Arguments In Normal English

Unit 4a Arguments In Normal English

27 Immediate Inferences The differences from a syllogism to normal English Immediate inference- a statement which can be inferred

directly from another statement (If...then) Examples – If All S is P then Some S is P – If No S is P then No P is S – If Some S is P then some P is S Last two are called a converse. Converse- a statement that reverses the subject and predicate (E and I) Observe- a statement of the opposite quality with a negated predicate (valid for all statements)

Complement- set of all terms non included in the given term

27 Immediate Inferences Obverses All to No, Some to Some not, No to All, Some not to Some P to non P Examples – All S is P to No S is non P • All boys are humans to No boys are non humans. – No S is P to All S is non P • No cats are dogs to All cats are non dogs. – Some S is P to Some S is not non P • Some incredible things are possible to Some incredible things are not impossible. – Some S is not P to Some S is non P • Some Americans are not capitalist to Some americans are non capitalists

27 Immediate Inferences Contrapositive- a statement that reverses and negates

both the subject and predicate of the original (A and O) All S is P ----No S is non P---- No non P is S-----All non P is non S All S is P to All non P is non S – All logic students are frustrated students to All non frustrated students are non logic students. Some S is not P-----Some S is non P----Some non P is S---Some non P is not non S. Some S is not P to Some non P is non S – Some humans are not boys to Some non boys are not non human.

27 Immediate Inferences All 11th graders are less than 2 meters tall, because all poor

logicians are non-11th graders, and nobody 2 meters tall or more is a good logician.

28 Translating Ordinary Statements Review

– Categorical Statements • All roads lead to Rome • All toads are ugly – All: Every, any, as many as – No: None, all.....not, never – Some: Many, most, a few Not all S are P? Not all students are bad?

28 Translating Ordinary Statements Review  Everybody needs a friend  Any number two pencil will work  As many as saw the accident may testify  None of the songs I heard were copyrighted  All of the pianos in that room were not in tune  Toddlers never study Statistics  Many Soldiers visited the memorial

28 Translating Ordinary Statements Review  Most people like ice cream.  A few people like spinach.  Not all soldiers fight on the front lines.

I. Singular statements- Statements that refer to a single

person or thing • Should be translated as universals. • John is a mailman – All John is a mailman • You are not my friends – No you are my friends

28 Translating Ordinary Statements II. Indefinite statements- Statements that seem to refer to a

singular statement • Should be translated as universals or particulars. • Dogs ate my homework – Some dogs were eaters of my homework • Cats are mammals • Cats sang outside my window • Therefore mammals sang outside my window • All cats are mammals • Some cats are outsside my window singers • Therefore some mammals are outside my window singers

28 Translating Ordinary Statements III. Hypothetical statements- Statements that use it/then

• Should be translated as universals. • If you like chocolate, you will love this cake • All chocolate lovers will be cake lovers • If it's a hard test I will not pass it • No hard test is a test I will pass

28 Translating Ordinary Statements Examples Paul is good. If you cheat you will get a zero I swim. A nice answer keeps others from getting angry If you don't study you will not learn.

29 Translating Inclusive and Exclusive Statements  Inclusives- a word, often a relative pronoun or adverb, that

refers to a broad range of things or times  (Ever words)Whoever, whatever, wherever, whenever, however, always, never...  Words following inclusive words usually become the subject • You should eat whatever your mother feeds you. • All things your mother feeds you are things you should eat.  Whenever often refers to a time • Whenever I go the US I always gain weight. • All times that I go the the US are weught gaining times.

29 Translating Inclusive and Exclusive Statements  Inclusives  Beware of always

• The poor you will always have with you • All time are times the poor will be with you • Joe always wins at chess – All times are times Joe wins at chess? • All times Joe plays chess are times Joe wins at chess  Never is similar with All times and not (an E statement)  Beware of shortened -ever words (where...wherever) • I will go where you go. • All places you go are places I will go.  That? (whatever....) • All's well that ends well to all things that end well are well

29 Translating Inclusive and Exclusive Statements  Exclusives- Words which exclude or set boundries  Only, unless, except

• Only the good die young • All good people are people who die young? • All people who die young are good people.  Nobody but, nothing but.... • Nobody but the Spartans could fight like that • All people who could fight like that are the Spartans • The plants will die unless you water them • All the plants that you don't water are plants that will die.  Except? 2 independent statements • Everyone was invited to the clubhouse except sisters • All non sisters were clubhouse invited people • No sisters were clubhouse invited people