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27-525: The sutta starts off by describing how the Buddha passes through the village of Kesaputta and is greeted by its inhabitants, a clan called the Kalamas . They ask for his advice: they say that many wandering holy men and ascetics pass through, expounding their teachings and criticizing the teachings of others. So whose teachings should they follow? He delivers in response a sermon that serves as an entry point to

54-496: A logical system has the soundness property if every formula that can be proved in the system is logically valid with respect to the semantics of the system. In most cases, this comes down to its rules having the property of preserving truth . The converse of soundness is known as completeness . A logical system with syntactic entailment ⊢ {\displaystyle \vdash } and semantic entailment ⊨ {\displaystyle \models }

81-434: A deductive system is the property that any sentence P of the language upon which the deductive system is based that is derivable from a set Γ of sentences of that language is also a logical consequence of that set, in the sense that any model that makes all members of Γ true will also make P true. In symbols where Γ is a set of sentences of L : if Γ ⊢ S   P , then also Γ ⊨ L   P . Notice that in

108-522: A fake quote attributed to the Buddha and this sutta that includes "when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it," which is in part the opposite of what the sutta actually states. Root texts Translations Essays Kesaputta Too Many Requests If you report this error to the Wikimedia System Administrators, please include

135-407: A semantic theory is strongly complete if every sentence P that is a semantic consequence of a set of sentences Γ can be derived in the deduction system from that set. In symbols: whenever Γ ⊨ P , then also Γ ⊢ P . Completeness of first-order logic was first explicitly established by Gödel , though some of the main results were contained in earlier work of Skolem . Informally,

162-407: A sound argument is the following well-known syllogism : Because of the logical necessity of the conclusion, this argument is valid; and because the argument is valid and its premises are true, the argument is sound. However, an argument can be valid without being sound. For example: This argument is valid as the conclusion must be true assuming the premises are true. However, the first premise

189-520: A soundness theorem for a deductive system expresses that all provable sentences are true. Completeness states that all true sentences are provable. Gödel's first incompleteness theorem shows that for languages sufficient for doing a certain amount of arithmetic, there can be no consistent and effective deductive system that is complete with respect to the intended interpretation of the symbolism of that language. Thus, not all sound deductive systems are complete in this special sense of completeness, in which

216-492: A system is sound when all of its theorems are tautologies . Soundness is among the most fundamental properties of mathematical logic. The soundness property provides the initial reason for counting a logical system as desirable. The completeness property means that every validity (truth) is provable. Together they imply that all and only validities are provable. Most proofs of soundness are trivial. For example, in an axiomatic system , proof of soundness amounts to verifying

243-578: Is sound if for any sequence A 1 , A 2 , . . . , A n {\displaystyle A_{1},A_{2},...,A_{n}} of sentences in its language, if A 1 , A 2 , . . . , A n ⊢ C {\displaystyle A_{1},A_{2},...,A_{n}\vdash C} , then A 1 , A 2 , . . . , A n ⊨ C {\displaystyle A_{1},A_{2},...,A_{n}\models C} . In other words,

270-429: Is false. Not all birds can fly (for example, ostriches). For an argument to be sound, the argument must be valid and its premises must be true. Some authors, such as Lemmon , have used the term "soundness" as synonymous with what is now meant by "validity", which left them with no particular word for what is now called "soundness". But nowadays, this division of the terms is very widespread. In mathematical logic ,

297-522: Is simply a freethinker's kit to truth which invites each one to accept and reject whatever he likes. Rather than supporting skepticism or subjective truths, in the sutta the Buddha continues to argue that the three unwholesome roots of greed, hatred and delusion lead to the opposite negative results, i.e. they are unskillful, blameworthy, etc. Consequently, behaviour based on these three roots should be abandoned. Moral judgements of actions can therefore be deduced by analysing whether these actions are based on

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324-426: Is sound if and only if every well-formed formula that can be proven in the system is logically valid with respect to the logical semantics of the system. In deductive reasoning , a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion must be true. An example of

351-520: Is the third solace found by him. 'Suppose evil (results) do not befall an evil-doer. Then I see myself purified in any case.' This is the fourth solace found by him. The disciple of the Noble Ones, Kalamas, who has such a hate-free mind, such a malice-free mind, such an undefiled mind, and such a purified mind, is one by whom, here and now, these four solaces are found. On these four solaces, Soma Thera wrote: The Kalama Sutta, which sets forth

378-546: The Buddha says, only when one personally knows that a certain teaching is skillful, blameless, praiseworthy, and conducive to happiness, and that it is praised by the wise, should one then accept it as true and practice it. Thus, as stated by Soma Thera , the Kalama Sutta is just that, the Buddha's charter of free inquiry: The instruction of the Kalamas (Kalama Sutta) is justly famous for its encouragement of free inquiry;

405-578: The Dhamma, the Buddhist teachings for those unconvinced by mere spectacular revelation. The Buddha proceeds to list the criteria by which any sensible person can decide which teachings to accept as true. Do not blindly believe religious teachings, he tells the Kalamas, just because they are claimed to be true, or even through the application of various methods or techniques. Direct knowledge grounded in one's own experience can be called upon. He advises that

432-399: The Noble Ones, Kalamas, who has such a hate-free mind, such a malice-free mind, such an undefiled mind, and such a purified mind, is one by whom four solaces are found here and now. 'Suppose there is a hereafter and there is a fruit, result, of deeds done well or ill. Then it is possible that at the dissolution of the body after death, I shall arise in the heavenly world, which is possessed of

459-422: The details below. Request from 172.68.168.226 via cp1108 cp1108, Varnish XID 211712007 Upstream caches: cp1108 int Error: 429, Too Many Requests at Thu, 28 Nov 2024 07:40:09 GMT Soundness In logic and deductive reasoning , an argument is sound if it is both valid in form and has no false premises . Soundness has a related meaning in mathematical logic , wherein a formal system of logic

486-450: The latter. Weak soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based. In symbols, where S is the deductive system, L the language together with its semantic theory, and P a sentence of L : if ⊢ S   P , then also ⊨ L   P . Strong soundness of

513-523: The overcoming of greed, hate, and delusion. The Kesamutti Sutta is often incorrectly used for advocating prudence by the use of sound logical reasoning arguments for inquiries in the practice that relates to the discipline of seeking truth, wisdom and knowledge whether it is religious or not. However, a plain reading of the text clearly states that one should not determine the validity of tradition based "by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by

540-453: The principles that should be followed by a seeker of truth, and which contains a standard things are judged by, belongs to a framework of the Dhamma; the four solaces taught in the sutta point out the extent to which the Buddha permits suspense of judgment in matters beyond normal cognition. The solaces show that the reason for a virtuous life does not necessarily depend on belief in rebirth or retribution, but on mental well-being acquired through

567-462: The spirit of the sutta signifies a teaching that is exempt from fanaticism, bigotry, dogmatism, and intolerance. However, as stated by Bhikkhu Bodhi , this teaching is not intended as an endorsement for either radical skepticism or as for the creation of unreasonable personal truth : On the basis of a single passage, quoted out of context, the Buddha has been made out to be a pragmatic empiricist who dismisses all doctrine and faith, and whose Dhamma

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594-460: The state of bliss.' This is the first solace found by him. 'Suppose there is no hereafter and there is no fruit, no result, of deeds done well or ill. Yet in this world, here and now, free from hatred, free from malice, safe and sound, and happy, I keep myself.' This is the second solace found by him. 'Suppose evil (results) befall an evil-doer. I, however, think of doing evil to no one. Then, how can ill (results) affect me who do no evil deed?' This

621-460: The statement of strong soundness, when Γ is empty, we have the statement of weak soundness. If T is a theory whose objects of discourse can be interpreted as natural numbers , we say T is arithmetically sound if all theorems of T are actually true about the standard mathematical integers. For further information, see ω-consistent theory . The converse of the soundness property is the semantic completeness property. A deductive system with

648-580: The thought, 'This contemplative is our teacher.'" While nothing in the text limits one from employing their own reasoning, the Buddha instructs not to make a decision based alone on it. Instead, the Buddha teaches that one can determine the validity of a tradition if "These qualities are skillful; these qualities are blameless; these qualities are praised by the wise; these qualities, when adopted & carried out, lead to welfare & to happiness' — then you should enter & remain in them." The misunderstanding of this sutta has become popular in part by reliance on

675-488: The unwholesome roots or not. The first and main part of the Kesamutti Sutta is often quoted, but an equally important section of the Kesamutti Sutta follows on from this. This section (17) features the Buddha's four assurances, or solaces. The Buddha asserts that a happy and moral life would be correct if there is no karma and reincarnation . The logic is comparable to that of Pascal's wager . The disciple of

702-412: The validity of the axioms and that the rules of inference preserve validity (or the weaker property, truth). If the system allows Hilbert-style deduction , it requires only verifying the validity of the axioms and one rule of inference, namely modus ponens (and sometimes substitution). Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of

729-487: The words of the wise should be heeded and taken into account. He proposes not a passive acceptance but, rather, constant questioning and personal testing to identify those truths which verifiably reduce one's own suffering or misery (Pali: dukkha ). The Kesamutti Sutta states (Pali expression in parentheses): Thus, the Buddha named ten specific sources whose knowledge should not be immediately viewed as truthful without further investigation to avoid fallacies : Instead,

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