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Propositional Logic. Common Argument Forms. “a shape or outline”. The many meanings of “form”. a way of being that gives something it’s character. “democracy” is a form of government. “Her form in serving tennis is very good.”. A way of doing something. Argument “form”.
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Propositional Logic Common Argument Forms
“a shape or outline” The many meanings of “form” • a way of being that gives something it’s character “democracy” is a form of government “Her form in serving tennis is very good.” • A way of doing something
Argument “form” • “An orderly arrangement; a way that something is put together” – distinguished from content • Operators create “statement forms” – single statements to complex statements • Typical patterns of thinking create “argument forms” – kinds of statements put together in unique identifiable ways
Valid Modus Ponens (in the affirming mode) p > q p___ q Invalid Affirming the Consequent p > q q___ p Valid and invalid argument forms 1
Affirming the Consequent • In a conditional statement, p is sufficient but not necessary to obtaining q. • The implication: it is possible to obtain q in a way other than p • P1. p > q • (a. r > q) • (b. s > q) • (Etc…) • P2. q • Con: p? r? s?
Challenges to identifying argument form • Argument form is not shape; we are looking for a logical, not a visual, “match” of argument elements to an argument form (M v N)>[S ≡ (Y v Z)] p>q M v N __p______________ [S ≡ (Y v Z)] q (M v N) > [S ≡ (Y v Z)] M v N [S ≡ (Y v Z)]
P1: ~ (M v N) > (F ● H) P2: ~ (M v N) F ● H P1:~ (M v N)>(F ● H) p>q P2:~ (M v N) ________p___ F ● H q Other examples
Hints for Identifying Argument Forms • Identify the premises and conclusion (and symbolize them all) • Identify the form of the component statements, including premises and conclusion (look for main operator) • Try to “match” all those statement forms to the patterns of statement forms found in argument forms
Identify premises and conclusion If TV viewing provides genuine relaxation, then TV enhances the quality of life. But TV viewing does not provide genuine relaxation. So TV does not enhance the quality of life. (P. 332, # 8) R > E ~ R____ ~ E
R > E ~ R ~ E Conditional statement: p>q Negation: ~p Negation: ~q Form and “match” of component statements R>E ~R ~E This is an example of “denying the antecedent” – an invalid argument form.
Example 2 “People just don’t listen to reason, and if they don’t there’s no way to have a productive conversation. So we can write off the possibility of productive political dialogue (c).” ~ R > ~ C ~ R__ ~ C ~ R>~ C ~ R__ ~ C ~ R ~ R > ~ C ~ C p>q q__ p
