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Logic 2

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zouhirgabsi

The document discusses logical concepts such as connectives, predicates, and referring expressions. It provides examples to illustrate that words like "and", "or", and "not" are connectives rather than predicates or referring expressions. Additionally, it presents two logical formulae that represent different interpretations of the ambiguous sentence "John and Mary are married."

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LOGIC 2 Words such as and, or and not are not predicates and cannot be used a referring expressions. Example:  Names are referring expressions, i.e. can be used to pick out individuals in the world. Can the word and be used in this way? Yes/no  Predicates express relations between individuals or properties of individuals (e.g. asleep). Can and be used to express property of an individual (e.g. John is and, or John ands) yes/no
LOGIC 2 Logic calls such words connectives. The kind of meaning that is involved is structural. Logical notation: &, V Example: John and Mary are married is an ambiguous sentence. Why? Answer: John and Mary are married to each other or as John is married to someone and Mary is married to someone . The logical notation of the first proposition is represented by the following formula: (jMARRIED TO m) & (m MARRIED TO j)
LOGIC 2 The second interpretation would be represented by: (Εx (jMARRIED TO x)) & (Ε y (m MARRIED TO y)) Logical calculations Mark the following examples as Valid (V) or (I) invalid (refer to examples p. 138, Textbook: Semantics, a discourse) Rule: Modus Ponens It is a rule stating that that is a proposition P entails a proposition Q, and P is true, then Q is true p→q P __________ Q
LOGIC 2 The formulae above the line in this diagram represent the propositions which are the premises of the argument, and the letter below the line represents the proposition which is the conclusion of the argument

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Logic 2

  • 1. LOGIC 2 Words such as and, or and not are not predicates and cannot be used a referring expressions. Example:  Names are referring expressions, i.e. can be used to pick out individuals in the world. Can the word and be used in this way? Yes/no  Predicates express relations between individuals or properties of individuals (e.g. asleep). Can and be used to express property of an individual (e.g. John is and, or John ands) yes/no
  • 2. LOGIC 2 Logic calls such words connectives. The kind of meaning that is involved is structural. Logical notation: &, V Example: John and Mary are married is an ambiguous sentence. Why? Answer: John and Mary are married to each other or as John is married to someone and Mary is married to someone . The logical notation of the first proposition is represented by the following formula: (jMARRIED TO m) & (m MARRIED TO j)
  • 3. LOGIC 2 The second interpretation would be represented by: (Εx (jMARRIED TO x)) & (Ε y (m MARRIED TO y)) Logical calculations Mark the following examples as Valid (V) or (I) invalid (refer to examples p. 138, Textbook: Semantics, a discourse) Rule: Modus Ponens It is a rule stating that that is a proposition P entails a proposition Q, and P is true, then Q is true p→q P __________ Q
  • 4. LOGIC 2 The formulae above the line in this diagram represent the propositions which are the premises of the argument, and the letter below the line represents the proposition which is the conclusion of the argument