, such as Aristotle’s Topics or Quintilian’s Institutio oratoria. Yet the renewed attention to the texts of Cicero and Quintilian, or those of Aristotle’s Greek commentators, in the fifteenth century does not seem to have produced an immediate challenge to scholastic usages of probability. In general, the terms probabilis or probabilitas appear to have been less central for humanists than for scholastic (moral) theology and jurisprudence. Many humanists prolifically used the wordprobabilis, but some shunned it and spoke instead of worthiness of belief (credibilitas). This may often signal not much more than a predilection for the Latin of some ancient author. A contrast to scholastic usage can at best be expected from authors who intended to make a break with scholastic dialectic such as Lorenzo Valla and Rudolph Agricola (Mack 1993, 31, 146; Nauta 2009, 233; Spranzi-Zuber 2011, 65).Lorenzo Valla (Repastinatio, 253) attacked scholastic dialectic, referring to worthiness of belief and belief-worthy things (credibilia) rather than to probability and probabilia. He follows Quintilian’s (the complete text of the Institutio oratoria was rediscovered in the Latin West in 1416) division of belief-worthiness into very firm (firmissimum), strongly disposed (propensius), and not ill-disposed (non repugnans).[39] Credibility and truth-likeness are also related to the modal category of possibility. Valla assumes degrees of possibility. Something can be very or slightly possible. Only propositions qualified as very possible were worthy of belief and truth-like (verisimilis). In this context, Valla never once uses the word probabilis. But he approvingly quotes Cicero’s connection of argumentation with probable (probabilis) invention in Book 3 of his Repastinatio dialecticae, where he gets down to dialectic and logic after much previous analysis of language. On the whole, Valla’s probability-related concepts do not seem to differ too starkly from the semantic and proto-frequentist notions of probability (or belief-worthiness) which he shared with the scholastics.Rudolph Agricola, another humanist innovator, put the word probabilis center stage in his path-breaking reinterpretation of dialectic. For him, dialectic was the art of speaking with probability on whatever issue. This definition appears traditional enough, but Agricola (De inventione dialectica, 210) explicitly distanced himself from Aristotle’s endoxon as the basis for probability in dialectic. As has been noted by modern scholars, “speaking with probability” is a feature of a process for Agricola rather than one grounded in a property of propositions used in a dialectical syllogism. Probability arises from the argumentative quality (argumentosus), aptness (aptus), and fittingness (consentaneus) of a reasoning process (Agricola, De inventione dialectica, 210, 306; Mack 1993, 170; Spranzi-Zuber 2011, 89). This directs dialectic away from the reliance on authority implied by Aristotle’s definition of reputable opinion. It is also significant that Valla and Agricola focus on the production of conviction (fides) instead of mere opinion. They thus seem to call for more rhetorical persuasion or for higher epistemological standards in dialectic’s quest for truth. It is difficult, however, to develop an uncontentious interpretation of what Agricola exactly meant by his peculiar, but undoubtedly influential, view of probability. In sixteenth-century century humanist discourse on probability, Agricola’s dialectic was a key innovation, as were the new interest in Aristotle’s Topics, the rise of a Protestant tradition of dialectic, and much more. Together with advancements in early modern scholasticism, these developments provide a justification for ending the present survey around 1500.6. Preview of early modern and modern probabilityMedieval and Renaissance notions of probability largely derived from the same ancient sources and remained related to each other through interchanges between scholastics and humanists. Yet soon after 1500, pre-modern probability discourse began to assume a new shape. Although the many differences between medieval and early modern scholastic and humanist uses of “the probable” cannot be summarized here, they should not be underestimated. Above all, at the end of the sixteenth century, the Aristotelian endoxon gave way in moral theology to a two-tiered definition of probability as either intrinsic (based on known reasons) or extrinsic (based on the opinions of others). How much such innovations fostered the rise of numerical probability in the middle of the seventeenth century is still largely an open question. Maryks (2008) claims that the humanist precedent prompted the Jesuits to introduce the distinction between internal and external probability. At present, however, the cross-pollinations between early modern humanism and scholasticism are scarcely better understood than the developments leading to the invention of numerical probability.In any case, the notions of probability of many philosophers, from Descartes and Locke to Kant, recognizably rely on a stock of meanings with roots in Renaissance humanism and medieval scholasticism. The philosophers in question deviated notably from this stock, but so did their scholastic contemporaries. The modernization of probability therefore occurred along a broad front of schools, trends and traditions in the seventeenth century. It is instructive to relate the four medieval concepts of probability listed above to their modern successors. On the modern side, three major groups of interpretations or concepts of probability have emerged (Hájek 2011):
- quasi-logical approaches: probability as a measure of objective evidential support;
- degree-of-confidence or degree-of-belief approaches: probability as a measure of subjective graded belief or confidence;
- feature-of-the-world approaches: probability as a measure for undetermined features of the world.
The first category mainly contains classical and logical concepts of probability.[40] Classical concepts define probability through the equal possibility of states of affairs. Logical concepts focus on evidential support for the truth of propositions. The most prominent variants of the second category are Bayesian theories of probability and mathematical representations of subjective expectation. The last category comprises frequentist and propensity interpretations of probability.[41] For frequentists, probability is the limit of a relative frequency in a series of events; for the propensity view, it is an irreducible feature of the physical world.Medieval notions of probability exhibit parallels to all modern groups of probability concepts. Endoxic and juridical probability are species of quasi-logical probability because they arise from evidential support for holding a proposition true. Endoxa, that is, probable opinions of others, are evidence for holding a proposition true. The witness testimony and indicia of juridical notions of probability are also, of course, kinds of evidence. The second category of modern interpretations of probability is related to medieval probability understood as a specific amount of confidence in the truth of a proposition. It is the confidence that characterizes opinions as the lowest rank of an epistemological order leading via fides (standing for fully confident belief or faith) to knowledge. Finally, probability is a feature of the world in modern propensity views, as well as for the medieval semantic notion of probability. Whether this also holds for proto-frequentist probability is, as indicated, a matter of interpretation.Conspicuously lacking in the period from 1200–1500 is an ancestor of the “classical” notion of probability, grounded on the equal possibility of events. This, then, seems to be a genuinely modern interpretation of probability.[42] | |
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