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Relating to or denoting principles that resemble laws, especially ones describing brute facts of the universe: things that are not explainable by theory, but are just “so”.
Relating to or denoting principles that resemble laws, especially ones describing brute facts of the universe: things that are not explainable by theory, but are just “so”.


A term coined by philosopher of science [[Nancy Cartwright]] to describe the limited conditions that must prevail for scientific laws to work.
A “[[nomological machine]]” is a term coined by philosopher of science [[Nancy Cartwright]] to describe the limited conditions that must prevail for scientific laws to work.
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“It is a fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behavior that we represent in our scientific laws” <ref>{{author|Nancy Cartwright}}. {{br|The Dappled World – A Study of the Boundaries of Science}}. (Cambridge University Press, 1999)</ref>}}
“It is a fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behavior that we represent in our scientific laws” <ref>{{author|Nancy Cartwright}}. {{br|The Dappled World – A Study of the Boundaries of Science}}. (Cambridge University Press, 1999)</ref>}}


This is fancy way of saying it’s a ''model''. So, for example, take Newton’s second law of motion, which describes the relationship between an object’s mass and the amount of force needed to accelerate it.  
As a piece of marketing, this is a ''terrible'', obscurant — if technically accurate — label.<ref>Like academics, lawyers learn to use the arcane vocabulary of the [[power structure]] while on the lower rungs of the profession: it is a credentialing strategy and part of the tribal identification ritual. By the time they get high enough on the latter to influence how their underlings write they have often lost the ability to write clearly and simply. Cartwright is a brilliant thinker, but her writing is dense and hyper-academic.</ref> A better name would be “regularity machine”: a device designed to generate ''regularities'': to winnow out any chattering and crosstalk and produce the pure, untrammeled outcomes your theory predicts.


This is stated as ''F=ma'' which means the ''force'' (F) acting on an object is equal to the ''mass'' (''m'') of an object times its [[acceleration]] (''a''). This is an immutable law of physics which holds in all non-relativistic, non-quantum scales.  
So, for example, take Newton’s second law of motion, ''F=ma''. The ''force'' (F) acting on an object is equal to its ''mass'' (m) times its ''[[acceleration]]'' (a).  


But the conditions in which it operates — zero friction, perfect elasticity, non-intertial frame of reference — circumstances which never exist in real life. So, a rolling ball with no force acting upon it will eventually stop. A [[crisp packet|crisp packet blowing across St. Mark’s square]] probably does still obey Newton’s laws of motion — once you have discounted all the contaminating effects of the real world, such as friction, convection and so on — but good luck calculating its trajectory using them in any case, so really it is impossible to know. We give Newton the benefit of a large and practically untestable doubt.
This is an immutable law of physics.<ref>For all non-relativistic, non-quantum scales.</ref> But the conditions in which it holds — zero friction, perfect elasticity, a non-inertial frame of reference — never prevail in “the field”. In life, there is always friction, energy loss through heat, wind, and impurity. The neat formula, with all these unrealistic conditions, is a ''nomological machine''. If the universe does not seem to obey the law, we can blame shortcomings in observed criteria. The nomological machine is not properly represented.  


Cartwright’s point is that we are not justified in extrapolating laws that hold for nomological machines to the real world: it does not follow that the behaviour of apparatus in tightly-constrained, not-naturally occurring laboratory conditions give any great insight into the mechanics of a wind-blown crisp packet, or any of the other myriad quotidian physical effects we see and take for granted.
A rolling ball with no force upon it will eventually stop. This is, so the theory goes, only because of the corruption of reality. So too, a [[crisp packet|crisp packet blowing this way and that across St. Mark’s square]]. Once you have discounted all the contaminating effects of the real world; the friction, convection, dust, drafts and so on, it still does, we ''assume'' obey Newton’s laws — but good luck proving that out. For every crisp packet, for every rolling ball, ''for every mass that ever accelerates in our imperfect human world'', we give Newton the benefit of a large and practically untestable doubt.


==== Tumbling dice as a nomological machine ====
But are we justified in extrapolating laws that hold for nomological machines to the real world? Do these imaginary regularity generators ''really'' tell us how wind-blown crisp packets, or any of the other myriad quotidian physical effects we see and take for granted every day, behave? Is this a ''conjuring'' trick?
When we calculate probabilities — when we roll dice — we are in situations of ''known risk''. Even though dice ''trajectories'' are chaotic; even though no two rolls are identical, all this intractable uncertainty is wiped out when the dice come to rest. At that stage we know the range of possible outcomes and their calculated probabilities. On a flat, hard surface, one side must come to rest face-up. There are six equal sides. We deduce each side has a ⅙ probability.


Now every fair die has these same characteristics. It is ''not'' just an average across all dice: that some some dice yield probabilities of ⅐, others ⅕ but, on average, they shake out at about ⅙. ''Every individual die'' must, within minimal tolerance, yield a ⅙ probability. ''All dice are functionally identical''.   
==== Tumbling dice as nomological machines ====
When we calculate probabilities — when we roll dice — we are in situations of ''known risk''. Even though their trajectories are chaotic; even though no two rolls are identical, all this intractable uncertainty is wiped out when the dice come to rest. At that stage, we know the range of possible outcomes and their calculated probabilities. On a flat, hard surface, one side must come to rest face-up. There are six equal sides. We deduce each side has a ⅙ probability.
 
Now ''every'' fair die has these same characteristics. We do ''not'' average the performance all dice, some of which yield probabilities of ⅐, others ⅕ and come out at about ⅙. ''Every individual die'' must, within minimal tolerance, yield a ⅙ probability. ''All'' dice must be functionally identical.   


Therefore, when we roll dice to ''determine'' an outcome we do not build a statistical model that predicts a ⅙ probability: we build the dice to yield that outcome. A rolling die on a flat surface is what [[Nancy Cartwright]] might call a “[[nomological machine]]”
Therefore, when we roll dice to ''determine'' an outcome we do not build a statistical model that predicts a ⅙ probability: we build the dice to yield that outcome. A rolling die on a flat surface is what [[Nancy Cartwright]] might call a “[[nomological machine]]”


By way of side-note, this is a ''terrible'', if accurate, label. “[[Nomological]]” means “denoting principles that resemble laws, especially ones describing brute facts of the universe”, so it is spot on, but it is intimidating to a lay reader. It sounds, and is meant to sound, ''clever''.<ref>Academics and lawyers, learn to do this sort of thing while they train and occupy the junior rungs: using arcane vocabulary of the power structure is part of the early tribal identification ritual, and a self-credentialing device. By the time they sit on the higher rungs in a position to write clear, simple prose, specialists often can’t. They literally don’t know any other way. Cartwright is a brilliant thinker, but her writing is dense and hyper-academic.</ref>
A “nomological machine” is carefully designed, constrained, hermetically-sealed: a [[simple system]] designed to generate the specific outcome an existing theory predicts. It is not a means of proving a theory so much as ''articulating'' it. It may be abstract and not even possible in the real world. Rolling fair dice on a flat surface illustrates probabilities. We can co-opt them for a game of monopoly, as a means of generating a random outcome. We can roll dice and say, “look: just as probability theory predicts, over time each side comes up one-sixth of the time.”  
 
A “nomological machine” is carefully designed, constrained, hermetically-sealed: a [[simple system]] designed to generate the specific outcome an existing theory predicts. It is not a means of proving a theory so much as articulating it. It may be abstract and not even possible in the real world. Rolling fair dice on a flat surface illustrate probabilities. We can co-opt them for a game of monopoly, as a means of generating a random outcome. We can roll dice and say, “look: just as probability theory predicts, over time each side comes up one-sixth of the time.”  


Note that if, over time, our dice ''don’t'' yield that outcome, we don’t conclude the ⅙ outcome is wrong: ''we throw out the defective dice''.
But if, over time, our dice ''don’t'' yield the outcomed expect, we don’t conclude our probability calculations are wrong: ''we throw out the defective dice''.


The [[The map and the territory|“map” and “territory”]] are, thus, transposed: where usually the have is the abstract simplification of an intractable real world territory, here the “real-world” dice is the map of the territory of a theoretical probability. But it is a map on a 1:1 scale: as far as engineering permits, ''identical'' to the territory. Its [[substrate]] need not take the form of dice: it could be any contraption that reliably yields a ⅙ probability. Now we all carry [[difference engine]]s in our pocket, we could get the same outcome with a random number-generator.
The [[The map and the territory|“map” and “territory”]] are, thus, transposed: where usually the map is the abstract simplification of an intractable real-world territory, here the “real-world” dice is the map of the territory of a theoretical probability. But it is a map on a 1:1 scale: as far as engineering permits, ''identical'' to the territory. Its [[substrate]] need not take the form of dice: it could be any contraption that reliably yields a ⅙ probability. Now we all carry [[difference engine]]s in our pocket, we could get the same outcome with a random number generator.


Machined dice and the flat, constrained surface on which they fall are not meant to represent “the real world”. They aspire to an idealised platonic utopia, free of friction and caprice, where abstract objects behave yield obediently to the expected statistical outcome: ⅙.  
Machined dice and the flat, constrained surface on which they fall are not meant to represent “the real world”. They aspire to an idealised platonic utopia, free of friction and caprice, where abstract objects yield obediently to the expected statistical outcome: ⅙.  


A “loaded” die is a ''flawed'' [[nomological machine]]. So is a surface like sand which allows a die an ambiguous resting place upon its edge. If, over time you get don't get the ⅙ outcome you expect you don't chuck out the probability theory: you chuck out the dice.
A “loaded” die is a ''flawed'' [[nomological machine]]. So is a surface like sand which allows a die an ambiguous resting place upon its edge. If, over time you get don't get the ⅙ outcome you expect you don't chuck out the probability theory: you chuck out the dice.
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