Proposition (Logic Slide 4)

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Proposition (Logic Slide 4)

  1. 1. Acts of the Intellect The Acts/Operations of the Intellect
  2. 2. Judgment The second act of the intellect by which it pronounces the agreement or disagreement between terms and ideas. It is the act by which the intellect compares and expresses the objective identity or non-identity between ideas. Ideas in themselves are neither true nor false. Truth comes in when the intellect compares and pronounces whether two ideas agree or disagree with each other.
  3. 3. Example : The term “ lady ” and the term “ beautiful ” are neither true nor false. But when the intellect compares these two terms and expresses whether they agree or disagree in a statement, then we can say whether the statement is true or false. Thus, the sentence “The lady is beautiful.” could now be said to be true or false. The intellect making judgment therefore either affirms or denies. The mental product of judgment is called “ enunciation ” and is defined as “ mental judgment ”.
  4. 4. PROPOSITION Definition: A PROPOSITION is a statement in which anything whatsoever is affirmed or denied. Example: “ A dog is an animal” “A dog is not a cat.” <ul><li>A proposition posits simple existence. </li></ul><ul><li>It affirms or denies the subject. </li></ul><ul><li>It is expressed by what grammarians call a “declarative” sentence. It must be distinguished from a question, exclamation, wish, command & entreaty. </li></ul>
  5. 5. Attributive Proposition A proposition in which the predicate (P) is affirmed or denied of a subject (S). Three basic elements of an attributive proposition: 1.) Subject that about which something is affirmed or denied. 2.) Predicate is what is affirmed or denied of the subject.
  6. 6. 3. Copula In the affirmative proposition, the copula (is, am & are) joins, unites or “copulates” the predicate with the subject; the subject is declared to exist as something identical with the predicate. In the negative copula (is not, am not & are not) separates, or divides the predicate from the subject.
  7. 7. Example: “ A dog is an animal” “ A dog is not a cat” Animals Dogs Pigs Rats Dog Cat
  8. 8. Note: For a proposition to be negative, the particles must modify the copula itself. If the negative particles modified either the subject or the predicate, but not the copula, the proposition is affirmative. Example: Socrates is not sick. Some are not seated. No cat has nine tails. None of the students will go. He will never go.
  9. 9. The Quantity (or Extension) of Proposition The quantity, or extension of the proposition is determined by the quantity, or extension of the subject term. Singular A proposition is particular if its subject term is standing for an indeterminately designated portion of its absolute extension. Particular A proposition is singular if its subject term is standing for one definitely designated portion of its absolute extension. Universal A proposition is universal if its subject term is standing for each of the subject that it can be applied.
  10. 10. If the subject term is indeterminate - that is if it is not modified by any sign of singularity (this, that, etc.), particularity (some, A portion of, etc.), or universality (all, every, each, etc) - the proposition is indeterminate. By its sense the quantity of the proposition can be determined. I n case of doubt, assume that it is “particular” and thus avoid attempting to draw more out of the premises that may actually be in them.
  11. 11. Exercise: Classify the following propositions as singular, particular, or universal. 1. Manila is a populous city. 2. That man is sick. 3. Some student is shouting at the top of his voice. 4. All men are mortal. 5. A dog is barking outside my window. 6. Fido is barking outside my window. 7. Our neighbors dog is barking outside my window. 8. A dog is an animal. 9. Dogs are not cats. 10. Pigeons are eating up the newly planted seed.
  12. 12. 11. Pigeons are not mammals. 12. Many men are suffering from arthritis. 14. Whatever is lighter than water floats on water. 15. All students in this room weigh over 2 tons. 16. No student in this room weighs over 200 pounds. 17. Woman is fickle. 18. Romeo is a romantic character. 19. Men are selfish creatures. 20. The Republic of the Philippines is a great nation. 13. Some Filipinos are communists.
  13. 13. The Symbols A, E, I, & O On the basis of both quality and quantity, attributive propositions are designed as A, E, I, & O. These letters are from the Latin words “ a ff i rmo”, which means “I affirm,” and “n e g o ”, which means “I deny”. A, E, I, & O have the following meanings: A & I (the first two vowels of affirmo ) signify affirmative propositions - A either a universal or a singular, and I a particular E & O (the vowels of nego ) signify negative propositions - E either a universal or a singular, and O a particular.
  14. 14. Affirmative Negative Universal & Singular Particular A I E O
  15. 15. Thus, the following are A Propositions: All voters are citizens. Every voter is a citizen. A dog is an animal. The following are E propositions: No dog is cat. Dogs are not cats. I am not a lawyer.
  16. 16. The following are I Propositions: Some houses are white. Many men are selfish. Dogs are pests. The following are O propositions: Some cat is not black. All horses can’t jump. Not every man is a saint.
  17. 17. Exercise: Classify the following propositions as A, E, I, or O 1. All cats are animals 2. No man is immortal by nature. 3. Some roses are red. 4. Gloria is the president of the Philippines. 5. Some roses are not red. 6. This man is not a sailor. 7. No zebras are native to Philippines. 8. Camels are not native to Philippines. 9. Not all basketball players are good students. 10. All basketball players are not good students.
  18. 18. 11. No one who does no work will get any pay. 12. All the members of that class are architecture majors. 14. Whatever is lighter than water floats on water. 15. All students in this room weigh over 2 tons. 16. No student in this room weighs over 200 pounds. 17. Woman is fickle. 18. Romeo is a romantic character. 19. Men are selfish creatures. 20. The Republic of the Philippines is a great nation. 13. Lindberg was not the first to fly across the Atlantic.
  19. 19. Quantity of the Predicate: Rule #1: The predicate is singular if it stands for one individual or group and likewise designates this individual or group definitely. Example: 1. John is not the tallest boy in the room. 2. He is not the first to do that. Rule #2: (Rule on Affirmative Proposition) The predicate of an affirmative proposition is particular or undistributed (unless it is singular). Rule #3: (Rule on Negative Proposition) The predicate of a negative proposition is universal or distributed (unless it is singular).
  20. 20. Exercise: State the quantity of and quality of the following propositions and then state the quantity of the predicate 1. Peter is a rational animal. 2. Peter is not a sailor. 3. Peter is the tallest man in the room. 4. Every man is mortal. 5. Some men are not aviators. 6. The man over there is a Filipino citizen. 7. Bantay is a dog. 8. The noisiest dog I ever heard is barking outside my window. 9. The dog that is barking outside my window is the noisiest dog I ever heard.
  21. 21. 10. No giraffes are native to Philippines. 11. Some athletes are not good students. 12. Bantay is not a cat. 13. A sphere is a solid. 14. A sphere is a solid body bounded by a surface that is equidistant at all its points from a point within that is called its center. 15. A sphere is not plane figure.
  22. 22. Logical Form The basic structure, or the basic arrangement of the parts, of a complex logical unit. Subject (S) - Copula - Predicate (P) The logical Form of the Attributive Proposition Su is P S a P A Su is not P S e P E Sp is P S i P I Sp is not P S o P O Ss is P S a P A Ss is not P S e P E
  23. 23. Reduction to Logical Form Example: “ He writes editorials . ” “ He is a writer of editorials” “ We should elect Smith ” “ The one we should elect is Smith” “ The ones who should elect Smith is we” “ What we should do is elect Smith” Supply words such as “one” thing “ All men have free will” “ All men are ones having free will.”
  24. 24. Example: “ He runs . ” Run - signifying present action “ He is running ” Run - signifying habitual action “ He is a runner ” Mixed type of proposition All but a few will go I - “Most (some) are ones who will go.” O - “The rest (some) are not the ones who will go.”
  25. 25. Exercise: Reduce the following propositions given below to logical form. 1. Time marches on. 2. Cats have whiskers. 3. A distinguished man called on me this afternoon. 4. Man seek wealth. 5. Hardly anyone will go. 6. All horses can’t jump. 7. Mothers generally love their children. 8. Nearly all voted against the bill. 9. Few manage to get all they want. 10. A few will be unable to go.

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