I personally find Sanneh's construct here crude and easily refutable.
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Evidence of regret is not refutable in the same way.
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These arguments are effective because they are intuitively appealing — but they are also easily refutable.
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After all, the staff union did not fire Meyer, they merely advanced some easily refutable causes.
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Speaking in a personal way about how he interacts with his faith, Mr. Rubio makes no refutable claims.
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Perhaps that is because even in a news conference setting, Trump didn't get any pushback for telling easily refutable lies.
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As a university student, I have witnessed adults spew false information and obviously biased talking points, that were refutable within seconds of research.
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"And it's all because you lied"—six of the least refutable words in English, all the moreso when an alien Queen Bey is presiding.
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And while there are documents that will refer to one testing methodology versus another, or an outcome, what we found is the outliers are either incomplete or, frankly, they're refutable based upon the methodology or the particular sample that they used.
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Congressional Memo PHILADELPHIA — For months, the strategies have been tested and recalibrated — the senatorial speed-walk, the winking deflection, the jittery laughter — honed through a presidential campaign season of refutable claims, racially charged rhetoric and tape-recorded boasts of sexual assault.
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Working my way through these tired, easily refutable, sometimes laughable pro-NCAA talking points—at times, I felt like Darth Vader moving through the corridor at the end of Rogue One; is likening Duke University basketball players to United States freakin' Marines really a winning analogy?
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Donald Trump's populist tax-cut policies are easily refutable, yet they will continue to appeal to people as long as Hillary Clinton focuses on Trump's personal tax avoidance issues instead of explaining to the public how her economic policies would address the limitations of Trump's proposed tax cuts.
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According to an editorial in The Harvard Crimson, the answer was "not much" as far as Spicer was concerned: I was in a classroom session with Spicer and he told the same stories, including several easily refutable lies, that he's told publicly since leaving the White House (some items were leaked).
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So the Lemma is proven. Now if D_n is refutable for some n, it follows that φ is refutable. On the other hand, suppose that D_n is not refutable for any n. Then for each n there is some way of assigning truth values to the distinct subpropositions E_h (ordered by their first appearance in D_n; "distinct" here means either distinct predicates, or distinct bound variables) in B_k , such that D_n will be true when each proposition is evaluated in this fashion.
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We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove "φ is either refutable or satisfiable". At the beginning we need to prove this for all possible formulas φ in our language. However, suppose that for every formula φ there is some formula ψ taken from a more restricted class of formulas C, such that "ψ is either refutable or satisfiable" → "φ is either refutable or satisfiable". Then, once this claim (expressed in the previous sentence) is proved, it will suffice to prove "φ is either refutable or satisfiable" only for φ's belonging to the class C. If φ is provably equivalent to ψ (i.e.
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If Theorem 1 holds, and φ is not satisfiable in any structure, then ¬φ is valid in all structures and therefore provable, thus φ is refutable and Theorem 2 holds. If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬φ is not satisfiable in any structure and therefore refutable; then ¬¬φ is provable and then so is φ, thus Theorem 1 holds.
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It follows now that we need only prove Theorem 2 for formulas φ in normal form. Next, we eliminate all free variables from φ by quantifying them existentially: if, say, x1...xn are free in φ, we form \psi=\exists x_1 ... \exists x_n \phi. If ψ is satisfiable in a structure M, then certainly so is φ and if ψ is refutable, then eg \psi = \forall x_1 ... \forall x_n eg \phi is provable, and then so is ¬φ, thus φ is refutable. We see that we can restrict φ to be a sentence, that is, a formula with no free variables.
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Columbia University Press. The emergence of such analysis has been attributed to a method that, like that of the physical sciences, permits refutable implicationsAs argued more generally in Paul A. Samuelson, 1947, Enlarged ed. 1983. Foundations of Economic Analysis, Harvard University Press.
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The interpretation of negation is different in intuitionist logic than in classical logic. In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable (i.e., that there is a counterexample). There is thus an asymmetry between a positive and negative statement in intuitionism.
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Together with Francisco Antônio Dória, Da Costa has published two papers with conditional relative proofs of the consistency of P = NP with the usual set-theoretic axioms ZFC. The results they obtain are similar to the results of DeMillo and Lipton (consistency of P = NP with fragments of arithmetic) and those of Sazonov and Maté (conditional proofs of the consistency of P = NP with strong systems). Basically da Costa and Doria define a formal sentence [P = NP]' which is the same as P = NP in the standard model for arithmetic; however, because [P = NP]' by its very definition includes a disjunct that is not refutable in ZFC, [P = NP]' is not refutable in ZFC, so ZFC + [P = NP]' is consistent (assuming that ZFC is). The paper then continues by an informal proof of the implication : If ZFC + [P = NP]' is consistent, then so is ZFC + [P = NP].
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The book has been described as "a work thoroughly debunked by scholars and critics alike".Elizabeth Sherr Sklar, Donald L. Hoffman (editors), King Arthur In Popular Culture, page 214 (McFarland & Company, Inc., 2002). Arthurian scholar Richard Barber has commented, "It would take a book as long as the original to refute and dissect The Holy Blood and the Holy Grail point by point: it is essentially a text which proceeds by innuendo, not by refutable scholarly debate".
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He argues that the first doctrine does not consider the agent's system of epistemic beliefs, whereas the latter considers it. The author postulates that the absolute justification in this system is refutable. He purposes to explain why the rejection of absolute justification does not raise objections to relativism. Considering that the set of epistemic beliefs are found in a system in a justified way, even if we suppose that this system of beliefs is coherent, one can have the problem of the circularity of justifications.
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There are two distinct senses of the word "undecidable" in contemporary use. The first of these is the sense used in relation to Gödel's theorems, that of a statement being neither provable nor refutable in a specified deductive system. The second sense is used in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of questions each requiring a yes or no answer. Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set.
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Approaches exist that allow for resolution of inconsistent beliefs without violating any of the intuitive logical principles. Most such systems use multi-valued logic with Bayesian inference and the Dempster-Shafer theory, allowing that no non-tautological belief is completely (100%) irrefutable because it must be based upon incomplete, abstracted, interpreted, likely unconfirmed, potentially uninformed, and possibly incorrect knowledge (of course, this very assumption, if non-tautological, entails its own refutability, if by "refutable" we mean "not completely [100%] irrefutable"). These systems effectively give up several logical principles in practice without rejecting them in theory.
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A statement that is neither provable nor disprovable from a set of axioms is called undecidable (from those axioms). One example is the parallel postulate, which is neither provable nor refutable from the remaining axioms of Euclidean geometry. Mathematicians have shown there are many statements that are neither provable nor disprovable in Zermelo–Fraenkel set theory with the axiom of choice (ZFC), the standard system of set theory in mathematics (assuming that ZFC is consistent); see list of statements undecidable in ZFC. Gödel's (first) incompleteness theorem shows that many axiom systems of mathematical interest will have undecidable statements.
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The connection between these two is that if a decision problem is undecidable (in the recursion theoretical sense) then there is no consistent, effective formal system which proves for every question A in the problem either "the answer to A is yes" or "the answer to A is no". Because of the two meanings of the word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense. The usage of "independent" is also ambiguous, however. It can mean just "not provable", leaving open whether an independent statement might be refuted.
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If the officer has sufficient probable cause that the suspect has been driving under the influence of alcohol, they will make the arrest, handcuff the suspect and transport them to the police station. En route, the officer may advise them of their legal implied consent obligation to submit to an evidentiary chemical test of blood, breath or possibly urine depending on the jurisdiction. Laws relating to what exactly constitutes probable cause vary from state to state. In California it is a refutable presumption that a person with a BAC of 0.08% or higher is driving under the influence.
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There are two distinct senses of the word "undecidable" in mathematics and computer science. The first of these is the proof-theoretic sense used in relation to Gödel's theorems, that of a statement being neither provable nor refutable in a specified deductive system. The second sense, which will not be discussed here, is used in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of questions each requiring a yes or no answer. Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set (see undecidable problem).
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Because of the two meanings of the word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense. Undecidability of a statement in a particular deductive system does not, in and of itself, address the question of whether the truth value of the statement is well-defined, or whether it can be determined by other means. Undecidability only implies that the particular deductive system being considered does not prove the truth or falsity of the statement. Whether there exist so-called "absolutely undecidable" statements, whose truth value can never be known or is ill-specified, is a controversial point in the philosophy of mathematics.
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16, 21 Feb.,'09.see also Baggini's additional comments on his talkingphilosophy site and the subsequent discussion A. C. Grayling wrote a highly critical review in the New Humanist. He states that the responses to questions concerning science and religion boil down to three strategies, God of the gaps, inference to the best explanation, and religion and science explain truths in different domains. He considers the first two refutable by undergraduates, and for the third strategy to work, he contends that one has to "cherry-pick which bits of scripture and dogma are to be taken as symbolic and which as literally true" in order to conveniently avoid the possibility of direct and testable confrontation with science.
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There are a number of equivalent ways to formulate rules for negation. One usual way to formulate classical negation in a natural deduction setting is to take as primitive rules of inference negation introduction (from a derivation of P to both Q and eg Q, infer eg P; this rule also being called reductio ad absurdum), negation elimination (from P and eg P infer Q; this rule also being called ex falso quodlibet), and double negation elimination (from eg eg P infer P). One obtains the rules for intuitionistic negation the same way but by excluding double negation elimination. Negation introduction states that if an absurdity can be drawn as conclusion from P then P must not be the case (i.e. P is false (classically) or refutable (intuitionistically) or etc.).
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Some countries are already adapting to the impending crisis by investing in broadband and reassigning spectrum bands. ITU is raising awareness to promote investment in broadband and keeps working to improve spectrum management worldwide. However, the argument about a looming bandwidth crunch is refutable according to some points of view. Former FCC official Uzoma Onyeije conducted a study that questions the existence of a broadband spectrum crisis, and further goes on to suggest alternatives to existing networks that would mitigate the need to reallocate spectrum. Onyeije argues that before claiming a “Spectrum Crisis” exists, carriers should leverage available marketplace solutions to appease the current infrastructure namely upgrading network technology, adopting fair use policies, migrating voice to internet protocol, leveraging consumer infrastructure, enhancing carrier Infrastructure, packet prioritization, caching, channel bonding and encouraging the development of bandwidth-sensitive applications and devices.
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Consumer theory is therefore based on generating refutable hypotheses about the nature of consumer demand from this behavioral postulate. In order to reason from the central postulate towards a useful model of consumer choice, it is necessary to make additional assumptions about the certain preferences that consumers employ when selecting their preferred "bundle" of goods. These are relatively strict, allowing for the model to generate more useful hypotheses with regard to consumer behavior than weaker assumptions, which would allow any empirical data to be explained in terms of stupidity, ignorance, or some other factor, and hence would not be able to generate any predictions about future demand at all. For the most part, however, they represent statements which would only be contradicted if a consumer was acting in (what was widely regarded as) a strange manner.
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