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Proof (truth)
Related concepts and fundamentals: * Agnosticism
Agnosticism
* Epistemology
Epistemology
* Presupposition * Probability
Probability
* v * t * e A PROOF is 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 , dialog , rhetoric , etc., a proof is a persuasive 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
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Mathematics
MATHEMATICS (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers ), structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics . Mathematicians seek out patterns and use them to formulate new conjectures . Mathematicians resolve the truth or falsity of conjectures by mathematical proof . When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic , mathematics developed from counting , calculation , measurement , and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry
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Axioms
An AXIOM or POSTULATE 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 Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.' The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy , an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic , an axiom is simply a premise or starting point for reasoning
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Theorem
In mathematics , a THEOREM is a statement that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms . A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system . The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive , in contrast to the notion of a scientific law , which is experimental . Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called HYPOTHESES or premises
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Rules Of Inference
In logic , a RULE OF INFERENCE, INFERENCE RULE or TRANSFORMATION RULE is a logical form consisting of a function which takes premises, analyzes their syntax , and returns a conclusion (or conclusions ). For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under an interpretation), then so is the conclusion. Typically, a rule of inference preserves truth, a semantic property. In many-valued logic , it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e
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Speech Act
A SPEECH ACT in linguistics and the philosophy of language is an utterance that has performative function in language and communication. According to Kent Bach , "almost any speech act is really the performance of several acts at once, distinguished by different aspects of the speaker's intention: there is the act of saying something, what one does in saying it, such as requesting or promising, and how one is trying to affect one's audience." The contemporary use of the term goes back to J. L. Austin 's development of performative utterances and his theory of locutionary , illocutionary , and perlocutionary acts . Speech acts are commonly taken to include such acts as promising, ordering, greeting, warning, inviting and congratulating
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Perlocutionary Act
A PERLOCUTIONARY ACT (or PERLOCUTIONARY EFFECT) is a speech act , as viewed at the level of its consequences, such as persuading, convincing, scaring, enlightening, inspiring, or otherwise affecting the listener. This is contrasted with locutionary and illocutionary acts (which are levels of description, rather than classifications of speech acts). Unlike the notion of illocutionary act, which describes the linguistic function of an utterance, a perlocutionary effect is in some sense external to the performance. It may be thought of, in a sense, as the effect of the illocutionary act via the locutionary act. Therefore, when examining perlocutionary acts, the effect on the hearer or reader is emphasized
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Conversation
CONVERSATION is interactive, communication between two or more people. The development of conversational skills and etiquette is an important part of socialization . The development of conversational skills in a new language is a frequent focus of language teaching and learning . Conversation analysis is a branch of sociology which studies the structure and organization of human interaction, with a more specific focus on conversational interaction
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Dialog
DIALOGUE (sometimes spelled DIALOG in American English ) is a written or spoken conversational exchange between two or more people, and a literary and theatrical form that depicts such an exchange. As a narrative , philosophical or didactic device, it is chiefly associated in the West with the Socratic dialogue
Socratic dialogue
as developed by Plato
Plato
, but antecedents are also found in other traditions including Indian literature . In the 20th century, philosophical treatments of dialogue emerged from thinkers including Mikhail Bakhtin , Paulo Freire , Martin Buber , and David Bohm
David Bohm
. Although diverging in many details, these thinkers have articulated a holistic concept of dialogue as a multi-dimensional, dynamic and context-dependent process of creating meaning
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Rhetoric
RHETORIC is the art of discourse , wherein a writer or speaker strives to inform, persuade or motivate particular audiences in specific situations. As a subject of formal study and a productive civic practice, rhetoric has played a central role in the European tradition. Its best known definition comes from Aristotle
Aristotle
, who considers it a counterpart of both logic and politics, and calls it "the faculty of observing in any given case the available means of persuasion ." Rhetoric
Rhetoric
typically provides heuristics for understanding, discovering, and developing arguments for particular situations, such as Aristotle's three persuasive audience appeals, logos , pathos , and ethos . The five canons of rhetoric, which trace the traditional tasks in designing a persuasive speech, were first codified in classical Rome: invention , arrangement , style , memory , and delivery
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Persuasive
PERSUASION is an umbrella term of influence . Persuasion
Persuasion
can attempt to influence a person's beliefs , attitudes , intentions , motivations , or behaviors . In business, persuasion is a process aimed at changing a person's (or a group's) attitude or behavior toward some event, idea, object, or other person(s), by using written or spoken words to convey information, feelings, or reasoning, or a combination thereof. Persuasion
Persuasion
is also an often used tool in the pursuit of personal gain, such as election campaigning, giving a sales pitch , or in trial advocacy . Persuasion
Persuasion
can also be interpreted as using one's personal or positional resources to change people's behaviors or attitudes
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Logic
LOGIC (from the Ancient Greek
Ancient Greek
: λογική, logikḗ ), originally meaning "the word" or "what is spoken" (but coming to mean "thought" or "reason"), is generally held to consist of the systematic study of the form of arguments . A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. (In ordinary discourse, the conclusion of such an argument may be signified by words like therefore, hence, ergo and so on.) There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions , below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference , including fallacies , and the study of semantics , including paradoxes
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Existence Of God
The EXISTENCE OF GOD is a subject of debate in the philosophy of religion , popular culture , and philosophy. Some people have tried to prove that God
God
exists. A wide variety of arguments for and against the existence of God
God
can be categorized as metaphysical , logical , empirical , or subjective . In philosophical terms, the question of the existence of God
God
involves the disciplines of epistemology (the nature and scope of knowledge ) and ontology (study of the nature of being , existence , or reality ) and the theory of value (since some definitions of God
God
include "perfection"). The Western tradition of philosophical discussion of the existence of God
God
began with Plato
Plato
and Aristotle
Aristotle
, who made arguments that would now be categorized as cosmological
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Forensics
FORENSIC SCIENCE is the application of science to criminal and civil laws , mainly—on the criminal side—during criminal investigation , as governed by the legal standards of admissible evidence and criminal procedure . Forensic scientists collect, preserve, and analyze scientific evidence during