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wittgenstein, tractatus testo

Wittgenstein uses, as an analogy, the field of vision. x . ." ed. In all these cases it seems natural to express the phenomenon in the form "A doubts p" "A desires p," etc., which makes it appear as though we were dealing with a relation between a person and a proposition. ) Cercherò di mettere in luce le affinità tra i due testi e, more. A proposition (true or false) asserting an atomic fact is called an atomic proposition. Merito di Russell è aver ) "In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all. 4.111 La Filosofia non è una scienza naturale. ) Ciò che accade, il Fatto, è il sussistere di Stati di Cose. This belongs to the part of logic which can be expressed, according to Mr Wittgenstein's system. The basic building blocks of reality are simple objects combined to form states of affairs. tautologia non ha condizioni di verità, poiché è incondizionatamente vera; e la contraddizione è sotto nessuna Our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary, since it has nothing outside it. Opera originale: Autore: - Titolo: Un'introduzione alla lettura del testo di Ludwig Wittgenstein: il Tractatus Logico-Philosophicus [Book (translation)] Ciò parrebbe infatti presupporre che noi escludiamo certe possibilità, Philosophy is not a theory but an activity. […]. 6.1 Le proposizioni della Logica sono tautologie. "But it is clear that 'A believes that p,' 'A thinks p,' 'A says p' are of the form p says p; and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects" (5.542). La filosofia è non una dottrina, ma un’attività. The psychological part of meaning, however, does not concern the logician. ¯ Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten. Einaudi. More interesting than such questions of comparative detail is Mr Wittgenstein's attitude towards the mystical. Facts may contain parts which are facts or may ​contain no such parts; for example : "Socrates was a wise Athenian," consists of the two facts, "Socrates was wise," and "Socrates was an Athenian." The right method of teaching philosophy, he says, would be to confine oneself to propositions of the sciences, stated with all possible clearness and exactness, leaving philosophical assertions ​to the learner, and proving to him, whenever he made them, that they are meaningless. The assertion that there is a certain complex reduces to the assertion that its constituents are related in a certain way, which is the assertion of a fact : thus if we give a name to the complex the name only has meaning in virtue of the truth of a certain proposition, namely the proposition asserting the relatedness of the constituents of the complex. Luciano Bazzocchi, The Form of the Tractatus and a False Perception of a Drawing by Wittgenstein The tree of the Tractatus, ... mento, non riusciamo a vedere il testo composto da Wittgenstein. Né meraviglia che i mostrargli che, a certi segni nelle sue proposizioni, egli non ha dato significato alcuno. We must take up next the question of molecular propositions which are at first sight not truth-functions, of the propositions that they contain, such, for example as "A believes p.". [Die Welt ist alles, was der Fall ist]. Infatti ogni avvenire ed The so-called logical "constants" are not represented by signs, but are themselves present in the proposition as in the fact. x Ci si concentra soprattutto sui due interventi da Jesi dedicati al filosofo viennese nel 1972 e nel 1977. N The definition of identity by means of the identity of indiscernibles is rejected, because the identity of indiscernibles appears to be not a logically necessary principle. * 2. 6.52 Noi sentiamo che anche qualora tutte le possibili domande scientifiche avessero 4.4611 Tautologia e contraddizione non sono però insensate; esse appartengono al simbolismo, cosí come lo “o” al Tractatus logico-Philosophicus. Any possible state of affairs can either be the case or not be the case, independent of all other states of affairs. 2. . Cosa muove Wittgenstein alla critica della concezione del linguaggio esposta nel Tractatus? Testo originate, versione italiana a fronte, introduzione critica e note a cura di G. C. M. COLOMBO, S. J. Fratelli Bocca, Milano-Roma, I954. 2. 1.12 Ché la totalità dei fatti determina ciò che accade, ed anche tutto ciò che non accade. This is perhaps the most fundamental thesis of Mr Wittgenstein's theory. 3. These projective properties correspond to that which in his theory the proposition and the fact must have in common, if the proposition is to assert the fact. e questo non può essere, poiché altrimenti la logica dovrebbe trascendere i limiti del mondo; solo cosí potrebbe Il mondo è tutto ciò che accade. 4.002 L’uomo possiede la capacità di costruire linguaggi, con i quali ogni senso può esprimersi, senza sospettare To all of ​them the logical structure is common. The proposition and the fact must exhibit the same logical "manifold," and this cannot be itself represented since it has to be in common between the fact and the picture. What we cannot think we cannot think, therefore we also cannot say what we cannot think. There are some respects, in which, as it seems to me, Mr Wittgenstein's theory stands in need of greater technical development. 2.14 L’immagine consiste nell’essere i suoi elementi in una determinata relazione l’uno al l’altro. ( Der Gedanke ist der sinnvolle Satz. 6.45 Intuire mondo sub specie aeterni è intuirlo quale tutto limitato. Testo originale a fronte, Libro di Ludwig Wittgenstein. What is meant is somewhat less complicated than it sounds. Logic, he says, fills the world. A truth-function of a proposition p is a proposition containing p and such that its truth or falsehood depends only upon the truth or falsehood of p, and similarly a truth-function of several propositions p, q, r … is one containing p, q, r … and such that its truth or falsehood depends only upon the truth or falsehood of p, q, r …. Essa deve delimitare l’impensabile dal di dentro, Kerro myös, millainen sinun työpaikkasi on. 6.43 Il buono o cattivo volere […] può alterare solo i limiti del mondo, non i fatti. (Esse sono della specie della questione, se il bene sia piú o meno identico del bello). Other readers will always be interested in your opinion of the books you've read. Questo è un testo molto interessante e molto impegnativo (anche in italiano), che richiede molta attenzione e dedizione. Ché dubbio può sussistere solo ove sussiste una domanda; domanda, solo ove sussiste una risposta; "Philosophy is not one of the natural sciences. The metaphysical subject does not belong to the world but is a boundary of the world. That which has to be in common between the sentence and the fact cannot, so he contends, be itself in turn said in language. Dev’essere fuori del mondo. tutte le possibilità di verità delle proposizioni elementari. Ludwig Wittgenstein iniziò a lavorare al Tractatus logico-philosophicus a partire dal 1910 e lo completò durante la prima guerra mondiale, quando si trovò prigioniero a Montecassino. ) 4.463 Le condizioni di verità determinano il margine che è lasciato ai fatti dalla proposizi one. 3i9. 6.54 Le mie proposizioni illustrano così: colui che le comprende, alla fine le riconosce They are all in a certain sense one) " (4.014). f ¯ 4.1 La proposizione rappresenta il sussistere o no degli stati di cose. Il mondo del felice è altro rispetto a quello dell’infelice. It follows that if we can define truth-functions generally, we can obtain a general definition of all propositions in terms of the original set of atomic propositions. At first sight, he goes on to explain, it seems as if a proposition could also occur in other ways, e.g. ... Eine zweite zweisprachige Ausgabe erschien 1933. "We must not say, the complex sign ‘aRb‘ says ‘a‘ stands in a certain relation R to b‘; but we must say, that ’a‘ stands in a certain relation to ‘b' says that a R b" (3.1432). Risultato della filosofia non sono «proposizioni f The object of philosophy is the logical clarification of thoughts. ) "] differs from previous methods by the fact that the generality comes only in specifying the set of propositions concerned, and when this has been done the building up of truth-functions proceeds exactly as it would in the case of a finite number of enumerated arguments "p, q, r, …". 2.1 Noi ci facciamo immagini dei fatti. This amounts to saying that "object" is a pseudo-concept. ξ The following is the explanation of this symbol: The whole symbol 6.4 Tutte le proposizioni sono d’egual Valore. condizione vera. Acquistalo su libreriauniversitaria.it! philosophicus di Wittgenstein, nonostante che l'unitarietà dell'opera e la coesa archi tettura rappresentativa renda più difficile riconoscere una analoga evoluzione di pen siero. A philosophical work consists essentially of elucidations. 4.115 Essa significherà l’indicibile rappresentando chiaro il dicibile [...] 6.53 Il Metodo corretto della filosofia sarebbe questo: nulla dire se non ciò che può PP. Ludwig Wittgenstein Tractatus logico-philosophicus Antologia a cura di Dario Zucchello . The Complete Poetry and Prose of William Blake. 1.11 Il mondo è determinato dai fatti e dall’essere essi tutti i fatti. eccezione di Ludwig Wittgenstein (1889-1951) negli ultimi anni della sua vita, ... Questo e il testo di una lezione tenuta il 31 marzo 2011 presso la 5a B Scienti co del Liceo ... (Tractatus, 6.53) Per illustrare la tesi (iv) partiamo dal fatto che, nelle lingue naturali, la forma fondamentale e quella soggetto-predicato. 6.522 Vi è davvero dell’ineffabile: esso mostra sé, è il Mistico. Il pensiero è la proposizione munita di senso. 185-262). The possibility of a proposition representing a fact rests upon the fact that in it objects are represented by signs. ( In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. 5.632 Il soggetto non appartiene al mondo, ma è un limite del mondo. We here touch one instance of Wittgenstein's fundamental thesis, that it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world. {\displaystyle ({\bar {p}},{\bar {\xi }},{\bar {N}}({\bar {\xi }}))} Nel primo caso noi chiamiamo la proposizione una tautologia; nel secondo, una contraddizione. cipale opera del primo periodo, fu proposto da G. E. Moore, quando si decise di pubblicarla in inglese, in omaggio al Tractatus theologico-poli-ticus di Spinoza, benché la stesura formale assomigli di più all'Etica di Hence, the author demonstrates that the solution to most philosophic problems becomes a critical method of linguistic analysis. There cannot, in Wittgenstein's logic, be any such thing as a causal nexus. linguaggio comune è una parte dell’organismo umano, né è meno complicato di questo. A geometrical figure may be projected in many ways: each of these ways corresponds to a different language, but the projective properties of the original figure remain unchanged whichever of these ways may be adopted. It has been sought to find such a property in self-identity, but the conception of identity is subjected by Wittgenstein to a destructive criticism from which there seems no escape. 2.12 L’immagine è un modello della realtà. A name is“semantically simple” in the sense that its meaning doesnot depend on the meanings of its orthographic parts, even when thoseparts are, in other contexts, independently meaningful. Il Pensiero è la Proposizione munita di Senso. He compares linguistic expression to projection in geometry. Ciò che è evento, il fatto, è il sussistere di stati di cose. It is this common structure which makes it capable of being a picture of the fact, but the structure cannot itself be put into words,since it is a structure of words, as well as of the facts to which they refer. Such an hypothesis is very difficult, and I can see objections to it which at the moment I do not know how to answer. 4.2 Il senso della proposizione è la sua concordanza o meno con le possibilità del ." Mr Wittgenstein begins his theory of Symbolism with the statement (2.1): "We make to ourselves pictures of facts." “We feel that even if all possible scientific questions be answered, the problems of life have still not … 6.21 La proposizione della matematica non esprime un pensiero. Such propositions may be called molecular. Most questions and propositions of the philosopher result from the fact that we do not understand the logic of our language. 1. Tractatus logico-philosophicus e Quaderni 1914-1916 Ludwig Wittgenstein. of our primitive function. In this way the naming of simples is shown to be what is logically first in logic. What does concern him in this problem of belief is the logical schema. What is relevant to logic is that common element among all these facts, which enables him, as we say, to mean the fact which the proposition asserts. {\displaystyle (\exists x).fx} His attitude upon this grows naturally out of his doctrine in pure logic, according to which the logical proposition is a picture (true or false) of the fact, and has in common with the fact a certain structure. It may be that this defence is adequate, but, for my part, I confess that it leaves me with a certain sense of intellectual discomfort. […]. L'immagine logica dei fatti è il pensiero. avuto un’intuizione genuina: che una proposizione fosse un’immagine 11. The manner in which other truth-functions are constructed out of "not-p and not-q" is easy to see. Allora vede The “names” spoken of in the Tractatus are notmere signs (i.e., typographically or phonologically identifiedinscriptions), but rather signs-together-with-their-meanings —or “symbols.” Being symbols, names are identified andindividuated only in the context of significant sentences. Of course, the problem applies not only to belief, but also to a host of other mental phenomena which may be called propositional attitudes: doubting, considering, desiring, etc. Everything, therefore, which is involved in the very idea of the expressiveness of language must remain incapable of being expressed in language, and is, therefore, inexpressible in a perfectly precise sense. Nevertheless he is capable of conveying his ethical opinions. Ludwig Wittgenstein’s Tractatus Logico-Philosophicus is in the Public Domain. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org According to this view we could only say things about the world as a whole if we could get outside the world, if, that is to say, it ceased to be for us the whole world. , f Gli otto capitoli in cui il volume si suddivide seguono la cronologia del pensiero e della produzione di Wittgenstein, scandita da tre testi di riferimento che compaiono proprio nell’indice: il Tractatus Logi- co-Philosophicus (1921), le Ricerche filosofiche e Della certezza (editi en- … Fuori della logica tutto è Accidente. ( First, there is the problem what actually occurs in our minds when we use language with the intention of meaning something by it; this problem belongs to psychology. Newly rev. Wittgenstein, Ludwig – Tractatus Logico-Philosophicus (German-English Side by Side Edition) ePub Edition – Read Online Now Wollstonecraft, Mary – A Vindication of the Rights of Women 3.03 Non possiamo pensare nulla d’illogico, ché altrimenti dovremmo pensare illogicamente. Objects can only be mentioned in connexion with some definite property. There is no way whatever, according to him, by which we can describe the totality of things that can be named, in other words, the totality of what there is in the world. According to this principle x is identical with y if every property of x is a property of y, but it would, after all, be logically possible for two things to have exactly the same properties. 5.61 La logica riempie il mondo; i limiti del mondo sono anche i suoi limiti. 4.001 La totalità delle proposizioni è il Linguaggio. This view may have been originally suggested by notation, and if so, that is much in its favour, for a good notation has ​a subtlety and suggestiveness which at times make it seem almost like a live teacher. ) This is, he says, the general truth-function and also the general form of proposition. avuto risposta, i problemi della vita non sarebbero stati ancora neppure toccati. to cases where the propositions which are arguments to our truth-function are not given by enumeration but are given as all those satisfying some condition. p Ciò, che non possiamo pensare, non possiamo pensare; né dunque Ciò che è pensabile è anche possibile. simbolismo dell’aritmetica. That the world is my world appears in the fact that the boundaries of language (the only language I understand) indicate the boundaries of ​my world. The theory with which he is disagreeing will be found in my articles on the nature of truth and falsehood in Philosophical Essays and Proceedings of the Aristotelian Society, 1906-7. Math. Wittgenstein makes use of the latter, assuming a ​knowledge of Dr Sheffer's work. Nel Tractatus Wittgenstein aveva . La 4.112 Scopo della filosofia è la chiarificazione logica dei pensieri. filosofiche», ma il chiarirsi di proposizioni. To say "x is an object" is to say nothing. "The events of the future," he says, "cannot be inferred from those of the present. Il piú 1 Il mondo è tutto ciò che accade. 6.41 Il senso del mondo dev’essere al di fuori di esso. What Solipsism intends is quite correct, but this cannot be said, it can only be shown. His defence would be that what he calls the mystical can be shown, although it cannot be said. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. ( Der Satz ist eine Wahrheitsfunktion […]. Il "primo Wittgenstein" Il titolo latino Tractatus logico-philosophicus, dato alla sua prin-7. 3.01 La totalità dei pensieri veri è un’immagine del mondo. what is the schema representing what occurs when a man believes. It can, in his phraseology, only be shown, not said, for whatever we may say will still need to have the same structure. It is clear that, when a person believes a proposition, the person, considered as a metaphysical subject, does not have to be assumed in order to explain what is happening. (Ma non nel senso di Mauthner). An atomic fact, although it contains no parts that are facts, nevertheless does contain parts. This is the same thing that he calls an atomic fact. If we may regard "Socrates is wise" as an atomic fact we perceive that it contains the constituents "Socrates" and "wise." 6.4311 La morte non è un evento della vita. In realtà, nel testo originale Wittgenstein si limita a . 1 The world is all that is the case. Tractatus logico-philosophicus online, Ludwig Wittgenstein, a cura di Luciano Bazzocchi. cipale opera del primo periodo, fu proposto da G. E. Moore, quando si decise di pubblicarla in inglese, in omaggio al Tractatus theologico-poli-ticus di Spinoza, benché la stesura formale assomigli di più all'Etica di possibile, impossibile: Ecco l’indizio di quella gradazione che ci serve nella teoria della probabilità). The series of words is a fact just as much as what makes it true or false is a fact. It is impossible, for example, to make a statement about two men (assuming for the moment that the men may be treated as simples), without employing two names, and ​if you are going to assert a relation between the two men it will be necessary that the sentence in which you make the assertion shall establish a relation between the two names. Non si dà Enigma. L’etica è trascendentale. IBS.it, da 21 anni la tua libreria online ... Tractatus logico-philosophicus e Quaderni 1914-1916. Even if this very difficult hypothesis should prove tenable, it would leave untouched a very large part of Mr Wittgenstein's theory, though possibly not the part upon which he himself would wish to lay most stress. The fact that nothing can be deduced from an atomic proposition has interesting applications, for example, to causality. 4.022 La proposizione mostra il suo senso. L'albero del Tractatus pdf . sussistere o meno degli stati di cose. In 1908 he began his studies in aeronauticalengineering at Manchester University where his interest in thephilosophy of pure mathematics led him to Frege. (La parola «filosofia» deve significare qualcosa che sta Ciò che accade, il fatto, è il sussistere di stati di cose. 4.114 Essa deve delimitare il pensabile e con ciò l’impensabile. , alcuna relazione di rappresentazione con la realtà. 2.11 L’immagine presenta la situazione nello spazio logico, il sussistere e non sussistere di stati di cose. The negation of this would be the proposition "there is at least one x for which fx is true" which is represented by " Le condizioni di verità sono contraddittorie. means whatever can be obtained by taking any selection of atomic propositions, negating them all, then taking any selection of the set of propositions now obtained, together with any of the originals—and so on indefinitely. 1.1 Il mondo è la totalità dei fatti, non delle cose. Corso di linguistica generale ... testo che apre visioni sull'essenza del linguaggio come "giuoco" mentale e associazione contestuale della realtà. The Wittgenstein family was one of the richest, most talented and most eccentric in Europe. He says (5-54): *' In the general propositional form, propositions occur in a proposition only as bases of truth-operations." volta, accidentale. 321 . [2] Le proposizioni del Tractatus sono numerate secondo un ordine crescente; maggiore è il numero di cifre associato alla proposizione, più questa è rilevante. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to epistemology. Il Tractatus Logico-Philosophicus: introduzione alla lettura, LONDON, Routledge, 2008, pp. possiamo dire ciò che non possiamo pensare. But to have constructed a theory of logic which is not at any point obviously wrong is to have achieved a work of extraordinary difficulty and importance. L’immagine logica dei Fatti è il Pensiero. In a logically perfect language nothing that is not simple will have a simple symbol. In logic, therefore, we cannot say, there is this and this in the world, but not that, for to say so would apparently presuppose that we exclude certain possibilities, and this cannot be the case, since it would require that logic should go beyond the boundaries of the world as if it could contemplate these boundaries from the other side also. You can write a book review and share your experiences. Fourthly, there is the question: what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other? insensate, se è salito per mezzo di esse, su esse, oltre esse. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. WITTGENSTEIN’S LADDER “My propositions serve as elucidations in the following way: anyone who understands them eventually recognizes them as nonsensical, when he has used them––as steps––to climb up beyond them. This cannot, of course, be the ultimate analysis, since persons are fictions and so are propositions, except in the sense in which they are facts on their own account. Tractatus and not 2 the Philosophical Investigations ; not all of them consider the most important ideas in the Tractatus but often discuss marginal points; above all they often make the discussion of Wittgenstein's ideas secondary to the development of their own thought. What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation" (2. Ludwig Wittgenstein, in his Tractatus Logico-Philosophicus, introduced the concept of logical space. His ground for maintaining that there must be simples is that every complex presupposes a fact. The totalities concerning which Mr Wittgenstein holds that it is impossible to speak logically are nevertheless thought by him to exist, and are the subject-matter of his mysticism. desumerne immediatamente la logica del linguaggio. linguaggio. It follows from this that we cannot make such statements as ** there are more than three objects in the world," or "there are an infinite number of objects in the world." which, as it stands, is only capable of dealing with finite numbers. That the sun will rise to-morrow is a hypothesis. There is one purely logical problem in regard to which these difficulties are peculiarly acute. * 2. The whole subject of ethics, for example, is placed by Mr Wittgenstein in the mystical, inexpressible region. In the first years after publication (in 1921) it was primarily read as a work aiming to put an end to nonsensical language and all kinds of metaphysical speculation. WITTGENSTEIN’S Tractatus Logico-Philosophicus, whether or not it prove to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an important event in the philosophical world. Thus the whole business of logical inference is concerned with propositions which are not atomic. valore. ∃ Di ciò di cui non si può parlare, si deve tacere. Accordingly, the proposition as a whole does not really enter into what has to be explained in explaining the meaning of a proposition. Facts which are not compounded of other facts are what Mr Wittgenstein calls Sachverhalte whereas a fact which may consist of two or more facts is called a Tatsache: thus, for example, "Socrates is wise" is a Sachverkalt, as well as a Tatsache whereas "Socrates is wise and Plato is his pupil" is a Tatsache but not a Sachverhalt. nel mondo. Berkeley vive a Dublino, dopo essersi immatricolato al Trinity College della stessa città. Infatti, quella ammette ogni possibile situazione; questa, nessuna. mostrato che la forma logica apparente della proposizione non ne è necessariamente la forma reale. In order to be able to do this we should have to know of some property which must belong to every thing by a logical necessity. Wittgenstein, however, by a very interesting analysis succeeds in extending the process to general propositions, i.e. Nel mondo tutto è come è, e tutto avviene come avviene; non v’è in esso alcun valore – né, se vi fosse, avrebbe un It might seem at first sight as though there were other functions of propositions besides truth-functions; such, for example, would be "A believes p," for in general A will believe some true propositions and some false ones: unless he is an exceptionally gifted individual, we cannot infer that p is true from the fact that he believes it or that p is false from the fact that he does not believe it. ) If we had started with not-fx instead oi fx we should have arrived at the proposition "fx is true for all values of x" which is represented by ... tractatus 127. que la 120. notre 119. ici 118. qui est 118. est pas 118. que le 118. de langage 118. vie 116. serait 115. cela 114 . . Find books Chiunque si senta respinto dalla complessità di questi lavori, o attratto dalla fama di Wittgenstein, ma troppo impaurito per leggerlo, troverà nel testo di John Heaton e nelle illustrazioni di Judy Groves, l'introduzione ideale a un grande filosofo del ventesimo secolo. In Tractatus Logico-Philosophicus, Wittgenstein “deals with the problems of philosophy and shows … that the method of formulating these problems rests on the misunderstanding of the logic of our language.”. p Ed. It may be any one of innumerable different things. Nella tautologia le condizioni della for Symbolism in which a sentence "means" something quite definite. Berkeley and Los Angeles: U of California Press, 1988. In practice, language is always more or less vague, so that what we assert is never quite precise. problemi piú profondi propriamente non siano problemi. 4.0031 Tutta la filosofia è «critica del linguaggio». {\displaystyle ({\bar {p}},{\bar {\xi }},{\bar {N}}({\bar {\xi }}))} Wittgenstein, Tractatus edizione di Colombo, 1954, Fratelli Bocca Editore La migliore edizione del Tractatus con testo a fronte e introduzione di Russell. (Non è forse per ¯ delle questioni e proposizioni dei filosofi si fonda sul fatto che noi non comprendiamo la nostra logica del A logically perfect language has rules of syntax which prevent nonsense, and has single symbols which always have a definite and unique meaning.

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