Diagonal Materialism and the Is-Ought Gap
Firstly, diagonalization is a three-stage process that involves two conceptual oppositions which were “previously glued together as apparently matched (quasi-)synonyms.” In this case, we have conceptual opposition 1, is-ought, and conceptual opposition 2, fact-value. Is-ought and fact-value are quasi-synonyms. And thus fit the bill for the diagnonalization process.
Secondly, “[d]iagnonalization is executed within a matrix, or exhaustive combinatorial array (with as many dimensions as there are elements in the assemblages to be composed, or sets to be enumerated).”
Thirdly, “diagonalization has successive parallel, orthogonal, and diagonal phases.”
Stage 1: The two conceptual oppositions are “adopted in parallel.” This first stage is “dominated by resonance or redundancy,” that is to say, the conceptual oppositions are still quasi-synonymous.
Stage 2: The two conceptual oppositions are “then twisted into the perpendicular.” The second stage is dominated “by combination or permutation,” that is to say, the conceptual oppositions are put (“combined”) into one matrix wherein the optimization (stage 3) of the two conceptual oppositions take place).
Stage 3: The two conceptual oppositions are then “finally inclined to the oblique.” The third stage is dominated “by optimization,” that is to say” the conceptual oppositions become no longer opposed, but rather synthesized and optimized.
Thus, is=value and fact=ought. This is also an example of why diagonal concepts “that can only appear – at their threshold of emergence – as paradoxical.”
Land specifically speaks of the two-dimensional nature of orthogonality. He says, “orthogonalism,” by emphasizing conceptual separations and divisions between, for example, is and ought and fact and value, “understands itself as a resolution of confusion. Rather than one axis there are two, with free conceptual variation upon each. In order to consolidate this articulation, it identifies the dispelled confusion as a fallacy. Hence the ‘Naturalistic fallacy’ or supposed in mistaking of values for matters of fact.” The second stage of the diagonalization process is where most people stop, they create a two-axis matrix, not even recognizing the possibility of diagonal reconstruction due to the fact they can only suppose such a thing to be a fallacious impossibility.
Land continues, “Upon diagonal reconstruction, it is not the ‘fallacy’ but rather the supposition of the fallacy which is found to be in error. That is to say, the orthogonal presupposition is withdrawn.” We, materialists, don’t even think to be a repetition of idealist metaphysics that presuppose orthogonalism: “[i]instead of independence and free variation of terms, the diagonal preserves reciprocal irreducibility only under conditions of mutual implication.”
Land thus concludes, “Values do not reduce to facts, or inversely, because neither reduces even to itself. In the fashion of metaphysics, orthogonalism is essentially erroneous.”
But what is the motor of this process? Nothing other than necessity (as in “logical” necessity): “Since it is articulated in two dimensions, orthogonalism can only be initially affirmed, or engaged, upon a plane. Within – and also without – such terms of engagement, the diagonal is a planar line. It is neither one-dimensional, nor two-dimensional, but inter-dimensional. A diagonal draws a plane into a line, in a process without terminus. Between diagonal thing and diagonalizing action there is no resilient distinction. The diagonal necessarily and continuously diagonalizes.”
As for materialism, Land recognizes that “[w]hen matter is liberated from its pre-critical conception, diagonal materialism becomes a redundant formulation (or pleonasm), in which each term fully reconstructs the positive sense of the other. Approached from the inverse, ideality undergoes diagonal subversion.”
[NOTE: Here is the essay on diagonalization by Land https://zerophilosophy.substack.com/p/note-on-diagonal-method]