This is ultimately derived from Kant, who taught that our senses are unreliable. This led later philosophers to dispense with external reality and start with sense perception.
This makes a certain kind of sense. If you do not believe that your senses observe reality as it really is, then why not dispense with external reality and start with sense perceptions? This is essentially what Kant followers, including Bohr, did.
Let’s now look at Bohr’s acceptance of the particle-wave duality that comes up when identifying the nature of light and hence his rejection of the Law of Identity.
Rejection of the Law of Identity
“The situation which we meet here is characterized by the fact that we are apparently forced to choose between two mutually contradictory conceptions of the propagation of light. One, the idea of light waves, the other, the corpuscular view of the of the theory of light quanta, each conception expressing fundamental aspects of our experience. As we shall see in the following, this apparent dilemma marks a particular limitation of our forms of perception which is bound up with the quantum of action.” 
We have already mentioned this particular quote when discussing Bohr’s acceptance of contradictions and the alleged failure of our forms of perceptions and his rejection of reality and objective facts.
But now, let’s take a look at the particular aspect of this quote that points to his belief on the nature of light.
Bohr accepts the contradiction that exists between the wave theory of light and the corpuscular or particle theory of light. He accepts this contradiction, taking it as an indication of the limitation of our faculty of perception and in doing so rejects the law of identity rather than reject the contradiction of particle-wave duality and accept the law of identity.
Is particle-wave duality a reasonable concept and could it be possible that this is a valid part of quantum mechanics? No, even a casual grasp of the Law of Identity makes it clear that particle-wave duality is an impossibility.
Everything that exists has a specific nature. Or, to put it simply: To be, is to be something. Everything that exists is subject to this basic principle, be it a mountain or the smallest subatomic particle.
To exist is to have a specific, non-contradictory nature. If something is a particle, it is not also a non-particle.
The concept of “particle” and “wave” are mutually exclusive. A particle is a kind of physical entity. It is one form physical entities exist in. It is simply one way of saying “that thing that exists, it is this kind of thing”.
But the concept of a wave is not the same kind of concept. A wave is not a form of physical existence. It is an abstraction which identifies relationships. It identifies relationships between the properties of entities, which might be physical entities or other abstractions.
For instance, “water waves” do not have a physical existence. The “wave” does not have physical existence.
What physically exists is water. What we refer to when we point to a “wave” of water is water arranged in a certain kind of spatial relationship. That is a certain kind of relationship between the position of water molecules.
[Editorial: Does this mean the water wave does not exist? Well, it means that the water and its relationships exist. But the wave is simply an abstraction].
It is no different when you talk about “light waves”, “electron waves” or any other kind of wave phenomena observed on the quantum scale.
Waves are not things. When someone says an electron is a wave, they are saying that an electron is an abstraction identifying relationships.
But, if an electron is a physical object, then it cannot also be an abstraction. Therefore, no physical entities can be both a particle, ie a physical object and a wave, ie an abstraction.
Whatever physical object you observe, it is not a wave. Whenever you observe a wave, you are observing relationships. Whether they be relationships of one or more physical entities or the changing properties of the same physical entities. If light is a wave, then there is something waving.
So, no there is no justification for alleging particle-wave duality. No experiment has ever actually proven this to be the case.
What then to make of the double slit experiments and the like which are purported to prove that electrons are both waves and particles? And other such experiments?
They do not show that electrons or anything else are both particles and waves. They show that when you perform such experiments, under certain conditions you observe particle behavior and under other conditions you observe waves.
But, that does not prove that electrons are both waves and particles. You cannot explain the behavior of electrons by appealing to non-physical so-called “explanations” which violate the Law of Identity.
What then does the double slit experiment demonstrate the nature of light? That remains to be seen. But, you cannot explain the observations of such experiments by appealing to non-physical explanations which attempts to establish a contradiction and to treat a physical entity as an abstraction.
And yet Bohr did just that, under the influence of philosophical tenets he already held. As we have mentioned already, his concept of “complementarity” was one of his most irrational and revealing philosophical notion, which embraces contradictions.
It is no wonder that this kind of philosophy ultimately led to the acceptance of the dual nature of light. The Law of Identity had already been rejected with the notion of “complementarity” and it is not a big leap from that to embracing the dual nature of light.
This is quite an example of how a philosophical idea such as complementarity has influenced and infected quantum mechanics. Let us now dive into a couple of quotes that shed light on his rejection of causality.
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.