Synthesized answer
In James's philosophy, a "Grenzbegriff" is something that "still remains undiscovered" [1, 2]. It represents an ultimate concept, like absolute unity, that philosophers strive towards but can never fully grasp or confirm through experience [1, 2]. Even after all rational efforts, an "opacity of the finite facts" remains, with unexplained peculiarities and different points of view [2].
The passages suggest that a "Grenzbegriff" is a limit-concept, a philosophical ideal that is approached but never definitively reached. It signifies the ongoing quest for ultimate understanding in philosophy, where complete certainty and a single, all-encompassing viewpoint remain elusive [1, 2]. The passages do not provide a more detailed definition of the term "Grenzbegriff" itself, beyond its characterization as an undiscovered or limit concept in the pursuit of absolute unity.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
of _radical empiricism_, in spite of the fact that such brief nicknames are nowhere more misleading than in philosophy. I say 'empiricism,' because it is contented to regard its most assured conclusions concerning matters of fact as hypotheses liable to modification in the course of future experience; and I say 'radical,' because it treats the doctrine of monism itself as an hypothesis, and, {viii} unlike so much of the half-way empiricism that is current under the name of positivism or agnosticism or scientific naturalism, it does not dogmatically affirm monism as something with…
lute unity, in spite of brilliant dashes in its direction, still remains undiscovered, still remains a _Grenzbegriff_. "Ever not quite" must be the rationalistic philosopher's last confession concerning it. After all that reason can do has been done, there still remains the opacity of the finite facts as merely given, with most of their peculiarities mutually unmediated and unexplained. To the very last, there are the various 'points of view' which the philosopher must distinguish in discussing the world; and what is inwardly clear from one point remains a bare externality and datum…
e_, etc.), what is that also but a synthesis,--a synthesis of a passive perception with a certain tendency to reaction? We are acquainted with a thing as soon as we have learned how to behave towards it, or how to meet the behavior which we expect from it. Up to that point it is still 'strange' to us. {86} If there be anything at all in this view, it follows that however vaguely a philosopher may define the ultimate universal datum, he cannot be said to leave it unknown to us so long as he in the slightest degree pretends that our emotional or active attitude toward it should be of…
d a fundamental part. {80} The term set up by philosophers as primordial has been one which banishes the incalculable. 'Substance,' for example, means, as Kant says, _das Beharrliche_, which will be as it has been, because its being is essential and eternal. And although we may not be able to prophesy in detail the future phenomena to which the substance shall give rise, we may set our minds at rest in a general way, when we have called the substance God, Perfection, Love, or Reason, by the reflection that whatever is in store for us can never at bottom be inconsistent with the…
be overlooked. More universality or extensiveness is, then, one mark which the philosopher's conceptions must possess. Unless they apply to an enormous number of cases they will not bring him relief. The knowledge of things by their causes, which is often given as a definition of rational knowledge, is useless to him unless the causes converge to a minimum number, while still producing the maximum number of effects. The more multiple then are the instances, the more flowingly does his mind rove from fact to fact. The phenomenal transitions are no real transitions; each item is the same…