Rejection of Causality
“These disintegrations [within nuclei] , so far as we are able to judge from all evidence, take place without any external cause. If we have a given number of radium atoms, we can merely say that there is a definite probability that a certain fraction of them will break down during the next second.” 
Is any justification given for this acausal statement? No, of course not. There can be no justification for this.
If something takes place, then there is a cause and evidence can be found for what that cause might be. There can be no evidence that something takes place without a cause.
Probability is not a cause nor does it explain anything. Probability simply states that A will happen X out of Y times. For instance, you can use probability to calculate that if you roll a normal six-sided die, then you will get a result of six about one in six times.
Probability is properly used when the outcome of some event is not known for certain in advance. There are many reasons why this uncertainty might exist.
It might be because the system is very complicated and it would be impractical to account for every possible factor required to predict the outcome.
Or, it might be because we lack sufficient knowledge of the workings of the event to be certain what the result might be. But, we know enough to approximate how often certain outcomes will occur.
Probability is, therefore, a mathematical method used to approximate the relative frequency of outcomes. It is an abstraction and does not have any actual explanatory power.
But, due to the influence of the likes of Bohr, probability is now alleged to have just that, explanatory power. Physicists treat probability as though it can explain how things like nuclear decay work or why electrons are *here* and not *there*.
Why did Bohr assert that probability is the cause of things? Because he had given up on physical causality, that is a connection between events in the physical world.
But, he wanted some kind of “explanation” for why things happen. If there is no physical cause for something, then it is often seen as convenient to pretend that it just happened by chance.
Which is essentially what he did when he abandoned physical causality and embraced probability. There is no causal reason why things happen, they just happen according to chance, as described by probability functions!
But, this is as good as no explanation at all.
“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.