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Erroneous method of proof
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is
Proof_by_example
Reasoning for mathematical statements
assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty
Mathematical_proof
Measure of alcohol content
in terms of ABV varies from country to country, for example in the United States, alcohol proof is defined as twice the percentage of ABV. The measurement
Alcohol_proof
Informal fallacy
can 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
Proof_by_assertion
Obligation on a party to prove their case
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
Burden_of_proof_(law)
Logical fallacy in which the conclusion provides the premise
defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion. As a consequence, the argument becomes a
Circular_reasoning
"classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
2007 American film
Death Proof is a 2007 American slasher film written, co-produced, shot and directed by Quentin Tarantino. It stars Kurt Russell as a stuntman who murders
Death_Proof
Proving validity without revealing other data
In cryptography, a zero-knowledge proof (also known as a ZK proof or ZKP) is a protocol in which one party (the prover) can convince another party (the
Zero-knowledge_proof
Informal fallacy
coined by philosopher John Locke in the late 17th century. In debates, appealing to ignorance is sometimes an attempt to shift the burden of proof. There
Argument_from_ignorance
Conclusion made on the basis of one or few instances of a phenomenon
phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions. For example, one may generalize about all people
Faulty_generalization
Marking an argument as obvious or trivial
Obscurantism – Practice of obscuring information Proof by example – Erroneous method of proof Bennett, Bo. "Proof by Intimidation". logicallyfallacious.com. Retrieved
Proof_by_intimidation
Type of trolling or harassment
considered harassment by opponents of the forum and that the term sealioning was used to silence legitimate requests for proof. In 2021, Maclean's compared
Sealioning
Form of incorrect argument and informal fallacy
it fails to address the proposition in question by misrepresenting the opposing position. For example: Quoting an opponent's words out of context—i.e
Straw_man
Expression in mathematics
can amount to an instance of proof by example – a logical fallacy of proving a claim by proving a non-representative example. Consider the following theorem
Without_loss_of_generality
essentially dissimilar concepts as though they were essentially similar. Proof by assertion – a proposition is repeatedly restated regardless of contradiction;
List_of_fallacies
Argument that leads to a logical absurdity
(empirical evidence). The second example is a mathematical proof by contradiction (also known as an indirect proof), which argues that the denial of
Reductio_ad_absurdum
Fallacy regarding hypocrisy
referring to an example of hypocrisy Two wrongs don't make a right – Philosophical expression Victor's justice – Biased application of justice by the victors
Tu_quoque
Logical fallacy of inconsistency
in set A and d2 in set B is cited to assert equivalence among the sets. Example: If apples and oranges are both fruits, and there are seeds in both apples
False_equivalence
Certain type of mistaken proof
a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there
Mathematical_fallacy
Type of fallacious argument (logical fallacy)
ISBN 978-1260091991. Lay, Steven (2014). Introduction to Analysis with Proof, 5th edition. Pearson. ISBN 978-0321747471. Hurley, Patrick J. (2012). A
Affirming_the_consequent
Misleading use of a term with multiple meanings
deceiving False equivalence: Fallacy based on flawed reasoning If-by-whiskey: An example Map-territory relation: Concept that words used to describe an underlying
Equivocation
Realization of a certain method or idea in order to demonstrate its feasibility
A proof of concept (POC or PoC), also known as proof of principle, is an inchoate realization of a certain idea or method in order to demonstrate its feasibility
Proof_of_concept
Exception to a proposed general rule
A counterexample is a specific example that contradicts a claim, hypothesis, or generalization. In logic a counterexample disproves a universally stated
Counterexample
Informal logical fallacy
of Mr Angus McSporran in Aberdeen. This clearly constitutes a counter example, which definitively falsifies the universal proposition originally put
No_true_Scotsman
Threat of force to make a conclusion accepted
from authority Formal fallacy In terrorem Legal threat Might makes right Proof by intimidation Henrik Dethlefsen, "Denmark and the German Occupation: Cooperation
Argumentum_ad_baculum
Branch of logic
deduction proof example. Natural deduction inference rules, due ultimately to Gentzen, are given below. There are ten primitive rules of proof, which are
Propositional_logic
Fallacy of incomplete evidence
Jumping to conclusions Othello error Pars destruens/pars construens Proof by example Prooftext Quasi-experiment Quoting out of context Selection bias Selective
Cherry_picking
Question containing an unjustified assumption
replies to be those that serve the questioner's agenda. The traditional example is the question "Have you stopped beating your wife?" Without further clarification
Loaded_question
Formal fallacy
negatively by some, makes the same claim as Group A. Therefore, Group A is viewed as associated with Group B, and is now also viewed negatively. An example of
Association_fallacy
Faulty deductive reasoning due to a logical flaw
Statement contradicted by facts and reality Mathematical fallacy, also known as Invalid proof – Certain type of mistaken proof Modus tollens – Rule of
Formal_fallacy
Fallacy of treating an abstraction as if it were a real thing
devices, by definition, do not apply literally and thus exclude any fallacious conclusion that the formal reification is real. For example, the metaphor
Reification_(fallacy)
Logical fallacy
is fallible. While all sources agree this is not a valid form of logical proof and therefore obtaining knowledge in this way is fallible, there is disagreement
Argument_from_authority
Building designed to withstand extreme floods
from high waves. This thus causes the building to be dubbed 'tsunami-proof'. An example of such an architecture is where a laminar flow around a building
Tsunami-proof_building
Method of proof in mathematics
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for
Constructive_proof
Discussion that has continued to the point of nausea
lie Carthago delenda est Filibuster Godwin's law List of Latin phrases Proof by assertion Pressure ulcer Rumination (psychology) Rut (roads) Sealioning
Ad_nauseam
Logic error due to ignoring the base rate
questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false
Base_rate_fallacy
In mathematics, a statement that has been proven
facts in the proof of a theorem. These basic properties that were considered as absolutely evident were called postulates or axioms, for example Euclid's
Theorem
Proof by Alan Turing
Turing's proof is a proof by Alan Turing, first published in November 1936 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem"
Turing's_proof
Type of informal fallacy
presented by another. Example: "Before you listen to my opponent, may I remind you that he has been in jail." Therefore, the claims made by person A will
Poisoning_the_well
Logical fallacy
following example offered by Alan Turing in the article "Computing Machinery and Intelligence": If each man had a definite set of rules of conduct by which
Denying_the_antecedent
Form of mathematical proof
to the next one (the step). — Concrete Mathematics, page 3 margins. A proof by induction consists of two cases. The first, the base case, proves the statement
Mathematical_induction
Subfield of automated reasoning and mathematical logic
dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development
Automated_theorem_proving
Attacking the person rather than their argument
of A by claiming they hold negative property x. A defends themself by attacking B, saying they also hold the same property x. An example given by professor
Ad_hominem
Logic founded on unproven premises
proof or demonstration as the conclusion itself." The formal name for this logical fallacy is petitio principii. Following are two classic examples:
Begging_the_question
Type of uncertainty of meaning where several interpretations are possible
the two makes sense, but an ambiguity like this should be avoided, for example by writing sin 2 ( α / 2 ) {\displaystyle \sin ^{2}(\alpha /2)} or 1 2
Ambiguity
17th-century conjecture proved by Andrew Wiles in 1994
other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums
Fermat's_Last_Theorem
Attempt to persuade or to determine the truth of a conclusion
form can be shown to be a logical truth by either (a) showing that it is a tautology or (b) by means of a proof procedure. The corresponding conditional
Argument
Type of informal fallacy
refute an assertion, Aristotle says we must prove its contradictory; the proof, consequently, of a proposition which stood in any other relation than that
Irrelevant_conclusion
Large number coined by Ronald Graham
Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's
Graham's_number
Fallacy that since an argument contains a logical fallacy, its conclusion must be false
English. The fact that Alice's argument was fallacious is not, in itself, proof that her conclusion is false. Charlie: Bob's argument that Ginger is not
Argument_from_fallacy
Formal fallacy, aka Linda Problem
the best-known example, researchers have developed dozens of problems that reliably elicit the conjunction fallacy. The original report by Tversky & Kahneman
Conjunction_fallacy
Informal fallacy in comparing actualities with ideals
of the problem would still exist after it were implemented. This is an example of black and white thinking, in which a person fails to see the complex
Nirvana_fallacy
Fallacy of claiming the majority is always correct
theorem Scientific consensus Social proof Wisdom of the crowd These ideas are paraphrased from this presentation by authors Andrew Potter and Joseph Heath
Argumentum_ad_populum
System that regulates the formation of blocks on a blockchain
Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the
Proof_of_work
Rhetorical tactic and potential fallacy
Machine "Of the Colours, or Common Opinions concerning Pleasure." Chap. XVI Archived 4 November 2016 at the Wayback Machine "Of Proofs Inartificial."
Appeal_to_nature
Fundamental theory of logical analysis
used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided a proof of the
Analytic_proof
Form of incorrect argument in natural language
that there is no proof for a certain claim. From this premise, the conclusion is drawn that this claim must therefore be false. For example, "Nobody has ever
Informal_fallacy
Fallacy of inferring on the whole from a part
whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber; therefore, the vehicle of which
Fallacy_of_composition
Bias in the sampling of a population
relative to others in the population. For example, a "man on the street" interview which selects people who walk by a certain location is going to have an
Sampling_bias
Phenomenon in decision theory and estimation theory
} from that point. For a sketch of the proof of this result, see Proof of Stein's example. An alternative proof is due to Larry Brown: he proved that the
Stein's_example
Purposefully unclear communication
of security through obscurity. A notable example of obfuscation of written communication is a message sent by September 11 attacks ringleader Mohamed Atta
Obfuscation
Type of mathematical proof
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof
Proof_by_exhaustion
Mistakenly drawing statistical inference from independent events
commonly associated with gambling, where it may be mistakenly believed, for example, that the next dice roll is more likely to give '4' because there have
Gambler's_fallacy
Assertion without proof
himself") is an assertion without proof, or a dogmatic expression of opinion. The fallacy of defending a proposition by baldly asserting that it is "just
Ipse_dixit
Informal fallacy
not understand why: Example: John is committing special pleading by saying that he only likes his own dog. Another common example comes from the conflation
Special_pleading
Branch of mathematical logic
formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures
Proof_theory
Planar maps require at most four colors
preceding decades. The Appel–Haken proof proceeds by analyzing a very large number of "reducible configurations", examples of maps with a particular property
Four_color_theorem
Formal argument for the existence of God
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development
Gödel's_ontological_proof
Psychological phenomenon regarding conformity
situation. The term was coined by Robert Cialdini in his 1984 book Influence: Science and Practice.[citation needed] Social proof is used in ambiguous social
Social_proof
Apparent, but false, correlation between causally-independent variables
(See also spurious correlation of ratios.) Another example of a spurious relationship can be seen by examining a city's ice cream sales. The sales might
Spurious_relationship
Question that has a built-in supposition
presupposes something that has not been proven or accepted by all the people involved. For example, "Is Mary wearing a blue or a red dress?" might be fallacious
Complex_question
Purported fallacy in explaining good reductively
necessarily accompanied by it, or both, this quality or combination of qualities is identical with goodness. If, for example, it is believed that whatever
Naturalistic_fallacy
Detection of errors in transcribed text
Proofreading is a phase in the process of publishing where galley proofs are compared against the original manuscripts or graphic artworks, to identify
Proofreading
Method of deriving conclusions
end of proofs to indicate that the original hypothesis has been demonstrated. There are different strategies used to formulate proofs. For example, reductio
Rule_of_inference
Formal fallacy
not a cat. This inference is unsound because all cats, by definition, are mammals. A second example provides a first proposition that appears realistic and
Affirming_a_disjunct
Informal fallacy involving falsely limited alternatives
trilemma is a famous example of this type of argument involving three disjuncts: "Jesus was either a liar, a lunatic, or Lord". By denying that Jesus was
False_dilemma
Logical reasoning method
Kling gave the example of analogy blindness in the case of comparison between a volcano and a geyser. A person objects to the analogy by complaining that
Argument_from_analogy
Logical paradox from vague predicates
paradox arises when a person's preferences patterns are investigated. As an example by Robert Duncan Luce, it is easy to find a person, say, Peggy, who prefers
Sorites_paradox
Formal fallacy about knowledge of objects
two objects cannot be identical. The name of the fallacy comes from the example: Premise 1: I know who Claus is. Premise 2: I do not know who the masked
Masked-man_fallacy
Bias towards recently acquired information
known as availability bias, is a mental shortcut that relies on immediate examples that come to a given person's mind when evaluating a specific topic, concept
Availability_heuristic
Formal language used to prove statements
In mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Formal language: The set
Proof_calculus
Proof in set theory
in the enumeration. The proof starts with an enumeration of elements from T, for example Next, a sequence s is constructed by choosing the 1st digit as
Cantor's_diagonal_argument
Type of logical fallacy
tactic is often sarcastic in their argument. This dialogue presents an example of appeal to ridicule: Person A: At one time in prehistory, the continents
Appeal_to_ridicule
Logical fallacy
For example: "Every time I score an A on the test it's a sunny day. Therefore the sunny day causes me to score well on the test." Here is the example the
Questionable_cause
Argument that uses faulty reasoning
or refute it, also called "guilt by association" (association fallacy) Claiming that a lack of proof counts as proof (appeal to ignorance) In humor, errors
Fallacy
Error in numerical data
presentation of data should be limited to what is warranted by the precision of those data. For example, if an instrument can be read to tenths of a unit of
False_precision
Print not counted in the number of a limited edition
edition that has sold out, marking such editions for example 'Artist's Proof no.8 of 50.' The term "proof" is generally, but not consistently, applied only
Artist's_proof
Logical fallacy
for example a law that would require a person wishing to lend money against a security to first ascertain the borrower's title to the property by inquiring
Appeal_to_consequences
Logical principle
the number is rational. The above proof is an example of a non-constructive proof disallowed by intuitionists: The proof is non-constructive because it doesn't
Law_of_excluded_middle
Relation between sides of a right triangle
numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic
Pythagorean_theorem
Mathematical proof technique using contradiction
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that
Proof_by_infinite_descent
Formal fallacy that occurs when a syllogism has four (or more) terms
argument sounds like the (valid) first example above, but is in fact structured like the invalid second example: Major premise: Nothing is better than
Fallacy_of_four_terms
Alternative decimal expansion of 1
number, there is a natural number that is greater (for example, by rounding up). Other proofs generally involve basic properties of real numbers and methods
0.999...
Limitative results in mathematical logic
formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Category of mathematical proof
as it is often necessary to develop a proof that works in general, rather than to just show a particular example. Impossibility theorems are usually expressible
Proof_of_impossibility
Logical fallacy
when the term that links the two premises is never distributed. In this example, distribution is marked in boldface: All Z is B All Y is B Therefore, all
Fallacy of the undistributed middle
Fallacy_of_the_undistributed_middle
1995 publication in mathematics
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Obligation on a party in a dispute to provide sufficient warrant for their position
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
Burden_of_proof_(philosophy)
Kind of proof calculus
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to
Natural_deduction
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
Boy/Male
Afghan, Arabic, Hindu, Indian, Muslim
Proof
Boy/Male
Muslim/Islamic
Proof
Boy/Male
Muslim
Proof
Girl/Female
Muslim
Guide, Proof
Boy/Male
Muslim
Evidence. Proof.
Boy/Male
Arabic, Muslim
Evidence; Proof
Boy/Male
Muslim/Islamic
Proof
Girl/Female
Indian
Witness; Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Boy/Male
Arabic, Muslim
The Proof
Girl/Female
Arabic, Muslim
Guide; Proof
Surname or Lastname
English
English : variant of Rolfe.German : from Ruffo, a short form of a personal name formed with hrÅd ‘renown’, ‘victory’.Probably an Americanized spelling of German Ruf and Ruff.
Boy/Male
Muslim
Proof
Boy/Male
Arabic
Proof; Evidence
Boy/Male
Arabic, French, German, Gujarati, Hindu, Indian, Malaysian, Muslim, Turkish
Proof; Evidence
Boy/Male
Indian
Proof
Boy/Male
Indian
Proof
Girl/Female
Muslim
Proof
Boy/Male
Muslim
Argument, Reasoning, Proof
Girl/Female
Muslim/Islamic
Guide Proof
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
Male
English
Pet form of English Sacheverell, SACHIE means "roe-buck leap."
Girl/Female
Indian
River
Girl/Female
Muslim
Gazing
Girl/Female
Indian, Telugu
Snake God
Boy/Male
Arabic, Muslim
Salvation; Peace; Free from Blemish; Ease; Name of a Sahaabi (RA)
Girl/Female
Australian, Danish, French, German, Hebrew, Swedish
Jehovah Increases; He will Increase; Feminine of Joseph
Girl/Female
American, Australian, British, Christian, Danish, English, French, German, Greek
Light; Shining Light; Variant of Helen
Boy/Male
Indian, Sanskrit
Carrying a Plough; Another Name for Krisna's Brother Balarama
Girl/Female
Finnish
Boy/Male
Tamil
Imperishable
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
PROOF BY-EXAMPLE
n.
Proof.
adv.
Passing near; going past; past; beyond; as, the procession has gone by; a bird flew by.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
v. t.
To cover with a roof.
n.
Proof.
a.
Out of the common path; aside; -- used in composition, giving the meaning of something aside, secondary, or incidental, or collateral matter, a thing private or avoiding notice; as, by-line, by-place, by-play, by-street. It was formerly more freely used in composition than it is now; as, by-business, by-concernment, by-design, by-interest, etc.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.
a.
Proof against penetration or permeation by water; impervious to water; as, a waterproof garment; a waterproof roof.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
a.
Used in proving or testing; as, a proof load, or proof charge.
pref.
With, as means, way, process, etc.; through means of; with aid of; through; through the act or agency of; as, a city is destroyed by fire; profit is made by commerce; to take by force.
n.
The cover of any building, including the roofing (see Roofing) and all the materials and construction necessary to carry and maintain the same upon the walls or other uprights. In the case of a building with vaulted ceilings protected by an outer roof, some writers call the vault the roof, and the outer protection the roof mask. It is better, however, to consider the vault as the ceiling only, in cases where it has farther covering.
a.
Proof against proofs; obstinate in the wrong.
adv.
Aside; as, to lay by; to put by.
n.
Proof.
n.
Proof.
n.
That which resembles, or corresponds to, the covering or the ceiling of a house; as, the roof of a cavern; the roof of the mouth.
n.
Proof by witness; attestation; testimony.
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.