“Causality may be considered as a mode of perception by which we reduce our sense impressions to order. At the same time, however, we are concerned in both cases with idealizations whose natural limitations are open to investigation and which depend upon the sense that the feeling of volition and the demand for causality are equally indispensable elements between subject and object which forms the core of the problem of knowledge.” 
Here he goes into detail about what he considers causality to be, a system of relationships between sensory experiences. According to this view, causality is not things acting according to their nature, but merely describing sensory experiences in a way which is orderly and self-consistent.
So, Bohr abandoned physical causality. But, not wanting to completely abandon the pretense of causality and a degree of order, he adopted the notion of causality as a way to structure sensory perceptions. According to this view, causality is merely a convenient ordering of sense impressions but does not necessarily reflect any causality in the actions of physical entities.
So there you have it, the three philosophical tenets that we set out to shed some light on, the rejection of reality and objective facts, the rejection of the Law of Identity and consequently, the rejection of causality.
Now we look at some of the core tenets of pragmatism, paraphrased from Wikipedia, and see if Bohr’s philosophy can be viewed as being consistent with pragmatism.
One of the core tenets of pragmatist epistemology is the coherentist theory of justification which claims that a system of beliefs is true if it is a coherent, self-consistent system of ideas which “fit-together”.
Bohr seems to have been influenced by the coherentist aspect of this pragmatist philosophy of William James as highlighted by this quote:
“As explained in detail, the concept of stationary states may indeed be said to possess, within its field of applications, just as much, or, if one prefers, just as little reality as the elementary particles themselves. In each case, we are concerned with expedients which enable us to express in a consistent manner essential aspects of the phenomena.” 
And as such, it seems that Bohr seemed to accept systems of beliefs as the truth as long as they were coherent, self-consistent and fit together, regardless of whether or not they actually described the physical reality.
One of the other core tenets of pragmatist epistemology is the pragmatic theory of truth, which is the claim that true statements are those which are useful-to-believe.
Consider that Bohr described language as more a matter of poetry than effective communication. The view that language is poetry useful for describing “images” and “mental connections” seems to have been influenced by the pragmatic theory of truth, which states that a theory is true if it is useful.
Consider also that what Bohr considers useful, is the description of “images” and “mental connections” between sense impressions. But, he does not assert that these are true, just useful.