Proof (truth), the Glossary

Table of Contents

1. 64 relations: Alibi, Anne Sjerp Troelstra, Antonella Cupillari, Argument, Aristotle, Author, Axiom, Belief, Bonnie Gold, Burden of proof (law), Burden of proof (philosophy), Communication, Conversation, Crime, David Hume, Determinism, Dialogue, Evidence, Evidence (law), Evil demon, Existence of God, Forensic science, Formal proof, Formal system, Geocentric model, Graphology, Harvard University Press, Indeterminism, J. L. Austin, John Henry Wigmore, John Locke, Jurisprudence, Jury, Justification (epistemology), Knowledge, Logic, Mathematical proof, Mathematics, Nature (philosophy), Necessity and sufficiency, Nicolaus Copernicus, Perlocutionary act, Persuasion, Proof complexity, Proof of concept, Proof procedure, Proof theory, Proposition, Provability logic, René Descartes, ... Expand index (14 more) »

2. Automated theorem proving
3. Evidence
4. Formal systems
5. Legal reasoning
6. Logical truth
7. Metatheory

Alibi

An alibi (from the Latin, alibī, meaning "somewhere else") is a statement by a person under suspicion in a crime that they were in a different place when the offence was committed.

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Anne Sjerp Troelstra

Anne Sjerp Troelstra (10 August 1939 – 7 March 2019) was a professor of pure mathematics and foundations of mathematics at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.

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Antonella Cupillari

Antonella Cupillari (born 1955) is an Italian-American mathematician interested in the history of mathematics and mathematics education.

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Argument

An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion.

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Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs; 384–322 BC) was an Ancient Greek philosopher and polymath.

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In legal discourse, an author is the creator of an original work, whether that work is in written, graphic, or recorded medium.

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Axiom

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.

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Belief

A belief is a subjective attitude that a proposition is true or a state of affairs is the case. Proof (truth) and belief are concepts in epistemology.

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Bonnie Gold

Bonnie Gold (born 1948) is an American mathematician, mathematical logician, philosopher of mathematics, and mathematics educator.

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Burden of proof (law)

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. Proof (truth) and burden of proof (law) are legal reasoning.

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Burden of proof (philosophy)

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. Proof (truth) and burden of proof (philosophy) are concepts in epistemology and evidence.

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Communication

Communication is commonly defined as the transmission of information.

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Conversation

Conversation is interactive communication between two or more people.

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Crime

In ordinary language, a crime is an unlawful act punishable by a state or other authority.

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David Hume

David Hume (born David Home; – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist who was best known for his highly influential system of empiricism, philosophical skepticism and metaphysical naturalism.

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Determinism

Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable.

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Dialogue

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.

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Evidence

Evidence for a proposition is what supports the proposition. Proof (truth) and Evidence are concepts in epistemology.

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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.

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Evil demon

The evil demon, also known as Deus deceptor, malicious demon, and evil genius, is an epistemological concept that features prominently in Cartesian philosophy. Proof (truth) and evil demon are concepts in epistemology.

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Existence of God

The existence of God is a subject of debate in the philosophy of religion.

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Forensic science

Forensic science, also known as criminalistics, is the application of science principles and methods to support legal decision-making in matters of criminal and civil law.

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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. Proof (truth) and formal proof are formal languages, formal systems, logical truth and proof theory.

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Formal system

A formal system is an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules. Proof (truth) and formal system are formal languages and formal systems.

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Geocentric model

In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center.

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Graphology

Graphology is the analysis of handwriting in an attempt to determine the writer's personality traits.

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Harvard University Press

Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing.

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Indeterminism

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

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J. L. Austin

John Langshaw Austin, OBE, FBA (26 March 1911 – 8 February 1960) was a British philosopher of language and leading proponent of ordinary language philosophy, best known for developing the theory of speech acts.

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John Henry Wigmore

John Henry Wigmore (1863–1943) was an American lawyer and legal scholar known for his expertise in the law of evidence and for his influential scholarship.

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John Locke

John Locke (29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Enlightenment thinkers and commonly known as the "father of liberalism".

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Jurisprudence

Jurisprudence is the philosophy and theory of law.

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Jury

A jury is a sworn body of people (jurors) convened to hear evidence, make findings of fact, and render an impartial verdict officially submitted to them by a court, or to set a penalty or judgment.

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Justification (epistemology)

Justification (also called epistemic justification) is the property of belief that qualifies it as knowledge rather than mere opinion. Proof (truth) and justification (epistemology) are concepts in epistemology and Metatheory.

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Knowledge

Knowledge is an awareness of facts, a familiarity with individuals and situations, or a practical skill. Proof (truth) and Knowledge are concepts in epistemology.

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Logic

Logic is the study of correct reasoning.

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Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. Proof (truth) and mathematical proof are proof theory.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Nature (philosophy)

Nature has two inter-related meanings in philosophy and natural philosophy.

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Necessity and sufficiency

In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.

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Nicolaus Copernicus

Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated a model of the universe that placed the Sun rather than Earth at its center.

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Perlocutionary act

A perlocutionary act (or perlocutionary effect) is the effect of an utterance on an interlocutor.

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Persuasion

Persuasion or persuasion arts is an umbrella term for influence.

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Proof complexity

In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Proof (truth) and proof complexity are Automated theorem proving and computational complexity theory.

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Proof of concept

Proof of concept (POC or PoC), also known as proof of principle, is a realization of a certain idea, method or principle in order to demonstrate its feasibility, or viability, or a demonstration in principle with the aim of verifying that some concept or theory has practical potential.

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Proof procedure

In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements. Proof (truth) and proof procedure are proof theory.

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Proof theory

Proof theory is a major branchAccording to Wang (1981), pp.

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Proposition

A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity.

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Provability logic

Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. Proof (truth) and Provability logic are proof theory.

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René Descartes

René Descartes (or;; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science.

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Rhetoric

Rhetoric is the art of persuasion.

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Rule of inference

In philosophy of logic and 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). Proof (truth) and rule of inference are formal systems and logical truth.

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Science

Science is a strict systematic discipline that builds and organizes knowledge in the form of testable hypotheses and predictions about the world.

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Scientific law

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena.

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Secrecy

Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals.

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Signature

A signature (from signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent.

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Simulated reality

A simulated reality is an approximation of reality created in a simulation, usually in a set of circumstances in which something is engineered to appear real when it is not.

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Speech act

In the philosophy of language and linguistics, a speech act is something expressed by an individual that not only presents information but performs an action as well.

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Sun

The Sun is the star at the center of the Solar System.

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Theorem

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.

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Thomas Aquinas

Thomas Aquinas (Aquino; – 7 March 1274) was an Italian Dominican friar and priest, an influential philosopher and theologian, and a jurist in the tradition of scholasticism from the county of Aquino in the Kingdom of Sicily.

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Truth

Truth or verity is the property of being in accord with fact or reality. Proof (truth) and Truth are concepts in epistemology.

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Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. Proof (truth) and well-formed formula are formal languages.

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Witness

In law, a witness is someone who, either voluntarily or under compulsion, provides testimonial evidence, either oral or written, of what they know or claim to know.

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See also

Automated theorem proving

• Anti-unification
• Automated reasoning
• Automated theorem proving
• Axiomatic system (logic)
• Burrows–Abadi–Needham logic
• Chaff algorithm
• Computer-assisted proof
• Concolic testing
• DPLL algorithm
• DPLL(T)
• Davis–Putnam algorithm
• F* (programming language)
• Fresh variable
• Geoff Sutcliffe
• Geometry Expert
• Harald Ganzinger
• Hilbert system
• Interactive Theorem Proving (conference)
• IsaPlanner
• LowerUnits
• Method of analytic tableaux
• Model elimination
• Non-surveyable proof
• Nuprl
• Occurs check
• POPLmark challenge
• Proof (truth)
• Proof assistant
• Proof complexity
• Propositional proof system
• Reasoning system
• Resolution (logic)
• Rippling
• Sequent calculus
• Substitution (logic)
• System on TPTP
• Thousands of Problems for Theorem Provers
• Unification (computer science)
• Unit propagation
• WalkSAT

Evidence

• Anecdotal evidence
• Archival research
• Burden of proof (philosophy)
• Case study
• Cherry picking
• Consilience
• Empirical evidence
• Evidence
• Evidence and documentation for the Holocaust
• Evidence and efficacy of homeopathy
• Evidence gap map
• Evidence law
• Evidence-based medicine
• Evidence-based practices
• Evidentialism
• Evidentiality
• Exclusion of evidence obtained under torture
• Exculpatory evidence
• Hierarchy of evidence
• Indicators
• Problem of the speckled hen
• Proof (truth)
• Psychoanalytic infant observation
• Real world data
• Real world evidence
• Scientific evidence
• Scientific method
• Security bag
• Self-evidence
• Smoking gun
• Sources
• Testimony
• Underdetermination

Formal systems

• Axiom schema
• Axiomatic system
• First principle
• Formal proof
• Formal system
• List of formal systems
• Physical symbol system
• Proof (truth)
• Rule of inference
• Rules of inference
• Substitution (logic)
• Term graph

Legal reasoning

• Adverse inference
• Alternative pleading
• Arbitrariness
• Argument in the alternative
• Argumentation theory
• Argumentum e contrario
• Burden of proof (law)
• Casuistry
• Causation (law)
• Clear statement rule
• Commanding precedent
• Contra principia negantem non est disputandum
• Deliberation
• Discourse ethics
• Distinguishing
• Egalitarian dialogue
• Ipse dixit
• Ipso facto
• Ipso jure
• Judicial interpretation
• Judicial populism
• Kuching Declaration
• Legalism (Western philosophy)
• Moral certainty
• Mutatis mutandis
• Open justice
• Precedent
• Prima facie
• Probable cause
• Proof (truth)
• Reasonable doubt
• Reasonable person
• Right of reply
• Social purpose
• Socratic questioning
• Statutory interpretation
• Substantial truth

Logical truth

• Degree of truth
• Direct proof
• Fact
• Faultless disagreement
• Formal proof
• Formation rule
• Logical constant
• Logical form
• Logical truth
• Proof (truth)
• Rule of inference
• Satisfiability
• Substitution (logic)
• Tautology (logic)
• Truth condition
• Truth function
• Truth predicate
• Truth value
• Truth-bearer
• Two Dogmas of Empiricism
• Vacuous truth
• Validity (logic)
• Veridicality

Metatheory

• Concision
• Contextualism
• Correspondence principle
• Eclecticism
• Emic and etic
• Explanatory power
• Facet theory
• Justification (epistemology)
• Metalogic
• Metamathematics
• Metatheory
• Metatheory of science
• Neopragmatism
• Proof (truth)
• Psychologism
• Relational developmental systems
• Semantic holism
• Sociology of sociology
• Theoretical definition

References

[1] https://en.wikipedia.org/wiki/Proof_(truth)

Also known as Disproof, Disproved, Disproven, Evidentification, Logical Proof, Proof (informal).

, Rhetoric, Rule of inference, Science, Scientific law, Secrecy, Signature, Simulated reality, Speech act, Sun, Theorem, Thomas Aquinas, Truth, Well-formed formula, Witness.