Two Kinds of Intelligibility / What Induction Cannot Explain
This morning I read an article by Peter Keeble in Philosophy Now magazine. He references two seminal texts in the history of philosophy and epistemology. Edmund Gettier “Is Justified True Belief Knowledge?” and Nelson Goodman “Fact Fiction and Forecast” (the famous “Grue” argument). Keeble seems to undermine the point of the “Grue” argument a bit. ”Causality works through various known regularities” – yes. However the fact that inductive reasoning is beset by accusations of circularity is not trivial for philosophy. Insofar as we are committed to statistical probability as the foundation for “a kind of knowledge,” that knowledge will always be relative. Consider the difference between maths and geometry – as per the ancients: in geometry, the intelligibility is in the figure itself. As David Lachterman puts it, this is ‘the difference between an Apollonian and a Cartesian locus’ (The Ethics of Geometry: A Genealogy of Modernity) - in the Cartesian case, intelligibility is imposed on the object through algebraic description; in the Apollonian, it is already there in the figure. The real issue here is not simply whether induction can be justified; it is that two different kinds of intelligibility are being conflated. Structural intelligibility, unlike inductive knowledge, is not susceptible to a temporal cut (something that happens before or after a given time T).
This distinction matters for how we handle “Grue” philosophically rather than just pragmatically. By reference to the metaphysician Kit Fine’s general view of “grounding relations,” “Grue” might be a “metaphysically necessary” but not “essential” property at some point in the future. About 20 years or so ago as an undergrad student I naively broke this down as the reason why Peter Geach misattributed something so badly wrong to Plato with the “Socratic Fallacy.” Because I knew intuitively at all and every level that Plato would never have been committed to the epistemic regress inherent in any definition of truth “in the empirical sense.”
The point of this is not so much a response to Gettier and Goodman as it is circling a deeper fracture in epistemology. The axis is the difference between knowledge that is tracked through regularity (inductive probability) and knowledge that is grounded in structure (essence, form, intelligibility – “architects can see the future” (from Sympathy Tower Tokyo by Rie Qudan). The architect doesn’t extrapolate from past buildings - the future form is already implicit in structural knowledge of what a building is - from structural knowledge of form - the future is already implicit in the figure. This is exactly what inductive knowledge cannot do, because inductive knowledge is always downstream of its evidence. Keeble deflates the Grue problem pragmatically (“we trust causal regularities.”) But this doesn’t resolve the philosophical issue – it sidesteps it. Keeble is basically saying “yes, induction is messy, but in practice we rely on causal stability.” However Goodman’s point is not practical; it’s structural. “Green” and “Grue” are equally compatible with past observations. So the data alone does not determine the law. This means induction is underdetermined, and therefore circular, because we justify it by its past success.
This is not trivial – it destabilises induction as a foundation for knowledge. This is (essentially) a distinction between relative and structural knowledge. This is extremely important: if knowledge is based on statistical probability, it will always be relative. I can sharpen this a bit – inductive knowledge is based on frequency, probability, and projection from past to future. Therefore it is always revisable and always relative to observed patterns and never fully grounded. Structural / Geometric / Essential knowledge is based on form / internal relations and necessity; therefore, it is self grounding, not dependent on temporal repetition and closer to what the Greeks meant by “epistēmē” (true, justified, and stable knowledge that is grounded in understanding why something is the case). Furthermore, in geometry, the intelligibility is not grounded in repeated observation. In Kit Fine’s metaphysical universe, “Grue” might be metaphysically necessary but not essential. A property can be true of an object (even necessarily true), but not a part of its essence. So an emerald might be “grue” under some bizarre predicate construction, but “green” tracks something essential or projectible. “Grue” does not – it is artificially demarcated. “Grue” only works as a destabilising predicate because inductive knowledge is indexed to time (before/after T). This is a distinction between properties that belong to the structure of a thing and properties that are merely projected onto it through language or induction. This is the real answer to Goodman but Keeble doesn’t go there.
Some predicates remain stable across transformations of description, while others collapse. This distinction marks a difference between what is structurally grounded and what is merely projected.
Plato would never have grounded knowledge in empirical definition. Peter Geach’s idea that “you must define something before you can know anything about it” Is a modern, analytic framing. Plato treats knowledge as a movement toward form (like a dancer!) Plato avoids the regress because knowledge is not built from induction upward; it is oriented toward structure already there. In this sense, analysis is not inductive but orientational - a movement toward structure rather than a generalisation from cases.
This is a distinction between two different types of intelligibility: inductive intelligibility assumes pattern recognition across time (unstable, relative). Temporally determined not spatially determined? Structural intelligibility is form-based necessity, stable and self grounding. spatially determined … things can conceivably change in time, but not in space? Modern epistemology has collapsed everything into the first, and forgotten the second.
*There is a family resemblance here to Kierkegaard’s critique of Hegel’s importation of “movement” into logic – the illegitimate introduction of transition – of “becoming” into what purports to be a purely logical system. This is a critique of a specific move within speculative idealism. Both are about the contamination of a knowledge claim by temporal indexing.
