There is a tendency among some or among many, depending on who you count, to reduce wholes to their parts when explaining the wholes. We see this kind of thing when, for example, some scientists or philosophers seek to reduce human consciousness to a specific physical location in the brain (see scientism, more generally). This kind of thinking has extraordinary implications, for if all higher order things (e.g., people) can be reduced to their lower level, basic physical parts (i.e., the wholes are merely summative of the physical aspects that comprise them), then all problems at the whole can be addressed simply by attending to the parts, especially the tangible, mechanistic parts. But is that necessarily true? For example, can all mental issues be addressed simply by attending to the physical processes or components in the brain, or to borrow an example from Polanyi, can we fix someone's grammar simply by fixing that person's vocabulary, since the grammar of a language is simply made up of its parts, the words? And then, can we attend to someone's style of writing simply by attending to that person's grammar, and so on?
This way at explaining things (and viewing the world -- i.e., defining reality or what is real [the ontological]) is common across all domains of knowledge and areas of practice. Another example: several years ago I was doing historical work at an institutional archives and reading some annual library reports from around the mid-20th century. One of the common problems that the head librarian described in those reports concerned his administration's view of the library as nothing more than a warehouse of books. As he described it, the administration at his academic institution ignored (or even failed to see) the complexities attached to managing and using a library, and as a result, repeatedly failed to invest in the library and the librarians who operated it (the practical implication of a reductionist viewpoint). For the head librarian, the library was more than a warehouse of books; in the process of acquiring, describing, managing, shelving, circulating, using, and so forth, and by virtue of the material (books, serials, etc.) that was being attended to in those processes, something emerged or came into existence that was beyond a basic warehouse. And the thing that emerged was as real as any of its constitutive parts (e.g., books and shelves), even if it could not be reduced to those parts. Thus, even though that administration would agree that the library was a real place, it seemed that for them, the librarian might have said, it was only real as "cobblestones" are real.
And since I regard the significance of a thing as more important than its tangibility, I shall say that minds and problems are more real than cobblestones (p. 33).
Polanyi's point in his lecture on emergence is simply this: higher order things (technically, coherent things), cannot be explained by or reduced to their constitutive parts ("the whole is greater than the sum of its parts") even if those parts are necessary for the whole to exist. Similarly, grammar requires a vocabulary, but cannot be reduced to a vocabulary. The reverse is true, too. A vocabulary cannot dictate a specific grammar, just as a grammar cannot dictate, or determine, a style of writing:
Take two points. (1) Tacit knowing of a coherent entity relies on our awareness of the particulars of the entity for attending to it; and (2) if we switch our attention to the particulars, this function of the particulars is canceled and we lose sight of the entity to which we had attended. The ontological counterpoint [my emphasis] of this would be (1) that the principles controlling a comprehensive entity would be found to rely for their operations on laws governing the particulars of the entity themselves; and (2) that at the same time the laws governing the particulars in themselves would never account for the organizing principles of a higher entity which they form (p. 34).
Polanyi, in all of this, is making a case for tacit knowing (the distal) as something that cannot simply be explained by or reduced to explicit knowledge (the proximate). In the final lecture, he will address some scientific consequences of this position -- issues that relate, in some respects, to problem-finding.