‘Political economists say that capital sets towards the most profitable trades, and that it rapidly leaves the less profitable and non-paying trades. But in ordinary countries this is a slow process, and some persons who want to have an ocular demonstration of abstract truths have been inclined to doubt it because they could not see it.’
What is capitalism?
To be clear, the question is one of definition. That shouldn’t, however, make it a wholly uninteresting question to both ask and answer.
I’ll endeavour to present one possible answer, an answer with which you might find interesting or informative.
First, let’s consider the term ‘capital’ as it would seem straight-forward that we should want the term in question, ‘capitalism’ to be in some way derivative of ‘capital.’ I am going to propose for my own use a wider notion for ‘capital’ than one might commonly encounter. Without arguing at length, I find problematic a traditional connotation for capital of ‘human produced means of production’ or a kind of productive artefact. Such a narrow term has outlived its usefulness in describing how value is created in the economy. Rather, I propose to use the term ‘capital’ to refer to any factor of production; any element necessary for creating value.
And so my definition: (A) Any arrangement is capitalist wherein enterprises compete for the voluntary allocation of capital amongst the diverse owners of capital. (B) This could be restated as any individual having a right to their labour, such a right being twofold. Firstly, they have the right to allocate their labour how they see fit. Secondly, they have a right to the fruits of their labour.
I propose each condition is necessary and sufficient for a system being capitalistic. Though they are not equivalent, I think where we find the one instantiated, we find the other. The tie is maybe neither straightforward nor obvious but nonetheless I maintain that it exists.
If B then A
As labour is a factor of production and we have defined capital to be any factor of production then A is permuted into ‘Any arrangement is capitalist wherein enterprises compete for the allocation of labour amongst the diverse owners of labour.’
If each individual has the right of allocation of his labour and the right to its fruits, he then owns his labour. When each individual owns his labour, there are diverse owners of labour and enterprises which would make use of labour must attract that labour.
If A then B
To begin, let’s consider the question, ‘what are the conditions necessary for A to persist? At what point has A failed to be the case?’ It has failed to be the case when either the nominal owners of capital are not permitted the voluntary allocation of that capital, or when the nominal owners of all capital are few. In the first alternative B fails to be the case as the owners of labor do not have the right of allocation of that labor. In the latter alternative B fails as individuals would not have the right to their labor at all. The first is serfdom, the second, slavery. This however, simply evidences what we have already shown.
To show that A implies B, let’s focus on the latter alternative. All physical capital could be concentrated in the hands of a few but as long as each individual has both a right to his labor and the fruits of said labor, capital as a whole has not concentrated.
And so what, you might say, of a situation in which there are diverse owners of physical capital but not labor? Such a situation may be capitalist for a moment and a moment only. Every poor investment of physical capital would make its owner both poorer and more the complete slave. For every poor allocation of physical capital, a person has lost forever his ownership of capital of any kind. As those who possess physical capital make poor investments one by one the diverse ownership of capital becomes less and less diverse and, like the game of Monopoly, a small set of people come to control all physical resources. Without the right to one’s own labor there ceases to be diverse ownership of capital.
And so, in order for A to endure, B must be true.
Nonetheless, it is worthwhile to investigate why the ‘right’ to one’s labour is expressed as such. It may not be obvious how the right to allocation and fruits are jointly necessary and sufficient for the endurance of A.
Constituent in A is a concept of ownership which is robust enough to create the market operation upon which the definition is based. With the right to allocate but not the incentive, the notion of capitalism that results is rather hollow.
Naturally the same considerations which apply so clearly in the case of physical capital apply when considering labour as capital. If you take away the right to fruits, you’ve diluted the sense of ‘ownership’ in A, a sense of ownership that would hold for all material capital.
So a free market in labor is both necessary and sufficient for an enduring capitalism.
 Another un-dealt with objection might run something like this: We can have A with a subset of people not having a right to their labour. This is true. The ante-bellum south might be such an example. Whether or not we admit such a counter argument is a matter of the extent of the ‘diverse’ condition. Where that diversity must be sufficiently great, B only may be satisfactory. Otherwise, we might have some alternate B’ where everyone but a subset of some size has a right to their labour.