The phrase "a foundational problem with" is correct and usable in written English.
It can be used to describe a fundamental issue or flaw in a particular concept, system, or argument.
Example: "The report highlights a foundational problem with the current approach to environmental policy, suggesting that it fails to address the root causes of climate change."
Alternatives: "a fundamental issue with" or "a core problem with".
Hill (2004, p. 627, 628) argues that the concept of superaddition "is quite out of place" in connection with cohesion, because Locke regards cohesion as a foundational problem, which thwarts our efforts to conceive of body.
These are fail-safe points in discussions of artistic freedom, and they sidestep a foundational problem: the decision to make art without regard for the lives involved, and no matter the consequences.
A foundational problem in kernel-based learning is how to design suitable kernels.
In (Wallace 2006) unitarily inequivalent representations are not considered a foundational problem for QFT, while in (Ruetsche 2003) and (Kronz and Lupher 2005) unitarily inequivalent representations are considered physically significant.
The second foundational problem was the lack of three critical planning tools: a realistic Theory of Change, an overarching Logic Framework and a tightly-integrated implementation plan.
The fourth foundational problem, the decision problem for predicate logic, was shown to have a negative solution in a short paper by Church in 1936 as a corollary to Gödel's incompleteness theorem.
Projective geometry has its own foundational problem, akin to that of distance in Euclidean geometry, which concerns the concept of cross-ratio, and we need to follow the moves to create projective geometry as an independent subject, to define cross-ratio in this setting, and to resolve the epistemological issues that are raised (an achievement associated with Klein's Erlangen Programme).
The foundational problem pushes the question about cohesion into the corpuscles themselves.
So although contemporary mainstream biology is an overtly materialist field, it has come to employ concepts that philosophers will recognize as intentional or semantic ones, concepts with a long history of causing foundational problems for materialists (and, to some extent, for everyone else).
The groundwork was a study of the four foundational problems in axiomatic formulations of pure logic.
