Logic

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Logic is more than reasoning. Usually it is reasoning conducted or assessed according to strict principles of validity. Aristotelian logic is a particular system or codification of the principles of proof and inference.

Educational level: this is a secondary education resource.

At a secondary level an introduction to logic may be helpful, where some of the more common operators are described. This introduction is a part of elementary logic at the undergraduate level. Here, there is at least one lesson available.

Educational level: this is a tertiary (university) resource.

This learning resource is partly an article, in some subareas an essay, and mostly a lecture.

Educational level: this is a research resource.

Resource type: this resource is an article.

Resource type: this resource contains a lecture or lecture notes.

Logic is often considered a part of philosophy. And, most often is used in science to help create knowledge consisting of facts and truths. But, it finds needed applicability in law and the practice of law. A third popular subject that confers a rigid structure on logic is mathematics.

Subject classification: this is a law resource .

Subject classification: this is a science resource .

Subject classification: this is a mathematics resource .

Nearly all intellectual efforts can be approached and have some understanding produced through the application of logic. This includes volition (e.g., emotion), affections, morality, and religion.

Notation

Notation: let the symbol Def. indicate that a definition is following.

Universals

To help with definitions, their meanings and intents, there is the learning resource theory of definition.

Def. evidence that demonstrates that a concept is possible is called proof of concept.

“[D]efinitions are always of symbols, for only symbols have meanings for definitions to explain.” A term can be one or more of a set of symbols such as words, phrases, letter designations, or any already used symbol or new symbol.

In the theory of definition, “the symbol being defined is called the definiendum, and the symbol or set of symbols used to explain the meaning of the definiendum is called the definiens.” “The definiens is not the meaning of the definiendum, but another symbol or group of symbols which, according to the definition, has the same meaning as the definiendum.”

Def.

1.a(1): "a science that deals with the canons and criteria of validity of inference and demonstration : the science of the normative formal principles of reasoning"

(2): "a branch of semiotic; [especially: syntactics]"

(3): "the formal principles of a branch of knowledge"

b: "a particular mode of reasoning"

c: "interrelation or sequence of facts or events when seen as inevitable or predictable"

is called logic.

Similar to the above dictionary, or lexical, definition is

Def. "[l]ogic is the study of correct argumentation."

Def. "[a] method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved" is called logic, from Wiktionary.

Computer logic

Computer logic is a system of principles behind the arrangements of elements in a computer or electronic device for performing a specified task.

Deduction

Def. "[a] process of reasoning that moves from the general to the specific, in which a conclusion follows necessarily from the premises presented, so that the conclusion cannot be false if the premises are true" is called deduction, from Wiktionary.

"The theory of deduction is intended to explain the relationship between premisses and conclusion of a valid argument and to provide techniques for the appraisal of deductive arguments".

Dialectics

From the Wikipedia article dialectics: "Dialectic (also dialectics and the dialectical method) is a method of argument for resolving disagreement ... The dialectical method is dialogue between two or more people holding different points of view about a subject, who wish to establish the truth of the matter by dialogue, with reasoned arguments. Dialectics is different from debate, wherein the debaters are committed to their points of view, and mean to win the debate, either by persuading the opponent, proving their argument correct, or proving the opponent's argument incorrect — thus, either a judge or a jury must decide who wins the debate. Dialectics is also different from rhetoric, wherein the speaker uses logos, pathos, or ethos to persuade listeners to take their side of the argument."

Induction

Def. "the derivation of general principles from specific instances" is called induction, from Wiktionary.

Inference

Beginning the Wikipedia article on inference is "Inference is the act or process of deriving logical conclusions from premises known or assumed to be true."

Logical calculus

"[A]n abstract logical calculus [consists of] "the vocabulary of logic, ... the primitive symbols ..., and the logical structure ... fixed by stating the axioms or postulates ... in terms of its primitive symbols."

Mathematical logic

In line with Boolean algebra which is a logical calculus is Boolean logic.

Natural deduction

Per the article about natural deduction on Wikipedia: "In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with the axiomatic systems which instead use axioms as much as possible to express the logical laws of deductive reasoning."

Principle

"A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored." from the Wikipedia article principle.

Propositional logic

Propositional logic uses or may result in declarative sentences.

Reasoning

Logic can also mean the quality of being justifiable by reason.

Def. "[t]he deduction of inferences or interpretations from premises" is called reasoning, from Wiktionary.

Another definition of reasoning may be

Def. "the drawing of inferences or conclusions through the use of" "statement[s] offered in explanation or justification" is called reasoning.

Sophistry

Def. "[a]n argument that seems plausible, but is fallacious or misleading, especially one devised deliberately to be so" is called sophistry, from Wiktionary.

Symbolic logic

The systematic use of symbolic techniques to determine the forms of valid deductive argument may be deductive symbolic logic.

Validity

Def. "the quality of state of" "having a conclusion correctly derived from premises" is called validity.

See also

• Categorical Syllogism
• Hypothesis
• Logical inference
• Logic Model
• Logic patterns
• Logical Proofs

Further reading

• Patrick Suppes (1967). Sidney Morgenbesser. ed. What is a scientific theory? In: Philosophy of Science Today. New York: Basic Books, Inc.. pp. 55-67. 

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This is a research project at http://en.wikiversity.org