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Proof (truth)
A proof is Necessity and sufficiency, sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, Dialogue, dialog, rhetoric, etc., a proof is a persuasive perlocutionary act, perlocutionary speech act, which demonstrates the truth of a proposition. In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and from other previously established theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In some areas of theory of justification, epistemology and existence of god, theology, the notion of Theory of justification, justification plays approximately the rol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessity And Sufficiency
In logic and mathematics, necessity and sufficiency are terms used to describe a material conditional, conditional or implicational relationship between two Statement (logic), statements. For example, in the Conditional sentence, conditional statement: "If then ", is necessary for , because the Truth value, truth of is guaranteed by the truth of . (Equivalently, it is impossible to have without , or the falsity of ensures the falsity of .) Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one (possibly one of several conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axioms
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a "logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. Non- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legal Burden Of Proof
In a legal dispute, one party has the burden of proof to show that they are correct, while the other party has no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts needed to satisfy all the required legal elements of the dispute. It is also known as the onus of proof. The burden of proof is usually on the person who brings a claim in a dispute. It is often associated with the Latin maxim ''semper necessitas probandi incumbit ei qui agit'', a translation of which is: "the necessity of proof always lies with the person who lays charges." In civil suits, for example, the plaintiff bears the burden of proof that the defendant's action or inaction caused injury to the plaintiff, and the defendant bears the burden of proving an affirmative defense. The burden of proof is on the prosecutor for criminal cases, and the defendant is presumed innocent. If the claimant fails to discharge the burden of proof t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophic Burden Of Proof
The burden of proof (Latin: ''onus probandi'', shortened from ''Onus probandi incumbit ei qui dicit, non ei qui negat'' – the burden of proof lies with the one who speaks, not the one who denies) is the obligation on a party in a dispute to provide sufficient warrant for its position. Holder of the burden When two parties are in a discussion and one makes a claim that the other disputes, the one who makes the claim typically has a ''burden of proof'' to justify or substantiate that claim, especially when it challenges a perceived ''status quo''. This is also stated in Hitchens's razor, which declares that "what may be asserted without evidence may be dismissed without evidence." Carl Sagan proposed a related criterion: " Extraordinary claims require extraordinary evidence". While certain kinds of arguments, such as logical syllogisms, require mathematical or strictly logical proofs, the standard for evidence to meet the burden of proof is usually determined by context and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evidence (law)
The law of evidence, also known as the rules of evidence, encompasses the rules and legal principles that govern the proof of facts in a legal proceeding. These rules determine what evidence must or must not be considered by the trier of fact in reaching its decision. The trier of fact is a judge in bench trials, or the jury in any cases involving a jury. The law of evidence is also concerned with the quantum (amount), quality, and type of proof needed to prevail in litigation. The rules vary depending upon whether the venue is a criminal court, civil court, or family court, and they vary by jurisdiction. The Quantum meruit, quantum of evidence is the amount of evidence needed; the quality of proof is how reliable such evidence should be considered. Important rules that govern Admissible evidence, admissibility concern hearsay, Authentication (law), authentication, Relevance (law), relevance, privilege (evidence), privilege, witnesses, opinions, Expert witness, expert tes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jurisprudence
Jurisprudence, also known as theory of law or philosophy of law, is the examination in a general perspective of what law is and what it ought to be. It investigates issues such as the definition of law; legal validity; legal norms and values; and the relationship between law and other fields of study, including Law and economics, economics, Applied ethics, ethics, Legal history, history, Sociology of law, sociology, and political philosophy. Modern jurisprudence began in the 18th century and was based on the first principles of natural law, Civil law (legal system), civil law, and the law of nations. Contemporary philosophy of law addresses problems internal to law and legal systems and problems of law as a social institution that relates to the larger political and social context in which it exists. Jurisprudence can be divided into categories both by the type of question scholars seek to answer and by the theories of jurisprudence, or schools of thought, regarding how those ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Justification
Justification (also called epistemic justification) is a property of beliefs that fulfill certain norms about what a person should believe. Epistemologists often identify justification as a component of knowledge distinguishing it from mere true opinion. They study the reasons why someone holds a belief. Epistemologists are concerned with various features of belief, which include the ideas of warrant (a proper justification for holding a belief), knowledge, rationality, and probability, among others. Debates surrounding epistemic justification often involve the ''structure'' of justification, including whether there are foundational justified beliefs or whether mere coherence is sufficient for a system of beliefs to qualify as justified. Another major subject of debate is the sources of justification, which might include perceptual experience (the evidence of the senses), reason, and authoritative testimony, among others. Justification and knowledge "Justification" involves the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existence Of God
The existence of God is a subject of debate in the philosophy of religion and theology. A wide variety of arguments for and against the existence of God (with the same or similar arguments also generally being used when talking about the existence of multiple deities) can be categorized as logical, Empirical research, empirical, Metaphysics, metaphysical, Subjectivity, subjective, or Science, scientific. In Philosophy, philosophical terms, the question of the existence of God involves the disciplines of epistemology (the nature and scope of knowledge) and ontology (study of the nature of being or existence) and the Value theory, theory of value (since some definitions of God include perfection). The Western philosophy, Western tradition of philosophical discussion of the existence of God began with Plato and Aristotle, who made arguments for the existence of a being responsible for fashioning the universe, referred to as the demiurge or the unmoved mover, that today would be c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Justification
Justification (also called epistemic justification) is a property of beliefs that fulfill certain norms about what a person should believe. Epistemologists often identify justification as a component of knowledge distinguishing it from mere true opinion. They study the reasons why someone holds a belief. Epistemologists are concerned with various features of belief, which include the ideas of warrant (a proper justification for holding a belief), knowledge, rationality, and probability, among others. Debates surrounding epistemic justification often involve the ''structure'' of justification, including whether there are foundational justified beliefs or whether mere coherence is sufficient for a system of beliefs to qualify as justified. Another major subject of debate is the sources of justification, which might include perceptual experience (the evidence of the senses), reason, and authoritative testimony, among others. Justification and knowledge "Justification" involves the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is generally effective, but there may be no method by which we can reliably find proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
