When a truth is necessary, the reason for it can be found by
When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached.
The great philosopher and mathematician Gottfried Wilhelm Leibniz, seeker of hidden harmonies and discoverer of profound laws, once declared: “When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached.” These words, like a lantern in the night, guide us toward the deep understanding of how the mind may travel from complexity to clarity. For truth, when it is necessary and eternal, is not suspended in air like a cloud, but rooted in foundations that can be uncovered, step by step, by the discipline of analysis.
Leibniz believed the universe itself was woven from reason, that every necessary truth could be unfolded like a scroll. To find its reason, one must take it apart, separating it into smaller ideas, until the first principles appear—self-evident truths that need no further proof. In this way, what seems mysterious becomes clear, and what seems complicated becomes simple. Just as a great edifice can be traced back to stone and mortar, so a great truth can be traced back to its primary ideas.
This vision was not born from idle speculation, but from Leibniz’s lifelong work. He gave the world calculus, a tool that resolved vast and intricate motions of planets into simple principles of change. He saw that behind the complexity of the cosmos, there were simple laws—orderly, necessary, and eternal. Thus, his words are not the musings of a dreamer, but the tested insight of a mind that had seen complexity dissolve into clarity through the art of analysis.
History shows us the power of this method. Consider the story of Euclid, whose Elements became the foundation of geometry for millennia. When asked to prove truths about triangles, circles, and lines, Euclid did not rely on authority or opinion. He resolved each proof into simpler steps, each resting on a prior truth, until all were traced back to the axioms—truths so simple and self-evident that no one could deny them. From those few axioms, an entire world of geometry was built. This is what Leibniz meant: necessary truths can always be unfolded until their roots in primary truths are revealed.
But Leibniz’s teaching does not belong only to mathematics. It belongs to life itself. When faced with a moral question, or a burden of decision, we too may practice this sacred analysis. Ask: why must I act so? What principle compels me? Break the situation down into its simplest truths—justice, compassion, honesty, duty—and soon you will find the root from which the answer springs. Just as the philosopher finds clarity in ideas, so the soul finds clarity in principles.
The lesson for us is luminous: when you are lost in confusion, return to first truths. Do not drown in the sea of complexity; resolve the waves into drops. Seek the primary ideas that no one can deny—fairness, truthfulness, love of life, reverence for the good. Upon such stones you can build a decision, a philosophy, a life. Just as Leibniz sought the harmony behind the universe, so you may seek the harmony behind your choices.
Practical wisdom must follow. When confronted with problems, practice the discipline of analysis. Write down the question. Break it apart. Search for the root truths beneath it. Ask yourself what cannot be denied, what is most fundamental. From those simple and necessary truths, climb upward again, and you will find your path. This method is not only for scholars, but for all who seek to live wisely.
Thus, remember Leibniz’s teaching: necessary truths are not arbitrary, but grounded in foundations waiting to be discovered. With patience, with discipline, and with courage to seek simplicity, you too can uncover them. And when you do, you will stand not upon shifting sands of opinion, but upon the bedrock of eternal truth, the very stones upon which the universe itself was built.
BBob
Leibniz’s notion that analyzing truths step by step can reveal the primary ones makes me think about how we approach problem-solving in general. When we encounter a complex issue, we often try to break it down to understand the root causes. But how do we know when we've reached the most fundamental level? Is it even possible to reach a universal primary truth, or does each person’s perspective alter what’s considered ‘primary’?
PNPth NgOc
I see the value in analyzing truths by reducing them to their simplest parts, but it seems like a lot of effort to uncover basic truths that may already be self-evident. Could there be situations where this method complicates things more than it helps? Or perhaps, as Leibniz suggests, once we understand the primary truths, everything else will naturally fall into place. It’s an interesting approach to understanding complex issues, but is it always applicable?
LMle mi
Leibniz’s concept of analyzing truth by breaking it into simpler components makes sense, but what happens when those primary ideas are themselves complex or ambiguous? Could this approach lead to misunderstandings if the simplest truths are still open to interpretation? Sometimes, the search for clarity can result in over-simplification, and I wonder if that would be the case with this method of resolving truth.
NKPhan Lac Nguyen Khang
The idea of resolving truth into simpler truths seems logical, but I wonder if it always works in practice. How do we know when we've reached the 'primary' truth? Often, our understanding of things is influenced by personal experiences and biases. Could the search for the primary truth lead to a distortion of reality? I’m curious whether Leibniz's method holds up in real-world situations or is more of a theoretical approach.
BPBao Phan
I find Leibniz's perspective interesting, as it suggests that truth is like a puzzle that can be dismantled and understood piece by piece. But what if some truths are so intertwined that they can’t be fully broken down into smaller ideas? Does this method always lead to the true essence of a matter, or can it sometimes oversimplify things and miss the bigger picture? It makes me wonder if some truths are inherently more complicated.