Logic Textbook by Ricky T. Maaño PDF

**LOGIC** **HISTORY OF LOGIC** \- was developed in the Ancient times: China, India, Greece Nyaya \- Indian logic (Nyaya) is a rich philosophical tradition that explores the nature of knowledge and reasoning. Rooted in ancient texts such as the Nyaya Sutras and Nyaya Bhasya, Indian logic offers a...

**LOGIC** **HISTORY OF LOGIC** \- was developed in the Ancient times: China, India, Greece Nyaya \- Indian logic (Nyaya) is a rich philosophical tradition that explores the nature of knowledge and reasoning. Rooted in ancient texts such as the Nyaya Sutras and Nyaya Bhasya, Indian logic offers a systematic framework for understanding how we acquire knowledge and make valid inferences. \- The Greek Logic, particularly the Aristotelian Logic, found wide application and acceptance in science and\... \- Aristotelian: In philosophy, the term Logic, is also known as Traditional Logic or Aristotelian Logic. \- Aristotelian Logic: It was further developed by Islamic and Christian philosophers in the Middle Ages. **SCHOOL OF LOGIC** Stoics- school of Greek logic in the 5th Century B.C. Chrysippus- an important member of the Stoic school He believed that logic and physics are necessary to differentiate between good and evil. **WHAT IS LOGIC?** 1. **LOGIC**: the term "Logic" originates from the Greek word; logos meaning speech,, word or reason..( In Defense of Logic ( An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.11) ·         Zeno, the stoic (c.340-265 B.C), was the first philosopher who used the Greek word : logike,  meaning human thought.( In Defense of Logic ( An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.11) ·         Aristotle, one of the great contributors in the field of logic, calls it organon, which means a tool for establishing truth.(In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.11) ·         Andrew H. Bachhuber defines logic as " the study of principles of correct reasoning".(Introduction to Logic. New York: Appleton-Century, Reprinted National  Bookstore, Inc., 1968) ·         Webster defines it as "the science that deals with the rules of correct reasoning and with proof by reasoning.( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.11) ·         Robert Baum asserts that "logic is concerned primarily with the type of thinking called reasoning, the process by which an inference or conclusion is drawn from a statement or series of statements".( In Defense of Logic.( An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.11) ·         Aristotle defines logic as the " study of proof". ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.11) ·         Irving Copi in his book define logic as " the study of the methods and principles used in distinguishing correct from incorrect arguments". ".(Introduction to Logic.7th ed. New York: Macmillan publishing Co., reprinted, Edca Publishing and Distributing Co., Quezon City , 1982.)  2. **LOGIC IS AN ART AND SCIENCE OF CORRECT RESONING** A. **Logic as an Art** ·         Art, in general, gives facility in doing things. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.11) ·         Art aims at beauty and perfection.(In Defense of Logic (An Introduction) , Revised Edition,  Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.12) ·         In logic, art facilitates our minds in making definitions, organizing concepts, formulating propositions, and analyzing arguments. (In Defense of Logic (An Introduction) , Revised Edition,  Ricky T. Maaῇo, Philippines Copyright 2010 , pg.12) ·         Logic as an art helps students to develop a habit of organized and correct reasoning. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.12) ** ** B. **Logic as a Science** ·         Logic is a science because it is a body of knowledge arranged in a systematic and consistent manner presented as valid reasoning. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010, pg.12) ·  It is a speculative science because it deals with what and why reasoning is correct. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.12) C. **Correct Reasoning** · Logic studies the principles governing correct reasoning,  these principles serve as the bases or standards of what is accepted or valid reasoning. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.12) · Reasoning can be classified as valid if it does not violate anyone of these principles. ( In Defense of Logic  (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.12) · Irving Copi states, " if the premises provide adequate grounds for accepting conclusions, if asserting the premises to be true warrants asserting the conclusion to be true also, then the reasoning is correct, otherwise the reasoning is incorrect".(Introduction to Logic.7th ed. New York: Macmillan publishing Co., reprinted, Edca Publishing and Distributing Co., Quezon City , 1982.) 3. **REASONING  VS. THINKING** Reasoning is different  from thinking. In the language of the layman , thinking refers to any activity of the mind.(In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.13) ·  Reasoning is only one form of thinking but there is an application of logical principles which is not true with other classifications of thinking.(In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.13) · 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. It is thinking with a purpose."(Introduction to Logic. New York: Appleton-Century, Reprinted National  Bookstore, Inc., 1968) · According to Camacho in his book introduction to logic, " when we do remember , imagine, reflect, envision, or daydream we simply make things present to our minds  without following the rules and principles of logic.(Introduction to Logic. Manila: St. Anthony Book Service, 1992 )  \ 4.  **CLASSIFICATIONS OF LOGIC** A. According to its Nature 1\. Natural Logic  Natural Logic is the natural ability of the man to reason in simple and ordinary manners affecting  his life. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.13) Natural Logic is also known as common sense. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.14) 2\. Scientific Logic  Scientific Logic is the reasoning ability of man fully cultivated and sharpened, in order to handle those difficult and complicated matters. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo Philippines Copyright 2010,, pg.14) B.  According to its Method 1\. Deductive  Logic  Deductive is one classification of logic that establishes specific conclusions based on universally assumed principles.(In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.15)  2. Inductive  Logic Inductive is one classification of logic that establishes universal or general truths based on specific or definite assumed principles. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.16) MATERIAL OBJECT OF LOGIC C. According to its Purpose 1\. Material Logic Material Logic refers to the content of the proposition. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.16) It investigates the truthfulness and falsity of every statement used in an argument. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.16) FORMAL OBJECT OF LOGIC 2\. Formal Logic Formal Logic refers to the structure of the argument. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.17) It offers different principles on how we may possibly arrange the argument in a logical manner.  (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.17) THE VALUE AND IMPORTANCE OF LOGIC 5\. THE VALUE OF LOGIC A. Proper understanding of the principles and methods of logical argument will develop skills and habits of reasoning out with clarity, coherence, validity, and spontaneity. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.19) B. Logic helps students in interpretation of facts and events. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.19) C. Logic is practical tool enabling students to decide more wisely. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.19) D. Logic helps students to approach other subjects or disciplines positively. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.19)          E. Logic contributes to the quality of life and to the growth of every individual.  (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo Philippines Copyright 2010, pg.20) F. Logic is necessary preparation for philosophy and law. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo Philippines Copyright 2010, pg.20)  \ 6.SCOPE OF LOGIC The ultimate objective of the study of logic is to assist the minds of the students in the discovery of truth. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010  ,pg.20) It studies the principles, methods and laws of correct reasoning as bases towards the attainment of truth. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.20) THE THREE ACTS/OPERATION OF THE MIND Mental Processes and Expression 1\. SIMPLE APPREHENSION The first act of the mind Is the formation of ideas which we call simple apprehension. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo,  Philippines Copyright 2010, pg.27) It is simple because there is no denial and affirmation of anything yet.(In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010,  pg.27) SIMPLE APPREHENSION(example) \- Students, study , lesson 2\. JUDGMENT Judgment is the second act of the mind that occurs after we perceive an idea. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.27) In judgment we carefully look at the similarities and differenc7es of two ideas ,compare them, and proclaim whether these ideas agree or disagree with one another. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.27) 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". (Introduction to Logic. Manila: National Bookstore, Inc. 1983) JUDGMENT(example)\ Students are studying their lessons. 3\. REASONING Reasoning is an activity of the mind by which we establish conclusions or new truths from formerly assumed truth. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.28) It is the mental process of establishing conclusion with high certainty from the given data. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.28) Reasoning is synonymous with inference.Inference is constructing a new propositions patterned  and based on the given data.. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.28) TWO KINDS OF INFERENCE 1\. Immediate Inference- is constructing new proposition  from the given propositions directly, i.e. without a medium. It is a revision of the given proposition without new truth involved.. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.28) Example: \- All students are studying their lessons\    Therefore, all students are not non-studying their lessons 2\. Mediate Inference on the other hand is establishing a conclusion based from the given data with medium. There is a new truth involved. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.28)\ \ Example: \- All students are studying their lessons\    Therefore , John Paul is studying his lessons. LIMITS OF LOGIC The limits of logic are based on two things: 1\. Because logic is an instrument of reason and rely on certain procedures to arrive at the truth , it does not offer a direct and instant knowledge of the material world. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.20) 2\. Logic is not a monopoly of truth. Many other truth exist outside the arena of logic. (In Defense of Logic (An Introduction), Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.20).  Andrew H. Bachhuber  in his book introduction to logic states, "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". (Introduction to Logic. New York: Appleton-Century, Reprinted National  Bookstore, Inc., 1968)   9.OTHER SOURCES OF TRUTHS OUTSIDE LOGIC:                                A.  Human Experience\ · Many philosophers and educators believe that "experience is the teacher ". This is so because we learn a lot from experiences. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo Philippines Copyright 2010, pg.21 ) B. Confidence and Reliance on the Authority\ · Confidence on the authority results to the acceptance of truth. Because logic and experience cannot provide all  truths, we need to accept other truths relayed by responsible authority. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 ,pg.21 ) C. Universally Recognized and Accepted\ · These principles are established and evident to us. Many of these principles exist for a number of years and understable by virtue of common sense. These principles include laws , norms, etc. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 , pg.21 ) SIMPLE APPREHENSION \- The first act of the mind is the formation of ideas which we call simple apprehension. 1.  SIMPLE  APPREHENSION AND TERMS A.  The Object of Simple Apprehension: THE ESSENCE OF A THING ·.Simple Apprehension as discussed in the previous chapter it is an activity of the mind by which we perceive the quiddity or essence of a thing. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) · Quiddity means the essence or whatness of a thing. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) · Webster defines essence as the "intrinsic nature or characteristic quality of a thing". It is what makes a thing as it is. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) · Essence of a thing is the characteristic intrinsic of a thing. In the absence of this intrinsic. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.21 )characteristic, a thing cannot be in itself. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) B. IDEA AND TERM b.1. **What is Idea?** · The term "idea" originates from the Greek word eidos, meaning image.(In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) · It is the intellectual image or picture of the essence of a thing..(In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.34 ) · Webster defines idea as a "mental representation of something perceived through the sense". (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35 ) · Phantasm of the imagination is considered the first step in forming an idea. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35) · An idea is a mental representation  of a thing expressed and made known through terms. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35 ) b.2.  **What is term?** · Terms are expressions of ideas or concepts. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35 ) · Terms comes from the Latin word terminus meaning, meaning last or final. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35 ) · Every term is a word but not every word is a term, like words fall under prepositions, conjunctions, adverbs and articles are co-significant words(also called "syncategorematic words" )and therefore in need of another word to form an idea. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.35-36 ) b.3. **First definition of Term** · Term is a necessary conventional sign expressing an idea or concept. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.36 ) b.4. **Necessary ** · A term is necessary because it is important in communication. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.36 ) · Without terms we will resort  to using other means of communication  such as : body language and facial expression. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.36 ) b.5.** Second definition of a Term** · Term is a word or combination of words used as as subject or predicate of  a proposition. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.38 ) C. THE COMPREHENSION AND EXTENSION OF TERMS · Comprehension of term refers to the sum-total  of all  the essential aspects signified by the term. These essential aspects could also mean those intelligible elements (or notes) that constitute the essence of  term. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.41 ) Comprehension of term does not include the following: a) Deducible elements derived from the essence , such as: (in the case if man)social being , abilityto speak,  etc. (In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.42 ) b) Accidentals or characteristics that are not totally necessary, such as: a black man, a Filipino or American, talented, a professional, etc.(In Defense of Logic (An Introduction) Revised Edition, Ricky T. Maaῇo, Philippines Copyright 2010 pg.42) c) Extension of term refers  to application of term to all subjects signified by the term(RM,pg.42)                                         Two kinds of Extension of Terms: 1.  Absolute Extension (RM,pg.42) \- Refers to application of term to all subjects that have existed before, that exist at the present moment, and will exist in the future. \- It is absolute because there is no restriction as to the application of terms 2.  Functional Extensions(RM,pg.43) \- Refers to application of term to all subjects as indicated in the proposition. \-  It is also called relative extension, because the application is limited to what is expressed by the proposition There are three kinds of functional extension(RM,pg.43)  a\. Universal term- applies to all subject b\. Particular term-applies to part of the whole that is determinately designated c\. Singular term- applies to  that part of the whole that is definitely designated.   **\ D. Classification of Terms** a\. According to Extension · Extension of term is defined as the application of a term to the subject explicitly indicated by the proposition.(RM,pg.51) · The terms according to extension are: universal, particular, and singular(RM, pg.51) · There are four considerations to determine the extension of terms(RM, pg.51) 1.  Identify the subject of the proposition 2. Identify the quantifier, article or any other indicator used  in the proposition. 3. Understand the meaning of the proposition 4. Look at the way the proposition is constructed and every word indicated therein A. UNIVERSAL TERM · Universal is an extension of term that stands for all subjects to which the term can be applied.(RM, pg.52) Indicators  of Universal  term: a\. Universal  Modifiers, such as: ·  Any, all, each, every, whoever, whatever, whichever, without exception.(RM, pg.52) b\. Universal Ideas · A term could still be universal even in the absence of any of these modifiers or articles as long as it refers to all subjects signified by the term..(RM, pg.52) c\. Articles "A", "An", and "The", that signify universal ideas.(RM, pg.53) B. PARTICULAR TERM · Particular is an extension of term that stands for an indeterminately designated part of a whole. · It could be an individual, object or more without specific or exact designation.(RM, pg.53) Indicators of Particular term: a\. Particular modifiers, such as: · A certain, a number of, some several, few , most, many, a lot of, more, etc. (RM, pg.53) b\. General Proposition · A proposition that is true  to some or great majority of subjects but not all as indicated in the proposition. (RM, pg.53) · The proposition is particular because the term does not apply to every subject. (RM, pg.53) c\. Use of Numbers · Numbers and philosophy are similar in terms of its infinite character.(RM,pg.54) · It cannot be taken  as a whole or a totality, but always a part of it.(RM,pg.54) · As philosophy is a never ending quest for meaning, number also has no end.(RM,pg.54) d\. Articles "A"and "An" that signify particular ideas.(RM,pg.54) C. SINGULAR TERM · Singular is an  extension of term that stands for one individual , object, or group specifically designated. (RM,pg.55) Singular Indicators: a\. Proper names, such as: ·  Quezon City, General Santos City, Corazon C. Aquino, etc. (RM,pg.55) b.  Superlatives, such as : ·  Wisest, most loyal, most behave, better, best, etc. (RM,pg.55) c\. Demonstrative Pronoun and Adjectives, such as: ·  This, that, those, these, etc. (RM,pg.55) ·   Nouns considered as plural English grammar are singular in logic as long as they are definitely  designated. (RM,pg.55) d\. Article "The" signifying definite ideas e\. Personal Pronouns, such as: ·We, they, he, she, our, you, me, her, etc. (RM,pg.55)  The General Principles on Comprehension and Extension · The greater the comprehension, the lesser the extension, and the lesser the comprehension, the greater the extension.(RM,pg.43) ·  According to Fr. Piῇon, there'is an  inverse relation between comprehension and extension(Piῇon, Manuel T. Logic Primer. Manila : National Bookstore, Inc., 1980.)\          **According to Signification** · Terms According to signification have three classifications: univocal, equivocal, and analogous.(RM,pg.73) A. Univocal Term · The term "Univocal" comes from the word "uni" meaning one.(RM,pg.73) · The word is sometimes called "homologous" originates from the Greek words: homo, meaning one or the same, and logos, meaning study.(RM,pg.73) · In univocal or homologous , we deal with terms  having the same or one meaning when they are applied to different contexts. (RM,pg.74) B. Equivocal Term · Equivocal are terms that maybe similar in writing or pronunciation but completely different in meaning when applied  to different contexts. · The term "equivocal" originates from the Latin words as aequae and vocis, meaning similarity in sound. C. Analogous Term\. An Analogous Term is one which is employed to express meanings partly, but not wholly, the same. After dealing with Simple Apprehension which is expressed in TERMS, and from these TERMS, we can now construct them into making PROPOSITIONS in the second act of the mind-JUDGMENT.  Lesson 3 refers to our discussion on the second mental operation which is JUDGMENT which is expressed in PROPOSITIONS.  Let us try to discuss JUDGMENT in a very specific way: First let us define what JUDGMENT is: Judgment is the second act of the mind that occurs after we perceive an idea (Maaῇo, 2010).  Meaning, we say something about what we perceive.  It is a kind of saying it in a statement way.  We tell or say something about what we see.  So, when I see an apple, I can say in my judgment that: That \"Apple is a fruit.\"  We categorize the term Apple in the group or class of fruits.   In judgment we carefully look at the similarities and differences of two ideas ,compare them, and proclaim whether these ideas agree or disagree with one another(Maaῇo, 2010).  Meaning, in Judgment, we try to check whether these TERMS that we use in the statement agree or disagree to each other as we compare them.  In doing specifically, we try to see their similarity as to whether \"S\"  is \"P\" or different like as to whether \"S\" is not \"P\".  Also, 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"(Maaῇo, 2010).  Meaning, If we affirm a statement, we are trying to say that S is P. It is like saying that S belong to the class of P.  On the contrary, if we negate a statement, we are trying to say that S is NOT P.  It is like saying that S does not belong to the class of P.\ \ FOR EXAMPLE:  \ \"Jose Rizal is a Philippine national hero.\"  In this statement, it appears that it is affirming that Rizal is a Philippine national hero.  Also, in comparing the two TERMS used in the statement, JOSE RIZAL and PHILIPPINE NATIONAL HERO, it shows that there\'s an agreement between the two.\ \"Jose Rizal is not an American national hero.\"  While this statement shows negation of Rizal\'s being an American national hero.  Also, in comparing the two TERMS used in the statement, JOSE RIZAL and AMERICAN NATIONAL HERO, it shows that there\'s an agreement between the two. REMEMBER:  JUDGEMENT is expressed into PROPOSITION.  \"Propositions are statements but not every statement is a proposition.\" Meaning, there are certain statements that we only use in logic.  But first, let us determine the different types of statements or sentences namely: 1.   DECLARATIVE SENTENCES\ 2.  INTERROGATIVE SENTENCES\ 3.  EXCLAMATORY SENTENCES\ 4.  IMPERATIVE SENTENCES\ \ In terms of their meanings and uses, check the picture below: IMG\_257\ \ Nota Bene:  Not all statements can be used in logical arguments.  Only statements that are expressed in declarative form but not all declarative sentences.  In English, we know that sentences are set of words that express a complete thought, but not all can be used as propositions in logic.  For example:\ \ 1.  Sentences with vague or ambiguous terms, such as **\"The sky is blue-ish.\"**\ 2.  Sentences with indexical or context-dependent terms, such as: **\"I am happy.\"\ **3.  Sentences with emotional or evaluate language, such as **\"This cake is awesome.\"\ **4.  Sentence with imperative or interrogative force, such as **\"Close the door!\"** or **\"What is your name?\"\ **5.  Sentences with modal or hypothetical language, such as **\"It might rain tomorrow.\"\ **\ As a general principle:  a declarative sentence can be used as a proposition in logic if it is CLEAR, SPECIFIC, and UNAMBIGUOUS, and if it can be definitively classified as TRUE or FALSE.\ \ PROPOSTIONS have **truth values**.  They are either **TRUE** or **FALSE**.\ \ Also, statement of FACTS can be used in logic, such as **\"Magellan arrived in the Philippines on March 16, 1521.\"  **The reason is that, such statements are considered propositions, which are **DECLARATIVE** sentences that can be either **TRUE or FALSE.  **In this case, the statement is a historical fact, and it can be verified to be true.  So, **STATEMENTS OF FACT** like this one can be used in logical reasoning and argumentation.\ \ \ There are two classifications of statement in logic:\ \ 1.  CATEGORICAL Statements/Propositions\ 2.  HYPOTHETICAL Statements/Propositions\ \ Both statements are used in logical arguments.  This will be fully utilized in arguments pertaining to Categorical and Hypothetical Syllogism.  But what is the difference between the two statements? \ **\ Categorical propositions **declare something unconditionally**, **while** hypothetical propositions **express a conditional relationship between two clauses. \ \ **1.  STANDARD CATEGORICAL STATEMENTS**\ \ CATEGORICAL PROPOSITIONS\ -In logic, a categorical proposition, or categorical statement, is **a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term)**.  When we say ASSERT, we AFFIRM; and when we say DENY, we NEGATE. \ Categorical proposition is an UNCONDTIONAL STATEMENT.\ \ In order for us to determine each type of categorical proposition we have to determine their QUANTITY and QUALITY.  When we say **QUANTITY**, we are referring whether the statement is **UNIVERSAL/Singular** or **PARTICULAR**.  But if we say the QUALITY of the proposition, we are referring whether the statement is \"**AFFIRMATIVE/ASSERTIVE or NEGATIVE/DENIAL.\" **\ \ There are four types of Categorical Propositions.  Below are the types and its corresponding Venn diagram symbol.\ \ \ IMG\_259\ \ Specifically, let us examine and explain each type of propositions:\ \ These are the elements of a proposition: The SUBJECT, the COPULA (this is the VERB that connects the subject and the Predicate)-this can be referred to as the AFFIRMATIVE/ASSERTIVE or NEGATIVE/DENIAL Copula (the quality of the proposition) and the PREDICATE.\ \ **A Proposition **- has a **UNIVERSAL** Quantity and **AFFIRMATIVE/ASSERTIVE** Quality.  This proposition has a UNVERSAL quantifier and an AFFIRMATIVE/ASSERTIVE copula.\ \ **E  Proposition** - has a **UNIVERSAL** Quantity and **NEGATIVE/DENIAL** Quality.  This proposition has a UNVERSAL quantifier and a  NEGATIVE/DENIAL copula.\ \ I  Proposition - has a **PARTICULAR **Quantity and **AFFIRMATIVE/ASSERTIVE** Quality.  This proposition has a PARTICULAR quantifier and an AFFIRMATIVE/ASSERTIVE copula.\ \ O Proposition - has a **PARTICULAR **Quantity and **NEGATIVE/DENIAL** Quality.  This proposition has a PARTICULAR quantifier and a  NEGATIVE/DENIAL copula.\ \ In terms of the **DISTRIBUTION** of the terms, we have to determine the distribution of the subject and predicate term. \ It is **DISTRIBUTED** if one class is **totally INCLUDED** in the other class or **totally EXCLUDED**from the other class.  While it is **UNDISTRIBUTED** if partially (not all)of the class are included in the other class.\ \ In A proposition, ALL S are P, it implies that all S are totally included in class of P but P is NOT TOTALLY INCLUDED the class of S.\ A proposition has a **Distributed** subject and an **Undistributed **predicate terms. **D-U**\ \ In E proposition. NO S are P. it implies that all S are TOTALLY EXCLUDED in the class of P, and vice-versa.\ E proposition has **both** **Distributed** subject and predicate terms. **D-D**\ \ In I proposition, SOME S are P, it implies that some S are partially included in class of P and vice-versa. \ I proposition has both **UNDISTRIBUTED** subject and predicate terms.** U-U\ **\ In O proposition, SOME S are not P, it implies that some S are not included in class of P (not all)(Undistributed) but P are totally excluded in the class of S (Distributed).  \ O proposition has an **Undistributed** subject and a **Distributed** predicate TERMS. **U-D\ ** 2.  HYPOTHETICAL STATEMENTS- are CONDTIONAL statements. This statement is a compound statement where the truth value of one statement i has something to do with the truth value of the other statement.  The second statement cannot happen (or is False) if the first statement is not possible (not True)  It is has three kinds. 2.1 CONDITONAL: STATEMENTS/PROPOSITIONS:\ IMG\_260IMG\_262\ \ \ TRUTH VALUE of a Conditional Statements:  Below are the rules.   1.   If the ANTECEDENT is TRUE and the CONSEQUENT is TRUE, then the conditional statement is **TRUE.\ 2. ** If the ANTECEDENT is TRUE and the CONSEQUENT is FALSE, then the conditional statement is **FALSE.**\ 3.  If the ANTECEDENT is FALSE and the CONSEQUENT is TRUE, then the conditional statement is **TRUE.\ 4.  **If the ANTECEDENT is FALSE and the CONSEQUENT is FALSE, then the conditional statement is **TRUE.** **2.2. CONJUNCTION-**A conjunction statement is an \'and\' statement. For a conjunction statement to be true, both of the statements must be true..  A conjunction is a statement formed by adding two statements with the connector AND. The symbol for conjunction is \'∧\' which can be read as \'and\'. When two statements p and q are joined in a statement, the conjunction will be expressed symbolically as p ∧ q. IMG\_265\ IMG\_267\ **CONJUCTIVE statements have correlative conjunction such as \"AND\"**\ \ **TRUTH VALUE** of a Conjunctive Statements: Below are the rules.  \ 1.   If it is **TRUE** that I am SMART and **TRUE** that I am HANDSOME, then, it is **TRUE **to say that **\"I am Smart AND Handsome.\"** 2.  If it is **TRUE** that I am SMART and **FALSE** that I am HANDSOME, then, it is **FALSE **to say that **\"I am SMART and Handsome.\"**  3.  If it is **FALSE** that I am SMART and **TRUE** that I am HANDSOME, then, it is **FALSE **to say that **\"I am SMART and Handsome.\"** ** ** **4.  **If it is **FALSE** that I am SMART and **FALSE** that I am HANDSOME, then, it is FALSE to say that **\"I am SMART and Handsome.\" ** **Always REMEMBER this students**, in conjunctive statements, both statements must INDEED be TRUE for the ENTIRE statement to be TRUE.  2.3. DINSJUNCTION or DISJUNCTIVE STATEMENTS: \ A disjunction is **a compound statement formed by joining two statements with the connector OR**. The disjunction "p or q" is symbolized by p q. A disjunction is false if and only if both statements are false; otherwise it is true.  **TRUTH VALUE** of a Disjunctive Statement: Below are the rules.  \ 1.   If it is TRUE to say that **the lights are either ON or OFF, then it is possible to say** that the lights are ON is TRUE, and possible to say that the lights are OFF is also TRUE. 2.   If it is TRUE to say that **the lights are either ON or OFF, then it is possible to say** that the lights are ON is TRUE, and possible to say that the lights are OFF is also FALSE. 3.   If it is TRUE to say that **the lights are either ON or OFF, then it is possible to say** that the lights are ON is FALSE, and possible to say that the lights are OFF is also TRUE. 4.   If it is FALSE to say that **the lights are either ON or OFF, then it possible to say** that the lights are ON is FALSE, and possible to say that the lights are OFF is also FALSE. Remember this, in disjunctive statements, at least one must be true or both to be true to be TRUE in its entirely.  Because if both are FALSE, then the whole is FALSE. Thank you for reading and I know this is very CONFUSING for you because you are not used to dissecting terms, propositions and later arguments.  You will understand little by little,  BE PATIENT!