On the usual interpretation, the 'fragment' of Anaximander affirms an incessant struggle among opposites, amounting to warfare: one side perpetrates 'injustice' against the other; the other side retaliates by repayment, yet claiming even more ('surfeit', as KRS speculate); this in turn elicits a corresponding counterattack and additional injustice by the other side; and so on, presumably without end.
Kahn, approving of this interpretation, goes so far as to say that:
His words suggest an exchange of crimes like that which Herodotus presents as the antecedent for the Persian War, in which Greeks and Orientals are alternative offenders against one another: "this was the beginning of the wrongs done (adikēmatōn) . . . after this the Greeks were guilty of the secondary wrongdoing (adikiēs)"(Hdt. 1.2.1).I've pointed out already that, whatever the words of the fragment may suggest to someone, they certainly require no such interpretation.
But here I simply wish to point out that it would be a contradiction to refer to a state of warfare, constituted by alternating injustice, as a taxis (order, arrangement). Warfare is not a taxis, nor can it be correct to speak of it as taking place in accordance with a taxis.
The proper phrase in Greek, I believe, for association under a taxis would be, not "paying dikē to each other" but rather, "paying and receiving dikē" -- the 'receiving' here being the crucial qualification, as it implies a willingness to be subject to arbitration and law. Warfare, in contrast, is precisely the lack of subordination to law.
This point is fudged in some translations by the use of a phrase such as "according to the assessment of time" to render kata tēn tou chronou taxin. By that phrase, the taxis mentioned in the fragment would be simply the rule whereby someone who commits an injustice has to make equivalent repayment (an 'assessment'). But that sort of taxis would exist only within any of the alleged cycles of injustice-repayment (and not even there, if, as KRS have it, the party requiring repayment looks for more than an equal share and attains to a 'surfeit'!). On that reading there would be no taxis that stretched across cycles of injustice-repayment, just as there is no taxis that governs warfare.
The standard interpretation, it seems, glides effortlessly from a putative taxis within a cycle to a taxis governing all cycles -- hiding the contradiction by which warfare is called lawfulness.
Of course one man's contradiction is another man's paradox, and I'm willing to allow that Heraclitus embraced a similar a paradox. But I cannot see any special merit antecedently in an interpretation that would turn Anaximander into Heraclitus.