Terms, Judgments, and Propositions
Term: an idea expressed in words either spoken or written
Classification of Terms:
Singular : one that stands for only one definite object
Examples:
1) Table
2) Socrates
3) Tree
Collective : one that is applicable to each and every member of a class taken as a whole but not to an individual taken singly.
Examples:
1) orchestra
2) platoon
Particular : one that refers to an indefinite number of individuals or groups. Some signifiers of a particular term: some, a number of, several, almostall, practically all, at least one, a few of, not all, and the like.
Examples:
1) some Sillimanians
2) almost all students
3) several politicians
Universal : one that is applicable to each and every member of a class. Some signifiers of a universal term: No, All, Each, Every
Examples:
1) All Sillimanians
2) Every politician
Judgment: the mental act of affirming of denying something.
Proposition: judgment expressed in words either spoken or written.
Example:
1) President Noynoy Aquino is a good president.
2) President Noynoy Aguino is not a good president.
Kinds of Propositions used in Logic
Categorical : a proposition that expresses an unconditional judgment.
Example: 1) The Japanese people are hard-working.
Hypothetical : a proposition that expresses a conditional judgment
Example: 1) If it rains today, then the road is wet.
Elements of a Categorical Proposition
- Subject (S)
- Copula (C)
- Predicate (P)
Quantity of a Categorical Proposition
Particular : one that contains a particular subject term.
Example: 1) Some Sillimanians are foreigners.
Universal : one that contains a universal subject term.
Example: 1) All Filipinos are Asian.
Note: It is the quantity of the subject that determines the quantity of the proposition. Thus, if the subject is particular, then the proposition is particular; if the subject is universal, then the proposition is universal.
Note: If the subject of the proposition does not contain a signifier, the quantity of the proposition must be based on what the proposition denotes.
Quality of a Categorical Proposition
Affirmative : if the copula of the proposition does not contain a negation sign “not”
Example: 1) Some Sillimanians are brilliant.
Negative : if the copula of the proposition contains a negation sign “not”
Example: 1) Some Sillimanians are not brilliant.
Four Basic Types of Categorical Propositions
Universal Affirmative (A) : All men are mortal.
Universal Negative (E) : No men are mortal.
Particular Affirmative (I) : Some men are mortal.
Particular Negative (O) : Some men are not mortal.
Translating Categorical Propositions into their Standard Form:
Standard Forms:
A proposition : All + subject + copula + predicate
E proposition : No + subject + copula + predicate
I proposition : Some + subject + copula + predicate
O proposition : Some + subject + copula + not + predicate
Examples:
- A: Every priest is religious.
Standard form: All priests are religious.
- E: Every priest is not religious.
Standard form: No priest is religious.
- I: Almost all politicians are corrupt.
Standard form: Some politicians are corrupt.
- O: Several politicians are not corrupt.
Standard form: Some politicians are not corrupt.
- Nuns are girls.
Standard from: All nuns are girls.
- Cheaters are not trustworthy.
Standard from: No cheaters are trustworthy.
- Fruits are delicious.
Standard form: Some fruits are delicious.
- Flowers are not fragrant.
Standard form: Some flowers are not fragrant.
Square of Opposition
Contrary: A E; differ only in quality
Rules: If one of the contraries is true, the other is false.
If one is false, the other is doubtful.
Examples:
1) A:
E:
2) E:
A:
Sub-contrary: I O; differ only in quality
Rules: If one of the sub-contraries is true, the other is doubtful.
If one is false, the other is true.
Examples:
1) I:
O:
2) O:
I:
Sub-alternation: A I and E O; differ only in quantity
Rules: If the universal is true, the particular is true.
If the universal is false, the particular is doubtful.
If the particular is true, the universal is doubtful.
If the particular is false, the universal is false.
Examples:
1) A:
I:
2) E:
O:
3) I:
A:
4) O:
E:
Contradiction: A O and E I; differ both in quality and quantity
Rules: One member of each part is a denial of the other
Examples:
1) A:
O:
2) E:
I:
3) O:
A:
4) I:
E:
Argument and Syllogism
Argument: consists of one or more propositions offered as evidence for another proposition
Syllogism: an argument which consists of three propositions which are so related so that when the first two propositions are posited as true, the third proposition must also be true.
Example: All lawyers are professionals.
Some criminals are professionals.
Therefore, some criminals are lawyers.
Elements of a Syllogism:
Major premise: the proposition that contains the major term
Minor premise: the proposition that contains the minor term
Conclusion: the third proposition whose meaning and truth are implied in the premise
Terms used in Syllogisms:
Major term (T): the predicate of the conclusion
Minor term (t): the subject of the conclusion
Middle term (M): the remaining term in the syllogism which does not appear in the conclusion
8 Rules of Syllogism: refer to the rules used in determining the validity of an argument
1) There must only be three terms in the syllogism: the major, minor, and middle terms.
2) The major and/or the minor term should only be universal in the conclusion if they are universal in the premises.
3) The middle term must be universal at least once.
4) If both of the premises are affirmative, the conclusion must also be affirmative.
5) If one premise is affirmative and the other negative, the conclusion must be negative.
6) The argument (syllogism) is invalid if both of the premises are negative.
7) One premise at least must be universal.
8) If one premise is particular, the conclusion must also be particular.