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# Primer in Logic

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### Primer in Logic

1. 1. PRIMER IN LOGIC Definition of Logic The term logic came from the Greek word logos, which is sometimes translated as sentence, discourse, reason, rule, and ratio. On a more specialized meaning, we might define logic as the study of the principles of correct reasoning. One thing one should note about this definition is that logic is concerned with the principles of correct reasoning. Logic is the study of the methods and principles used in distinguishing correct from incorrect reasoning. The main (not the only) thing that we study in logic are principles governing the validity of arguments - whether certain conclusions follow from some given assumptions. Science and Art Logic is a science because it is a systematize body of knowledge which is considered to be true. As a science, it follows procedures, structures, principles and rules that validate a certain statement or argument. It is an art since it has a order or rules to be followed in order to have a good and comprehensible presentation of ideas. This order gives us an easy way to understand an argument, hence as an art, it is a skill to be developed. Significance of studying Logic Why should anyone bother to study at least a little logic? Logic helps us to decide our decision. It also makes us analyze of what is good argument. If one understands logic one may able to adopt and grow using the same reasoning in times of difficulty. Logic is the arts of learning to think and communicate clearly and coherently. It chastens one's own thinking, and helps develop an appreciation for tenable arguments and a respect for good reasoning. Knowledge in logic helps us become more adept at solving problems, whether they're encountered in business, science, politics, or the law. The Logical Function of Language Language is man’s greatest invention. Without language, practically other human inventions would not have been possible. Language is the verbal form of our thoughts, and as such it is our vehicle or tool of communication. Man can communicate with others because of language. Language then may be defined as a set of symbols by which things, ideas, and thoughts or feelings are communicated to others. Language is used for many reasons, aims, or purposes. One of which is its logical function. Logical function is one in which language is used to reason, analyze, and clarify a problem or an argument. One may use language to prove or disprove the truth of some statements or theories. This is the function of logical reasoning. It is the very subject matter of logic.
2. 2. Terms A term is a word (verbal or written) which conveys an idea. It is a concrete expression of an idea which is agreed (conventional sign) upon by persons using the term. Without the term we cannot make any statement or proposition, since it I the basic components of it. Experience  Concept or Idea  Term Classification of Terms According to Extent of Meaning and Signification 1. UNIVOCAL – Terms are univocal if they exhibit similarity in meaning or signification even though they are used in at least two occasions. Ex. Honey Pie is a photographer. Tweety Cute is a photographer. 2. EQUIVOCAL – Terms may be considered equivocal if they exhibit difference in meaning or signification whenever they are used in at least two occasions. Ex. The wedding bells ring. Jerica receives a ring from Jerico. 3 Processes or Kinds: a. Spelling alone: terms are similar in spelling but different in meaning and pronunciation. Ex. Resume – bio data Resume – to continue b. Sound alone: terms maybe the same in pronunciation or utterances but their spellings remained to be different as well as their meanings. Ex. Maid - made Pool - pull c. Both Sound and Spelling: terms maybe have similarity in sound and spelling but still their meanings remained to be different. Ex. Right - right Left - left 3. ANALOGOUS – Terms are analogous if they express partly the same and partly different meanings when used in at least two occasions. - Proportionality and attribution are the key factors in understanding analogous terms. Ex. Orange – fruit, Orange – color Definition is a statement that gives the meaning of a term or a statement which explains what a term means. There are two elements of definition: (1) the definiendum or definitum, and (2) the definiens. The former is the term to be defined; it is the word whose meaning needs to be explained. The latter is the term which defines (explains) the definiendum. Ex. Logic is the science that deals with correct reasoning.
3. 3. Kinds of Definition 1. Nominal Definition -A definition which speaks about a term but not declaring anything about it. This is done by considering the origin of the term, by describing the term, by giving the synonym of the term or by citing an example that will represent the term Classification of Nominal Definition a. Nominal Definition by Etymology – attained by tracing the origin of the term. Ex.: Fraternity came from “frater”, which means “brother”. b. Nominal Definition by Description – attained by describing the term. Ex.: A rose is a flower. c. Nominal Definition by Synonym – it is done by giving a word equivalent to the term. Ex.: Being kind is being benevolent. d. Nominal Definition by Example – it is done by citing anything that will represent the term. Ex.: Our Chief Executive is Benigno Simeon Aquino III. 2. Real Definition -A definition, which declares something about the term. This kind of definition serves to explain about the nature and to distinguish it from other terms. Classification of Real Definition a. Real Definition by Genus and Specific Difference - a definition that explains the essence of a term by considering the intelligible elements that make up the term. Ex.: A triangle is a figure with three sides. “figure” – genus “three sides” – specific difference b. Real Definition by Description - It is done by stating the genus of the term but altering the specific difference by giving the logical property, which belongs to the term to be defined. Ex.: A Police Officer is a man bestowed with authority to enforce a law. “man” – genus “bestowed with authority to enforce a law” – logical property c. Real Definition by Cause -It is attained by stating the genus of the term but altering the specific difference by tracing its cause. A cause could be its purpose, function, reason for existence, make-up or origin. Ex.: A book is a written material made-up of several pages and is a source of information.
4. 4. Rules in Good Definition 1. The definition should explain the term clearly. 2. The definition should be precise. 3. The definition must be coextensive with the term defined. 4. The definition should be formulated positively. 5. The definition must not contain the term that is to be defined. Judgment, Sentence, and Proposition Judgement is the mental enunciation or pronouncement regarding the agreement or disagreement between two ideas. It is an act of the mind affirming an idea by another idea, or denying an idea from another. A judgment is either true or false. If a judgment agrees with reality, it is true; otherwise, it is false. Proposition is the verbal expression of a judgment. It is a statement in which something is affirmed or denied. All propositions are sentences, but not all sentences are propositions. A sentence does not always affirm or deny something. Sentence can be defined as a set of words that is complete in itself. As long as a word or group of words expresses an emotion or a complete thought it is a sentence. Proposition is not the same as definition despite the similarity in structure. The word is which is found in both proposition and definition functions differently. In propositions, the word is functions as a copula. A copula links the subject term and the predicate term in a proposition. It expresses either an affirmation or a denial, or an agreement or disagreement between the subject term and the predicate term. While in definition, the word is gives the meaning of the definiendum or the term being defined.