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Chapter 4

Chapter 4 Notes.docx

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University of Ottawa
Dean Lauer

Chapter 4 Notes: Some Valid Argument Forms I. Sentential Form A. Form and Variables One premise can be a conditional sentence (“If…then…”) The second premise is the same as the clause the comes after the “if” in the conditional The conclusion is the same as the clause that follows the “then” in the conditional Sentential Form- when letters replace the simple sentences that make up compound sentences Sentential Variables- stand for any sentence that might be substituted with them Ex: If P, then Q P Therefore, Q (3 dots or line above) B. Connectives We can use symbols to replace ordinary connective words like “and”, “or”, and “if… then…” They should be regarded as representing the logical function performed by a number of phrases that have a common role, rather than a translation Ex: Ordinary Words Symbol Name Either….or… v Disjunction Either it is a cat or it is a dog.C v D And, but, yet • Conjunction It is a dog, and it bites. D B If…then… Implication If it bites, then you should be waBy. W In a conditional/hypothetical sentence, the component immediately following the if is called the antecedent. The component sentence following the then is the consequent. C. Negation A symbol is used to show the denying of a claim. It is like putting, “It is not the case that” before a sentence. Ex: It is not a dog. D You can also add another symbol to deny the negative variable. D. An Example of Symbolizing Sentences are easier to deal with if we consider their constituent parts one at a time (antecedent, consequent) Ex: If cigarette advertising leads teenagers to smoke, and advertisers lie about their aims, then either cigarette advertising should not be allowed or it should be strictly regulated. Cigarette advertising leads teenagers to smoke, and advertisers lie about their aims. C L Either cigarette advertising should not be allowed or it should be strictly regulated. A v R (C L) ( A v R) Hints on Symbolizing Complex Sentences: 1. Identify the simple component sentences – those that are not made up of further sentences and connective phrases 2. Identify the main connective. This is the connective phrase that holds the whole together. 3. Try to symbolize the components that are connected by the main connective as separate sentences. This involves applying Steps 1 and 2 again to these subcomponents of the sentence. II. Valid Argument Forms 1. Modus Pones (MP) Ex: If P, then Q P Q P P Therefore, Q Q If Manning is healthy, then the Colts will win. Manning is healthy. The Colts will win. Four observations: Complex as well as simple sentences can occupy the places of P and Q. Components can be negative sentences. The order in which the premises are given does not matter. The f
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