formal logic - Definition. Was ist formal logic
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Was (wer) ist formal logic - definition

STUDY OF CORRECT REASONING
DefinitionOfLogic; Classical two-valued logic; Formal logic; Logical; Logician; Compound proposition; Logic of mathematics; Logically; Logic/alternate-start; Logics; Logicians; Formal symbolic logic; Logical rules; Logicus; Material logic; Types of logic; Logike; Logico; Subfields of logic; Formal logics; Formal logician; Formal logicians; Science of correct reasoning; Science of correct argument; Science of correct arguments; Science of correct argumentation; Science of good reasoning; Science of good argument; Science of good arguments; Science of good argumentation; Science of valid reasoning; Science of valid argument; Science of valid arguments; Science of valid argumentation; Study of correct reasoning; Study of correct argument; Study of correct arguments; Study of correct argumentation; Study of good reasoning; Study of good argument; Study of good arguments; Study of good argumentation; Study of valid reasoning; Study of valid argument; Study of valid arguments; Study of valid argumentation; Science of correct inference; Science of correct inferences; Science of good inference; Science of good inferences; Science of valid inference; Science of valid inferences; Study of correct inference; Study of correct inferences; Study of good inference; Study of good inferences; Study of valid inference; Study of valid inferences; Science of inference; Science of inferences; Study of inference; Study of inferences; Science of truth; Science of truth values; Science of logical truth; Study of truth; Study of truth values; Study of logical truth
  • access-date=25 September 2022}}</ref>
  • [[Gottlob Frege]]'s ''[[Begriffschrift]]'' introduced the notion of quantifier in a graphical notation, which here represents the judgement that <math>\forall x. F(x)</math> is true.
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  • Formal logic needs to translate natural language arguments into a formal language, like first-order logic, in order to assess whether they are valid. In this example, the colors indicate how the English words correspond to the symbols.
  • Logic studies valid forms of inference like the [[modus ponens]].
  • The [[square of opposition]] is often used to visualize the relations between the four basic [[categorical propositions]] in Aristotelian logic. It shows, for example, that the propositions "All S are P" and "Some S are not P" are contradictory, meaning that one of them has to be true while the other is false.
  • Conjunction (AND) is one of the basic operations of boolean logic. It can be electronically implemented in several ways, for example, by using two [[transistor]]s.
  • Young America's dilemma: Shall I be wise and great, or rich and powerful? (poster from 1901) This is an example of a [[false Dilemma]]: an informal fallacy using a disjunctive premise that excludes viable alternatives.
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Mathematical logic         
SUBFIELD OF MATHEMATICS
Symbolic Logic; Symbolic logic; Mathematical Logic; Logic (mathematics); Logic (math); Logic (maths); Logic (symbolic); Mathematical logician; Logic modeling; Logic modelling; Formal Logic; History of mathematical logic; Subfields of mathematical logic; Formal logical systems; History of symbolic logic; Applications of mathematical logic; 20th century in mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.
symbolic logic         
SUBFIELD OF MATHEMATICS
Symbolic Logic; Symbolic logic; Mathematical Logic; Logic (mathematics); Logic (math); Logic (maths); Logic (symbolic); Mathematical logician; Logic modeling; Logic modelling; Formal Logic; History of mathematical logic; Subfields of mathematical logic; Formal logical systems; History of symbolic logic; Applications of mathematical logic; 20th century in mathematical logic
¦ noun the use of symbols to denote propositions, terms, and relations in order to assist reasoning.
symbolic logic         
SUBFIELD OF MATHEMATICS
Symbolic Logic; Symbolic logic; Mathematical Logic; Logic (mathematics); Logic (math); Logic (maths); Logic (symbolic); Mathematical logician; Logic modeling; Logic modelling; Formal Logic; History of mathematical logic; Subfields of mathematical logic; Formal logical systems; History of symbolic logic; Applications of mathematical logic; 20th century in mathematical logic
<logic> The discipline that treats formal logic by means of a formalised artificial language or symbolic calculus, whose purpose is to avoid the ambiguities and logical inadequacies of natural language. (1995-12-24)

Wikipedia

Logic

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics.

Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually understood either as sentences or as propositions and are characterized by their internal structure; complex propositions are made up of simpler propositions linked to each other by propositional connectives like {\displaystyle \land } (and) or {\displaystyle \to } (if...then). The truth of a proposition usually depends on the denotations of its constituents. Logically true propositions constitute a special case, since their truth depends only on the logical vocabulary used in them and not on the denotations of other terms.

Arguments can be either correct or incorrect. An argument is correct if its premises support its conclusion. The strongest form of support is found in deductive arguments: it is impossible for their premises to be true and their conclusion to be false. Deductive arguments contrast with ampliative arguments, which may arrive in their conclusion at new information that is not present in the premises. However, it is possible for all their premises to be true while their conclusion is still false. Many arguments found in everyday discourse and the sciences are ampliative arguments, sometimes divided into inductive and abductive arguments. Inductive arguments usually take the form of statistical generalizations, while abductive arguments are inferences to the best explanation. Arguments that fall short of the standards of correct reasoning are called fallacies.

Systems of logic are theoretical frameworks for assessing the correctness of reasoning and arguments. Logic has been studied since antiquity; early approaches include Aristotelian logic, Stoic logic, Anviksiki, and the Mohists. Modern formal logic has its roots in the work of late 19th-century mathematicians such as Gottlob Frege. While Aristotelian logic focuses on reasoning in the form of syllogisms, in the modern era its traditional dominance was replaced by classical logic, a set of fundamental logical intuitions shared by most logicians. It consists of propositional logic, which only considers the logical relations on the level of propositions, and first-order logic, which also articulates the internal structure of propositions using various linguistic devices, such as predicates and quantifiers. Extended logics accept the basic intuitions behind classical logic and extend it to other fields, such as metaphysics, ethics, and epistemology. Deviant logics, on the other hand, reject certain classical intuitions and provide alternative accounts of the fundamental laws of logic.