Symbolic Logic and Other Forms of Deductive Reasoning - Softcover

Trammell, Dr. Richard L.

Softcover

ISBN 10: 1535230770 ISBN 13: 9781535230773

Publisher: CreateSpace Independent Publishing Platform, 2016

Synopsis

This text does not presuppose any technical background in math or logic. The first seven chapters cover all the basic components of a first course in symbolic logic, including truth tables, rules for devising formal proofs of validity, multiple quantifiers, properties of relations, enthymemes, and identity. (One exception is that truth trees are not discussed.) The five operator symbols used are: (.) and, (v) or, (~) not, and also if-then, represented by the sideways U and material equivalence represented by the triple line. There are also four chapters which can be studied without symbolic logic background. Chapter 8 is a study of 7 immediate inferences in Aristotelian logic using A, E, I, O type statements with a detailed proof concerning what existential assumptions are involved. Chapter 9 is a study of classic Boolean syllogism using Venn diagrams to show the validity or invalidity of syllogisms. Chapter 10 is a study of the type of probability problems that are deductive (example: having 2 aces in 5 cards drawn from a randomized deck of cards). Chapter 11 is a study of the types of problems that are often found on standardized tests where certain data are given, and then multiple-choice questions are given where the single correct answer is determined by the data. In the symbolic logic chapters, it is shown many times how putting English statements into symbolic notation reveals the complexity (and sometimes ambiguity) of natural language. Many examples are given of the usage of logic in everyday life, with statements to translate taken from musicals, legal documents, federal tax instructions, etc. Several sections involve arguments given in English, which must be translated into symbolic notation before proof of validity is given. Chapter 7 ends with a careful presentation of Richard’s Paradox, challenging those who dismiss the problem because it is not strictly mathematical. The conclusion of this chapter is the most controversial part of the text. Richard’s paradox is used to construct a valid symbolic logic proof that Cantor’s procedure does not prove there are nondenumerable sets, with a challenge to the reader to identify and prove which premise of the argument is false. There are several uncommon features of the text. For example, there is a section where it is shown how the rules of logic are used in solving Sudoku puzzles. Another section challenges students to devise arguments (premises and conclusion) that can be solved in a certain number of steps (say 3) only by using a certain 3 rules, one time each (for example, Modus Ponens, Simplification, and Conjunction). In proofs of invalidity, if there are 10 simple statements (for example), there are 1024 possible combinations of truth values that the 10 statements can have. But the premises and conclusions are set up so that only 1 of these combinations will make all the premises true and the conclusion false - and this 1 way can be found by forced truth-value assignments, with no need to take options. Another unusual section of the text defines the five operator symbols as relations (for example, Cxy = x conjuncted with y is true), and then statements about the operators are given to determine whether the statements are true or false. To aid in deciding what sections to cover in a given course or time frame, certain sections are labeled “optional” as an indication that understanding these sections is not presupposed by later sections in the text. Although there are a ton of problems with answers in the text, any teacher using this text for a course can receive free of charge an answer book giving answers to all the problems not answered in the text, plus a few cases of additional problems not given in the text, also with answers. Send your request to rltrammell151@gmail.com, and you will be sent an answer key using your address at the school where you teach.

About this title

About the Author

Professor Trammell was born and raised on a tobacco farm in Kentucky, though he never inhaled. He got his B.A. from Berea College, Kentucky, and received his B.D. from Union Theological Seminary, a hotbed of theological liberalism in New York City. Oddly enough, his systematic theology teacher had no required reading except Calvin’s Institutes, a fact which may help explain why he (i.e., Trammell, not Calvin) got a job at Grove City College four years later. During that four year period, Mr. Trammell became Dr. Trammell by writing a dissertation for the Department of Religion at Columbia University. The topic was “Charles S. Peirce’s Understanding of Religion.” In the fall of 1971, Dr. T. (as his students affectionately address him) began teaching philosophy at Grove City College. His favorite course is Symbolic Logic, because it is here that the suffering of his students is most easily observed. His other favorite course is Introduction to Philosophy, where he tries to concentrate into one course everything he has ever learned. Other courses taught by Dr. Trammell include Biomedical Ethics - an area of ethics where he has several publications; and Modern Philosophy - an area of the history of philosophy where he not only has no publications, but can barely understand other people’s publications. He also teaches 20th Century Philosophy, where he manages to make it up to 1910; General Logic, a course whose prime learning objective is to teach students to take three hour exams in seventy-five minutes; and once in a while a second course in symbolic logic, where students learn to demonstrate that “if p is true then p is true,” a proof that takes about 25 steps. Dr. Trammell’s current research projects include a paper whose thesis, if successfully established, will undermine at least half of mathematics. The mathematicians Dr. T. has talked to about this paper don’t seem worried. Although Dr. Trammell enjoys teaching immensely (a subject matter most students know little about) and spends a great deal of time thinking about logic, he also finds time to hug trees, wander through swamps, and carry cats to places they like to go. His children include Mark, Julie and John. His lovely wife Catherine, who never heard a word of French (except “we”) until she was in college but now speaks native French, is also a cat lover who wants to take our cats on trips to France so they can climb the Eiffel Tower, without using an elevator or steps.

Edition details

• Publisher: CreateSpace Independent Publishing Platform
• Publication date: 2016
• ISBN 10: 1535230770
• ISBN 13: 9781535230773
• Binding: Paperback
• Language: English
• Number of pages: 506