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logic - workbook summary

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Division of logic
Division of logic
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logic - workbook summary

  1. 1. Philosophy is an activity rather than a subject, you do philosophy rather than learn about it. Philosophy is thinking about thinking. Not a theory but a vision of life (darsan). Not merely “love of wisdom” but it signifies a real “possession” of it. Came from Greek words, philos “love” and Sophia “wisdom”
  2. 2. Man is gifted with his rational ability, has the capacity to create his ideas and express it in the manner he would understand and has a capability to organize his thoughts. The study of Logic is geared towards the honing the reasoning and critical ability of man as man would experience things in the world and as man would interact with other people. The study of Logic offers us the following:
  3. 3. 1. To understand the general rules or principles of correct reasoning. 2. To enable man to become a critical and logical thinker. 3. To develop the art and skill of expressing ideas and improve our reasoning skills. 4. To improve judgment skills in evaluating the validity of an argument or soundness of an argument. 5. To identify and avoid the faulty and misleading errors of formal and informal arguments of day to day experience.
  4. 4.  Logic derived from logikewhich means “thought”. Aristotle, the father of logic in his book Analytics, he considered logic as an “organon”. The science in gaining knowledge and a tool of correct thinking. Thus, logic is towards developing correct thinking or reasoning.  The science and art of correct inferential thinking. Logic is an art of reasoning.
  5. 5. An argument is a set of statements of which – the one being argued for – taken to be established as true on the basis of all the others. Supporting statements arecalled premises, while the statement taken to support are conclusion.
  6. 6.  Deductive is the process whereby a particular idea orpremise is established as true based from a general law or principle that is assumed to be true.  Inductiveprocess on the other hand is a reasoning process whereby the human mind processes particular instances to a universal/general truth.
  7. 7.  Logic gives emphasis on the validity of reasoning be it deductive or inductive. 1. Formal Logic concerns the forms of thought or the very structure or pattern of our reasoning process. 2. Material Logicis focused on the truth of the propositions.
  8. 8. 1. Simple Apprehension the simple understanding or grasping the meaning of an idea. This mental activity brings about the use of terms to express such idea. 2. Judgment the comparison of two ideas whether there is agreement or disagreement. This mental activity results with formulation of a proposition. 3. Reasoning the derivation of a new truth from previously established and known truth. This mental activity arrives at the construction of an argument.
  9. 9. The task of understanding, analyzing and evaluating an argument is considering the starting point. An idea is an outcome of a process. Known as an intellectual image or representation of a thin. Serves as a building block of the argumentative process.
  10. 10.  Using our senses, we are able to perceive external realities. Such sensory experience creates an image in the mind. This image is further identified as phantasm or a mental picture of the external object we perceive. The intellect now gives attention to this sense-image in order to make its own representation of the thing. Abstraction which is getting the essential characteristics or elements of the object perceived.
  11. 11. 1. It is a representation  But not a limited representation. 2. It is a representation of an essence  Essence of a thing that makes it what it is. 3. It is a representation of an essence of a thing in the mind  Not in the senses or in the imagination.
  12. 12. 1. Empirical. The kind of idea observable in its nature with use of sensory experience. 2. Theoretical. This idea entails the use of extending devices to perceive such concepts. 3. Metaphysical. This kind of idea exist beyond the realm of space and time.
  13. 13. 4. Fictitious. This kind of idea which is believed as a creation of the mind. 5. Abstract. An idea understood by the mind but not perceived by the senses. 6. Dispositional. An idea pertains to the observable manifestation of a certain operation 7. Evaluative. Used to signify our evaluative judgment on certain matters.
  14. 14.  An idea is just an abstract representation of a thing that we create in our mind. A sensible, artificial, material, arbitrary and conventional sign, expressive of an idea.
  15. 15. Sign is something which stands for something other than itself. Signified thing is made known. Signifying thing makes it known. Connection between the two is the power to signifying thing to convey knowledge.
  16. 16. Comprehension (designation/intention), is the sum total of the characteristics which make up an idea. Notes (intelligible elements) Extension (denotation), particular things were the comprehension can be applied to.
  17. 17. Greater the comprehension, the more specific the term becomes. But the greater the extension, the more general the term becomes.
  18. 18. 1. Singular terms stands for one individual/group and designates it definitely. 2. Particular terms stands for more than one but not all. 3. Universal terms stand for each of the subjects to which is applied to.
  19. 19. 1. Univocal terms signifies the same essence in at least two occurrences of the term. 2. Equivocal terms are used in two or more different senses or meanings. 3. Analogous terms one that is applied to unlike, but related things.
  20. 20. 1. Contradictory terms if one is the simple negation of the other. 2. Contrary terms belong to the same genus but differ from one another. 3. Relative terms one cannot bet understood without the other.
  21. 21. A definition is a statement which explains what a thing is. Definiendum the term to be defined. Definiens a cluster of words that defines that term.
  22. 22. 1. To increase vocabulary 2. To eliminate ambiguity 3. To reduce vagueness 4. To explain theoretically 5. To influence attitude
  23. 23. Stipulative Definitions “self-definition”. Lexical Definitions gives characteristics that can be true or false. Denotative/Extensional Definitions giving examples of the subject.
  24. 24. Ostensive/Demonstrative Definitions points the definition instead of naming. Connotative/Intentional Definitions giving the use of the subject. Synonymous Definitions using another word with the same meaning. Operational Definitions, states that the term is to be applied.
  25. 25. 1. Must be complete. 2. Must not be circular. 3. Must neither be too broad now too narrow. 4. Must not be expressed in ambiguous, obscure or figurative language. 5. Must not be negative where it could be affirmative.
  26. 26. A genus: an existing definition that serves as a portion of the new definition. Genera (more than one genus) The differentia: the portion of the new definition that is not provided by the genera.
  27. 27.  A proposition is defined as a statement in which anything is affirmed or denied. Expressed as a declarative sentence. A discourse that expresses either truth or falsity.
  28. 28. 1. Subject is that about which something is affirmed or denied. 2. Predicate is what is affirmed or denied of the subject. 3. Copula is either “is” or “is not”. It connects the subject and the predicate.
  29. 29. 1. Singular standing for one definitely designated individual or group. 2. Particular for an indeterminately designated portion of its absolute extension. 3. Universal standing for each of the subject of the subjects to w/c it can be applied to.
  30. 30. Affirmative is expresses a positive mood like the use “is” Negative it expresses a negative mood like the use “is not”
  31. 31. Universal-Affirmative(A) Universal-Negative (E) Particular-Affirmative (I) Particular-Negative (O)
  32. 32.  Logical form defined as the basic structure of the part of a complex logical unit.  Complex logical units include proposition and inferences, or arguments but not terms.
  33. 33. Devised by John Venn. It gives us a map of the logical relations between classes.
  34. 34.  A proposition “all S are P”  Diagrammed by shading the area of S which is not P.  E proposition “no S is P”  Diagrammed by shading the area which is both S and P.
  35. 35.  I proposition “some S are P”  Diagrammed by putting an X in the area which is both S and P.  O proposition “some S is not P”  Diagrammed by putting an X in the area of S which is not P.
  36. 36.  Originated with Aristotle. Opposition is recognized when two proposition are the same in terms of their subject and predicate but different or the same in their quantity or quality.
  37. 37.  every S is P” and “some S is not P” are contradictories.  “no S is P” and “some S is P” are contradictories.  “every S is P” and “no S is P” are contraries.  “some S is P” and “some S is not P” are sub contraries.  “some S is P” is a subaltern of “every S is P”.  “some S is not P” is a subaltern of “no S is P”
  38. 38.  Contradictory  difference inquantity and quality.  Contrary  difference in the quantity.  Sub-contrary  difference in the quality.  Sub-alternation  difference in the quantity but the qualityisthe same.
  39. 39.  Law of Contradictions:  1st rule: Contradictories cannot be true together  2nd rule: Contradictories cannot be false together  Law of Contrariety:  1st rule: contraries cannot be true together  2nd rule: contraries can be false together.
  40. 40.  Law of Sub-contrariety:  1st rule: both sub contraries cannot be false together  2nd rule: both sub contraries may be true together  Law of Sub-alternation:  1st rule: the truth of the universal involves the truth of the particular but the truth of the particular does not involve the truth of the universal.  2nd rule: the falsity of the universal involves the falsity of the particular but the falsity of the particular does not involve the falsity of the universal.
  41. 41.  Eduction is the process of immediate inference whereby, from any proposition taken as true, we derive other implied in it, though differing from the first in subject or predicate or both.
  42. 42.  Conversion  Obversion  Contraposition
  43. 43. It is the re-expression of a proposition by interchanging the places of the subject and predicate while preserving its quality.  Rules for Conversion ▪ Interchange S an P ▪ Retain quality ▪ Do not extend any term (retain the quantity except for A proposition)
  44. 44. It is the formulation of a new proposition by retaining the subject and quantity of an original proposition, changing its quality and using as predicate contradictory.  Rules for Obversion ▪ Retain the subject and the quantity of the obvertend ▪ Change the quality. If the obvertend is negative, the obverse must be affirmative ▪ As predicate, use the contradictory of the predicate of the original proposition
  45. 45. Combination of conversion and obversion.  Rules for Contraposition ▪ Contradict the subject and the predicate ▪ Exchange the subject and the predicate ▪ Retain the quality ▪ Retain the quantity except for E proposition (universal becomes particular)
  46. 46. Reasoning  The derivation of a new truth from previously established and know truth. Known as inference which is externally manifested with the construction of an argument.
  47. 47.  Argument  A set of statements of which one – the one being argued for – is taken to be established as true on the basis of all the others. ▪ The supporting statements are called premises. ▪ The statement they are taken to support is called the conclusion.
  48. 48. Deductive is the process whereby a particular idea or a premise is established as true based from a general law or principle that is assumed to be true. (from general to specific) Inductive a reasoning process whereby the human mind processes particular instances to a universal/general truth. (from specific to general)
  49. 49. oConclusion-indicators signals what follows next is the conclusion. oPremise-indicators are words or phrases serve to mark the premises.
  50. 50. To understand arguments and how the conclusion is supported by the premises.
  51. 51. A deductive argument in which a conclusion is inferred from two premises. Two type of Syllogism: Categorical Syllogism and Hypothetical Syllogism.
  52. 52. 1. Minor term = the subject term of the conclusion. 2. Major term = the predicate term of the conclusion. 3. Middle term = appears twice in the premises but not in the conclusion.
  53. 53.  – arrangement of the middle terms in the syllogism. 1.MP 2. PM 3.MP 4.PM SM SM MS MS SP SP SP SP
  54. 54. – order of propositions according to their quality and quantity.
  55. 55.  A valid standard-form categorical syllogism must contain exactly three terms, each which is used in the same sense throughout the argument.  Fallacy of Four Terms.  In a valid standard-form categorical syllogism, the middle term must be distributed in at least one premise.  Fallacy of Undistributed Middle.
  56. 56.  If either term is distributed in the conclusion then it must be distributed in the premises.  Fallacy of Illicit Major Term.  Fallacy of Illicit Minor Term.  No standard-form categorical syllogism having two negative premises is valid.  Fallacy of Exclusive Premises/ Fallacy of Two Negative Premises.
  57. 57.  If either premise of a valid standard-form syllogism is negative, then the conclusion must be negative.  Fallacy of Drawing an Affirmative Conclusion from a Negative Premise.  No standard-form categorical syllogism with a particular conclusion can have two universal premises.
  58. 58.  An argument can be evaluated by using the rule of categorical syllogism as exemplified in the previous chapter. But another approach is the use of Venn diagram. The technique is simply to draw in the premises. If we find that we have drawn in the conclusion follows, then the argument is valid.
  59. 59.  A deductive argument which uses hypothetical propositions.They do not contain direct, straightforward assertion of agreement or disagreement between the subject and predicate. They express the disagreement of the truth or falsity of one statement upon the truth or falsity of another statement.
  60. 60. A syllogism which contains a conditional proposition as the major premise. Conditional propositions are “if statements.” There are two parts to such a proposition. The truth of the antecedent follows the truth of the consequent;The falsity of the antecedent follows the falsity of the consequent.
  61. 61.  Antecedent (1st part) gives the ground, the reason, the cause.  Consequent (2nd part)gives the result, the dependent, the effect.  From the truth of the antecedent follows the truth of the consequent; the falsity of the consequent follows the falsity of the antecedent.
  62. 62. Fallacy of Denying the Antecedent. Fallacy of Accepting the Consequent.
  63. 63.  It is one whose major premise consists of a disjunctive proposition. A disjunctive proposition is an “either-or” statement.  Strict Disjunction – Proper Disjunction ▪ Components are called disjunct, can neither be true nor false together.  Broad Disjunction – Improper Disjunction ▪ Is a hypothetical syllogism whose major premise is broad disjunctive proposition. ▪ Is a complete disjunctive proposition in which one or both disjuncts must be true. The disjunction must be complete. Otherwise, truth may be found in the missing disjunct.
  64. 64.  The least difficulties among the hypothetical syllogisms. In the major premise states that two or more things are impossible at the same time.  Conjuncts can be true at the same time; but they may all, be false together.  From the truth of one member follows the falsity of the others; but from the falsity of one member, the truth of the other(s) does not follow.