Basic Terms in Logic Michael Jhon M. Tamayao

Learning Objectives Identify and define the basic terms in Logic. Differentiate the terms according to their use. Apply the terms in practical cases.

Introduction Terms – basic elements that make up a language system. The language of logic girds towards order.

What is LOGIC? “logos” = word, reason or principle Logic – science of correct reasoning. ! Systematized ! Evokes ORDER What does Logic put into order?

1.) All men are mammals All students are men :: All students are mammals. 2.) All monkeys eat banana George Lincoln eats banana :: George Lincoln is a monkey

What logic puts in order is the way we reason out. Logic makes explicit the rules of reasoning.

Inference – the process of deducing or Inference – the process of deducing or extracting a statement (conclusion) from the previous statement/s. Argument – the verbal expression of inference. Syllogism – the format of arguments with three statements. Conclusion – the statement being supported. Premises – the statement/s that support/s the conclusion.

Key Terms ARGUMENT PREMISES CONCLUSION INFERENCE SYLLOGISM

What is the importance of studying the Arguments? The answer: It is the way we support our claims to truth and validity. Truth and validity are the two aspects that measure the worth of an argument.

What is TRUTH in Logic? Truth – the correspondence or equivalence of the mind to reality/object. Statement Object “The Horse is white”

The truth value of a statement is not proven by logicians but of empirical scientists, researchers and private detectives. Logicians only study the reasoning found on statements and not the question of their truth values.

Judgment – the “act” by which the mind Judgment – the “act” by which the mind affirms or denies an attribute of a subject. – The simplest act of the mind in which it can attain truth. Proposition – “statement” that affirms or denies something. – verbal expression of judgment

– verbally expressed as a term/name. Simple Apprehension - more elementary “act” of the mind than judgment – conceiving a notion of something. “The Horse is white.” – verbally expressed as a term/name. Terms – the two notions in a proposition: subject and predicate

Acts of the Mind Verbal Expression Simple Apprehension Term/Name Judgment Inference Verbal Expression Term/Name Proposition Argument/Syllogism

Propositions: Quality and Quantity 1. Quality – affirmative negative Affirmative - predicate is affirmed of the subject. ex. The audience is kind. Negative - predicate is denied of the subject. ex. The audience is not kind.

2. Quantity – universal or particular Universal – the predicate is affirmed or denied of “the whole” subject. Ex. “All” men are beings with heart. “Not all” men are beings with heart. Particular – the predicate is affirmed or denied of only “part of” the subject. Ex. “Some” men are haughty. Some men not are haughty.

Four-fold Scheme of Proposition A-type: universal and affirmative “All men are mortal” I-type: Particular and Affirmative “Some men are philosophers” E-type: Universal and Negative “Not all philosophers are rich.” O-type: Particular and Negative “Some men are not rich.”

Terms also have “quantity” but not “quality” Singular terms ex. Socrates, Plato, Aristotle Universal Terms ex. Men, horse

What is meant by VALIDITY? An argument is valid if the premises do provide conclusive grounds for the conclusion. Otherwise, the argument is invalid. Validity follows the different rules of inference.

Validity pertains to arguments/reasoning. Truth pertains to propositions. Logic has for its first principle the independence of truth and validity.

Independence of truth from validity Example: All men are animals All creatures are men ::All creatures are animals. Although two statements are false, the argument is still valid. FALSE

Key Terms TRUTH and VALIDITY simple apprehension Judgment inference

All computers are technological products “Sound” Argument – the reasoning in the argument is valid and all the statements are true. Example: All computers are technological products All abacuses are computers :: All abacuses are technological products.

2 Kinds of Arguments e.g. All priests are humans. 1.) Deductive argument - An argument that has premises which gives conclusive grounds for the truth of the conclusion, or if the premises claim to support the conclusion with necessity. - The process is exact. e.g. All priests are humans. All Popes are priests. :: All Popes are humans.

2.) Inductive Argument - Makes the wilder claim that its premises support but do not guarantee the necessity of its conclusion. - The conclusion is only given a high probability of correctness and “not” exactly valid or invalid. Ex. Of all the 50 million swans I saw, nothing is black. :: No swan is black.

Key Terms DEDUCTIVE INDUCTIVE Exact Valid or invalid Not a matter of degree (All or Nothing) Probable Strong or weak A matter of degree (More or Less)

What is a FALLACY? Fallacy – bad method of argument, whether deductive or inductive. – one or more of its premises are false, or the reasoning from them may be invalid, or the language expressing them may be ambiguous or vague. – typical faults in arguments that sounds persuasive.

Ex. All Stars are hot. I am a Star. :: I am hot. There is ambiguity in the meaning of the word star.

Recap Logic – the science of correct reasoning. Inference – the process of deducing or extracting a statement (conclusion) from the previous statement/s. Argument – is a kind of reasoning/inference in which statements are offered to support or justify another statement. Syllogism – the format of arguments with three statements.

Conclusion – the statement being supported. Premises – the statement/s that support/s the conclusion. Truth – the correspondence or equivalence of the mind to reality/object. Judgment – the “act” by which the mind affirms or denies an attribute of a subject. Propositions – verbal expression of judgments.

Simple Apprehension – conceiving of the notion of something. Term – verbal expression of notions. Quality – may either be affirmative or negative. Quantity – may either be universal or particular.

Valid argument – an argument which has premises that provide conclusive grounds for its conclusion. Sound Argument – an argument with valid reasoning and all its statements are true. Deductive argument – an argument with premises that claim to support the conclusion with necessity.

Inductive Argument – argument with premises that support but do not guarantee the necessity of its conclusion. Fallacy – a bad argument that has one or more false statements and/or invalid reasoning that sounds persuasive.

END Thank you for listening!