The phrase now travels as a licence to disregard convention, which is close to the opposite of what it named. For Aristotle the archai are where justification terminates, reached by inquiry rather than assumed at its outset — and which of those two readings you take decides whether the method is rigour or vandalism.

Aristotle sets the problem in the Posterior AnalyticsAristotle, Posterior Analytics I.2–3, 71b–72b. Demonstration proceeds from premises that are true, primary, immediate, and prior to and explanatory of the conclusion. Since demonstration cannot regress without end, it must terminate in principles that are not themselves demonstrated. (I.2): demonstrative knowledge proceeds from premises prior to and explanatory of the conclusion, and because the chain cannot regress without end it must terminate in principles that are not demonstrated at all. But the direction of travel matters. In Physics I.1 the path of inquiry runs from what is more knowable to us toward what is more knowable by nature — the first principles are the destination of investigation, not equipment one begins with. The managerial usage reverses this, treating first principles as a starting position available on demand.

Euclid (c. 300 BC) gave the method its lasting expression, and Descartes gave it the shape now in circulation: the Discourse on Method (1637) and the Meditations (1641) demolish the inherited structure and rebuild from a foundation that cannot be doubted. The modern business version, popularised by Musk (2013) with the worked example of a battery pack priced against the spot cost of its constituent materials, is Descartes with a shorter timetable. Note that the example is the strong case: the quantities are physical, public, and independent of anyone's opinion. Most business premises are none of those.

The method, stated plainly

State the problem with the incumbent solution removed from it. Enumerate what is being assumed, including what seems too obvious to write. Separate fact from convention. Rebuild from what survives. The procedure is sound and the second and third steps are where it fails, for reasons that are well established and rarely mentioned alongside it.

The objections

Confirmation holism. Duhem (1906) and Quine (1951) established that hypotheses do not meet evidence one at a time: statements about the external world face the tribunal of sense experience not individually but only as a corporate bodyQuine, W. V. O. (1951). 'Two Dogmas of Empiricism.' The Philosophical Review 60(1). Duhem had made the narrower point for physics in 1906: an experiment tests a whole theoretical group, and when it fails, logic does not say which member to revise.. 'Test each assumption' is therefore not an operation available to you. A disconfirmed prediction tells you the conjunction is wrong; it does not say which conjunct, and the choice of what to revise is made on grounds the method cannot supply.

No dry dock. Otto Neurath (1932): we are sailors who must rebuild the ship on the open sea, never able to put in to dock and reconstruct from the best materials. Cartesian demolition is unavailable to anyone operating a going concern, which is everyone the advice is addressed to.

Tacit and dispersed knowledge. Polanyi (1966) — we know more than we can tell. Hayek (1945) — the knowledge that makes an arrangement work is distributed across the people in it and held nowhere in whole. Enumerating your assumptions can only reach the articulable ones, which are, by construction, the ones least likely to be load-bearing. Chesterton's fence (1929) is the practical corollary: the constraint a convention encodes is usually discovered by removing it.

The regress. Agrippa's trilemma, restated by Hans Albert (1968) as the Münchhausen trilemma, holds that every justification terminates in dogma, circularity, or infinite regress. 'First principles' names the first horn; it does not escape the trilemma. Aristotle's own answer — that the archai are grasped by nous rather than demonstrated — assigns the problem a location rather than solving it.

Cost. Herbert Simon (1955) showed that finite agents satisfice rather than optimise, and Gigerenzer and Todd (1999) that under genuine uncertainty simple heuristics frequently beat optimisation outright. Reasoning by analogy is not intellectual laziness; it is the rational default, and first-principles reasoning has to justify its cost against it rather than assume superiority.

When it earns the cost

Three conditions, and outside them analogy wins. When the standard method produces a result you cannot accept and cannot produce another. When the circumstances that generated the convention have demonstrably changed, so the encoded constraint has expired. And when an entire field is doing one thing, which locates whatever advantage exists inside what they have all assumed. The third has the payoff structure worth having: mostly wrong, occasionally very right, and cheap to be wrong about — which is the shape of antifragility rather than of good forecasting.

What it rules out

It rules out consensus as a premise: that a practice is prevalent is not a reason it is correct. It rules out the incumbent implementation standing in for the problem statement. It rules out authority in the justification of a conclusion, though not in the search for one.

It does not rule out convention as evidence. That an arrangement has survived is information about constraints, and the holist objections above make it strong information — stronger, often, than anything you can derive in an afternoon. The distinction is between treating convention as data, which is obligatory, and treating it as justification, which is the error the method exists to correct.

Sources

Albert, H. (1968). Traktat über kritische Vernunft. Mohr. · Aristotle. Posterior Analytics I.2–3; Physics I.1. · Chesterton, G. K. (1929). The Thing. Sheed & Ward. · Descartes, R. (1637). Discourse on the Method, Part II. · Descartes, R. (1641). Meditations on First Philosophy. · Duhem, P. (1906). La Théorie physique: son objet, sa structure. Chevalier & Rivière. · Gigerenzer, G. & Todd, P. (1999). Simple Heuristics That Make Us Smart. OUP. · Hayek, F. A. (1945). 'The Use of Knowledge in Society.' American Economic Review 35(4). · Neurath, O. (1932). 'Protokollsätze.' Erkenntnis 3. · Polanyi, M. (1966). The Tacit Dimension. Routledge. · Quine, W. V. O. (1951). 'Two Dogmas of Empiricism.' The Philosophical Review 60(1). · Simon, H. A. (1955). 'A Behavioral Model of Rational Choice.' Quarterly Journal of Economics 69(1).