Introduction to Logic

• The term "Logic" originates from the Greek word "logos," meaning speech, word, or reason.
• Zeno, a Stoic philosopher (c. 340-265 B.C.), was the first to use the Greek word "logike," referring to human thought.
• Aristotle, a significant contributor to logic, called it "organon," which means a tool for establishing truth.
• Andrew H. Bachhuber defines logic as the study of principles of correct reasoning.
• Webster defines logic as the science dealing with the rules of correct reasoning and proof by reasoning.
• Robert Baum asserts that logic is primarily concerned with the type of thinking called reasoning, which is the process of drawing inferences or conclusions from statements.
• Aristotle defines logic as the study of proof.
• Irving Copi defines logic as the study of methods and principles used to distinguish correct arguments from incorrect ones.

History of Logic

• Logic developed in ancient times, in China, India, and Greece.
• Indian logic (Nyaya) explores the nature of knowledge and reasoning, rooted in ancient texts and offering a systematic framework for acquiring knowledge and making valid inferences.
• Greek Logic, particularly Aristotelian Logic, found application and acceptance in science.
• Aristotelian Logic is also known as Traditional Logic.
• Islamic and Christian philosophers further developed Aristotelian Logic in the Middle Ages.

Schools of Logic

• The Stoics, a school of Greek logic, existed in the 5th Century B.C.
• Chrysippus was an important member of the Stoic school.
• The Stoics believed that logic and physics are necessary to differentiate between good and evi

What is Logic? Logic as an Art and Science of Correct Reasoning

• Art gives facility in doing things
• Art aims at beauty and perfection
• Logic as art enables the process of forming definitions, organizing concepts, formulating propositions, and analyzing arguments
• As an art logic helps develop organized and correct reasoning skills
• As a science, logic presents knowledge in a systematic and consistent manner for valid reasoning
• Logic is a speculative science because it deals with what and why reasoning is correct.
• Logic studies the principles governing correct reasoning, the standards for what is accepted or valid reasoning.
• Reasoning is valid if it does not violate any of these principles.
• Irving Copi states that reasoning is correct if the premises provide adequate grounds for accepting conclusions.

Reasoning vs. Thinking

• Reasoning differs from thinking, which refers to any activity of the mind in layman terms.
• Reasoning is one form of thinking that applies logical principles, which is not true for other classifications of thinking.
• Andrew Bachhuber states that reasoning is a kind of thinking in which we try to solve a problem, make a decision, or determine what is true, and therefore thinking with a purpose.
• According to Camacho, remembering, imagining, reflecting, envisioning, or daydreaming simply make things present to our minds without following the rules of logic.

Classifications of Logic: According to its Nature

• Natural Logic is the natural ability to reason in simple, ordinary manners affecting daily life.
• Natural Logic is known as common sense.
• Scientific Logic is the reasoning ability fully cultivated and sharpened to handle difficult and complicated matters.

Classifications of Logic: According to its Method

• Deductive Logic establishes specific conclusions based on universally assumed principles.
• Inductive Logic establishes universal or general truths based on specific or definite assumed principles.

Material/Formal Object of Logic

• Material Logic refers to the content of the proposition and investigates the truthfulness and falsity of every statement in an argument
• Formal Logic refers to the structure of the argument
• Formal Logic offers different principles on how to arrange the argument in a logical manner

The value and Importance of Logic

• Proper understanding of logical argument principles and methods develops skills and habits of reasoning with clarity, coherence, validity, and spontaneity.
• Logic helps in the interpretation of facts and events.
• Logic enables students to decide more wisely.
• Logic helps approach other subjects or disciplines positively.
• Logic contributes to the quality of life and the growth of every individual.
• Logic is necessary preparation for philosophy and law.

The Scope of Logic

• The study of logic aims to assist students' minds in discovering truth/reaching the ultimate objective.
• Logic studies principles, methods, and laws of correct reasoning as bases towards attaining truth.

The Three Acts/Operations of the Mind

• Simple Apprehension is the formation of ideas.
• Simple apprehension is simple because there is no denial and affirmation of anything yet
• example: Students, study, lesson
• Judgment is the second act of the mind that occurs after perceiving an idea.
• Judgment is looking at the similarities and differences of two ideas, comparing them, and proclaiming whether they agree or disagree.
• According to Corazon Cruz, Judgment is either an affirmation or negation.
• Affirmation is also called composition because we join two ideas together while negation is called division because we separate two ideas from one another
• example: students are studying their lessons
• Reasoning is an activity of the mind by which we establish conclusions or new truths from formerly assumed truth.
• Reasoning is the mental process of establishing a conclusion with high certainty from the given data
• Reasoning is synonymous with inference
• Inference is constructing new propositions patterned and based on given data

Two Kinds of Inference

• Immediate Inference constructs a new proposition directly from the given propositions, without a medium and is a revision of the given proposition without involving new truth
• example: All students are studying lessons --> Therefore all students are not non-studying their lessons
• Mediate Inference establishes a conclusion based on the given data with a medium which involves a new truth
• example : All students are studying their lessons--> John Paul is studying his lessons

Limits of Logic

• Logic is limited by the fact that It is an instrument of reason, relying on certain procedures to arrive at the truth
• therefore it does not offer direct, instant knowledge of the material world
• Logic is not a monopoly of truth
• Many other truths exist outside the arena of logic.
• Andrew H. Bachhuber states that since we cannot think unless we first have something in our minds to think about, logic presupposes means of attaining truth over which it has no control.

Other Sources of Truths Outside Logic

• Human experience is A source of truth
• Many philosophers and educators believe that "experience is the teacher" because we learn a lot from experiences.
• Confidence and Reliance on the Authority is A source of truth
• Confidence in authority leads to the acceptance of truths.
• Because logic and experience can't provide all truths, we often need to accept other truths relayed by responsible authorities.
• Universally Recognized and Accepted principles as a source of truth
• These established and evident principles have existed for many years and are understandable by virtue of common sense and include laws, norms, etc.

Simple Apprehension

• First act of the mind is the formation of ideas, the act of calling simple apprehension.
• It is an activity of the mind by which we perceive the quiddity or essence of a thing.

Simple Apprehension and Terms

• Quidity = the essence of something (whatness)
• Essence= intrinsic nature or characteristic quality that makes a thing what it is
• without it, it couldn't be itself

Idea & Term

• IDEA: originates from the Greek word eidos, meaning image
• Idea is the intellectual image or picture of the essence of a thing.
• Webster defines idea as a "mental representation of something perceived through the sense"
• The first step in forming an idea is through the phantasm of the imagination
• A mental representation expressed and known through terms (expressions of ideas or concepts)
• TERM: expressions of ideas or concepts. Comes for Latin term terminus (last/final).

Definitions of Terms

• Term is a necessary conventional sign expressing an idea or concept
• Term is necessary because it plays an important role in communication
• Without them, we resort to body language / facial expression
• Term is a word (or combo of words) used as the subject/predicate term expressing an idea or concept
• Not every word = a term (prepositions, conductions, adverbs, articles - co-significant, needs pairing to form an idea)

Comprehensive and Extensive Terms

• Comprehension of a term refers to the sum-total of all essential aspects signified by the term (intelligible elements/notes that constitute the essence of them).
• Comprehension does NOT include deducible elements derived from the essence OR accidentals/characteristics that are not totally necessary.

Extensive Divisions

• Extension of term refers to the application of term to all subjects signified
• Extension is absolute because there is no expression
• Functional applications refer to term to all subjects as indicated in the preposition (more limited)
• There are 3 kinds of functional extension:
  1. Universal term applies to all subjects
  2. Particular term applies to part of the whole that is determinately designated
  3. Singular term applies to that part of the whole that is definite designated

Classification of Terms

• The terms (according to expression): universal particulars, singular

To determine terms

• Identify the subject of the proposition
• Identify a quantifier article or any other indicator used in the position
• Understand the meaning of preposition
• Look at the way this proposition is constructing every word, indicated here in

Universal Terms Indicators

• Any all each every, whatever with out express modifiers
• Term could still be in universal even in the essence of absence of any of these modifiers or the tickles
• Long that will all 2 subjects signified by the term
• Articles "A" "AN" and "The"

Particular Terms Indicators

• Stand for and indeterminately designated part of a whole could be an individual object or more with out expression specified etc.
• Particular modifiers
• General proposition

Singular Terms Indicators

• Stands for one individual subject or group
• Singular Indicators: Proper names, Superlatives, Demonstrative pronoun adjectives, Nounds considered in plural(grammerically), The articles

Comprehension and Expression

• Greater the comprehension --> lesser the extension
• The greater the comprehension --> the greater the expression

Univocal/Equivocal

• Terms according to Signification
• Uni=One
• Univocal
• Homo= same, Logos = study. having one meaning apply to different contexts
• Equivocal -
• Terms with may be similar to our writing/pronunciation, but completely different meaning went applied
• Analogous -Term is one which is commonly used -To express meanings partly, but not holy the same

Judgement and Simple Apprehension

• Simple apprehension which expressed into TERMS --and building the terms we're now going to be contracting into making PROPOSITIONS, and it is the second act of the mind is judgment to a certain extent

Defining Judgement

• It is a second act mean that occurs after proceeding an idea
• Saying something about that we perceive
• We carefully look to at the similarities and differences of two of those ideas compare them, and and proclaim those agree or disagree within another
• Terms that agree, disagree in each to see if S is P, in order to see it is S is not P
• Affirmation and Negation - also meaning if you affirm is a statement that are saying as belong the classes of P vice versa if not not 1000
• Propostions have truth values - either true or false
• There are two classifications of statement in logic:
  1. Categorical propositions
  2. Hypothetical populations

Standard Categorical Statements

• In logic, categorical proposition is that asserts or denies that all or some of the members of the category
• Categorical proposition is an unconditional statements

Quantity and Quality

• Quantity(are we referring whether the categorical statements is universal / singular or particular

• Quality(are we referring that statements is(Affirmative/Assertive Negative or Denial)

Elements of a Preposition

• Subject
• the copula -VERB =Affirmitive/Assetsive or Negation
• Predicate

In terms of the Distribution, what constitutes:

• Distributed( totally included, totally excluded.

• Undistributed - Partially (not at all of the cross are include in the other other cost

Hypothetical Statements.

• These are conditional statement that has three kinds of classifications, here is that the first one is conditional proposition statement itself
• Expressed under condition or relation dependent that can depend between two populations

Conditional and Conjuction

• If and unless and and or and unless, where, suppose, in case - that the main objective is to find connectives Conjunction

• And is like and "and" statements for conjunctions. The statement can be true. Only of both of the statement must be true

• Disjunction:

• In order for the statement to be or false. Only if both the segment of polls, otherwise is true is or is the symbol or P or Q statement so conjunction "or" and now we have a disjunctive statement.

Explore the fundamentals of formal logic and its applications. Understand its primary focus, goals, and contributions to reasoning and critical thinking. Learn how logic functions both as a science and an art.