By Dagoy Dago y, Arlyn A. Curameng, Sheryl S. Dela Cruz, Kim C. Calso, Geli May N.
HYPOTHETICAL
SYLLOGISM
syllogism is one whose major premise is a hypo hy poth thet etica icall pr propo oposit sitio ion n while its minor premise and conclusion are cate categori gorical cal pr propos opositi itions ons.. Hypothetical
Hypothetical Proposition
Conditional
statement
If, then
Does not affirm nor negate the components only the nature and validity of their connection Categorical Proposition
All
S is P
No S is P
Some S is P
Some S is not P
S is the proposition is all about, the P affirms or denies
Three
kinds of Hypothetical Syllogism 1. Conditional
Syllogism
2. Disjunctive Syllogism 3. Conjunctive Syllogism
Conditional Syllogism
CONDITIONAL SYLLOGISM is one whose major premise is a conditional proposition consisting of an antecedent and consequent, while the minor premise affirms or denies either the antecedent or the consequent of the major premise and the conclusion merely expresses¶ whatever follows from its afffir af irm mat atio ion n or de deni nial al. Rules: osit the antecedent, posit the consequent cons equent P osit Sublate the consequent, sublate the antecedent osit the consequent, no conclusion P osit Sublate the antecedent, no conclusion
Posit the antecedent, posit the
consequent
In sy sym mbolic logic, this is known as MODUS PONENS. If the an antteced edeent is affirmed in the minor premise, the consequent must also be affirmed in the conclusion. The tru rutth of the con onse sequ quen entt fol olllow owss fr from om the tru rutth of the ant nteece cede dent nt. Example: If someone wins in the million-peso lotto draws, he becomes a millionaire. But, Nikki wins the million-peso lotto draw; Nikki becomes a millionaire. Sublate the consequent, sublate the antecedent
In symbolic logic, this is known as MODUS TOLLENS. If th thee co cons nseq eque uent nt is rejected in the minor premise, the antecedent must also be rejected in the conclusion . The falsity of the antecedent follows from the falsity of the consequent. Example: If someone wins in the million-peso lotto draws, he becomes a millionaire. But, Nikki does not become a millionaire; Nikki does not win in the million-peso lotto draw.
Posit
the consequent, no conclusion fall acy of affirming the consequent which This rule gives rise to the fallacy is committed when the consequent is affirmed in the minor premise.
Example: If someone wins in the million-peso lotto l otto draws, he becomes a millionaire. But, Nikki becomes a millionaire; Nikki wins in the million peso lotto draw.
Sublate the antecedent, no conclusion rej ecting the antecedent which is This gives rise to the fallacy of rejecting committed when the antecedent is rejected rej ected in the minor premise.
Example: If someone wins in the million-peso lotto l otto draws, he becomes a millionaire. But, Nikki didn¶t win in the million-peso lotto draw; Nikki didn¶t win become a millionaire .
Diff erent erent Patterns o f the f the Cond i it t i i onal o nal Syllog i ism s m A=
antecedent B = consequent The relation that exists between the two is expressed by the sign: (colon).
Exception: There
are few cases in which one can conclude with certainty (a) from the truth of the consequent to the truth of the antecedent, and (b) from the falsity of the antecedent to the falsity of the consequent. But this is due not to the legitimate nature of the conditional inferential procedure employed but to the formal necessity involved in th thee matt tteer in th thee con ond dit itiion onaal majo jorr pre rem mise. Example: If this month is December, next month is January; But this month is not December; Next month is not January
Disjunctive Syllogism
DISJUNCTIVE SYLLOGISM It is one whose major premise is a disjunctive proposition consisting of alternatives (disjuncts), while the minor premise afffir af irm ms or de deni nies es any of the dis isjjunct ctss, an and d th thee concl clus usiion mere relly expr ex pres essses what ateeve verr fol olllows fro rom m it itss affirm rmat atiion or de deni niaal. Both the minor premise and the conclusion are categorical propositions. It was mentioned that a true disjunctive pro p ropo possit itio ion n is on onee who hosse di disj sjun unct ctss ex excl clud udee ea each ch ot othe her r . Rules: Rules: (Compl (Complete ete disjun disjuncti ction) on) In the case of complete disjunction whose parts are mut utua uall lly y ex excl clus usiive ve,, i.e., the contradict each other, the following rule ru less ap appl ply: y: Rules: Pos osit it on onee al alte tern rnat ativ ive, e, sub ubla late te th thee ot othe her r . (Ponendo-tollens) Sub ubla late te on onee al alte tern rnat ativ ive, e, po possit th thee ot othe her r . (Tollendo-ponens)
**
Posit
one alternative, sublate the other. other. (Ponendo-tollens)
The
minor premise affirms one disjuncts and the conclusion rejects the other . Examples: The
accused is either guilty or not guilty;
But, he is guilty; (affirmed) He is not not guilty. (rejected) The
accused is either guilty or not guilty;
But, he is not guilty; (affirmed) He is not guilty. (rejected)
Sublate one alternative, posit the other. ( Tollendo-ponens)
**
The
minor premise rejects one disjuncts and the conclusion affirmss the other . affirm Example: The military operation in Basilan is either successful or unsuccessful; But it is not successful; (rejected) It is unsuccessful. (affirmed) The
military operation in Basilan is either successful or unsuccessful; But it is not unsuccessful; (rejected) It is successful. (affirmed)
Rules: (Incomplete disjunction) In incomplete disjunction whose parts are not mutually exclusive, i .e., they don¶t contradict each other, these rules apply: Rules: Posit one alternative, sublate the other . (Ponendo-tollens) Sublate one alternative, no conclusion .
**
Posit
The
one alternative, sublate the other. (Ponendo-tollens)
minor premise affirms one disjuncts and the conclusion rejects the other .
Examples: The test is either easy or difficult; But it is easy; (affirmed) It is not difficult. (rejected) The
test is either easy or difficult; But it is difficult; (affirmed) It is not easy. (rejected)
**
Sublate one alternative, no conclusion.
The
minors premise rejects one disjuncts disj uncts and the conclusion affirms the other .
Example: The test is either easy or difficult; But it is not easy; (rejected) It is difficult. (affirmed) The
conclusion, ³It is difficult´ does not necessarily follow from the premises. Why? Because the test can be average, in which case it is neither easy nor difficult. This forms the Fallacy or Tollendo-ponens,a fa fall llac acy y committed when one disjuncts in an incomplete disjunction is rejected in the minor premise and the other is i s affirmed in the conclusion. Example: This machine is either light or heavy; But it is not heavy; (rejected) It is light. (affirmed) This
syllogism is invalid. The machine may be moderate in i n weight.
Diff erent erent Patterns o f the f the Di Di sjunct sjunct ive ive Syllog i ism s m
It is for the posit-sublate the posit-sublate process and the sublate-posit the sublate-posit process. A=
first disjunct
B = second
The
relation that exists between A and B in disjunction is expressed by the wedge (v).
Conjunctive Syllogism
Conjunctive Syllogism It is one whose major premise p remise is a conjunctive proposition consisting consisting of alternatives (conjuncts), while the minor premise affirms or denies any of the conjuncts, and the conclusion merely expresses whatever follows from its affirmation or denial. Both the minor premise and the conclusion are categorical propositions . It was mentioned that a true conjunctive proposition is one whose alternative alternativess are incompatible.
Rules: Posit one alternative, sublate the other . (Ponendo-tollens) Sublate one alternative, no conclusion .
Posit The
one alternative, sublate the other. other. (Ponendo-tollens)
minor premise affirms one conjunct and the conclusion rejects the other .
Example: The passenger cannot be in the tricycle and in the Bus at the same time; But, he is in the tricycle; (affirmed) He is not in the bus . (rejected)
Sublate one alternative, no conclusion From
the falsity of one conjunct, the truth of the other does not necessarily follow. Example: tric ycle and in the The passenger cannot be in the tricycle Bus at the same time; But, he is not in the tricycle; (rejected) He is in the bus. (affirmed) The
conclusion, ³He is in the bus´ does not follow from the premise. There are vehicles other than the bus that he can take. This fallacy is called the Fallacy of TollendoPonens.
The End
