Immediate Inferences 7

Immediate Inferences 7. Assume that “Some chemicals are poisons” is true. What can you infer (if anything) in traditional categorical logic about the truth values of the following statements? Explain your answers. (3 pts. each) (a) All chemicals are poisons (b) Some non-chemicals are not nonpoisons (c) All chemicals are nonpoisons 8. Assume that “No psychiatrists are optimists” is true. What can you infer (if anything) in traditional categorical logic about the truth values of the following statements? Explain your answers. (3 pts. each) (d) Some nonoptimists are not nonpsychiatrists (e) No nonoptimists are psychiatrists Sorites 9. Put the following sorites into standard form by removing term-complements, then identify all subconclusions and determine the validity of the argument using either the Venn diagram or distribution rule method. (25 pts.) All U are non-T. All S are T. All non-S are non-R. All non-R are non-P. So, all P are non-U. 1 True False and Short Answers You may be asked true/false or short answer questions about the following material: 1. Paracomplete logic, paraconsistent logic, dialetheism 2. Problems for paracomplete responses to the Sorites and Liar paradoxes 3. Tautologies in K3, LP, and related non-classical logics 4. Existential import and differences between the traditional and modern squares of opposition Immediate Inferences 1 1. True. By contraposition, “All ideologues are fools” is equivalent to “All nonfools are nonideologues.” This implies “Some nonfools are nonideo- logues” by subalternation. 2. True. By obversion, “Some ideologues are not nonfools” is equivalent to “Some ideologues are fools,” which is the subaltern of “All ideologues are fools.” 3. False. By contraposition by limitation, “No nonideologues are nonfools” implies “Some fools are not ideologues,” which is the contradictory of “All ideologues are fools.” 4. Cannot determine. By contraposition, “All nonideologues are nonfools” is equivalent to “All fools are ideologues.” This is the converse of “All ideologues are fools,” and conversion is not valid for A statements. 3 Sorites 6. Put the following sorites into standard form, identify subconclusions, and use the Venn diagram and distribution rule methods to test it for validity. All folks who know that the oil reserves are running low are people who favor the development of alternative sources of energy. Every person who favors the development of alternative sources of energy is a voter who favors a tax increase. All well-informed citizens are folks who know that the oil reserves are running low. Not every highly educated person a voter who favors a tax increase. Therefore, not all highly educated people are well-informed citizens. 2 Sorites O= folks who know that the oil reserves are running low A people who favor the development of alternative sources of energy T voters who favor a tax increase W = well-informed citizens H = highly educated people Standard form: P1. All O are A. P2. All A are T. P3. All W are 0. P4. Some H are not W. So, 5. Some H are not W. Subconclusions: C1. All O are T (from P1 and P2). C2. All W are T (from C1 and P3). Valid Grant File Access Additional permissions are required to access the following files: /Users/gk/Downloads/20210414144443sorites.docx Microsoft Word needs access to the file named “20210414144443sorites.docx”. Select the item to grant access. Cancel Select… NO U are T All S are T AU R are s All Pare R No pare U o All S are 1 15) All Rare s (R) Subconclusion 1 All R are I predicate (R). Sorites All Rare T All p are R Put the following sorites into standard form by removing term-complements, then identify all subconclusions and determine the validity of the argument using either the Venn diagram or distribution rule method. (25 pts.) (R) (P) LP Subconclusions All p are T All U are non-T. All S are T. All non-S are non-R. All non-R are non-P. So, all P are non-U. No u are T All P are T (0,1) (P) Uu) NO P are U
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