DEDUCTION AND INDUCTION INDUCTION probable inference inference moving

DEDUCTION AND INDUCTION �INDUCTION (probable inference) : inference moving from specific facts to general conclusions. �DEDUCTION (necessary inference): inference moving from general premises to specific conclusions

DEDUCTIVE AND INDUCTIVE �DEDUCTIVE ARGUMENT: � Generally past or present-oriented � It draws from general information then extracts a specific conclusion which proves the past or present truth. �INDUCTIVE ARGUMENT: � Is generally future-oriented � It 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 LEARNING � TEAM X: RULE DRIVEN LEARNER � NECESSARILY! � DEDUCTIVE � TEAM Y: DISCOVERY LEARNER � PROBABLY! � Drawing conclusion through discovery – observing patterns or experiencing it for yourself. � INDUCTIVE � E. G. � 1: too much love = � will kill you � 2: study exams = � grades � 3. cigarette smoking � is dangerous to your health � 4. bugging the tough kids = � beat you

DEDUCTION & INDUCTION 1) DEDUCTION: “necessarily” –Ma-De-Cat-Hy-Di A. B. C. D. E. MATHEMATICS DEFINITION CATEGORICAL SYLLOGISMS HYPOTHETICAL SYLLOGISMS DISJUNCTIVE SYLLOGISM 2) INDUCTION: “probably” –PAGAS! A. B. C. D. E. PREDICTIONS ANALOGY GENERALIZATIONS AUTHORITY SIGNS

DEDUCTIVE ARGUMENTS � 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.

VALIDITY VS TRUTHFULNESS �Valid means: � PERFECT HOUSE VS. PERFECT HOME � argument 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

SIMPLE DEDUCTIVE ARGUMENTS � ALL POLITICIANS ARE LIARS � NOY IS A POLITICIAN � THEREFORE, IT FOLLOWS THAT NOY IS A LIAR � ALL MEN WILL DIE � MCREY IS INDEED A MAN � THEREFORE, MCREY WILL DIE � IT IS IMPOSSIBLE: � FOR THE PREMISES TO BE TRUE � THE CONCLUSION TO BE FALSE. � CONCLUSION FOLLOWS DIRECTLY FROM THE PREMISES.

DEDUCTIVELY INVALID ARGUMENT � ALL POLITICIANS ARE LIARS � ALL USED-CAR SALESMAN ARE LIARS � THEREFORE, IT FOLLOWS THAT ALL USED-CAR ARE POLITICIANS. � IF MCREY HAS NO TEETH, THEN HE IS MORTAL � MCREY IS MORTAL � THEREFORE, MCREY HAS NO TEETH. � THE CONCLUSION DOES NOT FOLLOW LOGICALLY FROM THE PREMISES

DEDUCTION: Ma-De-Cat-Hy-Di A. MATHEMATICS B. DEFINITION C. CATEGORICAL SYLLOGISMS D. HYPOTHETICAL SYLLOGISMS E. DISJUNCTIVE SYLLOGISM

ARGUMENT BASED ON MATHEMATICS � conclusion depends on some purely arithmetic or geometric computation or measurement � Exception: Statistics � E. 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 FROM DEFINITION �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.

CATEGORICAL SYLLOGISM �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.

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.

HYPOTHETICAL SYLLOGISM � 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.

DISJUNCTIVE SYLLOGISMS �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.

INDUCTIVE ARGUMENTS � MOST DOGS HAVE FLEAS � FULGOSO IS A DOG � THEREFORE, IT FOLLOWS THAT FULGOSO PROBABLY HAS FLEAS. � 98% OF SNAILS ARE SLIMY � THERE IS A SNAIL IN MY GARDEN � THEREFORE, 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 (sense of probability) � 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.

INDUCTIVE A. PREDICTIONS B. ANALOGY C. GENERALIZATIONS D. AUTHORITY E. SIGNS

PREDICTIONS ABOUT THE FUTURE � 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.

ANALOGY � 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.

GENERALIZATIONS � 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

ARGUMENTS FROM AUTHORITY � 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 BASED ON SIGNS � 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.