Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

The New Rhetoric is founded on the idea that since “argumentation aims at securing the adherence of those to whom it is addressed, it is, in its entirety, relative to the audience to be influenced,” says Chaïm Perelman and L. Olbrechts-Tyteca, and they rely, in particular, for their theory of argumentation on the twin concepts of universal and particular audiences: while every argument is directed to a specific individual or group, the orator decides what information and what approaches will achieve (...) the greatest adherence according to an ideal audience. This ideal, Perelman explains, can be embodied, for example, "in God, in all reasonable and competent men, in the man deliberating or in an elite.” Like particular audiences, then, the universal audience is never fixed or absolute but depends on the orator, the content and goals of the argument, and the particular audience to whom the argument is addressed. These considerations determine what information constitutes "facts" and "reasonableness" and thus help to determine the universal audience that, in turn, shapes the orator's approach. /// The adherence of an audience is also determined by the orator's use of values, a further key concept of the New Rhetoric. Perelman's treatment of value and his view of epideictic rhetoric sets his approach apart from that of the ancients and of Aristotle in particular. Aristotle's division of rhetoric into three genres–forensic, deliberative, and epideictic–is largely motivated by the judgments required for each: forensic or legal arguments require verdicts on past action, deliberative or political rhetoric seeks judgment on future action, and epideictic or ceremonial rhetoric concerns values associated with praise or blame and seeks no specific decisions. For Aristotle, the epideictic genre was of limited importance in the civic realm since it did not concern facts or policies. Perelman, in contrast, believes not only that epideictic rhetoric warrants more attention, but that the values normally limited to that genre are in fact central to all argumentation. "Epideictic oratory," Perelman argues, "has significant and important argumentation for strengthening the disposition toward action by increasing adherence to the values it lauds.” These values are central to the persuasiveness of arguments in all rhetorical genres since the orator always attempts to "establish a sense of communion centered around particular values recognized by the audience.”. (shrink)

The New Rhetoric is founded on the idea that since "argumentation aims at securing the adherence of those to whom it is addressed, it is, in its entirety, relative to the audience to be influenced," says Chaïm Perelman and L. Olbrechts-Tyteca, and they rely, in particular, for their theory of argumentation on the twin concepts of universal and particular audiences: while every argument is directed to a specific individual or group, the orator decides what information and what approaches will achieve (...) the greatest adherence according to an ideal audience. This ideal, Perelman explains, can be embodied, for example, in God, in all reasonable and competent men, in the man deliberating or in an elite." Like particular audiences, then, the universal audience is never fixed or absolute but depends on the orator, the content and goals of the argument, and the particular audience to whom the argument is addressed. These considerations determine what information constitutes facts and reasonableness and thus help to determine the universal audience that, in turn, shapes the orator's approach. The adherence of an audience is also determined by the orator's use of values, a further key concept of the New Rhetoric. Perelman's treatment of value and his view of epideictic rhetoric sets his approach apart from that of the ancients and of Aristotle in particular. Aristotle's division of rhetoric into three genres-forensic, deliberative, and epideictic-is largely motivated by the judgments required for each: forensic or legal arguments require verdicts on past action, deliberative or political rhetoric seeks judgment on future action, and epideictic or ceremonial rhetoric concerns values associated with praise or blame and seeks no specific decisions. For Aristotle, the epideictic genre was of limited importance in the civic realm since it did not concern facts or policies. Perelman, in contrast, believes not only that epideictic rhetoric warrants more attention, but that the values normally limited to that genre are in fact central to all argumentation. Epideictic oratory, Perelman argues, has significant and important argumentation for strengthening the disposition toward action by increasing adherence to the values it lauds." These values are central to the persuasiveness of arguments in all rhetorical genres since the orator always attempts to establish a sense of communion centered around particular values recognized by the audience.". (shrink)

This text is designed for the average to strong mathematics major taking a course called Transition to Higher Mathematics, Introduction to Proofs, or Fundamentals of Mathematics. It provides a transition to topics covered in advanced mathematics and covers logic, proofs and sets and emphasizes two important mathematical activities - finding examples of objects with specified properties and writing proofs.

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61students in six small sections of a “bridge" course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion of proof framework to indicate the top-level logical structure of a proof. For simplified informal (...) calculus statements, just 8.5% of unpacking attempts were successful; for actual statements from calculus texts, this dropped to 5%. We infer that these students would be unable to reliably relate informally stated theorems with the top-level logical structure of their proofs and hence could not be expected to construct proofs or evaluate their validity. (shrink)