Bohr on wholeness?
After an extended search through my copy of Pais' biography Niels Bohr's Times, I believe I have found what exactly what you are referring to. There were multiple times in his life when Bohr wrote about the definition of the word phenomenon. On pages 431-433 of my copy of Pais' book, Bohr's thoughts on this matter are summarized. I will now reproduce the entirety of what I think is the most relevant section:
Philosophy, at least natural philosophy, underwent a change which I would call dramatic — and which to my knowledge has not yet been digested by most professional philosophers — when in the late 1930s Bohr gave a new answer to an old question: What does one mean by the word 'phenomenon?' Next to complementarity, Bohr's new formulation is his most important contribution in philosophy.
Let us first go back and consider Bohr's earlier views. As mentioned before, in Como Bohr had said: 'Our normal [classical] description of physical phenomena is based entirely on the idea that the phenomena may be observed without disturbing them appreciably.' which carries the implications that quantum effects do cause such a disturbance and that one should distinguish between a phenomenon associated with an object on the one hand and the mode of observation on the other. In 1929 he employed a similar usage of 'phenomenon'. The finite magnitude of the quantum of action prevents altogether a sharp distinction being made between a phenomenon and the agency by which it is observed [his italics].' He used a similar formulation [...] at the Maxwell celebration in 1931. In 1937 he still talked of 'aspects of quantum phenomena revealed by experience under mutually exclusive conditions', which should be understood to mean, I think, that particle and wave properties refer to one and the same 'phenomenon'. I could well imagine that these various early statements may have added to misunderstandings of what complementarity is all about.
In 1938 Bohr abandoned all these formulations as inferior. He sharpened his own language, one might say, by defining the term 'phenomenon' to include both the object of study and the mode of observation. This is how he put it that year at an international conference in Warsaw:
Speaking, as is often done, of disturbing a phenomenon by observation, or even of creating physical attributes to objects by measuring processes, is, in fact, liable to be confusing, since all such sentences imply a departure from basic conventions of language which, even though it may sometimes be practical for the sake of brevity, can never be unambiguous. It is certainly far more in accordance with the structure and interpretation of the quantum mechanical symbolism, as well as with elementary epistemological principles, to reserve the word 'phenomenon' for the comprehension of the effects observed under given experimental conditions.$^1$
Thus, ten years after Bohr had begun talking about complementarity he had finally found the correct language in which to express what had been on his mind all that time. Another ten years later he slightly refined his Warsaw statement:
Phrases often found in the physical literature as 'disturbance of phenomena by observation' or 'creation of physical attributes of objects by measurements' represent a use of words like 'phenomena' and 'observation' as well as 'attribute' and 'measurement' which is hardly compatible with common usage and practical definition and, therefore, is apt to cause confusion. As a more appropriate way of expression, one may strongly advocate limitation of the use of the word phenomenon to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.$^2$
And, of course, he included this phraseology in the Schilpp book of 1949$^3$, his most readable account of the evolution of his ideas.
Bohr's usage of 'phenomenon', if not generally accepted, is the one to which nearly all physicists now subscribe.
The best known physicist to take exception was Einstein.
Having explained Bohr's concept of phenomenon, I can now state Einstein's objections to quantum physics in one brief phrase: Bohr's usage of phenomenon was unacceptable to Einstein. In contrast to the view that the notion of phenomenon irrevocably includes the specifics of the conditions of experimental observation, Einstein held that one should seek for a deeper-lying theoretical framework which permits the description of phenomena independently of these conditions. This is what he meant by the term objective reality [...]. It was his almost solitary conviction that quantum mechanics is logically consistent, but that it is an incomplete manifestation of an underlying theory in which an objectively real description is possible — a position he maintained until his death.
Note that, in the above, italicized brackets enclosing ellipses denote omissions by me, while non-italicized brackets are present in Pais' text itself. The essential references, used and indicated by Pais, are given below. I personally recommend the Dialectica paper. At the end of it, there is a brief summary by Bohr himself, which features the following sentence:
It is emphasized that the individuality of the quantum processes excludes a separation between a behaviour of the atomic objects and their interaction with the measuring instruments defining the conditions under which the phenomena appear.
Perhaps this statement is as succinct as one will find the idea stated in Bohr's own words: I have to say that I'm afraid you will have a very hard time finding a "single, easy-to-quote and easy-to-understand sentence" in the entirety of Bohr's writings, let alone in his philosophical musings! He was widely known for having a very terse, long-winded style both in speech and in writing.
N. Bohr, 'The causality problem in atomic physics', in New theories in physics, p.11, Nijhoff, the Hague 1939.
N. Bohr, 'On the notions of causality and complementarity', Dialectica 2, 312, 1948.
N. Bohr, in Albert Einstein: philosopher-scientist, p. 199, Ed. P. Schilpp, Tudor, New York, 1949.
Bohr's article "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" Phys. Rev. 48, 696-702 contains on p.700 the remark:
there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, [...]
which says that one needs to take the measurement boundary conditions into account when setting up a quantum mechanical model. This is substantiated by a quantitative derivation by Wiseman and Milburn 1993 where the effect of different kinds of continuous measurements on the behavior of the wave function is derived from a model of system + detector.