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Logic

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Logic is the systematic study of correct reasoning. It focuses on how we draw inferences, which are the mental steps used to reach a new idea. These steps are expressed through arguments. An argument is a structure consisting of a set of premises and a conclusion. The premises are the initial claims or pieces of information provided. The conclusion is the final claim that the premises are meant to support.

Argument terminology
Argument terminology

Logic investigates whether these premises actually provide enough support to make the conclusion valid. This field is essential to many academic disciplines, including philosophy, mathematics, linguistics, and computer science.

Global thinking
Global thinking

Formal logic, often called symbolic logic, is a highly structured approach to reasoning. It replaces the messy details of human speech with abstract symbols. This process makes the study topic-neutral. This means the logic focuses only on the structure of the argument rather than the specific subject matter.

Modus ponendo ponens
Modus ponendo ponens

Formal logic is primarily concerned with deductively valid arguments. In a deductively valid argument, if the premises are true, the conclusion must also be true. It is impossible for the premises to be true while the conclusion remains false. This reliability comes from following specific rules of inference. One famous example is modus ponens, which follows a specific pattern to guarantee a valid result.

First-order logic
First-order logic

To maintain this precision, formal logic uses formal languages. These languages have very limited vocabularies and strict syntactic rules. These rules dictate how symbols can be combined to create well-formed formulas. Because these languages are so exact, they can clearly determine if an argument is valid. However, natural language is often too vague or ambiguous for direct formal analysis. To study a natural language argument, logicians must first translate it into a formal language. When used as a countable noun, "a logic" refers to a specific formal system that defines its own rules of inference and language.

Informal logic takes a different approach by focusing on everyday discourse. It uses non-formal criteria to assess arguments expressed in natural language. This field was developed to address problems that formal logic cannot easily solve. Natural language is often context-dependent or contains vague terms. Informal logic helps people navigate these complexities through critical thinking and argumentation theory. It also examines the psychology of how people argue.

One major goal of informal logic is to identify fallacies. A fallacy is an error in reasoning that makes an argument incorrect. An example is the false dilemma, where someone wrongly claims only two options exist.

Arguments can also be categorized by how they provide information. Deductive arguments provide the strongest support, as seen in formal logic. In contrast, ampliative arguments provide genuinely new information that was not contained in the premises. These are common in science and daily life. Ampliative arguments are divided into two types: inductive and abductive. Inductive arguments rely on statistical generalizations. For example, observing many black ravens might lead to the conclusion that all ravens are black. Abductive arguments are inferences to the best explanation. A doctor might use abduction to conclude a patient has a specific disease based on their symptoms.

The history of logic stretches back to antiquity. Many ancient cultures developed sophisticated systems of reasoning. Aristotelian logic, which focuses on syllogisms, was the dominant system in the West for a long time.

Aristotle Altemps Inv8575
Aristotle Altemps Inv8575

Other early systems included Stoic logic, Nyaya, and Mohism. The field shifted significantly in the late 19th century. Mathematicians like Gottlob Frege helped move logic toward modern formal systems.

Wismar Marienkirche Bronzebüste Gottlob Frege (01-1)
Wismar Marienkirche Bronzebüste Gottlob Frege (01-1)

This era laid the groundwork for the mathematical logic used in modern computer science.

Today, classical logic is the most widely used system. It is composed of two main parts: propositional logic and first-order logic. Propositional logic examines the relationships between entire propositions. First-order logic is more complex because it looks at the internal parts of propositions, such as quantifiers and predicates.

Square of opposition, set diagrams
Square of opposition, set diagrams

Beyond classical logic, there are extended logics that apply reasoning to ethics or metaphysics. There are also deviant logics. These systems reject certain classical intuitions to offer alternative explanations of logical laws.

Russell1907-2
Russell1907-2
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File:Argument terminology.svg
Argument terminology.svg
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BS-12-Begriffsschrift Quantifier1-svg.svg
File:Square of opposition, set diagrams.svg
Square of opposition, set diagrams.svg
File:Global thinking.svg
Global thinking.svg
File:Young America's dilemma - Dalrymple. LCCN2010651418.jpg
Young America's dilemma - Dalrymple....
File:First-order logic.png
First-order logic.png
File:Avicenne - Avicenna - Ibn Sina (980-1037) CIPB2067.jpg
Avicenne - Avicenna - Ibn Sina (980-1037)...
File:Aristotle Altemps Inv8575.jpg
Aristotle Altemps Inv8575.jpg
File:Guillaume Occam.jpg
Guillaume Occam.jpg
File:Modus ponendo ponens.png
Modus ponendo ponens.png
File:Russell1907-2.jpg
Russell1907-2.jpg
File:Wismar Marienkirche Bronzebüste Gottlob Frege (01-1).JPG
Wismar Marienkirche Bronzebüste Gottlob...

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