You are absolutely right to make that distinction. While Popper's falsification is a famous and specific application of this way of thinking in science, the broader principle—that knowledge is advanced more robustly by negation and subtraction than by positive assertion—is indeed much older and more general.
This principle is most broadly known as the Via Negativa (Latin for "the negative way"), or Apophatic Reasoning.
The Via Negativa: Knowledge by Subtraction#
The via negativa is a mode of thought that defines or understands something by what it is not, rather than by what it is. The core insight is that positive descriptions are often limited, speculative, and hard to agree on, whereas negative descriptions—ruling things out—can be more certain and build a stronger foundation for consensus.
The classic analogy is that of a sculptor. To create a statue of a horse, the sculptor doesn't "add" horseness to a block of marble. Instead, they chip away everything that is not a horse. The masterpiece is revealed through subtraction. 🗿
By Whom, Most Famously?#
This idea has appeared in many domains, but here are its most famous proponents, long before Popper:
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Socrates and Platonic Philosophy: The Socratic method is a quintessential example of the via negativa in action. Socrates rarely offers a definitive answer for what concepts like "justice" or "piety" are. Instead, his dialogues consist of him taking someone's proposed definition and showing, through questioning, its contradictions and inadequacies. The result is often aporia—an awareness of what you don't know. The knowledge gained is the elimination of bad definitions.
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Apophatic Theology (Negative Theology): This is where the term is most famous. Philosophers and theologians like Pseudo-Dionysius the Areopagite (5th/6th century) and Maimonides (12th century) argued that any positive attribute we give to God (e.g., "God is good," "God is wise") is an inadequate human projection. We can't grasp the divine essence. Therefore, we can only speak truthfully about God by stating what God is not: not mortal, not finite, not corporeal, not ignorant. This clears the mind of false idols and leads to a more profound, if less defined, understanding.
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Nassim Nicholas Taleb (Contemporary): The contemporary author who has done the most to popularize the via negativa as a practical principle for life and decision-making. In his books like Antifragile, he argues that we know much more about what is definitively harmful (what to subtract) than what is definitively beneficial (what to add). For example:
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Health: It's easier to improve health by removing negatives (eliminating junk food, stopping smoking) than by finding the perfect "superfood."
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Wealth: The surest path is avoiding ruin (not taking on catastrophic debt, not gambling foolishly).
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Knowledge: We become wiser by identifying and eliminating our biases and false beliefs.
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In your example of textual analysis, the via negativa means we create a space for rigorous and plausible interpretations by first chipping away and agreeing on the bad ones: those that are anachronistic, logically flawed, or unsupported by the text. What remains is a refined set of better, more defensible interpretations.