TL;DR: Prior Analytics by the Greek philosopher Aristotle and the Laws of Thought by the English mathematician George Boole (1815-1864) are the two most important surviving original logical works from before the advent of modern logic as discussed by the authors.
Abstract: Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the ma...
TL;DR: The Public Theorist Acknowledgments: A "Potlatch of Signs"--Burning, Consuming, Wasting.
Abstract: The Public Theorist Acknowledgments PART I: All That Is Cultural Is Real-All That Is Real Is Cultural Chapter 1: Getting Class Out of Culture Chapter 2: Class Binaries and the Rise of Private Property PART II: Tracing Class Chapter 3: Class Is Chapter 4: Abu Ghraib and Class Erotics Chapter 5: Class and 9/11 Chapter 6: Eating Class Chapter 7: The Class Politics of "Values" and Stem-Cell Funding Chapter 8: Abortion Is a Class Matter Chapter 9: E-Education as a Class Technology Chapter 10: Gender after Class Chapter 11: The Class Logic of A Beautiful Mind PART III: Class Ecstasies of the Culture of Capitol Chapter 12: A "Potlatch of Signs"--Burning, Consuming, Wasting
TL;DR: It strikes me that the intuitive incorrectness of 0 c b constitutes an objection to defining 'a c b' as 'ab' = O.
Abstract: Student I've been studying the logic of classes, and can't see how any class can be included in its own complement Teacher Surely you've heard of the null class, which is included in every class, and hence in its own complement? Student That also strikes me as somehow implausible How do you define 'inclusion'? Teacher In the usual way a is included in b if and only if the intersection of a with the complement of b is null The intersection of 0 with any class b' is null, hence 0 c b Understand? Student Oh I understand all right, and I agree that Ob' = 0 But it strikes me that the intuitive incorrectness of 0 c b constitutes an objection to defining 'a c b' as 'ab' = O' If you constructed a system of class logic in which these two expressions were not equivalent, might you not be free to choose whether the null class ought to be included in every class or not, rather as mathematicians were (at one time) free to choose whether, in the limiting case of n = 0, xn should equal 1 ? Teacher Go ahead and construct such a system if you wish, but I suspect that, like the mathematicians, you'll end up discovering that 0 c b yields the most satisfactory results
TL;DR: For instance, the authors found that a majority of children succeed on DeMorgan's problems in additive contexts by age 7; success in multiplicative contexts lags significantly behind, and low performance scores are associated both with difficulty in computing complements and with poor discrimination between additive and multiplicative context.
TL;DR: A comparison of Aristotelian logic and quantificational first-degree logic revealed the shortcomings of the former versus the latter after analyzing the syllabi of the following state university departments as discussed by the authors.
Abstract: This study the Aristotelian logic requirement included on the admissions exams in eight of the eleven state universities in Lima, Peru. A comparison of Aristotelian logic and quantificational first-degree logic revealed the shortcomings of the former versus the latter after analyzing the syllabi of the following state university departments: Engineering at the National University of Callao, Education at the Enrique Guzman y Valle National University and the Jose Faustino Sanchez Carrion University; and Technology at the National Technological University of South Lima, the National University of Canete and the National University of Barranca. All content dealing with Aristotelian logic was extracted from the manual used by test preparation centers to teach prospective applicants. The objective was to determine contradictions and faults found in first-order quantificational logic questions. A qualitative analysis was performed through a literature review. Research for the logic in this study is divided into 1) Aristotelian Logic 2) Class Logic, 3) First-Order Quantifiable Logic, 4) Boethius Traditional Square of Opposition, 5) Special recommendations, 6) Immediate inferences based on operations and 7) Categorical Syllogisms. it is concluded that quantifiable first-order logic has progressed significantly within the study of logic, that it must be included within the areas to be studied within the Admissions exams for universities in Lima-Peru. There is a need for empirical research to fill any gaps found in this study.