Justification Attempt for The Process and Result of Interlanguage Translations

Ludwig Wittgenstein.

How do we tell a translation is correct — or the right one — or that is true? A translator could come up with the idea of subjective self bilingual ability, or the notions of language-cultural understanding, or the people-environment practical experience and repetition, or to state the reference from the general dictionaries that everybody uses and access widely. These are fine, but there’s possibility for these do not meet the demand, in the answer it provided, nor in the novelty it presented.

Hence, here we have a simple attempt to give us another idea and explanation of resolving the problem of justification for the interlanguage translations, using the fragments mainly taken from Ludwig Wittgenstein’s TLP and other related sources of the stated. The process of this operation is to apply some mathematical calculations and logical propositions, with familiar predicates and symbols.

For I am only capable in English and Indonesian, the example for this operation will be from these languages. The translations of a sentence to another sentence, and these sentences I shall call propositions. To put the example below:

I have a lot of money (1) English = Saya punya banyak uang (2) Indonesian

Dictionaries not only translate substantive (nouns) but also adjectives, conjunctions, etc., and treat them all the same. The meaning of simple signs (words) must be explained if we want to understand them. A process of translating from one language to another language is not a process of translating each proposition from one unity of a language to another of the same, but translating only the elemental part of the proposition, and it is important for the propositions to communicate to us a new mind.-Wittgenstein, Tractatus Logico-Philosophicus (1921).

I interpret the ‘elemental part’ by Wittgenstein as that a proposition in the context of (1), can only be translated into a proposition in the context of (2) — when it is done element by element, namely the word by word. Based on this, I translate not the proposition (1), but rather translates the elements in the proposition of (1) into the proposition (2).

Every statement regarding complexity can be analyzed in terms of its element parts, and in the results of the proposition from these elements, one can fully explain the complexity. Ferdinand de Saussure once said about how language consists of negative facts, which “if it’s Y that it is precisely, and not X, Z, etc.”. Language is “if not this then the other, but I cannot give an affirmation of the question why, as I understand it as it is”.

Saussure idea of language is rather a tautology because he does not devote any significant amount of reflection of linguistic negation. Nevertheless, when a negation is presented, the negation should not only be presented to one particular elemental — or a proposition but for the entire context of occurrence. We have to understand two propositions formed in ‘~p’ i.e. propositions ‘~(p q)’. Proposition (1) and Proposition (2), the negation (~) is absolute even in the form of tautology of a language. To use the formula of logical disjunction:

p: I have a lot of money = Saya punya banyak uang
q: I have a lot of money = Saya punya banyak duit
q): false

This is because, the concept of tautology does not have a truth condition, because within its scope “however it is correct” or “always true”. Wittgenstein in his term truth operation asserts that in one particular operation, only one logical symbolization may be given because if you use other logical symbolization it will produce a lot of consequences (fallacy). In the structure of propositions (1), we must use one by one different logical symbolization for each element part within, which in its attempt to become propositions (2). We can’t use the logic symbolization:

p: I have a lot of money = Saya punya banyak uang
p: Money = Uang

Since the first “p: I have a lot of money = Saya punya banyak uang” results in four elements out of six elements, is different from the second “p: Money = Uang” as a result of one element out of one element. This idea of the logic symbolization is vice versa. In Wittgenstein’s terms the expedient or the path to get things have changed and resulted in a new structure in the second p structure as taken partially from the first p structure.

Wittgenstein says, that the presence of new words needs justification, if there’s none, then it cannot proceed. Futhermore, Wittgenstein’s theory used by Ian Proops, Proops gives an example if “Every F is G”, then the results of the stated cannot exactly be said “Ga & Gb & Gc” even though in F there are only a, b, c (Fa & Fb & Fc). Wittgenstein does not justify the possibility of an additional clause required in the other/next proposition as probably Wittgenstein’s idea of ​​the exact equivalence of two propositions can only occur in specific cases such as a, b, c are individuals (which are absolutely equal to produce equal equivalence).

Proops assumes that Wittgenstein cannot provide justification for this because his theory bases its symbolization on things that are limited in nature. Still, as Wittgenstein quote Gottlob Frege, Frege’s idea of “the infinite axioms” in linguistic expression is to say there is no number limited to their names and meanings. In the statement of tautology which “q” is true and “p” is false, the basis of truth that lies in “q” is contained in “p”, and “p” follows from “q”.

p: I have a lot of money = Saya punya banyak uang (true)
q: I have a lot of money = Saya punya banyak duit (false)
q): Tautology (if not p then q)

Gottlob Frege.

To be able to find that “p” is true, we first know the truth that “q” is false. That “p” is followed by “q”, and vice versa, for that they said to be one and the same proposition. The solution to this is to release the possible outcomes of translation where “q” is wrong for then “p” is true — or vice versa (tautology), through other symbolization approaches.

Wittgenstein states, using two propositions as to become equal — or with the same meaning, we express it by putting the symbol “=” between the two signs. For example, “a = b” is to say “a” can be replaced by “b”. Using propositions (1) and (2), the sign “b” can replace the sign “a”, it cannot be said propositions (1) = propositions (2). Rather propositions (1) = propositions (2) Def. It needs an equation-definition on the form “a=b Def.”, and the word ‘Def’ (definition) is just a symbolic rule.

a = I have a lot of money
b = Saya punya banyak uang
b = Saya punya banyak uang Def. (in the context of using the symbolic rule Def)

The function f in the example proposition stating “(x): f (x). ⊃. x=a) with the symbol (⊃) means “if”, it is only “a” can be sufficient for the function f or any that has a relation with “a”, and if it is said that the only one that really has a relation with “a” is the only “a” alone. Therefore:

I have a lot of money = I have a lot of money

Can we understand two propositions without knowing they are the same or different? According to Wittgenstein, if he knew a word in English, which synonyms are known to him in German, it is impossible that he doesn’t know they mean the same. It’s impossible for him not to be able to translate each other. Wittgenstein then agrees with Frege’s idea that we cannot use the symbol “=” because according to Frege is impossible to say that two objects are truly equal. To say two things are equal or identical (a=b, b=a), is not reasonable, and to state that one thing is identical with itself (a=a) is not saying anything. Wittgenstein solves this problem by changing the form of the equation:

“ƒ (a, b). a=b”
“ƒ(a, a)” or (b, b).
Then “ƒ (a, b). ~a=b”,
“ƒ (a, b)”.

In the context of propositions (1) (2) above, Wittgenstein does not explain the term or the definition of the function f, therefore can be explained from another source, which is from Daniel Ashlock. The function f has the definition “a pair of ordered elements consisting of a collection of two, an element with an additional property of which the first element comes first from the second element”. Another definition explained by Mark Burgin, a function is a “special type of binary relation between two sets”.

The function f from Wittgenstein is to eliminate the use of “=”. Proposition (1) is not “=” Proposition (2), but instead becomes a function of f (a, b), or does not express such as equal, but rather the two is in the region of function f with “,” between “a” and “b”. Again, the symbol “,” is not defined or explained by Wittgenstein no more than not to use the symbol “=”. In the definition of a function f containing “binary and sequential relations” the symbol “=” is eliminated.

Different from Wittgenstein, explained by Ashlock, in an attempt for logic equivalence, with “a if and only if b”, is to say that “a” and “b” is a different way of conveying the same two things. This expression can be symbolized by the symbol ⇔ (not “=”).

After such an analytical — operation effort, not even what has been explained and can be the exact and true justification for the translation of Propositions (1) into Proposition (2) — other than stating why they cannot be justified. These processes and results, therefore, do not state true or false, nor can they state the similarity and equal in the translation.

A translator can use the concept of tautology or the negative facts by Saussure which explains “if not this then the other”, as if not this translation, then the other translation, but that is not to say anything. Translation from one language to another with the terms fair, safe, appropriate, usable, and approved reciprocally on the logical thinking from the translator and the recipient of the translation — and other translators, can be used.

The use of the dictionary (not without its disadvantages ) at once again expresses a more collective reference to help the approval process between everyone in terms of translating in addition to using — if the logical arguments is a pseudo-explanation. Not only the context of this operation of Propositions (1) (2), but almost every translator who does translations such as the use of interlanguage quotations, citations, sources, book translations, scientific journals, and so on. All of the operation above can be in the same domain to be used. The end.


Ashlock, Daniel. 2020. An Introduction to Proofs with Set Theory. USA: Morgan and Claypol.

Burgin, Mark. 2005. Super-Recursive Algorithms. USA: Springer Science+Business Media Inc.

Proops, Ian. 2004. Wittgenstein’s Logical Atomism on https://plato.stanford.edu/entries/wittgenstein-atomism/

Saussure, Ferdinand de. 1893. Course in General Linguistics. Translated by: Wade Baskin. New York: Columbia University Press.

Wittgenstein, Ludwig. 1921. Tractatus-Logico Philosophicus. Translated by: Kegan Paul. London: Routledge.

Frege, Gottlob. 1884. The Foundation of Arithmetic. Translated by: J.L Austin. New York: Harper & Brothers.



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