The Greek preposition "dia" has the literal positional meaning of passing through something, and the instrumentality meaning of by means of, because of or by reason of.
False. Δια can mean "passing through" only when governing the genitive. When it governs the accusative, it means something different. There is no "literal" meaning of a preposition by the time we get to the Koine period. A.T. Robertson's comments on δια are helpful here:
Passing Between’ or ‘Through.’ The idea of interval between leads naturally to that of passing between two objects or parts of objects. ‘Through’ is thus not the original meaning of διά, but is a very common one. The case is usually the genitive...
A. T. Robertson, A Grammar of the Greek New Testament in the Light of Historical Research (Logos Bible Software, 2006), 581.
Any student of Greek would know that the preposition occurs with its object and governs the meaning of its object, and the object (the noun) influences whether the preposition means something in terms of agency or instrumentality (to name a few). Robertson states:
The scientific method of studying the Greek preposition is to begin with the case-idea, add the meaning of the preposition itself, then consider the context. The result of this combination will be what one translates into English, for instance, but he translates the total idea, not the mere preposition. It is puerile to explain the Greek prepositions merely by the English or German rendering of the whole. (Ibid., 568)
So, your idea of holding on to a set, one-way interpretation of δια is quite wrong.
In the Greek construction of "through faith" the word "faith" is in the genitive case and according to the LEXICON I quoted, "dia" thus conveys the meaning of "by means of" or "because of."
False. Δια conveys the meaning of "because of" when governing the accusative, not the genitive. Again, we see Robertson: "With the accusative διά comes to be used with the idea of ‘because of,’ ‘for the sake of,’ ‘on account of.’" (Ibid., 583).
To spell it out for the deniers of the obvious, we are saved by grace through faith, with the meaning that we are saved because God credited our faith as righteousness. Now running from this obvious truth,we get off topic false charges non-stop. .
Since you have been saying "... God credited our righteousness as faith" for quite a few years on this board, it is quite clear you are trying to insert this meaning into the phrase "through faith." So, "To spell it out..." you are wrong.
The Archangel