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INFERENCE AND
SYLLOGISM
It is the mental activity whereby starting with several judgments which we relate to one another, we arrive at a new judgment which necessarily follows from the preceding ones.
Every reasoning process, involves a number of previously known truths. These truths are called premises. The reasoning process also involves the knowledge of a new truth (the conclusion).
It is the drawing of a conclusion from one or more premises. There are 2 kinds of inference: immediate and mediate.
Immediate – when a conclusion is drawn from only one premise.
Mediate – when a conclusion is drawn from two premises.
The mental product of inference is called an argument: The external expression of which is called a 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 (affirmative) or separates (negative) the first two terms
It is an inference that draws the conclusion in an absolute manner. Here, when the first 2 propositions are posited as true, the third must also be true.
All animals are substances.
But, a dog is an animal.
Therefore, a dog is a substance.
It is an inference which concludes with certainty, affirming or denying a statement, from the affirmation or denial of another.
If the students plagiarize, then they should be punished.
The students plagiarize.
Therefore, they should be punished. Either you pass the test, or you fail.
You pass.
Therefore, you did not fail.
All humans are mortal.
All Filipinos are humans.
Thus, all Filipinos are mortal.
Major premise: All humans are mortal.
Minor premise: All Filipinos are humans.
Conclusion: All Filipinos are mortal. Major term (T) – predicate of the conclusion
Minor term (t) – subject of the conclusion
Middle term (M) – found in both premises.
Figure 1 M T
t M
Thus, t T SUB-PRE Some scholars are wide-readers.
Some Filipinos are scholars.
Thus, Some Filipinos are wide-readers. III-1
Figure 2 T M
t M
Thus, t T PRE-PRE All great scientists are college graduates.
Some professional athletes are college graduates.
Thus, some professional athletes are great scientists
AII-2
Figure 3 M T
M t
Thus, t T SUB-SUB All artists are egoists.
Some artists are paupers.
Thus, some paupers are egoists. AII-3
Figure 4 T M
M t
Thus, t T PRE-SUB No gamblers are quitters.
All quitters are losers.
Thus, no losers are gamblers. EAE-4
1. No heroes are cowards.
Some soldiers are cowards.
Thus, some soldiers are not heroes.
2. All sacrifices are rewarding.
Some acts of cheating are rewarding.
Thus, all acts of cheating are sacrifices.
3. All pilots are risk-takers.
Some pilots are not happy-go-lucky.
Thus, some risk-takers are not happy-go-lucky.
4. No nuclear-powered submarines are commercial vessels, so no warships are commercial vessels, since all nuclear-powered submarines are warships.
Some animals are two-legged.
All people are animals.
Thus, all people are two-legged.
All animals are mortal.
Some animals are dogs.
Thus, some dogs are mortal.
1. There must only be 3 univocal terms, each of which occurs twice but not in the same proposition.
A father is a male parent.
The Holy Pope is a father.
Thus, the Holy Pope is a male parent.
*Fallacy of Equivocation
All flowers are beautiful.
All roses are flowers.
Thus, all roses are beautiful.
2. The middle term must not occur in the conclusion.
A goddess is a female.
A goddess is a deity.
Thus, a goddess is a female deity.
*Fallacy of Misplaced Middle Term
3. The middle tem must be distributed atleast once, in the premises.
All lions are animals. Tu (+) Mp
All men are animals. tu (+) Mp
Thus, all men are lions. tu (+) Tp
* Fallacy of the Undistributed Middle Term
All trees are plants.
All kamagong are plants.
Thus, all kamagong are trees.
4. If a term is distributed in the conclusion, then such term must be distributed in the premise.
Some lawyers are holy. Tp (+) Mp
No criminals are holy. tu (-) Mu
Thus, no criminals are lawyers. tu (-) Tu
* Fallacy of the Illicit Major Term
All birds have wings. Mu (+) Tp
All birds are animals. Mu (+) tp
Thus, all animals have wings. tu (+) Tp
* Fallacy of the Illicit Minor Term
5. There must be not 2 particular premises; one premise atleast must be universal.
Some priest are holy. Tp (+) Mp
Some nuns are holy. tp (+) Mp
Thus, some nuns are priests. tp (+) Tp
*Fallacy of Two Particular Premises
Some scholars are wide-readers.
Some Filipinos are scholars.
Thus, Some Filipinos are wide-readers.
6. If one premise is prticular, the conclusion must be particular.
All lawyers are professionals. Tu (+) Mp
Some criminals are professionals. tp (+) Mp
Thus, some criminals are lawyers. tp (+) Tp
* Fallacy of Undistributed Middle Term
Some animals are two-legged.
All people are animals.
Thus, all people are two-legged.
* Fallacy of Universal Conclusion drawn from a Particular Premise
7. If the conclusion is negative, only one premise must be negative.
No tenor is a soprano.
No soprano is a baritone.
Thus, no baritone is a tenor.
*Negative Premises
All lawyers are professionals.
Some criminals are not professionals.
Thus, some criminals are lawyers.
*Fallacy of Illicit Exclusion
8. Two affirmative premises cannot give a negative conclusion.
All stones are hard. Mu (+) Tp
Some diamonds are stones. tp (+) Mp
Thus, some diamonds are not hard. tp (-) Tu
* Fallacy of a Negative Conclusion drawn from Affirmative Premises
1. No heroes are cowards.
Some soldiers are cowards.
Thus, some soldiers are heroes.
2. All sacrifices are rewarding.
Some acts of cheating are rewarding.
Thus, all acts of cheating are sacrifices.
3. Some pilots are not happy-go-lucky.
All pilots are risk-takers.
Thus, some risk-takers are happy-go-lucky.
4. Some mosquitoes are blood-suckers.
All vampires are blood-suckers.
Thus, all vampires are mosquitoes
Figure 1 (SUB-PRE) M T
t M
Thus, t T
1. The major premise must be universal.
2. The minor premise must be affirmative.
The major premise must be universal. Some males are married.
All priests are males.
Thus, some priests are married.
The minor premise must be affirmative. All surgeons are doctors.
No anesthesiologists are surgeons.
Thus, no anesthesiologists are doctors.
BARBARA – AAA CELARENT – EAE DARII – AII FERIO - EIO
Figure 2 (PRE-PRE) T M
t M
Thus, t T
1. One premise must be negative.
2. The major premise must be universal.
One premise must be negative.
All great scientists are college graduates.
Some prof. athletes are college graduates.
Thus, some prof. athletes are great scientists.
The major premise must be universal.
Some lawyers are liars.
No honest citizens are liars.
Thus, no honest citizens are lawyers.
CESARE – EAE CAMESTRES – AEE FESTINO – EIO BAROCO - AOO
Figure 3 (SUB-SUB) M T
M t
Thus, t T
1. The minor premise must be affirmative.
2. The conclusion must be particular.
The minor premise must be affirmative.
All murdered are criminals.
No murderers are saints.
Thus, no saints are criminals.
The conclusion must be particular.
Some movies are violent.
All movies are works of art.
Thus, all works of art are violent.
DARAPTI – AAI DISAMIS – IAI DATISI – AII FELAPTON – EAO BOCARDO – OAO FERISON - EIO
Figure 4 (PRE-SUB) T M
M t
Thus, t T
1. If the MP is affirmative, the mp must be universal.
2. If the mp is affirmative, the conclusion must be particular.
3. If one premise is (-), the MP must be universal
If the MP is affirmative, the mp must be universal.
Some males are criminals.
Some criminals are females.
Thus, some females are males.
If the mp is affirmative, the conclusion must be particular.
All postmen are workers.
Some workers are professors.
Thus, all professors are postmen.
If one premise is negative, the MP must be universal.
Some criminals are terrorists.
No terrorists are women.
Thus, no women are criminals.
BRAMANTIP – AAI CAMENES – AEE DIMARIS – IAI FESAPO – EAO FRESISON - EIO
1. Is AOO a valid mood under figure 1?
2. Is OAO a valid mood under figure 2?
3. Is AEE a valid mood under figure 3?
4. Some politicians are pro-poor.
Some teachers are pro-poor.
Thus, some teachers are politicians.
5. All carabaos are black.
Some cats are black.
Thus, some cats are carabaos.
Its major premise is a hypothetical proposition, while its minor premise and conclusion are categorical propositions. Here, there is no major term (P), minor term (S), & middle term (M).
If the students plagiarize, then they should be punished.
The students plagiarize.
Therefore, they should be punished.
1. Conditional Syllogism
MP – Hypothetical Proposition
mp – Categorical Proposition
C – Categorical Proposition
1. Posit the antecedent, posit the consequent (MODUS PONENS)
-If the antecedent is affirmed in the mp, the consequent must also be affirmed in the conclusion. Consequent’s truth follows from the antecedent’s.
Ex: If someone wins in the lotto draw, one becomes a millionaire.
Son Gokou wins in the lotto draw.
Thus, Son Gokou becomes a millionaire.
* p כ q
p
q ؞ VALID
2. Sublate the consequent, sublate the antecedent.
(MODUS TOLLENS)
- If the consequent is rejected in the mp, the antecedent must also be rejected in the conclusion. Antecedent’s falsity follows from the consequent’s.
Ex: If the best pres. cand. is Miguel Imburnal, then the worst pres. cand. is Pepot Kuyukot.
The worst pres. cand. Is not Pepot Kuyukot.
Thus, the best pres. cand. is not Miguel Imburnal.
* p כ q
~q
p~ ؞ VALID
3. Posit the consequent, no conclusion (Fallacy of Affirming the Consequent)
- Committed when the consequent is affirmed in the mp.
Ex: If it is raining, then Rolando is absent.
Rolando is absent.
Thus, it is raining.
(There must be no conclusion)
* p כ q
q
p ؞ INVALID
4. Sublate the antecedent, no conclusion (Fallacy of Rejecting the Antecedent)
- It is committed when the antecedent is rejected in the mp.
Ex: If it is raining, then Roland is absent.
It is not raining.
Thus, Roland is not absent.
(There must be no conclusion)
* p כ q
~p
q~ ؞ INVALID
1. If this month is December, next month is January.
This month is not December.
Thus, next month is not January.
2. If you failed in the test, you did not pass.
You did not pass.
Thus, you failed.
*EXEMPTIONS
Identify the proper conclusion to these c.syllogisms if the mp is valid. If the mp is invalid, place NO CONCLUSION.
1. If you cheat, you will fail.
You did not cheat.
_________________________
2. If UST beats ADMU in this game, we will be exempted from the final exam.
UST did not win in this game.
_________________________
3. If each O is P, then no R is S.
All R is S.
_________________________
4. If every B is C, then each D is I.
No D is I.
_________________________
5. If every B is C, then each D is I.
No B is C.
__________________________
MP – Disjunctive Proposition
mp – Categorical Proposition
C - Categorical Proposition
Ex: Jojo Kulot is either guilty or not guilty.
Jojo Kulot is guilty. (affirmed)
Thus, Jojo Kulot is not guilty. (rejected)
1. Strict Disjunctive
- “Only one member is true & both cannot be true”
Ex: Either Angge is a truthful person or a liar.
She is telling the truth.
Thus, she is not a liar.
*p ˅ q
p
q~ ؞
*Strict Disjunctive follows the rule:
1. Posit one or more member of the MP in the mp, then sublate the remaining in the conclusion.
(Ponendo-tollens)
*p ˅ q *p ˅ q
p or q
q~ ؞ p~ ؞
The accused is either guilty or not guilty.
He is guilty.
Thus, he is not not guilty
2. Sublate one or more member of the MP in the mp, then posit the remaining in the conclusion.
(Tollendo-ponens)
*p ˅ q *p ˅ q
~p or ~q
q ؞ p ؞
The military operation in Basilan is either successful or unsuccessful.
It is not successful.
Thus, it is unsuccessful.
*Broad Disjunctive
- “Only one member is true, but both may also be true.”
- Sublate 1 or more members of the MP in the mp, then posit the remaining in the C.
Either Pepe likes to dive or play chess.
Pepe does not like to dive.
Thus, he likes to play chess.
*p ˅ q *p ˅ q
~p or ~q
q ؞ p ؞ It is possible that he does not likes to do both.
Pepe was not able to finish his thesis either because he is lazy or deadened.
He is not lazy.
Thus, he is deadened.
*p ˅ q
~p
q ؞ Pepe was not able to finish his thesis either because he is lazy
or deadened.
He is lazy.
Thus, he is not deadened.
*p ˅ q
p
q~ ؞
MP – Conjunctive Proposition
mp – Categorical Proposition
C - Categorical Proposition
Rule 1: Posit one alternative, sublate the other.
Ex: You cannot be a good husband and philosopher at the same time.
You are a good husband.
Thus, you are not a good philosopher.
* ~(p • q)
p
q~ ؞
Rule 2: Sublate one alternative, no conclusion
Ex: The passenger cannot be in the tricycle and in the bus at the same time.
He is not in the tricycle.
Thus, he is in the bus.
* ~(p • q)
~p
q ؞
1. (p כ q) כ r
~ q
(r כ p)~ ؞
2. (p כ q) ˅ (q ˅ r)
~(q ˅ r)
q כ p ؞
3. (p כ q) • r
p כ q
r~ ؞
4. If Angola achieves stability, then both Botswana and Chile will adopt more liberal policies. But Botswana will not adopt a more liberal policy. Thus, Angola will achieve stability.
1. If Montana suffers a severe drought, then, if Nevada has its normal light rainfall, Oregon’s water supply will be greatly reduced. Nevada does have its normal light rainfall. So if Oregon’s water supply is greatly reduced, then Montana suffers a severe drought.
2. p כ (q • r)
(q ˅ r) כ s
s כ p ؞
