A comprehensive model adding dimensions of certainty and access. Axis 1: A Priori-A Posteriori. Axis 2: Propositional-Procedural. Axis 3: Personal-Communal. Axis 4: Explicit-Tacit. Axis 5: Certain-Fallible (knowledge that can't be wrong vs. knowledge that might be mistaken). Axis 6: Direct-Inferential (known directly vs. known through reasoning). These six axes generate sixty-four knowledge positions. Mathematical knowledge is a priori, propositional, personal (when learned), explicit, certain (in ideal), inferential (proved). Perceptual knowledge is a posteriori, propositional, personal, explicit (usually), fallible, direct. The 6 Axes reveal that different kinds of knowledge have different epistemic statuses—certainty isn't the same for all.
The 6 Axes of the Knowledge Spectrum "You demand certainty. The 6 Axes ask: what kind of knowledge? Math can be certain (maybe). Perceptual knowledge can't—that's not its function. Certainty is a feature of some knowledge types, not a requirement for all. The axes help you see that demanding certainty from empirical knowledge is asking for the wrong thing."
by Dumu The Void February 25, 2026
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