Many people cornered with these facts will say it doesn't matter, their presuppositions still hold. That's hilarious!!
Where you are incorrect brother, but no worries.
1. Koine Greek Use of the Article as a Demonstrative:
In Koine Greek, especially in contexts of anaphoric reference (
when the speaker refers back to something just mentioned), the article alone can function semantically like an English demonstrative ("this" or "that")-especially when it follows a prior conceptual referent.
As F. Blass & A. Debrunner write in A Greek Grammar of the New Testament and Other Early Christian Literature (§253),
“The article may refer back to something previously mentioned (anaphoric), and in this use it may approach the demonstrative force of
'that.'”
In other words, ἡ πίστις here refers back to the kind of faith someone claims to have in the first clause--"if someone says he has faith (πίστιν)... but does not have works."
So, contextually, James is speaking not of faith in the abstract, but of a specific kind of professed faith: the workless, verbal-only faith.
Thus, "Can the faith save him?" naturally means, in idiomatic English:
“Can
that kind of faith [the kind without works] save him?”
And most modern translations reflect this sense--not because the demonstrative is present in the Greek, but because the article carries an anaphoric and qualifying function.
Daniel B. Wallace, Greek Grammar Beyond the Basics, p. 219:
q=Daniel+B.+Wallace%2C+Greek+Grammar+Beyond+the+Basics%2C+p.+219%3A&oq=Daniel+B.+Wallace%2C+Greek+Grammar+Beyond+the+Basics%2C+p.+219%3A&aqs=chrome..69i57j0i546i649l2j0i512i546j0i751.1711j0j7&sourceid=chrome&ie=UTF-8#:~:text=results%20with%3A%20219%3A-,GREEK%20GRAMMAR%20BEYOND%20THE%20BASICS,Good,-Neighbours%20Bookshop
“Anaphoric articles often appear where the article functions like a demonstrative in English (‘that X’).”
Craig L. Blomberg & Mariam J. Kamell, Zondervan Exegetical Commentary: James, p. 135:
Authors Craig Blomberg and Mariam Kamell use the historical, theological and literary elements of James to guide their interpretation of this often-overlooked early Christian text. Their concise discussion of how the book delivers consistent, challenging instruction will help pastors and church...
www.logos.com
“The presence of the article with pistis [faith] (‘the faith’) is likely anaphoric, referring back to the faith claimed in the first half of the verse. Hence many translations render it as ‘that faith.’”
You are correct in a strictly morphological sense: αὕτη ("that") is not in the Greek.
However, you err in
their semantic conclusion. In Koine Greek, the article ἡ before πίστις can-and here does-function anaphorically to mean
“that (just-mentioned) kind of faith”.
Therefore,
“Can that faith save him?” is an accurate and idiomatic rendering, even if it’s not a woodenly literal one.
But now we are nitpicking on words, neglecting the context of James, and this is not edifying @synergy since we are here to do exegetical, hermeneutical studies, not isolated "words" within a verse?!
Jas 2:14 What [is] Τί the τὸ profit, ὄφελος, my μου, brothers, ἀδελφοί if ἐὰν anyone τις says λέγῃ to have ἔχειν faith, πίστιν but δὲ has ἔχῃ; no μὴ works? ἔργα {Is} the ἡ faith πίστις vvv μὴ able δύναται to save σῶσαι him? αὐτόν;
Definite article---The phrase "the faith" in certain translations of the Bible is an anaphoric reference to a previously established concept of faith, according to Bible Hub and other textual analyses. Specifically, when the article "the" is added before the Greek word "pistis" (faith), it indicates that the faith being referenced is a specific, previously defined faith, often translated as "that faith" to reflect this specificity.
J. 
