Shared ground
These verses combine a personal prayer for well-being with a report of moral and spiritual reliability. The elder prays that the recipient would “prosper in all things” and have bodily health, and he frames that wish by pointing to the recipient’s already-thriving inner life (“even as your soul prospers”).
The elder’s joy is tied to public, credible testimony: traveling believers (“brothers”) have arrived and reported that the recipient’s life matches the truth. “Walking” presents truthfulness as a steady pattern, not a one-time claim. The elder then expands from this one person to a broader pastoral relationship: his greatest joy is hearing that his “children” continue to walk in truth.
Where interpretation differs (only where needed)
How broad is “prosper in all things”? Some read it as a general wish for overall well-being (life going well in many areas). Others think it naturally includes material provision and financial stability, while still being a greeting-like prayer rather than a guarantee.
What is “your truth”? Some take it mainly as the recipient’s integrity and reliability (his life shows what is true). Others hear “truth” as the shared Christian message, with “your truth” meaning “the truth evident in you” or “the truth you hold and live out.”
How strong is the comparison “even as”? Some read it as proportion (“to the same degree your soul is doing well”). Others read it as a simpler comparison (“just as your soul is doing well”), without implying a strict measure.
Why the disagreement exists
The wording is brief and personal, and it uses flexible terms: “prosper” can describe success broadly, not only money; “truth” can point to the Christian message, personal integrity, or both; and “even as” can signal either close correspondence or a looser comparison. The letter also assumes a network where reports about someone’s conduct mattered, making “truth” naturally connect both to belief and observable behavior.
What this passage clearly contributes
Explicitly, the passage shows that the elder values a whole-life picture: outward circumstances (health and general well-being) and inner life (“soul”) are both in view, and he assumes they can be meaningfully related. It also shows that “truth” is not merely spoken—its reality is confirmed by ongoing conduct (“walking”) and by community testimony (brothers who report what they saw). Finally, it portrays Christian leadership as relational (“my children”) and as deeply invested in perseverance in truth, not simply initial profession.