Principal: Syllogisms

Principal: Syllogisms Week 1 ENG 1005: Writing about Social Justice

What is an argument? Give me a definition of what you think an argument is: is it a report, testimony, example, warning, advice? What about a belief? Is a belief an argument?

Argument is that which argues. Neither belief, nor a news report, nor an example is an argument because it doesn’t seek to argue, but to explain. Things that explain tell you things, but they don’t seek to argue. They may be contained inside an argument, and they may be used to strengthen an argument, but they themselves do not—indeed cannot argue. Beliefs are not “grounded”. There’s no body of “evidence”, no “proof” to persuade based on belief alone. Example from Thank You for Smoking

Argument must be grounded in logic, math, or science. Arguments, on the other hand are grounded in logic, math, or science. Your argument then attempts to justify your claims. (Notice that claims never use the word: belief) All arguments have two parts: the premises and the conclusion. The premises contain the evidence (observation, examples, statements of fact) The conclusion is that which is justified by the evidence.

Two types of logic: inductive and deductive and humans suck at both. Most humans will only solve 50% of the deductive logical problems thrown at them; they’ll solve only 30% of the inductive logical problems thrown at them. Deductive arguments are purely about the structure of the argument. Inductive arguments are about the content.

Sylla-what? Syllogism = Aristotelian schematic used to test/analyze deductive reason Device we use for analyzing the “validity” of an argument Syllogisms are not necessarily concerned with the “T” truth but with the validity of the premise. We however, are concerned with the “T” truth of the argument and the validity of the premises. Logicians use the word premises, which is analogous the proposition. This is the format: If A = T and B = T C is also T It’s often important to decide if a proposition is arguing quantity or quality Quantity = universal or particular (whole class or part of a class) Quality = affirmative or negative (predicate asserts or denies)

Syllogistic Logic We can look to grammar to help us determine if an argument is particular or universal and to determine the class of things under review. Words like every, all, and no denote a quantity of universal Words like most, a few, the majority of, many denote a quality of particular Words that include (in the predicate) not, none of, not any are negative, but of course can be universal or particular.

What’s the contradictory of this statement? Some presidents are former movie actors. Contraries E Universal Neg. A Universal Affirm Subalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

Answer: No Presidents are former movie actors. Contraries E Universal Neg. A Universal Affirm Subalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

What’s the superaltern of…? Some CIA employees are defectors. Contraries E Universal Neg. A Universal Affirm Superalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

Answer: All CIA employees are defectors. However: why isn’t this a valid argument? Contraries E Universal Neg. A Universal Affirm Superalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

What’s the subaltern of…? No logic students are con artists. Contraries E Universal Neg. A Universal Affirm Superalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

Answer: Some logic students are not con artists. And: This premise is “T” Contraries E Universal Neg. A Universal Affirm Superalterns Subalterns I Particular Affirm O Particular Neg. Subcontraries

More Fun with Syllogisms All syllogisms have propositions/premises (usually, but not always two) and aresult These propositions are called the Major Premise, Minor Premise, and the Conclusion NOTE: They don’t always follow 1, 2, 3—in other words you can have a Minor, then Major Premise—and to compound matters, you can have implied premises(those tricky premises!) To test for “validity”, you must identify the conclusion. Look for words like because, therefore, thus, hence, consequently, because of this, so…

Distribution Happy Things Girls Distribution: a term is distributed if the premise in which the term appears tells you something about all of the members about that term class. [Can be positive/negative] All ________ are X = All ______ (distributed) and X (undistributed) Example: All girls are happy things. So, look for the nouns: girls/ happy things. What do we know about girls? What do we know about happy things?

Quick n’ Dirty Validity Rules All girls are happy All G are H Valid or Invalid Why? No clowns are girls No C are G Some C are H Some clowns are happy If you have a negative conclusion, you must have at least one negative premise. You can not have two negative premise in any one syllogism. If you have a positive conclusion you must have two positive premises. If you have two negative premises, you must have a negative conclusion. If your premises are universal, the conclusion cannot be particular. The “middle term” must appear once in each premises, but not in the conclusion. If a term is distributed in the conclusion, it must be distributed in the premise where it appears.

In-Class Exercise I Break into pairs. Create a syllogism that breaks each of the rules. Be prepared to write the syllogisms on the board. The teams that “solves” the syllogism by identifying the rule it breaks gets 1 point for each correct answer. The team that has the most points wins 5 extra credit points on the final draft of your argumentative essay. (That could mean a letter grade!)

Principal: Syllogisms