Now, it might seem that all that had been achieved thereby was to discover the abstract expression for the simplest and most ancient relation in which human beings – in whatever form of society – play the role of producers. This is correct in one respect. Not in another. Indifference towards any specific kind of labour presupposed a very developed totality of real kinds of labour, of which no single one is any longer predominant. As a rule, the most general abstractions arise only the midst of the richest possible concrete development, where one thing appears common to many, to all. Then it ceases to be thinkable in a particular form alone. On the other side, this abstraction of labour as such is not merely the mental product of a concrete totality of labours. Indifference towards specific labours corresponds to a kind of society in which individuals can with ease transfer from one labour to another, and where the specific kind is a matter of chance for them, hence of indifference. Not only the category, labour, but labour in reality has here become the means of creating wealth in general, and has ceased to be organically linked with particular individuals in any specific form. Such a state of affairs is at its most developed in the most modern form of existence of bourgeois society – in the United States. Here, then, for the first time, the point of departure of modern economics, namely the abstraction of the category “labour”, “labour as such”, labour pure and simple, becomes true in practice. The simplest abstraction, then, which modern economics places at the head of its discussions, and which expresses an immeasurably ancient relation valid in all forms of society, nevertheless achieves practical truth as an abstraction only as a category of the most modern society.
There are actually two different aspects of abstraction used here. The first is the idea of abstracting from, that is, comprehension of the concept as a universal: labor tout court. However, Marx goes on to clarify that this kind of abstraction is not adequate to grasp what is going on. Labor is not only a real abstraction, that is, an abstraction logically corresponding to a social experience in which the multiplicity of labors relevant to the reproduction of society means that no particular kind of labors occlude access to labor as generic concept. Labor is also a determinate abstraction insofar as labor in general has become the means of creating wealth in general. Thus only as a category of capitalist society does 'the simplest abstraction', 'labor', attain practical truth.
As such, I disagree with Pepperell's point, despite what I think is a clear enunciation of the difference between 'conceptual' or 'empiricist' abstractions (abstractions from an object, abstraction as a genus containing all manner of species) and 'real' abstractions:
Marx is no longer speaking about conceptual abstractions, and asking whether we can validly apply abstractions that we manufacture in thought, to specific kinds of real phenomena we encounter in history. He is speaking instead about abstractions that are somehow created in practice – that are produced as social realities by specific kinds of practical actions.
Marx is talking about both conceptual abstractions and their constitution, their attainment of "practical truth", their status as 'real'. If Marx was not including the conceptual aspect of abstraction, he would not refer to it as "valid in all forms of society", but he makes us aware that even if this abstraction is valid transhistorically, it lacks practical truth. This means more than that it is a real abstraction, that is, an abstraction generated in this society. It also has to be a determinate abstraction, that is, an abstraction with practical truth, one which is true in practice. That all labors exist as labor as such means that all labors thus act as labor as such. Labor in its simple form is thus determinate.
I believe this is why in the first chapter of Capital readers frequently miss the status of labor. There is a trinity of contradictory forms: Commodity, Value, Labor. Labor is not the odd man out, something trans-historically true while the Commodity and Value are social forms specific to capitalist society. Quite the contrary. If anything, we might say of the Commodity that it too "expresses an immeasurably ancient relation valid in all forms of society, [which] nevertheless achieves practical truth as an abstraction only as a category of the most modern society."