Chapter Nine in A Book of Abstract Algebra by Charles Pinter starts off in solid math fashion, with definitions.
Human perception, … is based on the ability to recognize the same structure in different guises. It is the faculty for discerning, in different objects, the same relationships between their parts.
The dictionary tells us that two things are “isomorphic” if they have the same structure. The notion of isomorphism of having the same structure is central to every branch of mathematics and permeates all of abstract reasoning. It is an expression of the simple fact that objects may be different in substance but identical in form.
There are lots of cool things that happen when objects, whether tangible in the material world or fabricated through logical thought, share a structure. Properties that apply to one, apply in the same way to another. The natural numbers are a system of 1, 2, 3 which will always multiply add and divide in a like manner, whether they are counting buffalo, beans or bananas.
A professor of economics at Harvard, Branko Milanovic, identifies capitalism as the sole surviving economic system in his book aptly titled, Capitalism Alone. The structure in this case is an economic one: ‘referring to production organised for profit using wage labour and mostly privately owned capital.’ He proposes that the creation of value through production and trade occurs in this manner across the world.
The West, and the US in particular, is the cradle of capitalism, home to Ayn Rand. But now that China in particular has shown how a communist country can harness this economic system, the different categorization of structures needs to be flushed out. Milanovic offers Liberal Meritocratic Capitalism for the West and Political Capitalism as representative of the Chinese system. The Economist summed it up:
Milanovic outlines a taxonomy of capitalisms and traces their evolution from classical capitalism before 1914, through the social-democratic capitalism of the mid-20th century, to ‘liberal meritocratic capitalism’ in much of the rich world, in particular America. He contrasts this with the ‘political capitalism’ found in many emerging countries, with China as the exemplar. These two capitalistic forms now dominate the global landscape. Their co-evolution will shape world history for decades to come.―The Economist
The idea is that the pursuit of value through private trade is the core structure, and yet it can be pushed around and molded by political actors from liberal democracies such as the US, to social democracies in northern Europe, to authoritarian countries in the East. But in its original state, capitalism produces private capital. All the other efforts in society to provide public services, or safeguard the poor, or educate the young are done somewhere else- but not in the economy.
Here lies the weakness in this argument. It is well established that all sorts of social structures provide value to individuals and communities, and these too are economic in nature. There are resources, and labor and transactions. There is capital. It seems necessary to incorporate all fields of economics into one structure rather than push off the inconvenient ones on politics.
What I propose is that at the core of capitalism is capital, but not just private capital. At the core of capitalism is capital which is often in blended ownership of private and public interests. There is capital which is much more private and unfettered by social concerns, like currency, stocks and bonds. But even these instruments are in part valued by their country of origin. The legacy of their political backing influences value.
And then there is capital which is moderately blended by public and private interests. The buy local movement in produce of today, or the buy USA textiles and Ford or Chevy of yesteryear. If you pay extra for these items, than that premium is to support the public interest of a local sub-group. But the mixing doesn’t stop in commodities. Utilities are mostly blended between public and private. Capital, it seems, has a complex nature.
On the seriously social end of the spectrum there are goods that society resists assigning any monetary or liquid value, such as human kidneys. The trading in this case depends on a string of interlocking transactions between group members who all share the similar ambition of gifting an organ to a friend or relative. But a trade still occurs, the capital has a social dimension and the outcome results in tangible value.
What determines the sliding scale of private to public divisions depends on the political management of the country and the multitude of social arrangements present where the economic transactions occur. But the structure of capitalism, which dictates the rules of how the system works, contains private and public capital, not private alone.