INTRODUCTION to LOGIC

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INTRODUCTIONtoLOGIC

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

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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

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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.

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Part IThe Basic Concepts

• We will discuss in this section the fundamental
  concepts in logic.

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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.

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HOW DO WE DEFINE LOGIC?

• Rules should be understood, not memorized.
• Understanding means being able to apply.

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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 mans statements.
  
• Logic is a discovery of the norms of correct
  thinking.
• Logic is primarily concerned with arguments.

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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
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WHAT IS THE CORE OF LOGIC?
LOGIC
PSYCHOLOGICAL PROCESSES
ARGUMENTS
ANALYSIS OF LANGUAGE
STANDARD FORMS OF PROPOSITIONS
ANALYSIS OF PROPOSITIONS TERMS
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WHAT IS THE DIFFERENCE BETWEEN LOGIC AND
PSYCHOLOGY?

• Logic ? Psychology

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

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WHAT ARE THE OPERATIONS HAPPENING IN THE
REASONING PROCESS?
KNOWING JUDGING INFERING
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WHAT ARE THE OPERATIONS HAPPENING IN THE
REASONING PROCESS?
BLACK
HAIR
I AM YOUNG
YOUNG
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WHAT ARE THEIR VERBAL EXPRESSIONS?
Mental Operations Verbal Expression
Simple Apprehension Term
Judgment Proposition
Inference Argument
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WHAT ARE THE OPERATIONS HAPPENING IN THE
REASONING PROCESS?
BLACK
BLACK
HAIR
HAIR
I AM YOUNG
I AM YOUNG
YOUNG
YOUNG
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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.
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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
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WHAT ARE THEIR VERBAL EXPRESSIONS?
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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.

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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.

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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.

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WHAT ARE THE TYPES OF LOGIC?
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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.

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

• Example 2
• All actors love the spotlight
• Wowowilly is an actor
• Therefore, Wowowilly loves the spotlight.

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ARISTOTELIAN SYLLOGISTIC LOGIC
Spotlight-lover
Actor
Willy
1st premise All actors love the spotlight
2st premise Wowowilly is an actor.
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ARISTOTELIAN SYLLOGISTIC LOGIC
1st premise All actors love the spotlight
Willy
2st premise Wowowilly is an actor.
Conclusion Wowowilly loves the spotlight.
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Recap for Part I
LOGIC (RULES)
CORRECT ARGUMENTS
SIMPLE APPREHENSION
TERMS
REASONING PROCESS
JUDGMENT
PROPOSITION
INFERENCE
ARGUMENT
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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 Aristotles syllogistic logic.

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Part IILogic 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.

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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.

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Logic as a means to attain truth

• Truth is the correspondence of the mind with the
  reality.

I won the Democratic Presidential race!
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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.

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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)

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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.

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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.

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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.

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LOGIC AND ETHICS
truly true
THEORETICAL
REASON
TRUTH
PRACTICAL
MIND
truly good
GOOD
WILL
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LOGIC AND ETHICS
Truth about the nature of concepts
truly true
THEORETICAL
REASON
TRUTH
PRACTICAL
truly good
Truth about the value of actions
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LOGIC AND ETHICS
LOGIC
Truth about the nature of concepts
THEORETICAL
REASON
PRACTICAL
MORALITY
Truth about the value of actions
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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
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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.
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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.
ethics Recognition of the value of the action. (practical reason) To know the undesirability of this reality. (practical reason)
logic Identification of the definition or meaning of the concept. (theoretical) How it is positioned in the argument Identification of the definition or meaning of the concept. (theoretical) How it is positioned in the argument
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Recap of Part II
SOUND ARGUMENTS
VALIDITY
TRUTH
CONCLUSION
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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?

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Part IIISummary

• This section will summarize through questions and
  answers the different topics discussed in
  preceding sections.

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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.

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IV. Summary (Q A)

• What are the types of logic?

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IV. Summary (Q A)

• What are the operations of the mind and their
  corresponding verbal expressions?

Mental Operations Verbal Expression
Simple Apprehension Term
Judgment Proposition
Inference Argument
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IV. Summary (Q A)

• What are the parts of an argument?
• An argument is composed of two parts, the
  premise(s) and the conclusion. The premises are
  the supporting propositions, while the conclusion
  is the proposition being supported.
• What are the different kinds of arguments?
• Deductive arguments - arguments that start with
  a more universal statement and conclude with a
  less universal statement.  
• Inductive arguments - arguments that start with a
  sufficient list of particular statements and end
  with a probable universal statement as inferred
  from the premises.

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IV. Summary (Q A)

• What is truth?
• Truth is the correspondence of the mind with the
  reality.
• Truth is strictly ascribed to propositions, and
  validity is to arguments.
• Truth is independent from Validity
• A sound argument is a valid argument with true
  propositions.