------------------------------------------------------------------------ Subject: Position Paper #1: Argument Analysis ------------------------------------------------------------------------ Let me reiterate a few of the points about argument analysis that came to light while grading your position papers. ------------------------------------------------------------------------ First, you might wonder why it's important. As I wrote in an article about this course a few years ago, "Computing Curricula 2001's 'Social and Professional Issues' knowledge area includes the item 'Methods and Tools of Analysis'..., which covers precisely these sorts of argument- analysis techniques (http://www.computer.org/education/cc2001/final/sp.htm#SP-MethodsAndTools)" (Rapaport 2005: 322-323). (CC2001 is one in a series of computer-science curricula officially recommended by the ACM and the IEEE Computer Society.) ------------------------------------------------------------------------ 1. Many of you are not using the technical terms correctly: You need to distinguish between premises, on the one hand--which can be *true* or *false* (but cannot be "valid", "invalid", "sound", or "unsound")--and arguments, on the other hand--which can be *valid* (if the conclusion must be true whenever the premises are true), *invalid* (= not valid; the conclusion could be false even if the premises are true), *sound* (if it's valid *and* all premises are true), or *unsound* (= not sound; either invalid or valid-with-at-least-one-false-premise) (but cannot be "true" or "false"). And you should avoid using such non-technical (hence ambiguous) terms as "correct"/"incorrect" or "right"/"wrong". You also have to be careful about calling a conclusion "valid", because that's ambiguous between meaning that you think it's true (and are misusing the word "valid") and meaning that you think it follows validly from the premises. ------------------------------------------------------------------------ 2. Some of you said things like this: "Since one of the premises is false, the conclusion is invalid." That's not right. The conclusion of an invalid or unsound argument can still be true! Here are some examples: a) An *invalid* argument with a true conclusion: Cats meow. (true) Birds fly. (true) .'. dogs bark. (true) But that's invalid, because it has the form: P Q .'. R and there are arguments with that form that have true premises and *false* conclusions, so the form of argument is invalid. b) Here's a *valid* argument that's *unsound*, yet has a true conclusion: Cats fly. (false) If cats fly, then they have tails. (true!) .'. Cats have tails. This is *valid*, because it has the form of "modus ponens": P If P, then Q .'. Q and all such arguments are valid--the conclusion can't be false if the premises are both true. But here, one of the premises *is* false, so the argument is unsound. Yet the conclusion is true. By the way, the second premise is true because of the truth-table (or "logic gate") for "if-then": Whenever the "if"-clause (the "antecedent") is false, the conditional statement is true (no matter whether its "then"-clause (the "consequent") is true or false!). c) And here's an *invalid* and *unsound* argument with a true conclusion: Cats fly. (false) Birds meow. (false) .'. Dogs bark. (true) It's invalid for the same reason as argument (a), above, and it's unsound because--in addition to being invalid--both premises are false. ------------------------------------------------------------------------ 3. Also, validity requires *all* premises to be stated. A missing premise renders an argument invalid, even if the argument would be valid if the missing premise weren't missing. Consider this argument form: All Ps are Qs All Rs are Ss .'. No R is a P That's invalid; here's an example why. Let P = dogs, Q = animals, R = mammals, S = vertebrates. The following argument has the above invalid form: All dogs are animals. (true) All mammals are vertebrates. (true) .'. No mammal is a dog. (false) So we have a way for that argument form to have true premises but a false conclusion; therefore, it's invalid. The 2 premises are irrelevant to each other, so no conclusion relating them can be inferred from them alone. You can see this by drawing Euler circles or Venn diagrams. I can't do this easily in this plain-text file, but if you want to see it, let me know in class, and I'll draw it on the board. However, if we add a missing premise that connects the two premises: No Ss are Ps. we then have a link that makes the new, 3-premise argument valid. ------------------------------------------------------------------------ 4. Finally, "phenomenons" and "phenomenas" are not words :-) You can, however, talk about a single *phenomenon* or several *phenomena*. ------------------------------------------------------------------------ 5. And a reminder: Those of you who lost points for a missing first draft with peer-editing comments can get those points back by bringing in those first drafts. And those of you who lost points for incorrect citation formats can get those points back by fixing the citations. ------------------------------------------------------------------------ Reference: --------- Rapaport, William J. (2005), "Philosophy of Computer Science: An Introductory Course", Teaching Philosophy 28(4): 319-341. http://www.cse.buffalo.edu/~rapaport/Papers/rapaport_phics.pdf