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Dead Greeks

Explore the development of logic from the ancient Greeks to modern symbolic logic, including key figures, argument schemes, and the importance of context.

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Dead Greeks

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  1. Dead Greeks Plato: There is a truth (absolute truth), you can reach it by deduction, and nothing else matters much. The process is called “dialectic,” and today we’d probably think of it as math and science. Student of Socrates, founded the academy, was the first ever professor

  2. Aristotle: Rhetoric matters; it’s not just the absolute truth, it’s how to make the best case possible. Advisor to Alexander the great, student of Plato, ran for his life after Alex was overthrown.

  3. Protagoras (a sophist) that all arguments have 2 sides, and if you know your crap you should be able to argue both equally well. Plato wrote a book slamming him called “Progtagoras”

  4. Romans follow the greeks; they don’t come up with anything new but they rip off the greeks. The big thinker is Quintillian: his big quote is: “A liar needs a good memory,” which makes sense, but isn’t really theoretically groundbreaking.

  5. The dark ages • Nothing really happened because the Catholic church took over, burned books, ran crusades who burned books in the libraries of Europe, • It was all saved by Saint Patrick, who drove all the snakes off of Ireland and saved the original writing.

  6. The Renaissance • Guys like Da Vinci re-read the classics and added stuff • But he was weird, had 17 brothers and sisters, started a bunch of crap he never finished, and did a bunch of gross work with dead bodies. And he painted the Mona Lisa.

  7. Pascal: A Renaissance hero • All humans have 2 basic psychological instincts: The rational (math, science, reason) and the intuitive (feeling, emotion, love). • A good scheme of argument includes both.

  8. The Renaissance and Logic • Science was really going well; language became mathematicized. • The easiest form was the syllogism, which goes: • Ps are Qs • X is a P • Therefore, X is a Q

  9. The example in all the text books: • Socrates is a human • All humans are mortal • Therefore, Socrates is a mortal

  10. A better example: • All Atlanta Braves are scum-sucking satan-worshippers who torture babies for fun • Gary Sheffield is an Atlanta Brave Sep 03, 2003 NL FINAL 1 2 3 4 5 6 7 8 9 R H E - ATLANTA 0 1 0 0 0 0 0 0 2 3 7 4 NY METS 1 3 0 1 1 0 0 3 x 9 10 0 (FINAL)

  11. This all resulted in modern symoblic logic Consider first the argument scheme: (1) Don't let x happen. (2) If you do y, then x. Therefore, (3) Don't do y. This is a clearly valid scheme containing a mixture of declaratives and imperatives, which reduces to: (1') x->s (2') y->x Therefore, (3') y->s A typical instance of this is: (1») Don't let the cat escape. (2») If you open the front door, the cat will escape. Therefore, (3») Don't open the front door.

  12. The second argument scheme is similar: • (4) Do x. (5) In order to do x, you must do y. Therefore, (6) Do y. • This is also a clearly valid scheme containing a mixture of declaratives and imperatives, and it reduces to: • (4') ~x->s (5') x->y Therefore, (6') ~y->s • A typical instance of this is the inference from «Clean up your room» to «Hang up your coat.»

  13. A third valid argument scheme, but one which is far more complex, is: (7) Do p or q. (8) If you do p, then do r. (9) If you do q, then do s. Therefore, (10) Do r or s. It may not be presumed here that the sanctions for not doing p, q, r, and s are the same; they may or may not be. Hence this argument scheme reduces to: (7') ~(pVq)->x (8') p->(~r->y) (9') q->(~s->z) Therefore, (10') ~(rVs)->(xVyVz), where x is at least yVz. A typical instance of this scheme is: (7») Either tell her nothing or tell her everything. (8») If you decide to tell her nothing, feign ignorance of the entire matter. (9») If you decide to tell her everything, tell it in a way that coheres credibly. Therefore, (10») If you neither feign ignorance of the entire matter nor tell her the whole story so that it coheres credibly, you'll be suspected of leaving something out or of lying.

  14. I leave an appropriate context to the imagination of the reader. Notice that our choice of x was simply yVz, but it could well be something stronger (y & z comes to mind, as well as more complicated propositions that entail y, z, or both). However, the validity of the three schemata above depends critically on the assumption of a common context in which the premises and conclusion are asserted or else we have the usual problem with indexicals. Indeed, without this assumption, even the following argument scheme is invalid: (11) Do x. Therefore, (12) Do x. Since it does not follow from «Give me ten dollars or I will starve» that «Give me ten dollars or I will shoot» and since the sanction is, in both the premise and the conclusion, left implicit, the notion of validity for arguments with imperatives read as material (bi)conditionals depends critically on a common context. As another example, consider the imperative «Tell me who did it!» Asked by a curious friend, the sanction for not answering is mere displeasure; asked in a court of law, the sanction for not answering is being found in civil contempt and incarcerated -- quite different!

  15. Besides the problem of context, a more subtle problem arises if it is not clear whether the sanction will be applied only if the imperative is ignored or at least when the imperative is ignored, i.e. when it is not clear whether the conditional is a simple conditional or a biconditional. Thus it may appear that the following argument is surely valid: (13) Give me ten dollars. Therefore, (14) Give me at least five dollars. However, if the conditional corresponding to (13) is a biconditional, i.e. the sanction will be avoided if the command is obeyed (e.g., the criminal will not shoot if he is paid off), (14) may simply not be sufficient to avoid the sanction. Verily, our ability to analyze arguments is hampered by lack of knowledge of context, intention, and the like, and this is the situation for declaratives just as for imperatives. If it seems like it is more troublesome for the latter, that is, indeed, the case, since often when imperatives are issued as commands (as opposed to requests) they are an abrogation of the rights and will of others, in which case the context is such that the intentions are necessarily less clear than when two people are having a (consensual) conversation: The situation of the starving beggar can be resolved more easily than the situation of the street criminal, i.e. it is surely a simpler matter to ascertain whether something less than ten dollars will do to satisfy the man's hunger than it is to ascertain what the man with his hand on the trigger will do if he is given less than he demands.

  16. The modern approach • Answer one: Fallacies • Answer two: Toulmin • Answer three: Give up and study power or persuasion or something

  17. Fallacies: • Look for classic errors of reasoning and if you don’t find any, it’s a good argument. • Throw around latin terms like you really learned something in college • FAULTY CAUSE: (post hoc ergo propter hoc) mistakes correlation or association for causation, by assuming that because one thing follows another it was caused by the other. example: A black cat crossed Babbs' path yesterday and, sure enough, she was involved in an automobile accident later that same afternoon. example: Since the Anaheim Angels introduced the rally monkey, the team has one a lot more come-from-behind victories. Never underestimate the power of the rally monkey.

  18. More fallacies APPEAL TO IGNORANCE: (argumentum ad ignorantiam) attempts to use an opponent's inability to disprove a conclusion as proof of the validity of the conclusion, i.e. "You can't prove I'm wrong, so I must be right." BIFURCATION: (either‑or, black or white, all or nothing fallacy) assumes that two categories are mutually exclusive and exhaustive, that is, something is either a member of one or the other, but not both or some third category. example: Either you favor a strong national defense, or you favor allowing other nations to dictate our foreign policy. example: Either you are with the terrorists or you are with the United States. SLIPPERY SLOPE: (sometimes called a snowball argument or domino theory) suggests that if one step or action is taken it will invariably lead to similar steps or actions, the end results of which are negative or undesirable. A slippery slope always assume a chain reaction of cause-effect events which result in some eventual dire outcome. example: If the Supreme Court allows abortion, next think you know they'll allow euthanasia, and it won't be long before society disposes of all those persons whom it deems unwanted or undesirable.

  19. Problems with fallacies • Not making a mistake doesn’t prove you’re right; it’s all about form and not substance • Sometimes fallacies are really good arguments; sometimes slopes are really slippery • Most arguments aren’t structured the right way • Many arguments have implied parts

  20. The Toulmin approach • All arguments have their own internal structure, you can’t force them into syllogisms or hope that fallacies will fit. • What all arguments have in common is a claim, supported by data, and the two are connected with a warrant. • The warrant can be implied

  21. Problems with “The Toul” • The warrants are based on “fields,” and nobody knows what those are. • Indeterminacy: Any word can mean any thing at any time, so you can’t ever prove anything. Study persuasion instead. • You don’t just have one argument.

  22. Better Answers: • Pragmatism: An argument is a good argument if it works. Don’t worry about fields. • Drop qualifier, backing, and rebuttal • Focus on “serial connectivity,” ways that arguments connect. • There are facts and they do seem to matter. Example: Abortion debate.

  23. Evaluate an argument like this: • An argument is a good argument if the claim and only the claim is supported by the data, and all the best data is out there. • Focus on who has more and better evidence, because data is more important than warrant.

  24. Take home points • How to evaluate an argument started back with Aristotle and Plato, Pascal kinda got it, Toulmin is the recent hotshot, and we’re still trying to figure it all out. • There are 4 basic approaches: symbolic logic, fallacies, Toulmin approaches, and giving up on rationality. • I think you should take Pascal and find a scheme that does both.

  25. The payoff • All argument is 2 things: Proving your claims and having a valid structure. There’s a lot of debate about structure. • The better structure will: • (a) Help you see how all the little points fit together • (b) Help you evaluate the argument

  26. Class exercise Read an article and come up with 4 things: • Outline • Fallacy check • Toulmin diagram • Serial connectivity diagram

  27. Possible diagram 2.7 millions have become unemployed while Bush is in office Losses are permanent says the FRB Tax cuts aren’t working to improve jobs An under-secretary for the Dept of Commerce isnt’ enough Big problem Current efforts are lame Job loss is a big problem and needs more attention

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