Edit Note : I am not attempting to discover the grammatical subject of the text. I do not believe there is one. The passive indicative has no subject. The predicate of the verse is clearly a concept regarding how faith relates to righteousness. It is this relationship I am seeking to establish, whatever may be established from this place. Then, other places furnish more information.
Neither 'in heart' or 'with heart' (or however one translates the dative) nor 'unto righteousness' are subjects. Nor does the passive indicative provide a subject, only stating that it is 3rd person and singular, whatever it may be.
But I cannot see that the subject is defined, here, within the clause : καρδια γαρ πιστευεται εις δικαιοσυνην.
καρδια γαρ πιστευεται εις δικαιοσυνην
[TR : Beza, Stephens, Elzevir and Scrivener all identical.]
For with the heart man believeth unto righteousness [KJV -1769]
I am interested in what Paul conveys about the relationship between faith and righteousness in this particular place.
The KJV inserts 'man' but neither Paul dictated nor Tertius transcribed either anthropos, aner, arrhen or arsen. The exact meaning of these would be another question but my understanding is they are human, man, bachelor and male - but none is there in Greek so neither should they be in English.
Πιστευεται pisteuetai is the present passive indicative, 3rd person singular and the various translations render this as :
for with the heart doth [one] believe [Young's Literal]
with heart for [one] believes [Green's Literal]
For with [the] heart is belief [Eng Greek NT]
for with [the] heart is believed [J N Darby]
for by heart men believe [Wycliffe - from Jerome's Vulgate]
for with the heart we believe [Douay-Rheims from Jerome's Vulgate]
Καρδια kardia is the dative case and of the very same word in Matthew 5:8 Daniel B Wallace, in Beyond the Basics (p194 1996 ed), ascribes it to be a 'dative of reference', of which he says 'the dative is the most common case used for reference'. He adds that this place could also be considered to be the 'dative of sphere', that is to say the expression of the realm in which the key word operates.
Moreover the preposition is εις which I would suggest should be rendered 'unto' and not merely 'to'. It conveys a 'toward' meaning, not a mere direction of operation. There is a force to it - unto.
Paul's words are minimal in this place. The concept he is conveying must be very precise and it must be that he is not enlarging - here - but focusing on one aspect.
How should these few, concise words be rendered in English ?
My own thoughts lean in the direction of :
For [within the realm of the] heart [is there that which] is believed unto righteousness.