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1976 book by Imre Lakatos
Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics
Proofs_and_Refutations
2023 compilation album by John Fahey
Proofs & Refutations is a compilation album by American fingerstyle guitarist and composer John Fahey, released in 2023. It reissues Double 78 alongside
Proofs_&_Refutations
Argument that leads to a logical absurdity
freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof. This argument form traces back
Reductio_ad_absurdum
Comes Back To Haunt You: The Fonotone Years 1958–1965 Dust-to-Digital 2023 Proofs & Refutations (Reissues Double 78 alongside new material) Drag City
John_Fahey_discography
Hungarian philosopher of mathematics and science (1922–1974)
thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and also for introducing
Imre_Lakatos
Textbook
in 1993. It is referenced several times in Imre Lakatos's book Proofs and Refutations, where it is described as "outstandingly good within the deductivist
Principles of Mathematical Analysis
Principles_of_Mathematical_Analysis
Austrian–British philosopher of science (1902–1994)
1956–57 (as privately circulated galley proofs; published as a book 1983), ISBN 0091514509 Conjectures and Refutations: The Growth of Scientific Knowledge
Karl_Popper
2011 box set by John Fahey
Prince Georges Avenue: Essential Recordings (2009) Your Past Comes Back to Haunt You: The Fonotone Years, 1958–1965 (2011) Proofs & Refutations (2023)
Your Past Comes Back To Haunt You: The Fonotone Years 1958–1965
Your_Past_Comes_Back_To_Haunt_You:_The_Fonotone_Years_1958–1965
Any informal mathematical practices used in everyday life
ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his Proofs and Refutations aimed to sharpen the formulation of informal mathematics, by reconstructing
Informal_mathematics
Topological invariant in mathematics
additional proofs, see Eppstein (2013). Multiple proofs, including their flaws and limitations, are used as examples in Proofs and Refutations by Lakatos
Euler_characteristic
Philosophical question
Ontological Proofs Today. Frankfurt: Walter de Gruyter. pp. 28, 150. ISBN 978-3-86838-181-8. Szatkowski, Miroslaw (2013). Ontological Proofs Today. Piscataway
Existence_of_God
Field in logic and theoretical computer science
(1999) provided a proof method reducing lower bounds on size of Resolution refutations to lower bounds on width of Resolution refutations, which captured
Proof_complexity
Chart for the analysis of legal evidence in trials
reasoning, explanations, refutations, and conclusions; and shapes which represent facts, claims, explanations, and refutations. Although Wigmore taught
Wigmore_chart
17th-century conjecture proved by Andrew Wiles in 1994
complicated proof was simplified in 1840 by Lebesgue, and still simpler proofs were published by Angelo Genocchi in 1864, 1874 and 1876. Alternative proofs were
Fermat's_Last_Theorem
incorrect (or no) proofs? Moritz. Theorems demoted back to conjectures Mei Zhang, Proofs shown to be wrong after formalization with proof assistant Steven-Owen
List_of_incomplete_proofs
Informal fallacy
also be a form of brainwashing. Modern politics contains many examples of proofs by assertion. This practice can be observed in the use of political slogans
Proof_by_assertion
Jordanian Islamic scholar (born 1967)
for others to openly critique Salafi beliefs. He is also known for his refutations of the Sufi master Ibn Arabi (in particular, wahdat al-wujud) and Aristotelian
Sa'id_Foudah
Characteristic of some logical systems
\implies \ \Gamma \vdash _{\mathcal {S}}\varphi .} A formal system S is refutation complete if it is able to derive false from every unsatisfiable set of
Completeness_(logic)
Islamic theological treatise
Umm al-Barahin (Arabic: أم البراهين, lit. 'The Mother of Proofs, or The Foundational Proofs'), also known as al-'Aqida al-Sanusiyya al-Sughra (Arabic:
Umm_al-Barahin
12th century Indian philosopher poet
("Sugar-candy Pieces of Refutations" or just Sweets of Refutation). Śrīharṣa thinks that any philosophical argument or view is subject to refutation-arguments (khaṇḍana-yukti)
Shriharsha
On partitions into intersecting convex hulls
r {\displaystyle r} by Bárány, Shlosman and Szűcs. Matoušek presents a proof using deleted joins. The theorem was proved for r {\displaystyle r} a prime-power
Tverberg's_theorem
Interplay between observation, experiment, and theory in science
based on Polya's idea of heuristics. In Proofs and Refutations, Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He
Scientific_method
Exception to a proposed general rule
Imre Lakatos, Proofs and Refutations (1976) Cambridge University Press ISBN 0521290384 James Franklin and Albert Daoud (2011) Proof in Mathematics:
Counterexample
German mathematician
University of St Andrews, Scotland. May 2000. Lakatos, Imre (1976). Proofs and Refutations. Cambridge University Press. p. 141. Biography, University of St
Philipp_Ludwig_von_Seidel
Arab Christian philosopher (893–974)
versions in Syriac. These include: Plato's Laws; Aristotle's Sophistical Refutations (from a Syriac translation by Theophilus of Edessa) and Topics (from
Yahya_ibn_Adi
Type of informal fallacy
"ignorance of the nature of refutation". To refute an assertion, Aristotle says we must prove its contradictory; the proof, consequently, of a proposition
Irrelevant_conclusion
Unique positive real number which when multiplied by itself gives 2
other proofs that the square root of any non-square natural number is irrational, see Quadratic irrational number or Infinite descent. A simple proof is
Square_root_of_2
Logical operation
of a proposition P {\displaystyle P} is the proposition whose proofs are the refutations of P {\displaystyle P} . Classical negation is an operation on
Negation
Spiegelhalter Introduction to Probability Models — Sheldon M. Ross Proofs and Refutations — Imre Lakatos The Principles of Mathematics — Bertrand Russell
List_of_mathematics_books
Faulty deductive reasoning due to a logical flaw
ISBN 1-55591-539-6. Retrieved 2011-10-04. Bibliography Aristotle, On Sophistical Refutations, De Sophistici Elenchi. William of Ockham, Summa of Logic (ca. 1323)
Formal_fallacy
Addition to a theory to prevent falsification
Scotsman Special pleading The Structure of Scientific Revolutions Proofs and Refutations "The Dragon in My Garage" Paraconsistent logic Moving the goalposts
Ad_hoc_hypothesis
Propositional proof system
In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally
Frege_system
Inference rule in logic, proof theory, and automated theorem proving
allowed one to instantiate the formula during the proof "on demand" just as far as needed to keep refutation completeness. The clause produced by a resolution
Resolution_(logic)
Book by Augustine of Hippo
IV: a proof that the power and long duration of the Roman empire was due not to the pagan gods but to the Christian God. Book V: a refutation of the
The_City_of_God
Proposition in mathematics that is unproven
proof, some have even proceeded to develop further proofs which are contingent on the truth of this conjecture. These are called conditional proofs:
Conjecture
American professor of philosophy (born 1968)
Superstition: A Refutation of the New Atheism, Aquinas, Scholastic Metaphysics: A Contemporary Introduction, Neo-Scholastic Essay, and Five Proofs of the Existence
Edward_Feser
Obsolete physics theory
30..262., doi:10.1103/PhysRevSeriesI.30.262 De Sitter, Willem (1913), "A proof of the constancy of the velocity of light" , Proceedings of the Royal Netherlands
Emission_theory_(relativity)
Philosophical question
advanced in his De Aeternitate Mundi (On the Eternity of the World) eighteen proofs for the eternity of the world, resting on the divinity of its creator. John
Eternity_of_the_world
1781 book by Immanuel Kant
one concept and its general object, and (3) only direct proofs can be used, never indirect proofs (e.g., a proposition is true because its opposite is false)
Critique_of_Pure_Reason
Argument that uses faulty reasoning
opponent's thesis and thus win an argument. Aristotle's Sophistical Refutations (De Sophisticis Elenchis) identifies thirteen fallacies. He divided them
Fallacy
Mathematical fallacy Superseded theories in science List of incomplete proofs List of unsolved problems in mathematics List of disproved mathematical
List_of_conjectures
Logic founded on unproven premises
trivial and uninteresting). Aristotle discusses this in Sophistical Refutations and in Prior Analytics book II, (64b, 34–65a 9, for circular reasoning
Begging_the_question
Book by Abu Mansur al-Maturidi
in defence of Monotheism, including his cosmological doctrines such as proofs for the creation and ontology of the Universe. He also focuses on God, his
Kitab_al-Tawhid_(Al-Maturidi)
Cambridge University Press, Cambridge, UK, 1983 Lakatos, Imre (1976), Proofs and Refutations. Cambridge: Cambridge University Press. ISBN 0-521-29038-4
Quasi-empiricism in mathematics
Quasi-empiricism_in_mathematics
Ecumenical Patriarch of Constantinople from 806 to 815
thoroughness with which he traced the literary and traditional proofs, and his detailed refutations are serviceable for the knowledge they afford of important
Nikephoros I of Constantinople
Nikephoros_I_of_Constantinople
Epistemological philosophy advanced by Karl Popper
theories. This led him to posit that "only attempted refutations which did not succeed qua refutations should count as 'verifications'". A little later,
Critical_rationalism
Computer software for model generation
Most automated theorem provers try to perform a proof by refutation on the clause normal form of the proof problem, by showing that the combination of axioms
Models_And_Counter-Examples
of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation complete—given unlimited resources and a fair derivation
Superposition_calculus
Approach in philosophy of mathematics and logic
Kleene's wonderfully-clear style. Lakatos, Imre (2015) [1976]. Proofs and Refutations The Logic of Mathematical Discovery. Cambridge Philosophy Classics
Intuitionism
that it could withstand innumerable empirical contradictions, logical refutations, and moral revulsions at its effects. The Marxian vision took the overwhelming
Criticism_of_Marxism
Rule in logic programming
parents is the previous clause C i {\displaystyle C_{i}\,} . The proof is a refutation if the last clause C l {\displaystyle C_{l}\,} is the empty clause
SLD_resolution
Pakistani Islamic scholar
written I'la Al-Sunan, a 20-volume Hadith encyclopedia of Hanafi proofs, written as a refutation by the Hanafi school against the objections raised by the growing
Zafar_Ahmad_Usmani
Genre of literary prose
peasants, Berto and Giorgio, on the topic of anarchy. Imre Lakatos Proofs and Refutations is a 1976 book on the logic of discovery and progress in mathematics
Socratic_dialogue
Consistency of the axioms of arithmetic
question would in particular provide a proof that Peano arithmetic is consistent. There are many known proofs that Peano arithmetic is consistent that
Hilbert's_second_problem
Lakatos. In particular, it initially made use of Lakatos' work on proofs and refutations. Subsequently, development has been influenced by the work of Geof
Scientific_community_metaphor
Obsolete theories in natural history and natural philosophy
address covid-19". Washington Post. Popper, Karl (1963), Conjectures and Refutations, Routledge and Kegan Paul, London, UK. Reprinted in Theodore Schick (ed
List of superseded scientific theories
List_of_superseded_scientific_theories
Logical fallacy
known as ignoratio elenchi (Latin for "ignoring the list" or "ignoring refutation") or missing the point, follows a similar structure to appeal to the stone
Appeal_to_the_stone
Internet adage
information technology, refutations lag nonsense production to a greater degree than in fields with less rapid change." Big lie Burden of proof Firehose of falsehood
Brandolini's_law
Topics referred to by the same term
Mythology of Lost § The Island "Lost Island" refutation, the response by Gaunilo of Marmoutiers to Anselm's logical proof of the existence of God All pages with
Lost_island
Any of 4 regular star polyhedra
9, pp. 16–48, 1810. Lakatos, Imre; Proofs and Refutations, Cambridge University Press (1976) - discussion of proof of Euler characteristic Anthony Pugh
Kepler–Poinsot_polyhedron
Method of logical reasoning
of deductive reasoning. Mathematical induction is used to provide strict proofs of the properties of recursively defined sets. The deductive nature of mathematical
Inductive_reasoning
Islamic honorific title
context, as a title for the 11th-century theologian al-Ghazali, due to his refutations of Hellenistic-influenced philosophers and Isma'ilis. It was later used
Hujjat_al-Islam
Truth-based approach to semantics
performs. Dummett further argues that a theory based on inference, such as proof-theoretic semantics, provides a better foundation for this model than truth-conditional
Truth-conditional_semantics
Two geometries based on axioms closely related to those specifying Euclidean geometry
at trying to formulate non-Euclidean geometry, however, provided flawed proofs of the parallel postulate, depending on assumptions that are now recognized
Non-Euclidean_geometry
English by Eli Franco. *Refutation of Pratyabhijñā Philosophy *Vādasthānāni (Grounds for Argumentation) Vijñaptimātratāsiddhi (Proof of Consciousness-only)
Jitāri
Informal fallacy
thirteen fallacies originally identified by Aristotle in Sophistical Refutations. For example: People who commit crimes are criminals. Cutting people
Accident_(fallacy)
Latin Library. Retrieved 10 September 2008. Aristotle, Sophistical Refutations, ch. 5 "Osborne Wrigley-Pimley-McKerr III", United States Heraldic Registry
List_of_Latin_phrases_(S)
Philosopher (born 1946)
interest in my studies and, later, my early career. Studying his Proofs and Refutations was the intellectual event of my undergraduate study." Worrall continued
John_Worrall_(philosopher)
In proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. The developed algorithms
Proof_compression
Theological text written by Augustine of Hippo
over several topics, and includes an attempted proof of the existence of God. Intended also as a refutation of Manichaeism, De libero arbitrio denied God's
De_libero_arbitrio_voluntatis
Prominent Iranian Baháʼí scholar
Abu'l-Faḍl began working on refutations of that book. When he learned that other Baháʼí scholars had also started working on refutations that had reached an advanced
Mírzá_Abu'l-Faḍl
Ascetic frequently claimed to be Subhas Chandra Bose
and what compelled Justice Mukherjee to accept official DNA result as a proof to dismiss Bhagwanji being Netaji. The high court raised concern about accepting
Bhagwanji
Latin Library. Retrieved 10 September 2008. Aristotle, Sophistical Refutations, ch. 5 "Osborne Wrigley-Pimley-McKerr III", United States Heraldic Registry
List_of_Latin_phrases_(full)
Form of incorrect argument and informal fallacy
different proposition (i.e., "stand up a straw man") and the subsequent refutation of that false argument ("knock down a straw man"), instead of the opponent's
Straw_man
Computer security method
fields. Usually, this refers to mathematical proofs, which are common in cryptography. In such a proof, the capabilities of the attacker are defined
Provable_security
with meal) Mathematical fallacy – Certain type of mistaken proof Sophistical Refutations – Text by Aristotle on logical fallacies, in which Aristotle
List_of_fallacies
Interpretation of Karl Marx's value theory
recent survey of the debate, a proponent of the TSSI concludes that "the proofs of inconsistency are no longer defended; the entire case against Marx has
Temporal single-system interpretation
Temporal_single-system_interpretation
American philosopher, sanskritist, academic
of metaphysics in India, he published Classical Indian Metaphysics: Refutations of Realism and the Emergence of the "New Logic," highlighting the increasing
Stephen_Phillips_(academic)
Portuguese Shi'ite apologist (d. c. 1722)
mentioned by Tiburcio. The four volumes are: (1) "The refutation of Christianity and the proofs of the principles of Islam" (Radd-e uṣūl-e dīn-e Naṣārā
Aliqoli_Jadid-ol-Eslam
Finding an optimal algorithm for playing chess
require evaluation to confirm that a forced-win exists (i.e. with no refutations from Black). Furthermore, Shannon's calculation for the complexity of
Solving_chess
in the socialized aspects of a proof. In particular, proofs are rarely written in full details, and some steps of a proof are generally considered as trivial
Philosophy_of_mathematics
Term in mathematical logic
cannot be proved in ZF, and few working set theorists expect to find a refutation in ZF. However ZF cannot prove that they are independent of ZF, even with
Independence (mathematical logic)
Independence_(mathematical_logic)
Conspiracy theory about race and culture
platform. Ferral, Katelyn (1 March 2024). "Undocumented immigrants are not proof of a scheme to replace whites with nonwhites". PolitiFact. The 'great replacement
Great Replacement conspiracy theory
Great_Replacement_conspiracy_theory
English philosopher (1873–1958)
his Principia Ethica, and his essays, "The Refutation of Idealism", "A Defence of Common Sense", and "A Proof of the External World". Moore was an important
G._E._Moore
French Benedictine monk and philosopher
island than which none greater is possible does not exist." Gaunilo's refutation is also criticized on the grounds that it misinterprets the argument set
Gaunilo_of_Marmoutiers
Material supporting an assertion
detected some characteristics that are present in evident arguments and proofs. The more they are evident, the more these characteristics will be present
Evidence
Quranic exegesis by Fakhr al-Din al-Razi
concerns was the self-sufficiency of the intellect. [...] [He] believed [that] proofs based on tradition (hadith) could never lead to certainty (yaqin) but only
Tafsir_al-Kabir
Hypothetical situation
'Beweisen' ", Maia N.S. 10 pp. 1–26 as cited by Imre Lakatos (1976) in Proofs and Refutations p. 9. (John Worrall and Elie Zahar, eds.) Cambridge University Press
Thought_experiment
School of theology in Sunni Islam
rejected Taqlid, would use scriptural proofs from the Quran and sunnah but also in some cases rational proofs. The Athari denunciations of Taqlid would
Atharism
Book by Ludwig Wittgenstein
presupposes certainty" (OC115). Wittgenstein also sketched (then-)novel refutations of philosophical skepticism in various guises: "If you are not certain
On_Certainty
Mathematical theory by Shinichi Mochizuki
from Mochizuki's arguments a proof of a quantitative result on abc, which could in principle give a refutation of the proof.[non-primary source needed]
Inter-universal Teichmüller theory
Inter-universal_Teichmüller_theory
German rabbi and community leader (1470s–1554)
should be put in prison or sentenced for this crime without sufficient proof. Josel was anxious to obtain this order because in 1543 at Würzburg five
Josel_of_Rosheim
Video game urban legend
Bratt contacted 2K and Sid Meier once again but did not receive a direct refutation. Meier stated that he did not know the correct answer, but he thinks that
Nuclear_Gandhi
of his treatise, Al-Kilabi outlines four rational proofs for God's freedom from location. These proofs assert that ascribing location to God subjects God
Ibn_Jahbal_al-Kilabi
Israeli-British historian (born 1945)
Shlaim, Avi (2009). Israel and Palestine: Reappraisals, Revisions, Refutations. Verso. ISBN 978-1844673667. OL 23913926M. Shlaim, Avi (2023). Three
Avi_Shlaim
Trilemma in computer science concerning network naming schemes
to four-syllable, human-readable names. Several platforms implement refutations of Zooko's conjecture, including: Twister (which use Swartz' system with
Zooko's_triangle
demonstrative proof. Both Thales and Pythagoras of the Pre-Socratic philosophers seemed aware of geometric methods. Fragments of early proofs are preserved
History_of_logic
Type of cooperative argumentative dialogue
science through policies on environmental issues, math through mathematical proofs, health through nutrition labels, and physical education through fitness
Socratic_method
Approach to mathematics using computation
Doron Zeilberger A.J. Han Vinck Borwein integral Computer-aided proof Proofs and Refutations Experimental Mathematics (journal) Institute for Experimental
Experimental_mathematics
Various systems of symbolic logic
computerized tools, known as proof assistants. These tools assist their users in the generation and verification of large-scale proofs, whose size usually precludes
Intuitionistic_logic
PROOFS REFUTATIONS
PROOFS REFUTATIONS
Boy/Male
Arabic, Muslim
The Proof
Boy/Male
Arabic, French, German, Gujarati, Hindu, Indian, Malaysian, Muslim, Turkish
Proof; Evidence
Boy/Male
Muslim
Proof
Boy/Male
Muslim/Islamic
Proof
Boy/Male
Arabic, Muslim
Evidence; Proof
Girl/Female
Indian
Witness; Proof
Girl/Female
Muslim
Proof
Surname or Lastname
English
English : from the possessive case of Brook (i.e. ‘of the brook’).Jewish (Ashkenazic) : Americanized form of one or more like-sounding Jewish surnames.Americanized spelling of German Brucks.This name was brought independently to North America from England by numerous different bearers from the 17th century onward. Among them were William Brooks, who brought the name to Scituate, MA, from Kent, England, in 1635, and Henry Brooks, who came to Woburn, MA, in or before 1649.
Surname or Lastname
Dutch (also de Roos) and Swiss German
Dutch (also de Roos) and Swiss German : habitational name for someone living at a house distinguished by the sign of a rose.Dutch (also de Roos) : metonymic occupational name for someone who grew roses, from roos ‘rose’.Dutch : from the female personal name Rosa (Latin rosa ‘rose’).Dutch : nickname from roos ‘erysipelas’, an infection which causes reddening of the skin and scalp, applied presumably to someone with a ruddy complexion.Swiss German : from a personal name formed with hrÅd ‘renown’.Swedish and Danish (of German origin) : as 1.Swedish : variant of Ros.English and Scottish : variant of Ross 2.
Male
English
English surname transferred to forename use, BROOKS means "of the brook."
Boy/Male
Indian
Proof
Boy/Male
Muslim
Proof
Boy/Male
Afghan, Arabic, Hindu, Indian, Muslim
Proof
Girl/Female
Arabic, Muslim
Guide; Proof
Boy/Male
Indian
Proof
Boy/Male
Arabic
Proof; Evidence
Boy/Male
Muslim/Islamic
Proof
Girl/Female
Muslim
Guide, Proof
Boy/Male
Arabic, Australian, Muslim
Proofs; Arguments
Boy/Male
Muslim
Evidence. Proof.
PROOFS REFUTATIONS
PROOFS REFUTATIONS
Girl/Female
Muslim/Islamic
Deliriously in love
Boy/Male
Indian
Servant of the forbearing one, Servant of the patient one
Girl/Female
Arabic, Muslim
Daughter of the Prophet
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi
With Beautiful Hands
Girl/Female
Indian, Sanskrit
One who Comes Repeatedly
Girl/Female
Gujarati, Hindu, Indian, Kannada, Mythological, Rajasthani, Sanskrit
An Apsara; Shakuntala's Mother
Girl/Female
Hindu, Indian
Blue Complexioned
Girl/Female
Muslim/Islamic
Clouds
Girl/Female
Hindu, Indian
Daughter of the Moon
Boy/Male
Dutch, Finnish, French, German, Greek, Latin, Swedish
Kingly; Royal
PROOFS REFUTATIONS
PROOFS REFUTATIONS
PROOFS REFUTATIONS
PROOFS REFUTATIONS
PROOFS REFUTATIONS
n.
Demonstration; proof.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.
n.
Proof.
n.
Proof; evidence.
a.
Proof against proofs; obstinate in the wrong.
a.
Used in proving or testing; as, a proof load, or proof charge.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
v. t.
To cover with a roof.
n.
Proof.
n.
The act of proving; also, that which proves anything; proof.
n.
Proof; trial.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
a.
Having roofs.
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.
n.
Full of pores; having interstices in the skin or in the substance of the body; having spiracles or passages for fluids; permeable by liquids; as, a porous skin; porous wood.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
n.
Proof.
n.
Proof; attestation.
n.
Proof.
n.
Trial; proof.