Logic part1


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Logic part1

  2. 2. FORMAL ANALYSIS<br />Formal logic: evaluate the validity of argument based upon its form NOT the content of its premises and conclusion<br />Much like math, variables take the place of statements and we deal solely with the variables<br />Propositional logic: system of formal logic in which we can take simple atomic propositions and build more complex arguments<br />
  3. 3. Propositional logic uses 2 main building blocks: propositions and propositional connectives<br />Propositions: statement that is either true or false (has a truth value)<br />“Atomic” without propositional connectives<br />Propositional connectives: Used to connect smaller propositions into larger ones<br />Very similar to mathematical connectives: */-+<br />Larger propositions that include connectives also have a truth value<br />PROPOSITIONAL LOGIC<br />
  4. 4. CONNECTIVES<br />Conjunction, disjunction, negation, conditional & biconditional<br />Each connective is governed by its own truth conditions (conditions under which propositions that include the connective are true)<br />We can discover the truth conditions of non-atomic propositions that include many connectives through the use of truth tables<br />Each connective has its own truth table<br />
  5. 5. VARIABLES<br />Replace propositions in English with variables that can stand in for any proposition<br />Propositions, once replaced by variables, are put in propositional forms<br />Propositional form: a pattern that can represent any number of actual propositions<br />Example: p&q is a propositional form in which “p” and “q” can stand for any proposition<br />Substitution instance: replace variables by actual propositions – many possible sub. instances for each prop. form<br />
  6. 6. RULES<br />Each proposition can be replaced by one or several variables in a series of propositional forms (argument) but each variable must represent the same proposition throughout<br />P & Q can both represent the same proposition but P cannot represent two different propositions within the same series/argument<br />Variables can represent atomic propositions or more complex ones that, themselves, include connectives<br />
  7. 7. ARGUMENT FORMS<br />Once we have propositional forms, we can combine them into argument forms<br />Argument form: offers a pattern of argument that we is always valid pattern for any number of arguments<br />Example: 1) p&q<br /> 2) p<br />
  8. 8. ARGUMENT FORMS<br />An argument is valid IF it is a valid argument form<br />Note: not all valid arguments are so in virtue of their argument form – here we offer a sufficient, but not necessary, condition for validity<br />An argument form is valid IF AND ONLY IF it has no substitution instances in which the premises are true and the conclusion false<br />
  9. 9. CONJUNCTION<br />Propositional conjunction: [while still in English] “and” expresses the conjunction of two or more propositions (called “conjuncts”)<br />Non-propositional conjunction: “and” does not express the conjunction of two or more propositions<br />Test: can you separate the proposition into two separate conjuncts without changing the meaning of the sentence?<br />
  10. 10. DISJUNCTION<br />Propositional connective: “or”<br />Unless specified, meant as an inclusive “or”<br />Exclusive “or” generally implied by context and not the actual proposition itself<br />
  11. 11. NEGATION<br />Propositional connective: “not”<br />The negation of a proposition is true if and only if the proposition is false and vice versa<br />“Not” is tricky so a good test for whether a proposition is an instance of negation is to reformulate the sentence so it starts with “It is not the case that x” … if it is possible without affecting the meaning of the sentence, it is probably an instance of negation<br />