Logic: A Concise Introduction
Logic
Logic is defined as the organized body of knowledge or science that evaluates arguments.
The aim of logic is to develop methods and principles for evaluating arguments and constructing sound arguments.
An argument consists of one or more statements (premises) claimed to provide support for another statement (conclusion).
Arguments are classified as good if the premises support the conclusion and bad if they do not.
The term "argument" in logic does not refer to a verbal fight but to a structured set of statements.
Statements
A statement is a sentence that is either true or false, typically a declarative sentence.
Examples of statements: "Chocolate truffles are loaded with calories," "Melatonin helps relieve jet lag."
Truth and falsity are the two possible truth values of a statement.
Sentences that are questions, proposals, suggestions, commands, or exclamations are not statements.
Premises and Conclusions
Premises provide reasons or evidence, and the conclusion is the statement that the evidence is claimed to support.
Example: "All film stars are celebrities. Halle Berry is a film star. Therefore, Halle Berry is a celebrity."
Distinguishing premises from conclusions is crucial for argument analysis.
Indicator Words
Conclusion indicators signal the conclusion of an argument (e.g., therefore, thus, hence, consequently).
Premise indicators signal the premises of an argument (e.g., since, because, as, for).
Example of conclusion indicator: Tortured prisoners will say anything just to relieve the pain. Consequently, torture is not a reliable method of interrogation.
Example of premise indicator: Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the development of the fetus.
Some arguments lack indicators, requiring the reader to identify the statement claimed to follow from others.
Restructuring Arguments
When restructuring arguments, maintain fidelity to the original version while ensuring premises and conclusion are complete and meaningful.
Passages may contain statements that are neither premises nor conclusions; only statements supporting the conclusion should be included in the list of premises.
Inference and Proposition
Inference is the reasoning process expressed by an argument.
Proposition refers to the meaning or information content of a statement; used interchangeably with statement in this text.
History of Logic
Aristotle (384–322 B.C.):
Credited as the father of logic; devised systematic criteria for analyzing and evaluating arguments.
Chief accomplishment: syllogistic logic.
Originated modal logic.
Catalogued informal fallacies.
Chrysippus (280–206 B.C.):
Developed a logic based on propositions.
Laid the foundation for the truth functional interpretation of logical connectives.
Introduced natural deduction.
Middle Ages:
Peter Abelard reconstructed and refined Aristotelian logic, originated a theory of universals, and distinguished between formal and content-based validity.
William of Sherwood and Peter of Spain made contributions to logical treatises and textbooks.
William of Ockham extended modal logic theory and developed the idea of a metalanguage.
Gottfried Wilhelm Leibniz (1646–1716):
Attempted to develop a symbolic language for resolving disputes; sometimes credited as the father of symbolic logic.
Nineteenth Century:
Symbolic logic work by Augustus De Morgan, George Boole, William Stanley Jevons, and John Venn.
John Stuart Mill initiated a revival in inductive logic.
Charles Sanders Peirce developed a logic of relations and invented symbolic quantifiers.
Gottlob Frege (1848–1925):
Laid the foundations of modern mathematical logic with his Begriffsschrift, which introduced the theory of quantification.
Twentieth Century:
Alfred North Whitehead and Bertrand Russell attempted to reduce mathematics to logic in Principia Mathematica.
Kurt Gödel proved the incompleteness theorem.
Logic has contributed to technology through the conceptual foundation for electronic circuitry in digital computers.
Recognizing Arguments
A passage contains an argument if it purports to prove something.
Two conditions must be fulfilled for a passage to purport to prove something:
At least one statement must claim to present evidence or reasons.
There must be a claim that the alleged evidence supports or implies something.
The second condition expresses an inferential claim.
An inferential claim can be either explicit (using indicator words) or implicit (without indicator words).
Example of explicit inferential claim: Mad cow disease is spread by feeding parts of infected animals to cows, and this practice has yet to be completely eradicated. Thus, mad cow disease continues to pose a threat to people who eat beef.
Example of implicit inferential claim: The genetic modification of food is risky business. Genetic engineering can introduce unintended changes into the DNA of the food-producing organism, and these changes can be toxic to the consumer.
Nonarguments
Not all passages contain arguments; it is important to distinguish arguments from nonarguments.
Simple Noninferential Passages
Lack a claim that anything is being proved; missing the claim that any potential premise supports a conclusion or that any potential conclusion is supported by premises.
Include warnings, pieces of advice, statements of belief or opinion, loosely associated statements, and reports.
Warning: intended to put someone on guard against a dangerous or detrimental situation.
Piece of advice: makes a recommendation about some future decision or course of conduct.
Statement of belief or opinion: expresses what someone happens to believe or think about something.
Loosely associated statements: lack a claim that one is proved by the others.
Report: conveys information about some topic or event.
Expository Passages
Begin with a topic sentence followed by sentences that develop the topic sentence; if the aim is not to prove the topic sentence, there is no argument.
Skin and the mucous membrane lining the respiratory and digestive tracts serve as mechanical barriers to entry by microbes. Oil gland secretions contain chemicals that weaken or kill bacteria on skin. The respiratory tract is lined by cells that sweep mucus and trapped particles up into the throat, where they can be swallowed. The stomach has an acidic pH, which inhibits the growth of many types of bacteria.
Example: If the purpose of the subsequent sentences in the passage is not only to flesh out the topic sentence but also to prove it, then the passage is an argument.
Illustrations
An expression involving one or more examples that is intended to show what something means or how it is done.