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INTRODUCTION to LOGIC

INTRODUCTION to LOGIC. Michael Jhon M. Tamayao, M.Phil. PHILO 11 Cagayan State University. Topic Outline. I. The Basic Concepts Definition of Logic The core of logic Logic vs. Psychology The three operations of the mind The corresponding verbal expressions The two types of arguments

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INTRODUCTION to LOGIC

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  1. INTRODUCTIONtoLOGIC Michael Jhon M. Tamayao, M.Phil. PHILO 11 Cagayan State University

  2. Topic Outline I. The Basic Concepts • Definition of Logic • The core of logic • Logic vs. Psychology • The three operations of the mind • The corresponding verbal expressions • The two types of arguments • The first logician II. Logic as an “Organon” of the Mind towards Truth • (Logic) As a tool • (Logic) As a means to attain truth • Truth is independent from Validity

  3. Objectives • At the end of the discussion, the participants must be able to: • Define logic. • Understand the fundamental concepts and principles of logic. • Distinguish the two types of logic and their subdivisions. • Understand why and how Logic is an organon towards truth.

  4. Part I:The Basic Concepts We will discuss in this section the fundamental concepts in logic.

  5. HOW DO WE DEFINE LOGIC? • “Logic is the science of correct reasoning.” • It is systematic body of knowledge. • It pertains to the study of rules and principles for making correct arguments. • “Logic is a science that serves as a tool for the mind to reason out correctly.”

  6. HOW DO WE DEFINE LOGIC? • Rules should be understood, not memorized. • Understanding means being able to apply.

  7. WHAT IS THE CORE OF LOGIC? • The core of the science of logic lies in its collection of universal and eternal rules that ascertains truth in the flow of man’s statements. • Logic is a discovery of the “norms” of correct thinking. • Logic is primarily concerned with “arguments.”

  8. WHAT IS THE CORE OF LOGIC? LOGIC PSYCHOLOGICAL PROCESSES LOGICAL RULES (for making arguments) ANALYSIS OF LANGUAGE STANDARD FORMS OF PROPOSITIONS ANALYSIS OF PROPOSITIONS & TERMS

  9. WHAT IS THE CORE OF LOGIC? LOGIC PSYCHOLOGICAL PROCESSES ARGUMENTS ANALYSIS OF LANGUAGE STANDARD FORMS OF PROPOSITIONS ANALYSIS OF PROPOSITIONS & TERMS

  10. WHAT IS THE DIFFERENCE BETWEEN LOGIC AND PSYCHOLOGY? • Logic ≠ Psychology LOGIC (Logical Rules) Psychology

  11. WHAT IS THE DIFFERENCE BETWEEN LOGIC AND PSYCHOLOGY? tells what the mind ought to do Studies the actual Way the mind works, i.e. what the mind is. It is a normative science; it imposes rules and norms for thinking. It is an empirical science; it studies actual facts.

  12. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? • The three operations of the mind… • Simple apprehension is the mental operation by which the mind knows the meaning of a term. • Judgment is the mental operation that affirms (or denies) something about anything whatsoever. • Inference is the mental operation that proves a judgment by using supporting judgments.

  13. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? KNOWING JUDGING INFERING

  14. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? BLACK HAIR I AM YOUNG YOUNG

  15. WHAT ARE THEIR VERBAL EXPRESSIONS?

  16. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? BLACK BLACK HAIR HAIR I AM YOUNG I AM YOUNG YOUNG YOUNG

  17. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? MENTAL OPERATION HAVING BLACK HAIR IS A MANIFESTAION OF YOUTH, I HAVE BLACK HAIRS. I AM YOUNG.

  18. WHAT ARE THE OPERATIONS HAPPENING IN THE REASONING PROCESS? HAVING BLACK HAIRS IS A MANIFESTAION OF YOUTH, I HAVE BLACK HAIRS. I AM YOUNG. HAVING BLACK HAIRS IS A MANIFESTAION OF YOUTH, I HAVE BLACK HAIRS. I AM YOUNG. MENTAL OPERATION

  19. Inference (Mental Operation) Supporting Judgment Inferred Judgment Argument (Verbal Expression) Premise(s) Conclusion WHAT ARE THEIR VERBAL EXPRESSIONS?

  20. WHAT ARE THE TYPES OF ARGUMENTS? 1. Deductive arguments - arguments that start with a more universal statement and conclude with a less universal statement. Ex. All Filipinos are Asians; (most universal) All Cagayanos are Filipinos; Therefore, all Cagayanos are Asians. (least universal) • If the premises are true, then the conclusion is necessarily true.

  21. WHAT ARE THE TYPES OF ARGUMENTS? • 2. Inductive arguments - arguments that start with a sufficient list of particular statements and end with a probable universal statement as inferred from the premises. Ex. Mike, Paul, Bong, & Ton are Cagayanos Mike has a dark complexion. Paul has a dark complexion. Bong has a dark complexion. Ton also has a dark complexion. :: Cagayanos probably have dark complexions. • The conclusion is only “probably” true.

  22. Aristotle (384-322 BC) WHO IS THE FIRST “LOGICIAN”? • Aristotle came up with the first complete system of Logic, which was written under the title of “Organon” or “Instrument” (of Knowledge). • His Logic is classified as “syllogistic.”

  23. LOGIC Expressed in language Expressed in symbols propositional predicate syllogistic categorical hypothetical WHAT ARE THE TYPES OF LOGIC?

  24. ARISTOTELIAN SYLLOGISTIC LOGIC • Aristotelian syllogistic logic is “categorical.” • This type of logic is based on the mechanism of correlating three terms or categories in the premises to arrive at a necessarily true conclusion. • Example 1: All dogs are animals; All terriers are dogs; Therefore, all terriers are animals.

  25. ARISTOTELIAN SYLLOGISTIC LOGIC Animals Dogs terries 1st premise: All dogs are animals. 2st premise: All dogs are terries.

  26. Animals Dogs ARISTOTELIAN SYLLOGISTIC LOGIC 1st premise: All dogs are animals. terriers 2st premise: All terriers are dogs. Conclusion: All terriers are animals.

  27. ARISTOTELIAN SYLLOGISTIC LOGIC • Example 2: All actors love the spotlight; Wowowilly is an actor; Therefore, Wowowilly loves the spotlight.

  28. ARISTOTELIAN SYLLOGISTIC LOGIC Spotlight-lover Actor Willy 1st premise: All actors love the spotlight 2st premise: Wowowilly is an actor.

  29. Spotlight-lover Actors ARISTOTELIAN SYLLOGISTIC LOGIC 1st premise: All actors love the spotlight Willy 2st premise: Wowowilly is an actor. Conclusion: Wowowilly loves the spotlight.

  30. Recap for Part I LOGIC (RULES) CORRECT ARGUMENTS SIMPLE APPREHENSION TERMS REASONING PROCESS JUDGMENT PROPOSITION INFERENCE ARGUMENT

  31. Recap for Part I • Define Logic. • What is the core of logic? • How is logic different from psychology? • What are the three operations of the mind? What are their corresponding verbal expressions? • What are the two kinds of arguments? • Briefly discuss Aristotle’s syllogistic logic.

  32. Part II:Logic as an “Organon” of the Mind Towards Truth This section will discuss the nature of logic as an instrument of the mind towards truth. With this in mind, we will also discuss the notion of truth and its independence from validity.

  33. Logic as a tool… • Logic is not an exclusive science studied for its own sake. Rather, it is an instrument used by all the sciences in clarifying their points and arguments. • Logic is the ideal tool of the mind.

  34. Obama Clinton Logic as a means to attain truth… Truth is the correspondence of the mind with the reality. I won the Democratic Presidential race!

  35. Logic as a means to attain truth… • The truth-value of a statement is whether it is “true” or “false.” • Truth is not the same with validity. • Truth is strictly ascribed to propositions, and validity is properly ascribed to arguments. • Proving the truth of propositions properly lies in the hands of the empirical scientists. • Valid arguments become tools for truth because it “conserves” the “presupposed” truth of the propositions.

  36. Truth is independent from Validity… • An argument can be valid but at the same time have false propositions. • Ex. All animals are man; (False) Valid Form (AAA-1) All chairs are animals; (False) Therefore, all chairs are man. (False)

  37. Truth is independent from Validity… • An argument can have true propositions but at the same time have invalid form. • Ex. All creatures have a purpose; (True) All angels are creatures; (True) Therefore, all angels are not man. (True) • The argument is invalid because it has four terms.

  38. Truth is independent from Validity… • The truth of propositions does not necessarily make the argument valid, and the validity of the argument does not necessarily make its propositions true. • But, if the given propositions in the premises of the argument are recognized as true, then the conclusion is necessarily true. • If the propositions of the arguments are all true and the entire form of the argument is valid, then it is said to be a “sound” argument.

  39. WHAT IS A SOUND ARGUMENT? • Example of a Sound Argument. All men are rational animals; All teachers are men; Therefore, all teachers are rational animals. • Logic aims at giving sound arguments.

  40. LOGIC AND ETHICS “truly” true THEORETICAL REASON TRUTH PRACTICAL MIND “truly” good GOOD WILL

  41. LOGIC AND ETHICS Truth about the nature of concepts “truly” true THEORETICAL REASON TRUTH PRACTICAL “truly” good Truth about the value of actions

  42. LOGIC AND ETHICS LOGIC Truth about the nature of concepts THEORETICAL REASON PRACTICAL MORALITY Truth about the value of actions

  43. LOGIC AND ETHICS LOGICAL REASONING All man are mortals Socrates is a man. Socrates is mortal. THEORETICAL TRUTH & VALIDITY OF CONCEPTS MORAL REASONING We should not kill This situation urges me to kill Pedro. Thus, I must not succumb to the urge of killing Pedro in this situation. PRACTICAL TRUTH OF THE VALUE OF CONCEPTS

  44. HOW CAN WE RELATELOGIC AND ETHICS? Killing is a sin. To terminate the life of Pedro is killing. Thus, To terminate the life of Pedro is a sin.

  45. HOW CAN WE RELATELOGIC AND ETHICS? Killing is a sin. To terminate the life of Pedro is killing. Thus, To terminate the life of Pedro is a sin.

  46. Recap of Part II SOUND ARGUMENTS TRUTH VALIDITY CONCLUSION

  47. Recap of Part II • Discuss the idea of Logic as a tool. • Explain the propositional notion of truth. • What is the difference between truth and validity? • Give examples of a valid argument with false propositions. • Give examples of an invalid argument with true propositions. • How can validity be an avenue for truth? • How can we relate logic and ethics?

  48. Part III:Summary This section will summarize through questions and answers the different topics discussed in preceding sections.

  49. IV. Summary (Q &A) • What is Logic? • “Logic is the science of correct reasoning.” • Logic is a discovery of the “norms” of correct thinking. And as such, it is primarily concerned with “arguments.” • Logic is a “prescriptive” or “normative” science, and not a “descriptive” science.

  50. LOGIC Expressed in language Expressed in symbols propositional predicate syllogistic categorical hypothetical IV. Summary (Q &A) • What are the types of logic?

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