Ivan Ilyich, dying in 1886, remembers the syllogism from his schoolboy logic: Caius is a man, men are mortal, therefore Caius is mortal. Tolstoy's point is that the proposition is impeccable and useless. It had always been true of Caius, that abstraction in a textbook, and it had never once been true of Ivan, who had a mother and a smell of leather in his father's study and a particular way of holding a cigarette. Forty years later Heidegger gave the structure its name. In Being and Time (1927), section 51, he observes that the public interpretation of dying takes the form man stirbt: one dies. Death is levelled to an occurrence that reaches Dasein, certainly, but belongs to nobody in particular, and the chatter that circulates this formula is not a lie but a tranquillising service, performed daily, free of charge.

The trades have their own version of the formula, and it is now recited at every industry conference, in every consultancy deck, on every earnings call where a chief executive is asked about headcount: one is automated. The grammar is identical. A class is named, a probability is attached to the class, and the sentence is true of the class while being false, or at least undecidable, about every member of it. Christopher Frey and Michael Osborne's 2013 paper The Future of Employment produced the canonical instance, with its estimate that some forty-seven per cent of United States employment fell into a high-risk category; the figure travelled for a decade, detached from its own stated method, precisely because it said everything about occupations and nothing about anyone. David Autor's 2015 reply in the Journal of Economic Perspectives, and the task-level framework Daron Acemoglu and Pascual Restrepo set out in the American Economic Review in 2018, improved the economics considerably. They did not touch the grammar. The subject of the sentence remained nobody.

What interests me is not the accuracy of the forecasts, which is a question for labour economists, but the fact that Heidegger reached for the workplace when he needed something that death was not. In section 47 he considers whether we can know death through the dying of others, and answers by way of Vertretbarkeit, representability: one person can stand in for another, and everyday life runs on this substitution, most obviously in an occupation, where a role is filled, a shift is covered, a colleague deputises and the work proceeds without remainder. Representability, for Heidegger, is the ordinary condition of being with others in a world of concern. Dying alone refuses it: no one can take another's dying away from him. The whole architecture of authenticity rests on there being one act at the bottom of a life that cannot be delegated, and Heidegger located everything else, including the entirety of a person's working existence, on the delegable side of the line.

Call that line the representability frontier: the moving boundary between acts a substitute can perform without loss of what the act was, and acts that lose their character the moment a substitute performs them. Every craft guild in history has defended a stretch of it. What distinguishes the current decade is not that the frontier moves, since it has moved since the Jacquard loom, but that its movement has become an explicit capital project, surveyed by measurement, financed by quarterly budget, and reported as progress against a benchmark. I have argued in earlier work that model deployment is best read as a re-description of tasks rather than a replacement of workers. I want to tighten that claim: re-description is not the milder alternative to replacement but its precondition, and the sector that has described its own work exhaustively has already conceded the frontier.

Consider radiology, where the public sentence was pronounced earliest. Geoffrey Hinton told a Toronto audience in 2016 that we should stop training radiologists, since the work would be finished within five or ten years. The decade that followed did not produce the contraction he predicted; what it produced was a mutation inside the practice, which is the more instructive outcome. The radiologist's act was once perceptual and terminal: a trained eye moved across a field, found or failed to find, and signed. Under statistical triage the perceptual act arrives pre-performed, and the human contribution migrates towards adjudication, exception handling, and the bearing of liability. Gilbert Simondon described this migration precisely in Du mode d'existence des objets techniques (1958): when the machine assumes the role of technical individual, the human is displaced either downward, into attendance on the machine, or upward, into the organisation of ensembles, and in neither position does he remain the bearer of the tool. The radiologist has been displaced upward, which sounds like promotion and reads, in the reporting room, like a signature attached to a judgement one did not originate. That is a change in the ontology of the trade, not in its payroll.

Here Max Weber supplies what Heidegger cannot. In Science as a Vocation, delivered in 1917, Weber contrasts Abraham, who died old and satiated with life because life had given him what it had to give and the cycle had closed, with civilised man, placed inside an infinite progression of knowledge, who can only ever become tired of life and never satiated with it, and for whom death is therefore a meaningless occurrence. A completable trade is one whose competence can in principle be finished within a working life: the mastery has a shape, the shape has an end, and the practitioner can be satiated. What model deployment does to a sector is convert it into what I will call the interminable trade, in which the standard of competence is revised on the release schedule of the instruments, the practitioner is permanently behind a frontier that no amount of effort closes, and the craft can no longer be completed and therefore can no longer be honourably lost. The grief reported by mid-career professionals across medicine, translation, illustration and code is frequently misdescribed, by them and by their critics, as fear of unemployment. It is more exactly Weber's fatigue: the withdrawal of the possibility of a finished mastery, which is to say the withdrawal of a death within the trade that would have been one's own.

Law shows the same mutation with a documentary record, because the American judiciary wrote it down. In Da Silva Moore v. Publicis Groupe (S.D.N.Y. 2012), Magistrate Judge Andrew Peck held that computer-assisted review was an acceptable method of searching electronically stored information, and in doing so converted a question of diligence into a question of recall and precision. Document review had been a trade whose content was reading: a junior lawyer's eye on a page, hour after hour, a form of attention that also, incidentally, taught the reader what a case looked like from underneath. After Peck, the defensible act is the design and validation of a sampling protocol. Nobody was forbidden to read. Reading simply ceased to be the thing for which one was paid, and a stage of formation that was never on anyone's balance sheet was quietly struck from the profession's account of itself. The Cravath system, with its deliberate up-or-out schedule, had at least made a career finite on purpose, which is a kind of honesty; the newer structure removes the lower rungs and leaves the ladder advertised.

Agriculture completes the taxonomy by demonstrating a form of extinction Heidegger never treats. The knowledge of a particular field, its cold corner, its drainage, the year the subsoil was compacted, was historically non-representable in the strict sense: it could be transmitted only by a body standing in that field across seasons, which is why farms were inherited rather than merely sold. Precision agriculture, with its yield maps and prescription files held on vendor platforms, makes that knowledge portable. The practice does not die of neglect; it dies by becoming repeatable. What was ownmost becomes, in the most literal commercial sense, transferable, and the trade loses the very property that made it resemble a life rather than an office.

Against these mortal practices stand the entities in the room that cannot die. Chief Justice Marshall, in Dartmouth College v. Woodward (1819), enumerated the properties conferred on the corporation by its charter and named immortality first. Marx, in the tenth chapter of Capital, described the machine as dead labour that lives, vampire-like, by sucking living labour. And a deployed model is closest of all to the intelligence Aquinas describes in the Summa Theologiae, where each angel constitutes its own species, knows without discursive reasoning, and arrives complete, having had no youth and no formation and therefore no vocation. Such a knower cannot die. It can only be deprecated, which is the withdrawal of a version from support, a purely administrative event with no interior. Deprecation is not death. A firm that is legally immortal, operating instruments that are structurally biographyless, retains exactly one mortal element on the floor, and it is the worker, whose finitude is now the only finitude in the building and is priced accordingly.

What, then, would anticipatory resoluteness look like inside a trade? Not retraining, which is the chatter's own prescription and keeps the practitioner inside the interminable progression. Not refusal, which mistakes an instrument for an agent. Heidegger's Vorlaufen means running ahead into the possibility and returning from it with the shape of one's own existence disclosed; the occupational analogue is to run one's practice forward to the point at which every describable act within it has been described, and to see what one is still doing there. Whatever is still being done is the ownmost remainder of the trade. There is a trap in this, and it should be stated plainly rather than resolved: the frontier advances by articulation, so every eloquent account of what only a practitioner can do is also a specification document for the system that will next attempt it. The remainder cannot be safely named; it can only be practised.

A trade does not end when its workers leave. It ends when its last non-representable act has been written down, and what survives that moment is not a vocation but an office: a position that can be filled indefinitely, by whatever is cheapest and can hold the signature.