INDUCTION (probable inference) : inference moving from specific facts to general conclusions.

DEDUCTION (necessary inference): inference moving from general premises to specific conclusions

DEDUCTION AND INDUCTION

DEDUCTIVE ARGUMENT:Generally past or present-orientedIt draws from general information then

extracts a specific conclusion which proves the past or present truth.

INDUCTIVE ARGUMENT:Is generally future-orientedIt first gathers specific information, then draws

a general conclusion which predicts what the future can be.

The conclusion can be proven false if we find one contrary example.

DEDUCTIVE AND INDUCTIVE

TEAM X: RULE DRIVEN LEARNER NECESSARILY! DEDUCTIVE

TEAM Y: DISCOVERY LEARNER PROBABLY! Drawing conclusion through discovery –

observing patterns or experiencing it for yourself.

INDUCTIVEE.G.1: too much love =

will kill you2: study exams =

grades3. cigarette smoking

is dangerous to your health 4. bugging the tough kids =

beat you

DEDUCTIVE AND INDUCTIVE LEARNING

1) DEDUCTION: “necessarily” –Ma-De-Cat-Hy-DiA. MATHEMATICSB. DEFINITION C. CATEGORICAL SYLLOGISMSD. HYPOTHETICAL SYLLOGISMSE. DISJUNCTIVE SYLLOGISM

2) INDUCTION: “probably” –PAGAS!F. PREDICTIONSG. ANALOGYH. GENERALIZATIONSI. AUTHORITYJ. SIGNS

DEDUCTION & INDUCTION

premises are claimed to support the conclusion. Impossible:

premises to be true and the conclusion false.

conclusion is claimed to follow necessarily from the premises.

Indicators: ‘‘certainly,’’ ‘‘absolutely,’’ and ‘‘definitely.’’

E.G.The meerkat is a member of the

mongoose family.All members of the mongoose family are carnivores.Therefore, it necessarily follows that the meerkat is a carnivore.

All saleswomen are charming.C. Reyes is a saleswoman.Therefore, C. Reyes is charming.

DEDUCTIVE ARGUMENTS

Valid means: PERFECT HOUSE VS.

PERFECT HOMEargument has necessary

logical structure.logical construction.

The particular way the premises and conclusion fit together.

“truth preserving”The truth of the premises

are preserved onto the conclusion

VALIDITY VS TRUTHFULNESS

ALL POLITICIANS ARE LIARSNOY IS A POLITICIANTHEREFORE, IT FOLLOWS THAT

NOY IS A LIAR

ALL MEN WILL DIEMCREY IS INDEED A MANTHEREFORE, MCREY WILL DIE

IT IS IMPOSSIBLE: FOR THE PREMISES TO BE TRUE THE CONCLUSION TO BE FALSE.

CONCLUSION FOLLOWS DIRECTLY FROM THE PREMISES.

SIMPLE DEDUCTIVE ARGUMENTS

ALL POLITICIANS ARE LIARSALL USED-CAR SALESMAN ARE

LIARSTHEREFORE, IT FOLLOWS THAT

ALL USED-CAR ARE POLITICIANS.

IF MCREY HAS NO TEETH, THEN HE IS MORTAL

MCREY IS MORTALTHEREFORE, MCREY HAS NO

TEETH.

THE CONCLUSION DOES NOT FOLLOW LOGICALLY FROM THE PREMISES

DEDUCTIVELY INVALID ARGUMENT

A.MATHEMATICSB.DEFINITION C.CATEGORICAL

SYLLOGISMSD.HYPOTHETICAL

SYLLOGISMSE.DISJUNCTIVE SYLLOGISM

DEDUCTION: Ma-De-Cat-Hy-Di

conclusion depends on some purely arithmetic or geometric computation or measurement

Exception: StatisticsE.g.

a shopper might place two apples and three oranges into a paper bag and then conclude:that the bag contains five

pieces of fruit.a surveyor might measure a

square piece of land and, after determining that it is 100 feet on each side, conclude that it contains: 10,000 square feet

ARGUMENT BASED ON MATHEMATICS

conclusion is claimed to depend merely upon the definition of some word or phrase used in the premise or conclusion.

E.G.Because Gloria is

untruthful, it follows that:she tells lies.

Because a certain paragraph is flowery, it follows that: it is excessively wordy.

ARGUMENT FROM DEFINITION

SYLLOGISM? inference

an argument consisting of exactly two premises and one conclusion

a syllogism in which each statement begins with one of the words ‘‘all,’’ ‘‘no,’’ or ‘‘some.’’

E.g.All lasers are optical devices.Some lasers are surgical

instruments.Therefore:

some optical devices are surgical instruments.

CATEGORICAL SYLLOGISM

TYPES EXAMPLES

UNIVERSAL AFFIRMATIVES

All humans are mortal.

UNIVERSAL NEGATIVES No humans are perfect.

PARTICULAR AFFIRMATIVES

Some humans are healthy

PARTICULAR NEGATIVES Some Humans are not

clever.

A syllogism having a conditional statement for one or both of its premises.

E.G. If electricity flows through a

conductor, then a magnetic field is produced.

If a magnetic field is produced, then a nearby compass will be deflected.

Therefore, if electricity flows through a conductor,

then a nearby compass will be deflected.

If quartz scratches glass, then quartz is harder than glass.

Quartz scratches glass.Therefore:

quartz is harder than glass.

HYPOTHETICAL SYLLOGISM

a syllogism having a disjunctive statement (i.e., an ‘‘either . . . or . . .’’ statement) for one of its premises.

E.G.Either breach of contract

is a crime or it is not punishable by the state.Breach of contract is not a crime.Therefore: it is not punishable by the state.

DISJUNCTIVE SYLLOGISMS

MOST DOGS HAVE FLEASFULGOSO IS A DOGTHEREFORE, IT FOLLOWS THAT

FULGOSO PROBABLY HAS FLEAS.

98% OF SNAILS ARE SLIMYTHERE IS A SNAIL IN MY

GARDENTHEREFORE, THE SNAIL IN MY

GARDEN IS HIGHLY LIKELY TO BE SLIMY

IT IS ENTIRELY POSSIBLE FOR ALL THE PREMISES TO BE TRUE AND FOR THE CONCLUSION TO BE FALSE.

INDUCTIVE ARGUMENTS

premises are claimed to support the conclusion

Arrives at a conclusion, but with less certainty

Improbable: that the premises be true and the

conclusion false. conclusion is claimed to follow only

probably from the premises. indicators are ‘‘improbable,’’

‘‘plausible,’’ ‘‘implausible,’’ ‘‘likely,’’ ‘‘unlikely,’’ and ‘‘reasonable to conclude.’

E.g. The meerkat is closely related to the

suricat.The suricat thrives on beetle larvae.Therefore, probably the meerkat thrives on beetle larvae.

The vast majority of saleswomen are extroverts.Elizabeth Taylor is a saleswoman.Therefore, Elizabeth Taylor is an extrovert.

INDUCTIVE ARGUMENTS (sense of probability)

A.PREDICTIONSB.ANALOGYC.GENERALIZATIONSD.AUTHORITYE.SIGNS

INDUCTIVE

the premises deal with some known event in the present or past, and the conclusion moves: beyond this event to some event in the relative future.

future cannot be known with certainty; thus, whenever an argument makes a prediction about the future, one is usually justified in considering the argument inductive.

E.G.someone might argue that because

certain meteorological phenomena have been observed to develop over a certain region of eastern Luzon, a storm will occur there in 26 hours.

one might argue that because certain fluctuations occurred in the prime interest rate on Friday, the value of the pesos will decrease against foreign currencies on Monday.

PREDICTIONS ABOUT THE FUTURE

if two things have certain characteristics: (A) in common, then they are also

probably have one or more additional traits (B) in common.

E.G.

Because Christian’s Porsche is a great handling car, it follows that Israel’s Porsche must also be a great handling car

Christian likes Justin Bieber, Charice Pempengco, and Kpop.

I know Israel likes Justin Bieber, Charice Pempengco, and Glee.

 Israel will probably like Kpop also, so I will buy this CD for him.

ANALOGY

an argument that proceeds from the knowledge of a selected sample to some claim about the whole group.

Portion of the members = all the members of the group have that same characteristic?

These examples illustrate the use of statistics E.G.

Because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are: especially tasty and juicy.

Because six out of a total of nine members sampled from a certain labor union intend to vote for Aquino for union president, two-thirds of the entire membership intend to vote for Johnson.

FHM: sexiest girl

GENERALIZATIONS

argument in which the conclusion rests upon a statement made by some presumed authority or witness.

QUESTION ON THE AUTHORITY: either mistaken or lying? such arguments are essentially probabilistic.

E.G.A person might argue that

earnings for Hewlett-Packard Corporation will be up in the coming quarter because of a statement to that effect by an investment counselor.

A lawyer might argue that Mack the Knife committed the murder because an eyewitness testified to that effect under oath.

ARGUMENTS FROM AUTHORITY

argument that proceeds from the knowledge of a certain sign to a knowledge of the thing or situation that the sign symbolizes

What is marked on a sign does not have to be true though it usually seems to be. So, there is good but not conclusive reason

to believe it.

E.G.

One might argue that the road does indeed make several sharp turns one mile ahead. Because the sign might be misplaced or in error about the turns, the conclusion is:

only probable.

ARGUMENTS BASED ON SIGNS

1) William is a bachelor, all bachelors are single; hence William is single.

2) Socrates was a Greek. Most Greeks eat fish. Socrates ate a fish.

3) If Dennis misses work and at work there is a party, then Dennis will miss the party.

4) To earn a master’s degree, a student must have 32 credits. Tim has 40 credits, so Tim will earn a master’s degree.

5) Red meat has iron in it and beef is red meat, so beef has iron in it.

6) The elm is a tree and all trees have bark, so elms have bark.7) Acute angles are less than 90 degrees and this angle is 40

degrees so this angle is acute.8) Jimmy got bitten by a dog. Jimmy is now scared of all dogs.9) Magnolias are dicots and dicots have two embryonic leaves;

therefore magnolias have two embryonic leaves.10) 2 episodes of the Big Bang Theory made me laugh so hard. The

Big Bang Theory is always a funny show.

SEATWORK: DEDUCTIVE OR INDUCTIVE