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# PHIL-P 162 Logic Week w Notes PHIL-P 162

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This 13 page Class Notes was uploaded by Tanner Brooks on Friday January 22, 2016. The Class Notes belongs to PHIL-P 162 at a university taught by Professor Chris Kraatz in Spring 2016. Since its upload, it has received 19 views.

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Date Created: 01/22/16

Logic PHIL-P 162 Week 1: Content - what is contained in a statement? Main emphasis on “what." Form - emphasis on “how" Aristotle’s Metaphysics: Accidental Properties - properties you can change but you still have the same thing. Essential Properties - properties that makes a thing that thing. (According to Aristotle everything must have some Essential property.) Rationality - essential property for man. (According to Aristotle) Proposition: the idea that gets expressed by a descriptive statement. Description, by its very nature, is either accurate or inaccurate. Since every proposition expresses a descriptive idea, every proposition must be either accurate or inaccurate. If a proposition is accurate, then it is called “true.” If a proposition is inaccurate, then it is called “false.” This is the “truth value” of a proposition, and every proposition must have one (and only one) truth-value. Whatever truth value a proposition has, it has always had that truth value and it always will – truth values cannot be changed. We say this is so because propositions express descriptive ideas, and descriptions are always about how something is at some time. That the door was open during class last Monday is still true, and there is nothing we can do now to change the truth value of that proposition. Argument: a collection of propositions in which some of the propositions are alleged to count as good reason for believing another proposition. Arguments don’t have truth- values. The propositions that are alleged to count as evidence or good reason for believing something are called premises. Every argument must have premises. The proposition that is alleged to receive support from the premises is called the conclusion. Every argument must have a conclusion. Arguments are not random collections of ideas, arguments contain an inference. That is, in an argument, there is a “therefore.” The person who expresses an argument alleges that the premises support the conclusion (“these ideas, therefore that idea”). Every argument must be valid or invalid. Validity: an argument is valid when it is not possible for all the premises to be true and the conclusion false. In a valid argument, if the premises are all true, then the conclusion must be true. It doesn’t matter whether or not the premises and conclusion really are true, this is hypothetical – validity tells us what would happen if all the premises were true; the conclusion would be true also. Deductive Reasoning - always involves valid arguments. Inductive Reasoning - always involves invalid arguments. Soundness: an argument is sound when (a) it is valid, and (b) all of its premises really are true. If either of these features is absent, then the argument is unsound. Since a sound argument is always valid [the truth of the premises guarantees the truth of the conclusion], and since sound arguments have all true premises, every sound argument is guaranteed to have a true conclusion. The Three Classic Laws of Thought: The Law of Identity: A = A [identical propositions must have identical truth values] The Law of Non-Contradiction: A ≠ not-A [opposite propositions must have different truth values] The Law of Excluded Middle: either A or not-A. [every proposition must have one, and only one, truth value] • Gunther likes dark beer. Premise • Miller Lite is not dark beer. Premise ______________________________ • Gunther does not like Miller Lite. Conclusion Invalid Argument – The argument is invalid because Gunther liking Dark Beer does not guarantee that he dislikes light beer. If the word only was inserted after the word Gunther in the first premise this would become a valid argument. Unsound Argument – The argument is unsound because the argument is invalid. ------------------------------------------------------------------------------- 1. The sun rose yesterday. 2. The sun rose the day before that. 3. The sun rose the day before that. . . . (10,000,000) The sun rose the day before that. ______________________________________ (10,000,001) The sun will rise tomorrow. Invalid Argument - The argument is invalid because although the conclusion is highly likely that the sun will rise on the 10,000,001 day it is not guaranteed by the premises above it. Unsound Argument - The argument is Unsound because the argument is invalid. --------------------------------------------------------------------------- 1. All cheese orbits the earth. 2. The moon is made of cheese. ___________________________ 1. The moon orbits the earth. Valid Argument – although this statement has a truth value of false it is still a valid statement because the conclusion is supported by the premises. Unsound Argument – the argument is unsound because of the arguments truth value which is false. ------------------------------------------------------------------------ 1. All dogs are cats. 2. All cats are fish. _________________ 1. All dogs are fish. Valid Argument – although the statement is ridiculously false the argument is valid because the premises support the conclusion. Unsound Argument – the argument is unsound because it has a truth value of false. ------------------------------------------------------------------------ 1. The earth is round. 2. A hydrogen atom has 1 electron. ___________________________________ 1. The Indianapolis Colts play in the NFL. Invalid Argument – the argument is invalid because these premises in no way whatsoever support the conclusion. Unsound Argument – the argument is unsound because it has a truth value of false and its invalid. ------------------------------------------------------------------------------- 1. All mammals are warm-blooded. 2. Some pets are mammals. ______________________________ 1. Some pets are warmblooded. Valid Argument – the argument is valid because the premises support the conclusion. Sound Argument – the argument is sound because it has both a truth value of true and it is also a valid argument PHIL-P 162 Logic Week Two Categorical statements - always name two groups (or categories) and assert a relation between them. •The first category named is called the Subject Group. •The second is called the Predicate Group. •The words that are used to name the Subject group are referred to as the Subject Term •The words that are used to name the Predicate group are referred to as the Predicate Term. Example: All dogs are mammals. • The Subject Group is a large collection of dogs. • The Subject Term is the word “dogs” as it appears in the statement. • Similarly, the Predicate Group is a large collection of mammals. • The Predicate Term is the word “mammals” as it appears in the statement. Every categorical statement must have a Subject Term and a Predicate Term. The variable S is a place-holder for the Subject Term (dogs) The variable P is a place-holder for the Predicate Term (mammals) Standard Forms of Categorical Logic with examples: (A) All S are P (All dogs are mammals) (E) No S are P (No sharks are mammals) (I) Some S are P (Some students are geniuses)* (O) Some S are not (Some dogs are not hounds)* *The word some here means that there is at least 1 Venn Diagrams of Standard Forms of Categorical Logic: (A) (E) (I) (O) By focusing on form and structure rather than content you can simplify the ways to categorize them. The standard form of a statement never changes. The quantity and quality of a statement never change as well. • Quantity is a function of how much information is being expressed about the Subject group • Universal Statement - a statement that makes a claim about every member of the subject group. • Particular statement - a statement that does not make a claim about every member of the Subject group • Quality is a function of whether a statement connects or separates the subject and predicate groups • Affirmative - if a statement does connect the subject and predicate group. • Negative - if a statement does not connect the subject and the predicate group. Statements that separate groups have words of negation in their Form (“no” or “not”). Form with distributions* [quantity/quality] (A) All S are P. [universal/affirmative] (E) No S are P. [universal/negative] (I) Some S are P. [particular/affirmative] (O) Some S are not P. [particular/negative] • Distributed - when a statement asserts complete information about the group being named • Undistributed - when a statement does not assert complete information about the group being named. *Distributions are shown with underlines. Consider the previous example: All dogs are mammals. Universal Statement -the statement makes a claim about every member of the Subject Group (dogs). Affirmative Statement – the statement asserts a connection between the subject and predicate groups. Distributed -a statement makes a claim about every member of the Subject group (dogs). Undistributed - a statement does not make a claim about every member of the Predicate group (mammals). Immediate Inferences: •An immediate inference is a short argument (one premise and one conclusion). •The conclusion is produced by changing specific features (the quantity, quality, or terms) of the premise according to a brief set of instructions. •The premise and conclusion may then be examined to find out how they are related to one another by virtue of the inference performed. For any two categorical statements, the relation between them will be one of the following: •Logically equivalent - the statements must have the same truth value •Logically opposite - the statements must have different truth values •Logically independent - any combination of truth values is possible Immediate inferences: Obversion (finding the Obverse) 1. change the quality of the statement: aff − neg, neg − aff. 2. Replace the predicate term with compliment:
P − non-P, non-P − P. Produces logically equivalent result for (A), (E), (I), (O). (A) All S are P (E) Obverse: No S are non-P (E) No S are P (A) Obverse: All S are non-P (I) Some S are P (O) Some S are not non-P (O) Some S are not P (I) Some S are non-P Contradiction (finding the contradictory) 1. change the quality of the statement:
aff − neg, neg − aff. 2. change the quantity of the statement:
univ −part, part − univ. Produces a logically opposite result for (A), (E), (I), (O). (A) All S are P. (O) Contradictory: Some S are not P (E) No S are P (I) Contradictory: Some S are P (I) Some S are P (E) Contradictory: No S are P (O) Some S are not P (A) Contradictory: All S are P

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