Slide 1

Inference and Syllogism

Group 3: AstillaBriginoCaoLegaspiTiuReasoning, Premises and ConclusionReasoning is a mental act whereby starting with several judgements which we relate to one another, we arrive at a new judgement which necessarily follows from the preceding ones.Premises - every reasoning process, involves a number of previously known truths.Conclusion -knowledge of a new truth which is inferred from the premises.

Example:

All vehicles are instruments of transportation;But, jeep is a vehicle;Therefore, Jeep is an instrument of transportation.INFERENCE

-It is he drawing of conclusion from one or more premises. -a mental process by which we reach a conclusion based on specific evidence

Immediate- when a conclusion is drawn from only one premise Example:A student says she cant anymore afford to enrol next semester.It indicates that the student has no money to pay for the tuition.

=Two kinds of inference=

Mediate- when a conclusion is drawn from two premisesExample: No statesmen are good politicians. Some journalists are good politicians. Therefore, Some journalists are not statesmen.=Two kinds of inference=

It is the external expression of an argument (the mental product of inferential thinking) SYLLOGISM Categorical syllogism is an inferential thinking that draws conclusion in an absolute manner.

Example:Law implies order;But, Ten Commandments are laws;Therefore, Ten Commandments imply order. =Two kinds of syllogism= Hypothetical syllogism is an inferential thinking, which concludes with certainty, affirming, or denying a statement, from the affirmation or denial of another.

Example:If the students cheat, then they should be punished;But, the students cheated;Therefore, they should be punished. =Two kinds of syllogism= The matter refers to the proposition that comprises the reasoning process.The form is the link that joins the premises to the conclusion.A syllogism is considered valid when it is impossible to have a false conclusion if the premises are true.=Nature of Categorical Syllogism=Examples:False premises but seemingly true conclusion

Money makes man live comfortably;But, mans goal is money;Therefore, mans goal is to live comfortably.=Nature of Categorical Syllogism=Example:True premises but false conclusion

A square is a geometrical figure;But, a circle is a geometrical figure;Therefore, a circle is a square. A correct syllogism is, therefore both sound and valid.=Nature of Categorical Syllogism=major term (P) which is the predicate term of the conclusion and is contained in the major premiseminor term (S) which is the subject term of the conclusion and is contained in the minor premisemiddle term (M) which is common to, and found in both premises. Major term and minor term are called extremes.=Constituents of Categorical Syllogism=Example:

All animals are substance; (Major premise, substance major term)But, a dog is an animal; (Minor premise, dog minor term)Therefore, a dog is a substance. (Conclusion, animal middle term)=Constituents of Categorical Syllogism=It is the logical process in which, the premises relate two terms with a third (middle), and the relationship is expressed in the conclusion that either unites or separates the first two terms.CATEGORICAL SYLLOGISMRule #1: The middle term must always be taken in the same sense; otherwise, the syllogism would contain more than three terms and would therefore commit Fallacy of Equivocation or Fallacy of Four Terms.

Example:A father is a male parent;But, the Holy Pope is a father;Therefore, the Holy Pope is a male parent.Rules of Categorical SyllogismRule #2: The major term and the minor term cannot have a greater extension in the conclusion than in the premises; otherwise the effect (conclusion) becomes greater than the cause (premise), which is impossible.

The fallacy committed here is the Fallacy of Illicit Process, which is two kinds: Illicit Major and Illicit Minor.

Rules of Categorical SyllogismRules of Categorical Syllogism Illicit Major, when the predicate is universal in the conclusion not in the major premise.

Example:

All hammers are tools;But, no chisels are hammers;Therefore, no chisels are tools.

Illicit Minor, when the subject is universal in the conclusion but not in the minor premise.

Example:

All birds have wings;But all birds are animals;Therefore, all animals have wings.Rule #3: The middle term should not occur in the conclusion. Violation of this rule is called Fallacy of Misplaced Middle Term.Example:Rules of Categorical SyllogismYou are happy;You are gay;Therefore, you are happy and gay.

A steward is a flight attendant;But, a steward is a male;Therefore, a steward is a male flight attendant

Rule #4: The middle term must be distributed universally, at least once, in the premise. Violation of this rule is called Fallacy of Undistributed Middle Term.

Example:All stewardesses are female;But, all mothers are female;Therefore, all mothers are stewardesses.Rules of Categorical SyllogismRule #5: Two affirmative premises cannot give a negative conclusion. Violation of this rule is called Fallacy of a Negative Conclusion drawn from Affirmative Premises. Example:All pets are domestic animals;Some turtles are pets;Therefore, some turtles are not domestic animals.Rules of Categorical SyllogismRule #6: From two negative premises, nothing follows. If we draw a conclusion from two negative premises, we commit Fallacy of Negative Premises.

Example:No tenor is a soprano;No soprano is a baritone;Therefore, no baritone is a tenor.Rules of Categorical SyllogismRule #7: From two Particular premises, nothing follows.If both particular premises are affirmative, then the subjects and the predicates are particular.Example:Some men are gays;But, some gays are artists;Therefore, some artists are men.If both particular premises are negative, then the syllogism violates Rule #6.Rules of Categorical Syllogism Example:Some wives are not naggers;Some wives are not mature;(Then what?)If one particular premise is affirmative, and the other negative, then we have the following fallacious syllogisms:Rules of Categorical Syllogism Example: Fallacy of Illicit Major TermSome cats are pets;But, some pythons are not cats;Therefore, some pythons are not pets. Fallacy of Undistributed Middle TermSome horse-back riders are not males;But, some drivers are horse-back riders;Therefore, some drivers are not males.Rules of Categorical SyllogismRule #8: The conclusion follows the weaker premise. If one premise is universal, and the other is particular, the conclusion should be particular; otherwise, it commits Fallacy of Universal Conclusion drawn from a Particular Premise.

Example:All mongoloids are mentally retarded;But, some mongoloids are special children;Therefore, all special children are mentally retarded.Rules of Categorical SyllogismTHE END