Propositional logic uses atomic propositions and propositional connectives like conjunction, disjunction, negation, conditional, and biconditional to build more complex arguments. These connectives have specific truth conditions defined by truth tables. Variables are used to represent propositions, forming propositional forms that can represent different arguments. An argument is valid if it follows a valid argument form where the premises cannot be true and the conclusion false for any substitution instances.

1. PROPOSITIONAL LOGIC

2. FORMAL ANALYSISFormal logic: evaluate the validity of argument based upon its form NOT the content of its premises and conclusionMuch like math, variables take the place of statements and we deal solely with the variablesPropositional logic: system of formal logic in which we can take simple atomic propositions and build more complex arguments

3. Propositional logic uses 2 main building blocks: propositions and propositional connectivesPropositions: statement that is either true or false (has a truth value)“Atomic” without propositional connectivesPropositional connectives: Used to connect smaller propositions into larger onesVery similar to mathematical connectives: */-+Larger propositions that include connectives also have a truth valuePROPOSITIONAL LOGIC

4. CONNECTIVESConjunction, disjunction, negation, conditional & biconditionalEach connective is governed by its own truth conditions (conditions under which propositions that include the connective are true)We can discover the truth conditions of non-atomic propositions that include many connectives through the use of truth tablesEach connective has its own truth table

5. VARIABLESReplace propositions in English with variables that can stand in for any propositionPropositions, once replaced by variables, are put in propositional formsPropositional form: a pattern that can represent any number of actual propositionsExample: p&q is a propositional form in which “p” and “q” can stand for any propositionSubstitution instance: replace variables by actual propositions – many possible sub. instances for each prop. form

6. RULESEach proposition can be replaced by one or several variables in a series of propositional forms (argument) but each variable must represent the same proposition throughoutP & Q can both represent the same proposition but P cannot represent two different propositions within the same series/argumentVariables can represent atomic propositions or more complex ones that, themselves, include connectives

7. ARGUMENT FORMSOnce we have propositional forms, we can combine them into argument formsArgument form: offers a pattern of argument that we is always valid pattern for any number of argumentsExample: 1) p&q 2) p

8. ARGUMENT FORMSAn argument is valid IF it is a valid argument formNote: not all valid arguments are so in virtue of their argument form – here we offer a sufficient, but not necessary, condition for validityAn argument form is valid IF AND ONLY IF it has no substitution instances in which the premises are true and the conclusion false

9. CONJUNCTIONPropositional conjunction: [while still in English] “and” expresses the conjunction of two or more propositions (called “conjuncts”)Non-propositional conjunction: “and” does not express the conjunction of two or more propositionsTest: can you separate the proposition into two separate conjuncts without changing the meaning of the sentence?

10. DISJUNCTIONPropositional connective: “or”Unless specified, meant as an inclusive “or”Exclusive “or” generally implied by context and not the actual proposition itself

11. NEGATIONPropositional connective: “not”The negation of a proposition is true if and only if the proposition is false and vice versa“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