Formal Technologies

The tools and systems designed to manipulate abstract symbols according to strict rules, enabling everything from simple arithmetic to complex computer programs. This includes calculators (slaves to the algorithm), programming languages (formal systems that are surprisingly forgiving of missing semicolons), and the humble spreadsheet, which has launched a thousand careers and caused a thousand nervous breakdowns when someone sorted the wrong column. Formal technologies give us power over abstraction, which we primarily use to make pretty charts about things that don't matter.

Example: "She used formal technologies to build a complex financial model that predicted market trends with 95% accuracy. Unfortunately, the model was based on historical data, and the market, not being a formal system, promptly did something unpredictable and made all her charts wrong. She blamed the model; the model blamed reality."

by Abzugal February 14, 2026

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Formal Sciences

The branch of knowledge that studies abstract structures and symbolic systems, unconcerned with whether they correspond to anything in the real world. Mathematics, logic, and theoretical computer science live here, in a pristine realm where 2+2 always equals 4 and arguments are either valid or invalid, not just "like, your opinion, man." Formal sciences are beautiful, consistent, and utterly indifferent to the messy reality of human existence, which is why mathematicians are so calm and everyone else is so confused.

Example: "He loved the formal sciences because in mathematics, unlike in relationships, things either worked or they didn't, and when they didn't, you could prove why. His girlfriend pointed out that this attitude might be why he had so much time for mathematics."

by Abzugal February 14, 2026

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Formal Laws of Logic

The immutable, mathematical rules that govern valid reasoning, regardless of content. Think of them as the operating system of rational thought. The big three are the Law of Identity (A is A), the Law of Non-Contradiction (A cannot be both A and not-A at the same time and in the same sense), and the Law of Excluded Middle (either A is true, or not-A is true—no middle option). These aren't suggestions; they're the bedrock upon which all sound arguments are built. Violate them, and your reasoning collapses into incoherence faster than a house of cards in a hurricane.

"You say you both love me and don't love me simultaneously, and that this is somehow a valid emotional state? I don't care what your therapist says—the Formal Laws of Logic demand you pick a lane, or this conversation is over."

by Dumu The Void February 23, 2026

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Formal Infrasciences

The branch of infrascience that examines the infrastructure underlying the formal sciences—logic, mathematics, systems theory, and related fields that study formal structures rather than empirical phenomena. Formal infrasciences investigate the foundational systems, structures, and conditions that make formal inquiry possible: logical infrastructure (rules of inference, proof systems) that enables deductive reasoning; conceptual infrastructure (definitions, axioms, frameworks) that provides foundations; computational infrastructure (formal systems, algorithms, software) that extends formal capabilities; notational infrastructure (symbol systems, languages) that enables formal expression; and institutional infrastructure (departments, journals, conferences) that supports formal research. Formal infrasciences reveal that even the most abstract formal systems depend on infrastructure—that logic doesn't float free but is practiced by communities using tools developed over centuries, and understanding formal science requires understanding this infrastructure.

Example: "His formal infrasciences research examined how the development of computer proof assistants is transforming mathematical practice—not by replacing human reasoning, but by providing infrastructure that extends what humans can prove. New tools, new proofs, new mathematics."

by Abzugal March 16, 2026

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Formal Metasciences

The systematic study of the formal sciences themselves—a second-order discipline that takes logic, mathematics, systems theory, and related fields as its objects of inquiry. Formal metasciences ask meta-level questions about formal knowledge: How do formal scientists know what they claim to know? What methods do different formal disciplines use? How does formal knowledge change over time? How do social, cultural, and institutional contexts shape formal science? What are the limits of formal understanding? Formal metasciences are the formal sciences reflecting on themselves—the attempt to understand what formal science is, what it can achieve, and how it relates to other forms of knowledge. They're essential for formal science to be self-aware rather than merely practiced, for formal scientists to understand their own activities rather than just engaging in them.

Example: "Her formal metasciences research examined how Gödel's incompleteness theorems transformed logic's understanding of itself—showing that formal systems have inherent limits, and that the dream of complete, consistent foundations for mathematics is impossible. Logic studying itself discovered its own boundaries."

by Abzugal March 16, 2026

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