The verbal expression of the mental judgment is called proposition Proposition is group of ideas of which anything is affirmed or denied For ancient thinkers, proposition is the enunciation of truth or falsity.
Types of Proposition
Categorical: A categorical proposition unites or separates two concepts by means of the linking verb “to be.”
Hypothetical: A hypothetical proposition unites or separates, not two concepts but two enunciations by means of a non-verb copula
PROPOSITIONS
Examples of Categorical Propositions
Some sharks are not dangerous. Every kind act is meritorious.
PROPOSITIONS
Examples of Hypothetical Propositions
If it is a car, it has a motor. If you are a Filipino, then you are a native of the Philippines.
PROPERTIES OF PROPOSITIONS
Every proposition has quality and quantity
Quality: the quality of a proposition maybe affirmative or negative A proposition that has “no” or “not” is negative. This is oftentimes determined by the copula
PROPERTIES OF PROPOSITIONS
Quantity: the quantity of a proposition is either universal or particular. The proposition is universal when what is being affirmed or denied of the subject term is its whole extension and particular when what is being affirmed or denied is just part of its extension.
THE FOUR CATEGORICALS
A – stands for affirmative and universal propositions (All S is P) Examples: All bachelors are unmarried men. Every butterfly is an insect.
FOUR CATEGORICALS
I – stands for affirmative and particular propositions (Some S is P) Ex. Some Filipinos are Moslems. Some OLAS students are naughty.
FOUR CATEGORICALS
E – stands for negative and universal propositions ( No S is P or All S is not P) Examples: No speaker of Congress in the Philippines has become the president. No bird has four legs. Cagayan is not a Visayan province.
FOUR CATEGORICALS
0 – stands for negative and particular propositions (Some S is not P or Not All S is P) Examples: Some senators are not lawyers Not every journalist gives accurate and well-founded report.
State the class of each of the proposition
No one who died for his country died in vain. Some students in this class are Cebuanos. Pentagons are polygons. Centipedes are not snakes. Dr. Jose Rizal is a national hero. Most congressman are not giving up their pork barrel.
Three senators are running for the presidency. No one is above the law. The mantis is an insect. Not every plant bears fruits.
RECOGNIZING ARGUMENTS
An argument is a group of propositions in which one proposition is asserted to be true on the basis of the other proposition An argument is not categorized as true or false but as either logical or illogical, valid or invalid sound or unsound
ARGUMENTS
The proposition which is claimed to be true is called c alled the “conclusion” while the proposition which serves as support of the conclusion is called “premise.”
Premise and Conclusion Indicators
Premise-indicators: some, because, for, given that, as indicated by, if
Conclusion-indicators therefore, thus, hence, so, accordingly, consequently
PROPERTIES OF ARGUMENTS
TRUTH – refers to the conformity of proposition to reality LOGIC – refers to the connection between the premises and the conclusion SOUNDNESS – property of argument as a whole
PROPERTIES OF ARGUMENT
An argument maybe logical while one or more of its premises are false. For example: All Filipinos are Asians. But Bill Clinton is a Filipino. Therefore, Bill Clinton is Asian.
PROPERTIES OF ARGUMENTS
There are arguments whose premises are true but are not logical: Cows have horns. Horses are not cows. Therefore, horses have no horns.
Using your common-sense knowledge, which of the following are sound arguments, which are merely logical and which are not logical at all?
If you win the lotto jackpot, you will be a millionaire. Lucio Tan is a millionaire. Therefore he must have won the lotto jackpot. All birds fly. But eagles are birds, therefore, eagles fly.
No one under the age of eighteen is eligible to vote in national elections. My philosophy teacher is not under the age of 21, therefore, he is eligible to vote in national elections. If a figure has five sides, it is a polygon. A pentagon is a polygon. Therefore, a pentagon has five sides.
Miriam College is in Katipunan avenue. Katipunan avenue is in Marikina. Therefore, Miriam College is in Marikina. Fidel Ramos is older than Joseph Estrada. Estrada is older than Miriam Santiago. Therefore, Santiago is younger than Ramos. No fish have lungs. Whales have lungs. Therefore, whales are not fish.
Determine whether the following are argument or non-arguments
I believe we must use clean, safe nuclear power. The more dependent we become on foreign oil., the less l ess our national security is enhanced. Many people think that thunder is caused by lightning. This is a mistake There ought to be a law prohibiting the use of animals in research. After all, we would not tolerate that kind of treatment to humans.
There are three things that last: faith hope and love. But the greatest of this is love. He who does not love does not know God for God is love. There is a plan to make former Pres. Marcos a national hero. However, several groups of people, including the Church and the CPP-NPA are strongly protesting the plan.
SYLLOGISMS
The verbal expression of a deductive reasoning or inference is the syllogism. A syllogism is an oral discourse showing the agreement or disagreement between two terms on the basis of their respective relation to a common third term.
The Minor Term (S) is the subject of the conclusion and found in the minor premise The Major Term (P) is the predicate of the conclusion and found in the major premise The Middle Term (M) is the term that appears both in the premises but not in the conclusion.
Examples of Valid Syllogisms: All heroes are freedom loving Andres Bonifacio is a hero. Therefore, Bonifacio is freedom loving. All humans are rational. The elephant is not rational. Therefore the elephant is not human.
Examples of Invalid Syllogisms Every mother is pregnant. But Lakambini is a mother Therefore, Lakambini is pregnant. All Catholics are Christians. But, Anglicans are not Catholics. Therefore, Anglicans are not Christians
Supply the missing proposition: A body of knowledge is a science. But ___________________. Therefore, Logic is a science. No voter is an alien ________________. Therefore, some citizens are not aliens.
_______________________. But a chair is material. Therefore, a chair is not a spirit. Words are symbols. But nouns are words. Therefore, __________________. Every X is Y. But __________________. Therefore, no W is Y.
Human is the subject matter of psychology. But an eagle is not human. Therefore, ________________. ______________________. But you are honest. honest. Therefore, you are not a liar. All false beliefs are dangerous. But some religious beliefs are false. Therefore, ______________________.
Rules of Syllogism 1.
2.
3.
4.
There must be three and only three terms No term must have a greater extension in the conclusion than it has in the premises. The Middle Term must not appear in the conclusion. The middle term must be universal at least once
Rules of Syllogism Two affirmative premises yield an affirmative conclusion. Two negative premises yield no conclusion. When one premise is negative, conclusion must be negative; when one premise is particular, conclusion must be particular. When both premises are particular, there is no conclusion.
Valid Moods and Figures
First Figure (sub-prae) Second Figure (prae-prae) Third Figure (sub-sub) Fourth Figure (prae-sub)
Valid Moods and Figures
First – BARBARA, CELARENT, CELARENT, DARII, FERIO Second – CESARE, CAMESTRES, FESTINO, BAROCO Third – DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON Fourth – BRAMANTIP, CAMENES, DIMARIS, FESAPO, PRESISON
No gentlemen is cruel. But Some policemen are cruel Therefore, some policemen are not gentlemen. Some scientists are Filipinos But some scholars are scientists. Therefore, some scholars are Filipino. No goat is able to speak But no cat is able to speak Therefore, no cat is a goat.
Every dictator is powerful But the president is powerful Therefore, the president is a dictator. Nobody is perfect But he is a nobody. Therefore, he is perfect. Every book has a title But some men have titles Therefore, some men are books.
No poor is rich But every beggar is poor. Therefore, no beggar is rich. No rebel is loyal to the constitution But some soldiers are rebels. Therefore, some soldiers are loyal to the constitution. Every murder is immoral But euthanasia is murder. Therefore, euthanasia is immoral.
Exercises on Categorical Syllogisms Morphines are analgesics Aspirins are not morphines Therefore, aspirins are not analgesis All snakes are reptiles All reptiles are cold-blooded Therefore, all snakes are cold-bloo c old-blooded ded Some plants are not green. Mushrooms are plants Therefore, some mushrooms are not green A dog is four-legged animal A parrot is not a four-legged animal animal A parrot is not a dog.
No angel has a body. A man is not an angel Therefore, a man has a body. Most amphibians lay their eggs in ponds or rivers Frogs are amphibians amphibians Therefore, most frogs lay their eggs in ponds or rivers. Cats are domesticated animals. A mountain lion is a cat. Therefore, a mountain lion is a domesticated animal
Some figures are round. The circle is a figure. Therefore, the circle is round. Bachelors are unmarried men. Joey is unmarried. Therefore, Joey is a bachelor. Everything visible is real. The soul is not visible. Therefore, the soul is not real.
HYPOTHETICAL SYLLOGISMS
A hypothetical syllogism is a syllogism that contains hypothetical proposition as its premise. Hypothetical syllogism is of three kinds: Conditional Disjunctive Conjuctive
Conditional Syllogism
A conditional syllogism is a syllogism whose major premise is a conditional proposition. A conditional proposition is a compound proposition which asserts that one member is true (the “then” clause), on the condition that the other is true (the “if” clause)
Implications or Connections
Logical implication – the implication means that the antecedent flow with logical necessity into the consequent
Examples: If he is a catholic, then he believes in Christ. If he is a fiscal, then he must be a lawyer.
Causal implication
Its implication is suggestive of cause and effect relationship.
Examples: If you touch a live wire, you will be electrocuted. If the plants are always in the shade, then they will not flower well.
Contextual implication The implication depends on the will of the person or on particular circumstances Examples: If I win the lotto jackpot, then I will travel around the world. If you do not pay your debt now, I will never lend you money again.
Rules for Conditonals When the minor premise affirms the antecedent, the conclusion must affirm the consequent Example:
If it rains, then the ground will be wet. It rained. Therefore, the ground is wet.
Rules for Conditionals
When the minor premise denies the consequent, the conclusion must deny the antecedent.
If you are alive, then you are not dead. But you are dead. Therefore, you are not alive.
Exercises for Conditional Conditional Syllogism If Moises has weak lungs, he will not be able to join the team. He was not able to join the team. Therefore, he has weak lungs. If Mark is not quiet, we will frighten the fish away. Mark made a lot of noise. Therefore, he frightened the fish away. If this syllogism commits the fallacy of illicit major, it is invalid. It does not commit the fallacy of illicit major Therefore, it is valid.
If Fr. Chris will not go abroad, the seminarians will be happy. The seminarians will not be happy. Therefore, Fr. Chris will go abroad. Unless he gets a tutor, Wilmar will fail in logic. He did not get a tutor. Therefore, he will fail in logic. Anyone who earns a bachelor degree must take up logic. Procopio has not taken up logic yet. Therefore, he does not have a bachelor degree.
The coach is worried that the football team will lose if it rains during the game next Saturday. He thinks the team doesn’t play very well when the field is muddy. But the weather is forecast is for sunny weather for the whole weekend. That’s good news, it means the team will win the game on Saturday. Lyndon has decided to run for president of the student’s council. That’s a pity because he is bound to lose. If Lyndon is going to win the election, he will have to be known to a lot of students. But hardly anyone knows Lyndon.
