Hypothetical Arguments

  Advanced Hypothetical Arguments 355 are followed by consideration of tactics you can follow to determine the answer to the question. If you will be taking one of these standardized tests, it is advisable to purchase one of the many practice books available. !e other set of questions is based on tests given some years ago. While there are many books available to help you to prepare for standardized tests, to prepare for the “critical thinking” part of a test, practice with the problems in such a book is quite helpful. I would give the following book the highest rating: David Killoran, Power Score LSAT Logic Games Bible (Charleston, S.C.: PowerScore, 2015). Problem Set 31: Standardized Test–Style Arguments Logic Games–Style Questions Instructions Read the scenario and the initial conditions set out, which I call “rules.” !en try to answer each of the questions. A&er each question I have set out some suggestions, labeled “Tactics,” for answering that question. !e format follows standardized tests. Scenario: Plato examines some students in his Academy. !ere is a story in the ancient sources that about 380 b.c., Plato decided that he should examine the students in his new school, the Academy. !e students he examined were Isocrates, Xenophon, Aristotle, !eatetus, Speusippus, and Eudoxus. In order to make it easier to use logical symbols, from now on, we will just use the +rst letter of each student’s name: Isocrates = I, Xenophon = X, Aristotle = A, !eatetus = T, Speusippus = S, and Eudoxus = E. !e examinations were rather strenuous. Plato would devote one whole day to examining each student, and all six students would be examined on six consecutive days, leaving one day of the week to rest. !e schedule for the examination must be in accord with the following rules: Rule 1. I is examined either on day 1 or day 6. Rule 2. T is examined on some day earlier than S is examined. Rule 3. S is examined on the day immediately before E is examined. Rule 4. If X is examined on day 3, then S is examined on day 5. Problem 1. Which of the following orders could be a list of the students, in the order of their scheduled examinations, moving from day 1 through day 6? 356 The Logic of Arguments a. I, S, E, A, T, X. d.X, T, S, E, I, A. b.X, A, T, S, E, I. e. T, A, X, S, E, I. c. X, T, S, A, E, I. Problem 2. Which of the following must be false? a. "e exam for X is scheduled for Day 4. b. "e exam for A is scheduled for Day 6. c. "e exam for T is scheduled for Day 4. d."e exam for S is scheduled for Day 3. e. "e exam for E is scheduled for Day 2. Problem 3. Which student of Plato cannot take his exam on Day 5? a. E d.T b.X e. S c. A Problem 4. "e examinations for Day 3 and Day 5, in this order, could be those of a. X and E d. E and T b.X and A e. E and A c. A and X Tactics for Solving the Problems Overall Strategy Before Reading the Questions Note any facts or inferences that can be drawn directly from the scenario or rules. a. List the 6 days in order: Day 1: ___ , Day 2: ___ , Day 3: ___ , Day 4: ___ , Day 5: ___ , Day 6: ___. b. Note that A can take the exam on any day. c. Write out the rules in a convenient notation. Rule 1. I takes exam on (Day 1 v. Day 6) Rule 2. T → (= precedes) S and Rule 3. S → (= precedes by 1 day) E Inference: T →S →1 E Rule 4. (X is Day 3) → (S is Day 5) Question #2 (from Lesson 32): Question #3 (from Lesson 33): 372 The Logic of Arguments Inductive Arguments in Context Instructions Find any inductive arguments that are contained in the following passages. (a) State the conclusion of the inductive argument. (b) State the premises of the inductive argument that are given in the passage. (c) Identify what kind of inductive argument is used. (d) State whether you think the induction is valid or invalid. Remember that there are no rules for induction, as there are for deduction; so you will have to use your judgment here. 1. “"e cow, the goat, and the deer are ruminants. "e cow, the goat, and the deer are horned animals. "erefore, all horned animals are ruminants.” (Adapted from Aristotle) 2. “"e history of all hitherto existing society is the history of class struggles. “Freeman and slave, patrician and plebeian, lord and serf, guild-master and journeyman, in a word, oppressor and oppressed, stood in constant opposition to one another, carried on an uninterrupted, now hidden, now open $ght, a $ght that each time ended, either in a revolutionary reconstitution of society at large, or in the common ruin of the contending classes. “In the earlier epochs of history, we $nd almost everywhere a complicated arrangement of society into various orders, a manifold gradation of social rank. In ancient Rome we have patricians, knights, plebeians, slaves; in the Middle Ages, feudal lords, vassals, guild-masters, journeymen, apprentices, serfs; in almost all of these classes, again, subordinate gradations. “"e modern bourgeois society that has sprouted from the ruins of feudal society has not done away with class antagonisms. It has but established new classes, new conditions of oppression, new forms of struggle in place of the old ones. “Our epoch, the epoch of the bourgeoisie, possesses, however, this distinct feature: it has simpli$ed class antagonisms. Society as a whole is more and more splitting up into two great hostile camps, into two great classes directly facing each other—Bourgeoisie and Proletariat.” (Karl Marx and Friedrich. Engels, 19th-cen. revolutionaries, Communist Manifesto, 1848) 3. “Now it is scarcely possible to conceive how the aggregates of dissimilar particles should be so uniformly the same. If some of the particles of water were heavier than others; if a parcel of the liquid on any occasion were constituted principally of these heavier particles, it must be supposed to a*ect Complex Arguments 379 Humans Deductive syllogism: Animals acting in di!erent ways act based, not on instinct, but on “reason and custom.” Humans build their homes in di!erent ways (either individually or culturally). "erefore, humans act based on “reason and custom.” Inductive reasoning (= proof of the minor premise): Greeks build their houses in way G. Paci#c islanders build their houses in way P. Americans build their houses in way A. "erefore, humans build their homes in di!erent ways (either individually or culturally). Problem Set 33: Complex Arguments Arguments Including both Deduction and Induction Instructions "e following arguments may include deduction, induction, or both. Analyze. Identify both deductive and inductive arguments. "en check them for validity. 1. “Animals do not possess a language in the true sense of the word. In the higher vertebrates, as also in insects, particularly in the socially living species of both great groups, every individual has a certain number of innate movements and sounds for expressing feelings.