§ 20 Rational testing

Sometimes all we have is beauty, that is, the satisfaction of something that fits with an idea we have about things.¹

Our conceptual apparatus can produce propositions that are logically consistent with our frame of reference without empirical testing for accuracy. It is fair to call these propositions true. So, for example, if I believe that the spaghetti monster created the world, the proposition “The spaghetti monster created the world” would count as true. In fact, such a proposition cannot be tested empirically. And this is true for many of our beliefs.

In this case, we rely exclusively on the conceptual apparatus as it stands, and taking our belief as a starting point, we infer any implications on purely rational grounds.

A logically consistent proposition must therefore fit with the belief structure. In other words, they are subject to aesthetic judgment.

The truths that we thus produce rely solely on their aesthetic coherence and consistency within a given conceptual framework and its inferential structures.

Alethic judgments whereby truth is exclusively meant as ‘consistent with my beliefs’ are, in fact, a special form of aesthetic judgment.

Logic is as much an aesthetic as an alethic concern.

In this way, theology and mathematics become curious bedfellows, in that both make use of this feature. Theology by making assumptions about reality that it cannot prove and working out its consequences rationally á la Thomas Aquinas.

In the case of mathematics, those unprovable assumptions and their grammar of operational possibilities deliver us the deep exploration of the game with its rules, its field of play and its pieces, resulting in an enormously rich conceptual work of art, an exploratory construction whose worldly applicability may well lag far behind, if it is ever allowed to catch up.

Until more mundane uses and purposes catch up with this harmoniously composed city of mathematical relations, it serves as a simple source of contemplative joy and pleasure, as well as a horizon for our further explorations in other disciplines.

Rationalist explorations of an extant conceptual framework also occupy people interested in words and images.

The architecture of the Rationalists (the Rats, as Charles Jencks called them) represents the outcomes of such intricate games in which the exploration of formalised rules of play systematically seeks out possibilities.

However, when making an actual design decision based on such a game, a responsible designer would want to test it for its implications for stability, utility, and attractiveness, as well as its potential effects on people’s lives and the quality of the environment.

In music, we recognise such rationalist explorations in all their manifestations, but most emphatically in the work of Johann Sebastian Bach, Arnold Schonberg, and Steve Reich.

In the exploration of language, we see it in the disciplines of logic and linguistics, as well as in prose and poetry. One should certainly not say that analysis without empirical testing is worthless.

The purely inferential exploration of an existing and ‘closed’ conceptual framework and its space of implications has given us the extraordinary profundity of chess, where Qxf6# is final if true.

Analytical explorations can be tested empirically and rationally and then evaluated critically when used. Rational testing of such analytical assertions looks at whether an inferential outcome is legitimate and therefore true, that is, that it is coherent and consistent with the conceptual framework and its inferential grammar.

With that, rational truths have no necessary relationship to reality other than that they are products of that reality’s behaviour, but that may not offer much comfort.

© Jacob Voorthuis, 2026. Please cite Jacob Voorthuis as the author, The Theoria Project as the title and the page address as the location. This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially under the following terms: No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made.

1. A slightly older version of this paragraph was first published in Jacob Voorthuis, Theoria, use, intention & design, a philosophical reckoning; Analysis & Critique: Gardening in the metaphysics of the beautiful, the true, and the good, AHT, TU/e (2024) ↩︎