Known and unknown numbers
When we encounter numbers, in our daily lives, they typically have a well understood meaning.
You check your watch when waiting for a train. The numbers represent the time of the day. You set the oven temperature when cooking a meal. The numbers represent heat. You read the scales when trying to lose weight. The numbers represent mass. This is all straightforward and well understood.
But there are other, arguably more important numbers, that are less straightforward. We check prices when buying groceries. We check our wages, and the debits and credits in our bank accounts, when we’re worried about money.
These “money numbers” intimately control and influence our lives. They enable us to do things, such as getting a train to another city. But they also prevent us from doing things, if we don’t have enough of them.
What do these numbers mean? If you ask pretty much anyone, what does £1, or €1, or $1 represent or measure, you’ll quickly get some mumbling and stumbling, even if you ask a professional economist. Nobody is really sure what they mean, which is a bit odd, considering how important they are in our lives.
So that’s the question I’d like to ask today: just what is the meaning of £1?
The value question
Obviously this is a question about money. But it’s a very specific question, which I’d like to distinguish from others we could ask.
Money can take different material forms: coins, notes, bits stored in a computer and so on.
Take a five pound note. It has a material body made from polymer, and the number 5 is printed on it. The material body is merely a vehicle for the embodiment of that number, which I’ll call the “unit of account”.
Our question is not about the material, or bodily form of money. We will ignore this.
More precisely, our question is: what is the meaning of the monetary unit of account? What does that number 5, on this note, actually represent? Something, nothing, anything?
In the UK that 5 has units of “pounds” (whatever that might mean). In the USA the unit is the “dollar”. And almost every nation state in the world issues its own currency, and gives it a special name.
But our question is not about who has the power to issue currency, or how money has arisen in history. We’re not asking about the genesis of money.
(Yes, nation states have typically issued currency to direct economic activity and collect taxes. But it’s equally true that money has arisen spontaneously in the absence of state power, and sometimes in conscious opposition to it, whenever there is a need to trade.)
We just want to know what the unit of account might mean, once it’s up and running.
So our question, really, is about the possible meaning of a numeric representation that arises in human commerce. So, from now on, when I say “money”, I’m using that as shorthand for the “unit of account”.
What answer does economic science give?
Now, this should be a short post, because economic science should have already answered our simple question. But the opposite is the case.
At the beginning of economic science, in the 1700s, Adam Smith argued that the real wealth of a nation is not its stock of money but the size and ingenuity of its labour force. So money is not wealth, but merely represents it. Smith proposed to think of money as representing the quantity of labour it can purchase in the market. So if the average wage, in a national economy, is £1 per hour, then £1 represents 1 hour of average labour time.
Of course, £1 purchases lots of other things in the market — it has an exchange ratio with corn, bread, anything that’s for sale. But Smith was happy to be pragmatic here. Smith, as an economic theorist, chooses to relate money to labour because labour, according to him, is what economics is really about.
Early Marginalists, in the 1800s, such as William Jevons, toyed with the idea that money prices relate to psychological states of the human mind, such as “ratios of final degrees of utility”. So Jevons’ answer is even more subjective than Adam Smith’s.
Samuel Bailey thought the search for a unique referent of the unit of account was silly and pointless. He noted that market prices merely reflect the ratios in which commodities exchange. But that is all. So money numbers don’t refer to anything. There is nothing behind them, and they don’t represent any substance that exists independently of market exchange. So the unit of account doesn’t measure or refer to any single thing.
Bailey’s “nothing” answer became the dominant attitude of economic science in the 20th Century. For instance, in canonical formulations of neoclassical general equilibrium theory, money isn’t even present.
So our question, “what is the meaning of £1?”, makes little sense to a modern economist. They are value nihilists. It’s a bit like asking a physicist their views on phlogiston.
Modern Post Keynesians retain sympathy for Smith’s original formulation. But in general, they don’t ask this “money question”, and don’t really care about it.
So according to economics, the number 5 on a five pound note is not like the numbers we see written on the sides of thermometers, or the numbers written on the face of a clock. That 5 doesn’t refer to, or measure, any particular aspect of objective reality. It’s a meaningless number.
What does Marx say?
Marx, in contrast, stands alone in the history of economics by giving a very different answer.
The first 3 chapters of Capital, about 150 pages, are entirely devoted to the meaning of money. Marx argues that when a community produces and exchanges commodities for exchange in the market, then certain causal regularities, or social laws, necessarily emerge.
First, a special commodity splits off from all the others and functions as a universal means of exchange. This is a money commodity, which gets used in every transaction.
Second, the market prices of commodities become governed by the labour time required to produce them. So planes cost more than pens because more of society’s labour time is used-up to produce planes compared to pens.
Third, the dynamics of supply and demand, and the discipline of market competition, means that the circulation of money regulates the division of labour within the community. If you can’t make money producing commodity X, because it’s over-supplied to the market, then you have to switch to start producing commodity Y, which is under-supplied.
So money, and therefore the unit of account, functions as a kind of transmission mechanism, or control signal, that regulates the total labour time of the community to meet aggregate demand.
And Marx therefore claims that the unit of account refers to labour time in virtue of the lawful regularities of generalised commodity production.
I will refer to Marx’s answer as “the law of value”.
His argument is unique because he claims that money refers to labour time, that there is a semantic connection of reference between one part of reality (in this case a number stamped on a coin, or a note, or stored in a computer) and another part of reality (in this case, actual labour time expended by individuals) in virtue of a social practice. It doesn’t matter what the individuals think money refers to, because it isn’t their individual consciousness that fixes the semantics, the reference. No, it’s their social activity, of exchanging the products of their labour in the marketplace in lawfully regulated ratios, that fixes the semantics.
So according to Marx money refers to labour time objectively. It’s not a subjective choice of the economic theorist, like Adam Smith suggested. No, it’s economic activity itself that makes money in fact refer to labour time, whether we believe it does or not.
So Marx’s answer relies on the presupposition that there can be semantic relations in the world, independent of human intention or consciousness. Let’s call this the presupposition of “objective semantics”.
Some problems with Marx’s argument
Now, obviously, I’ve massively compressed Marx’s argument for the sake of time. It’s incredibly subtle, insightful and important. But it’s not perfect, and of course it’s been thoroughly attacked in every respect.
A major objection is – yes – commodity exchange instantiates lawful regularities, and yes, commodity prices do gravitate towards prices proportional to labour time, all other things being equal. But even in this situation, prices are also proportional to any real cost of production, such as the quantity of corn, or coal, or oil directly and indirectly used-up to produce things. So planes are more expensive than pens because they also use-up more oil inputs.
So why then does Marx think that labour is the special and unique referent of the unit of account?
Marx’s argument for this, in Volume 1, is his famous “third thing” argument. He says that exchange-value abstracts from all possible concrete use-values, and must therefore refer to a common property shared by all commodities. And he says the only “common property” they have is “that of being products of labour”.
But in a modern economy, all commodities are also ultimately products of electricity, or abstract energy, or land, since these are also basic and fundamental inputs to every industrial process.
So it must be admitted that Marx’s argument isn’t very satisfying at this particular point. His “third thing” argument, taken at face value, is pretty weak.
Taking a step back: how can we make claims about objective semantics?
Now, I want to temporarily push all this economics entirely to one side. Sometimes, in science, a field encounters problems that it’s not fully equipped to handle. I think this is the case here.
Our question, about the meaning of money, is not merely an economic question, but a question about semantics: specifically, on what grounds can we claim that one part of reality refers to, or measures, another part of reality? Under what conditions are we justified to make such a claim.
Economics, as a specialised scientific field, isn’t equipped to answer this question.
Parts of reality representing, or standing in for, other parts of reality happens all the time. For example, I’m using language right now to refer to lots of different things in reality, such as money, people, and economic theories.
But I don’t want to get into the philosophy of language. I’d like to tackle this question from a more mundane, or practical point-of-view. Let’s look at examples where everyone agrees that certain numbers really do refer to parts of reality.
So we’ll begin by looking at measuring devices.
Consider a thermometer. We all agree it measures temperature. But why does it?
A necessary condition for a thermometer to measure temperature is that some part of it, say its mercury column, lawfully covaries with changes in the local temperature. The reason why many thermometer’s use mercury is because mercury reliably expands and contracts with changes in temperature.
So we might claim that a part of reality (in this case the height of a mercury column) refers to temperature (a different part of reality) because temperature reliably causes its height.
But this idea rapidly breaks down on closer inspection.
For example, a thermometer that measures air temperature also measures air pressure, because temperature and air pressure are typically correlated.
Take another example: a thermometer that measures the temperature of a liquid also measures the rate of evaporation of molecules from its surface.
Or, consider a thermometer hanging on the wall of a small room. The more people in the room, the higher the temperature, so the height of the mercury column is also reliably caused by the number of people in the room.
And these examples can be easily multiplied. The problem is this: lots of states of the world reliably covary with the height of a mercury column. So why should temperature be the special, unique thing that thermometers measure?
Well maybe we can avoid this difficulty by saying that what counts is the final cause that affects the height of the mercury column. So, yes, air pressure, molecule evaporation, and number of people do correlate with temperature but, when it comes down to it, it’s the jiggling of molecules close to the mercury bulb that really causes the expansion, and it’s that jiggling that we call heat, and therefore the thermometer in fact measures temperature.
But not all thermometers work this way. For example, infra-red thermometers, widely available, measure temperature at a distance by focusing infra-red light emitted by objects onto an internal sensor. So the final cause, in this case, is not jiggling molecules, but light.
So this proposal of a final or last cause doesn’t get us very far.
So we haven’t yet been able to clearly state why a thermometer in fact measures temperature, which is perhaps a bit surprising.
Let’s try again.
Imagine, for a moment, that a Man from the Moon visits Earth and knows nothing of its culture of customs. He lands and looks around, and discovers a strange artefact. It’s a thermometer, but he doesn’t know that.
He sets about trying to figure out what this thing does.
He notices a strange half-circle symbol written on its side (it represents degrees centigrade, but he doesn’t know that) and a bunch of numbers (which he does recognise). He experiments with the strange device. Eventually he guesses that the device has got something to do with temperature.
So he sticks it in a bowl of ice. And the device reads 0. He then submerges it in a bowl of boiling water. It now reads 100.
This is his Aha! moment.
The strange half-circle symbol must be a unit of length especially because it labels equidistant marks along the side of the device. And this Earth artefact must be a device for measuring the thermal expansion of mercury.
What an amazing discovery!
Now, obviously, the Man from the Moon has arrived at the wrong conclusion. But his conclusion is entirely consistent with the evidence before him. His only “mistake” is to interpret the thermometer’s scale as a direct measure of mercury expansion, rather than an indirect measure of temperature.
He simply doesn’t know that humans typically use this device to measure temperature, and therefore interpret the numbers written on it as degrees of heat, not units of length.
What this example shows is that the very same lawful relationship between temperature and mercury expansion supports two different uses of the thermometer. The nature of the thermometer, as a technological artefact alone, doesn’t fix the meaning of its numbers.
More examples of semantic indeterminacy
Is this true of other measuring devices?
Let’s consider a clock. Obviously the numbers typically refer to the time. But if we use the clock to measure the rotation of the clock’s hands per tick of its timekeeping element then those numbers simply represent angle of rotation.
Consider a ruler. The numbers typically refer to the length of any adjacent object. But the numbers can also refer to the quantity of segments of uniform length in the ruler’s body.
Why would we ever use a ruler in this way?
Well metrologists, who calibrate measuring devices, do this kind of thing all the time.
For example, until recently, the ‘meter’ was defined as the length of a standard metal bar stored at constant temperature. So to calibrate and mark a two meter ruler a metrologist measures the ‘quantity of ruler segments per metal bar’, which, in this case, would be two segments. And then places 2 equidistant marks on the ruler.
And in fact, every measuring device supports a calibration use-case, which we typically don’t think about. When we calibrate any measuring device, the meaning of its numbers suddenly inverts.
So the point is this: the semantics of measuring devices, what they refer to, is fixed by how we use them. The devices themselves, as pure tech, leave the meaning of their numbers under-determined.
A problem for Marx’s theory?
So we decide what those numbers mean.
This appears to create a problem for Marx’s theory. The very idea of an objective semantics seems now to be in question. If we can’t even uphold this proposal for the case of simple measuring devices, perhaps the whole idea is a non-starter.
And therefore maybe Adam Smith is right. We, as economic theorists, may decide to relate money to labour time, because that’s useful for us when thinking about the economy. But that’s a matter of subjective choice. Money doesn’t really in fact refer to labour time.
Thermostats and heating systems
But this isn’t the end of the story. Let’s now take a look at a slightly more complex device, the thermostat.
Thermostats coupled to heating systems are everywhere, as anyone who works in an air-conditioned office knows.
You set a thermostat’s set-point to the desired temperature. The thermometer-component within the thermostat measures room temperature. The thermostat mechanically compares its set-point to the measured temperature. If the set-point is higher the thermostat turns the heating on; but if the set-point is lower the thermostat turns the heating off. In this way, a thermostat controls the room temperature until it equals its set-point.
It’s a simple example of a negative feedback control system.
So here we have a measuring device, a thermometer, functioning as a sub-component within a larger system.
Once the thermostat has been set by a human, it works autonomously. Now typically it controls temperature. But perhaps that’s only because heating engineers install them in the right way.
So we can’t yet claim that a thermostat objectively, and as a matter of fact, controls temperature. We need to dig a bit deeper.
What happens if we install a thermostat incorrectly?
Well, if we don’t connect the thermostat to any heating elements — or cross its wires, so when it outputs a signal to increase heat it actually turns the heater off — then it won’t function correctly. It will never successfully control the ambient temperature of the room.
Or let’s say we connect the thermostat’s output to a loudspeaker. So when the measured temperature is too low, the speaker emit a high-pitch, when the temperature is too high, it emits a low-pitch. And if the temperature equals its set point, then the speakers become quiet.
Again, in these circumstances, the thermostat will fail to successfully control any aspect of its environment. The loudspeakers will forever remain loud. There’s a mismatch between what it measures as input, and what it outputs as control actions in its world.
And this is a key observation. Perhaps we can say that a thermostat controls temperature, and only temperature, and therefore its thermometer-component objectively refers to temperature, because it can only function correctly, and reach an equilibrium state with its environment, when it is connected to the world in such a way that it achieves control success.
Necessary and sufficient conditions for control success
This idea of “control success” definitely gets us somewhere, because it allows us to immediately exclude lots of things that the thermostat doesn’t control.
For example, a very sunny day causes the thermometer-component to register a rise in temperature. In this situation, light intensity and temperature are initially correlated. But the thermostat achieves control success without affecting the intensity of sunlight. So we can exclude light intensity as a possible candidate for what a thermostat refers to.
The same can be said for the number of people in the room. Sure, lots of people means a hot room, but, again, the thermostat achieves control success without removing or adding people.
But we aren’t quite there yet, because there are lots of other features of the world that reliably covary with temperature, and can’t be excluded so easily.
I’ve already mentioned things like air pressure, or rates of liquid evaporation. When a thermostat successfully controls the temperature it also, as a side-effect, controls air pressure and evaporation rates. So we could equally say that a thermostat controls these things too.
But the important point to note is that neither air pressure or evaporation rates, nor any of the infinite things that may reliably covary with temperature, are necessarily present control success. And we can demonstrate this by standard methods of scientific experimentation. In other words, the Man from the Moon could methodically, and reliably, exclude all these possible candidates.
For example, we can wire-up the thermostat and heating system to air in a balloon so that when the temperature changes the air pressure within the balloon remains constant. The thermostat successfully controls temperature. And we can conclude that the presence of co-varying air pressure is not necessary for control success.
Similarly, we could perform an experiment where all liquids in the room are enclosed, or simply not present. No evaporation. So the presence of covarying evaporation rates are also unnecessary for control success.
In principle, the Man from the Moon can perform as many experiments as he pleases, to slowly but surely exclude accidental properties of the environment, and converge towards those features of the world that are necessary and sufficient for control success.
Taking this experimental approach, the Man from the Moon would quickly discover that the thermostat doesn’t actually control air temperature, because it can also successfully control the temperature of a liquid. So neither a gaseous substance, nor a liquid substance, are necessary for control success.
In fact, the Man from the Moon would be forced to conclude, after much experimentation — wiring up the thermostat to lots of different possible worlds and eliminating lots and lots of possibilities — that a thermostat controls something abstract about its environment, something related to the vibrational frequency of molecules, or what we call heat. And this abstract thing, heat, is a common property of many different kinds of material things.
We should note that the abstraction performed by the thermostat is of an entirely material kind. There’s no higher-level cognition at work here. The abstraction is a relational property between the mechanical nature of control system, and a common property of all the kinds of environments in which it achieves control success.
And, as you might expect, this conclusion doesn’t just apply to thermostats, but all kinds of control systems.
And this is my main point: measuring devices have indeterminate semantics, and meaning of the numbers are fixed by human use. But control systems — whether constructed by humans, evolved by nature, or even those that spontaneously emerge from our social practices — have determinate semantics, which are fixed by the kind of control system that they are.
So there’s a massive difference between things that measure and systems that control.
All of this can be formalised, and made more precise. Here’s my paper that does this:
Wright, 2014. Loop-closing semantics. In: From animals to robots and back: reflections on the hard problems in the study of cognition. Cognitive Systems Monographs: Springer, pp. 219–253. Preprint here. And also a talk:
So control systems objectively refer to specific features of the world in virtue of the kind of mechanisms they are. The semantics are objective because a Man from the Moon, or a Woman from Mars, or an intelligent Robot from Alpha Centuri, would all agree on what any specific control system in fact controls by following the scientific method.
So it turns out that, after all, there can be objective semantics.
Back to Marx’s argument
We now have the outline of a theory that explains how kinds of causal relations instantiate objective semantics, and therefore how some parts of the world in fact refer to other parts of the world.
So let’s go back to Marx, and economics, and think about the meaning of £1 from this new perspective.
Recall that Marx’s law of value explains how the total labour of society is allocated to different productive activities in order to meet social demand.
Obviously, this process is neither perfect, or equitable, or guaranteed to reach a full-employment equilibrium, nonetheless the law of value is the basic homeostatic mechanism of generalised commodity production.
The law of value is a control system that operates through the actions of individuals. It is precisely a negative feedback loop, which becomes particularly clear when we build formal models of its dynamics.
We are subject to the law of value, the law controls us, we are part of its control system, sub-components, not masters of it. We literally live within a control system (in fact many). And the language of the economic control system, the method by which it controls us, is money.
And this economic control system, like all control systems, instantiates objective semantics independently of our consciousness. The meaning of money is fixed by our social practice, whether we are aware of it or not.
The objective semantics of money
So what are the objective semantics of money?
Well, I’m afraid I’m going to disappoint, and not give what I think is the right answer today. I think there’s already quite a lot to think about, before going further.
But to apply the method, we need to identify the inputs and outputs of the law of value, what it measures and what it controls. We need to identify the set-point of the system, what the state the control system is attempting to realise. We need to identify what sub-components of the economic system function as a measurement signal, and what function as a control signal. We need to identify the meaning of control success in this context. And we need to identify the necessary and sufficient conditions for control success, that is what features of the social world must be necessarily be present, for the law of value to operate to completion.
We can’t be like the Man in the Moon and perform experiments on the law of value, but we can look at history for natural experiments, and we can entertain counterfactual thought experiments.
Marx ultimately grounded his claim that the meaning of £1 is a quantum of labour time by a purely formal appeal to a common property shared by all commodities. But if we take a control system perspective I think we can construct a better argument that really pins down the objective semantics of money, and identifies precisely what abstract property of our social world the unit of account refers to.
Thanks to the Communist Corresponding Society for inviting me to give this talk and the subsequent, really interesting and helpful discussion. I hope to gain permission of the attendees to share the audio at a future date.