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The Tetrast2 - Speculation Lounge
Sketcher of various interrelated fourfolds.

Contrarian, partisan, neutralist, conformist; & digressions on the light cone & classes of math

June 13, 2014.

Latest significant edit: June 19, 2026.

Here is a logical system of four dispositions to form an opinion in reaction to the definite opinions of the rest of the group on a given topic, so as to agree or to disagree with all or some or none of them. Adjust it to taste; for example, replace every instance of "some" with "as many as possible" and replace every instance of "none" with "as few as possible".
Contrarian:
disposed so to react to the rest
as, without remainder, to
AGREE with NONE and
DISAGREE with SOME (indeed all).
Partisan:
disposed so to react to the rest
as, without remainder, to
AGREE with SOME and
DISAGREE with SOME.
Neutralist:
disposed so to react to the rest
as, without remainder, to
AGREE with NONE and
DISAGREE with NONE.
Conformist:
disposed so to react to the rest
as, without remainder, to
AGREE with SOME (indeed all) and
DISAGREE with NONE.

By "neutralist" here I mean a person capable of a non-neutral opinion as long as the opinion avoids both agreement with the other people and disagreement with the other people. Note: I've changed the post's title to replace "insularist" with "neutralist". Much earlier I had used such words as "quasi-solipsist" and "solipsoidist", and had thought of "outsiderist" and a Latinate word "exsularist" from the conjectured *exsul, see etymonline.com's quote from De Vann.

Contrarian

Partisan		 X Neutralist

Conformist

The opposition between contrarian and comformist seems diametrical. Likewise the opposition between partisan and neutralist. The contrarian tries to disagree with others, all of them; the conformist tries to agree with others, all of them. The partisan tries to have allies and adversaries; the neutralist tries to lack allies and adversaries.

There also seems a diametrical opposition between the neutralist and the equivocalist, who aims to support both (or all) sides in opining. But the neutralist diametrically opposite to the euivocalist would be in a case of an alternative so exclusive that denial of both (or all) sides in an actual discussion would amount to an equivocation from the start. All four of the dispositions discussed above, including conventional neutralism, tend to lead one into contradictions and some at-least seeming equivocation, but those four are on a kind of logical tier distinct from the absurdism, self-contrarianism, and the like, that arrives in full force with equivocalism. What seems most diametrically opposite to an equivocalist is an opiner who has no such isms at all.

Digression: A striking affinity with special relativity's light cone

The four main dispositions portrayed in this discussion are classified systematically in terms of possible combinations of agreement and disagreement, but they also have in common a temporal element, insofar as they involve reactions to the already given (or supposed) opinions of other people. So it ought not to be too surprising (although it puzzled me in the past) that the dispositions have a one-to-one affinity with temporally, indeed somewhat lightcone-ishly, varied modes of the willful or cocksure: impetuous, pertinacious, smug, hidebound. Inspect the following correlations (not equivalences or formal implications).

■ Contrarian ≘ impetuous, radicalistic, pushing too far, too fast, like with too much ∆s⁄∆t, vis-à-vis the almost-now, more or less along the surface of the future.
■ Partisan ≘ pertinacious, programmatic, putting too much time regularly into it, like with too much ∆τ⁄∆t, vis-à-vis the gradually addressable future.
■ Neutralist ≘ smug, committing too little of one's own time & energy, like with too little ∆τ⁄∆t, vis-à-vis the just-now, the barely-now, more or less along the surface of the past.
■ Conformist ≘ hidebound, hanging too far back, too slow, like with too little ∆s⁄∆t, vis-à-vis the settled, layered past.

* * * *

Only in the case of the idea of smug neutralism (or "smug insularism" as I was calling it) did a term (neutralism) in the agreement-disagreement series influence my idea of the correlated term (smugness) in the temporally varied series. Instead of the smug, I had previously thought of the impulsive, over-reactive, etc. The correction was corroborated for me by its resulting in better correlations elsewhere, for example:

■ Impetuous ≘ too desirous, not disgusted enough (vis-à-vis the almost-now).
■ Pertinacious ≘ too hopeful, too confident, not scared enough (vis-à-vis the gradually addressable future).
■ Smug ≘ too pleased, not pained enough (vis-à-vis the just-now, the barely-now).
■ Hidebound ≘ too attached, not resentful enough (vis-à-vis the settled past).

(Also see "Political dispositions".)

* * * *

The likeness to special relativity's light cone, in the arrangement of the temporally varied terms above, arises from seeing time as encompassing not merely a chronological series (which tends to make us think simply in terms of past, present, future) but instead zones of possibility of communication and of control (cause and effect) and involving some sort of practical speed limits and practical looseness about the difference between high speed and top speed. In other words, in discussing temporal orientations of behavior, affectivity, etc., we need to distinguish not only among past, present, and future, but furthermore between the more-or-less present as it can affect one (the just-now) and the more-or-less present as one can affect it (the almost-now). In everyday situations, the spacetime wedge, so to speak, between the just-now and the almost-now is phenomenologically small to vanishing; but there remains the stark and equally phenomenological difference between inbound and outbound causal, communicational directions. Now, I did not simply come up with the light cone's outlines by considering common experience; instead I had read about the light cone many years earlier, and later I looked for its like in common experience. Are its lineaments really less phenomenological than time seen as a chronological series divided simply into past, present, and future? I doubt it. Both views involve ideas about what ought to count as parts of time's form.

Further digression: The light cone and the mathematics of structures of alternatives in timelike, quasi-modal perspectives

The light cone's divisions echo divisions of the mathematics of structures of alternatives, implications, and the like:

Lightcone-like Structure Compounded of (Quasi-)Modal Cases

■ Optimal & feasible cases: for, or as if for, the almost-now (mathematics of optimization, longer known as linear & nonlinear programming).
■ Probabilities: for, or as if for, the gradually addressable future (probability theory).
■ Information, news: from, or as if from, the just-now (information theory, including information algebra).
■ Contingent facts, data: from, or as if from, the settled past (mathematical logic).

So, a considerable portion of mathematics — 'applied' but highly general — is concerned with temporal or at least timelike perspectives. (Also see "Plausibility, verisimilitude, novelty, nontrivialness, versus optima, probabilities, information, facts" at The Tetrast.) Part of my point here is to suggest that the light cone is not just some idiosyncrasy of the physical world, and that consideration of pure-mathematical underpinnings of the above mathematical applications may find the light cone's lineaments emerging already in the divisions of pure mathematics. Of course some would say that it would instead show, or at least suggest, that mathematics is a more of a mere generalization from concrete experience than mathematical platonists like to think it to be. Still, I'd hold that, if the pure-mathematical underpinnings of the above-listed applied areas collectively form a mathematically non-arbitrary pattern of topics, then it could show that the structure of the light cone is rooted more deeply than many suppose it to be.

Update 2026-3-18 & succeeding days: the mathematical underpinnings:

Zone of the light cone, or of its like. Deductive maths of structures of (quasi-)modal (quasi-)temporal alternatives. Such maths focus on total populations, gamuts, etc. Underpinnings in pure maths.
The almost now, the imminent.Maths of optima (& feasible cases).
Ordinally focused;—not generically focused on amounts or degrees of optimality or feasibility. 		Some maths of: many-to-many equations; extrema & critical points (in topology); & graph theory.
The gradual future.Probability theory.
Cardinally focused;—generically considers amounts of probability.
Zadeh's possibility theory belongs here too if, as he said somewhere, it does the same work as probability theory. 		Some maths of: one-to-many relations (multi-valued functions); integrals; measure; & counting (a.k.a. enumeration).
The just now, barely now. Maths & algebra of information (news).
Cardinally focused;—generically considers amounts of informativeness. 		Some maths of: many-to-one functions; derivatives; abstract algebra (theory of groups of operations).
The layered past. Maths of contingent facts, data, monadic or polyadic etc., i.e., maths of logic.
Not generically about degrees of truth (MVL). Focused on orderings and numbers of individual facts, including relation instances.		 Some maths of: one-to-one correspondences, bijective functions; convergence, ideal limits; & order.

End of update.

Some less digressive remarks

Each of the dispositions to reactive opinion tends to lead one into inconsistencies. If one generally aims in the first place both to agree and to disagree with somebody (such as oneself) in one same time, place, and regard, then one's disposition could be called equivocalist, self-contrarian, inconsistentist, absurdist, or the like.

- posted by The Tetrast, initially @ 6/13/2014 02:14:00 PM [top of post] [top of page] Copyright © BenjaminðA.ðUde11.
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