Foundational Primitives & Basic Reasoning

Primes about the elemental building blocks of formal and everyday thought: basic mathematical structures and operations (addition, power sets, limits, transitive relations), core philosophical categories (identity, property, referent, truth value), and basic epistemic moves and fallacies (inference, causal reasoning, wishful thinking).

61 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Addition — Combine two or more quantities, elements, contributions or increments through a typed binary operation that produces their sum.
• Anisotropy — Make a property or response depend on direction, orientation, or axis in the carrier, so rotating the same probe changes the measured relation.
• Appeal to novelty — Treat newness, recency, or modernity itself as sufficient evidence that an idea, method, product, or institution is truer, better, safer, or more effective.
• Argument from incredulity — Treat one's inability to imagine, understand, or intuit how a proposition could be true or false as evidence that it therefore is false or true.
• Attractor — Identify an invariant state set toward which a nontrivial neighborhood of initial conditions approaches under a system's evolution, with the basin and mode of attraction stated explicitly.
• Bow tie (biology) — A many-to-few-to-many architecture in which diverse inputs converge on a small conserved core of protocols or intermediates and then fan out into diverse outputs.
• Camouflage — Reduce reliable detection or identification by altering how a target’s observable features relate to its background or expected category.
• Causal reasoning — Infer, compare, test, or revise cause–effect structure by distinguishing interventions and counterfactual alternatives from association alone.
• Coincidence — A conjunction of events or circumstances that is experienced as notably aligned despite lacking an established causal connection.
• Continuum (measurement) — Represent variation as admitting gradual quantitative transitions across an ordered range rather than only abrupt membership in discrete categories.
• Coordinate-free — Define and reason about an object through intrinsic relations whose truth is invariant under every admissible change of coordinates, basis, chart, or component representation.
• Data collection — Deliberately acquire and record observations about defined variables, events, texts, or experiences under a protocol that preserves provenance, quality, and fitness for a stated question.
• Design — Deliberately specify and shape an artifact, system, service or arrangement so its structure can realize valued purposes under interacting constraints.
• Disjoint union — Combine collections while tagging every member with its source so equal values from different sources remain distinct in the result.
• Downtime — A bounded interval during which a system, service, asset, role, or capability is unavailable for its intended demand, whether the interruption is planned or unplanned.
• Due diligence — Investigate and exercise the care appropriate to a consequential commitment before relying, approving, acquiring or acting.
• Enforcement — Cause a rule, requirement, agreement or boundary to be complied with by monitoring conduct and applying credible consequences or corrective action.
• Estimation — Derive a usable value, range or state for an unknown quantity from incomplete, noisy or indirect information, with assumptions, uncertainty and decision purpose made explicit.
• Fail-fast system — Detect an invalid state at the earliest trustworthy boundary, report it explicitly and stop the affected operation before corruption propagates.
• Finiteness — Bound a collection, process, horizon, description, or resource so its members or steps can in principle be exhausted, completing enumeration rather than opening an unending remainder.
• Idea — A mentally or symbolically entertainable content that presents a possible form, object, relation, action or state of affairs for thought and communication.
• Identity (philosophy) — Treat two occurrences, descriptions, states, or presentations as numerically the same entity only when a declared persistence and reidentification criterion licenses one referent across the difference.
• In situ — Observe, preserve, create or act on something in its original location so the surrounding relationships that constitute its behavior remain present.
• Indexed family — Organize a collection by assigning one object to every element of a declared index set, allowing repetition and preserving the identity of positions.
• Inference — Move from premises, evidence or observations to a conclusion licensed by an explicit rule or support relation.
• Information — A difference, constraint, or patterned selection that can change an interpreter's uncertainty, representation, or action when carried through a usable relation between possible states.
• Information overload — When incoming information exceeds the receiver's finite capacity to select, integrate and act, additional input reduces understanding and decision quality instead of improving it.
• Input/output — The typed exchange boundary through which a system receives state-changing signals or data and emits signals, data, actions or effects to its environment.
• Inquiry — Pursue a question through disciplined evidence-seeking and reasoning in order to reduce uncertainty, resolve doubt or improve understanding.
• Jacobi identity — A skew bracket's three cyclic nestings cancel, making each element's adjoint action behave as a derivation and allowing local pairwise generators to compose into coherent higher-order structure.
• Limit (mathematics) — Identify a value or object that a varying process approaches arbitrarily closely under a declared notion of neighborhood, direction, indexing, and convergence.
• Metatheory — A theory whose objects of study are the claims, language, inference rules, models or performance of another theory.
• Mottle — An otherwise continuous surface or field carries irregular, nonuniform patches of contrasting color, tone, texture, or intensity whose distribution is recognizable without forming a regular repeat.
• Multiple realizability — The same higher-level role or property can be instantiated by materially different lower-level structures.
• Multistability — A dynamical system supports multiple simultaneously stable long-run states or attractors, so history, perturbations, and initial conditions determine which persistent regime is realized.
• Mutual knowledge — A fact is mutual knowledge in a group when every member knows it, without requiring anyone to know that the others know it or any higher-order awareness.
• Order — Defines ranking or sequencing relationships.
• Other (philosophy) — Model a self, identity or social order through its constitutive relation to what it marks as distinct, exterior or not-self, with recognition, asymmetry and exclusion treated as variable structural consequences.
• Pattern — Recognize a repeatable organization of elements or relations that remains identifiable across instances or transformations and supports compression, expectation or comparison beyond accidental resemblance.
• Pigeonhole principle — Whenever more items are assigned to fewer available categories or slots, at least one slot must receive multiple items.
• Planning — Construct a revisable sequence, dependency structure, or policy that connects a represented present state to a desired future state before committing the corresponding actions.
• Power set — For a set S, form the set whose members are exactly all subsets of S, including the empty set and S itself.
• Praxis (process) — Turn an idea, theory or learned capability into situated action whose consequences can in turn revise understanding.
• Proof of impossibility — Demonstrate that no object, procedure or arrangement can satisfy a declared set of requirements under stated assumptions.
• Property (philosophy) — Represent a repeatable characteristic that can be instantiated by objects, events or states and used in predication, comparison and explanation.
• Qualitative property — A property records kind, state or category without its identity depending on a numerical magnitude or arithmetic distance.
• Reference class problem — Choose which relevant comparison class should govern a probability or generalization about one case when that case belongs to many classes with different rates.
• Referent — The entity, event, property, place, value, or abstract object that a sign, name, variable, record, or representation is used to pick out in a declared context.
• Ripple effect — A localized disturbance produces successive indirect consequences that propagate outward through connected parts of a system.
• Sanity check — Apply a fast, coarse test of units, scale, sign, invariants or obvious boundary cases to reject results that cannot plausibly be correct before investing in detailed verification.
• Self-awareness — Represent oneself as the subject of one’s present states, traits, motives or actions and use that representation in reflection and regulation.
• Strategic thinking — Reason about a goal as a changing system of actors, constraints, leverage points and future consequences in order to choose a coherent direction.
• Suspension of judgment — Deliberately withhold commitment to a conclusion when the applicable grounds or decision threshold are not yet satisfied.
• System — A bounded whole whose interacting or interdependent elements, relations, rules, and exchanges generate organized behavior that cannot be specified by listing parts alone.
• Theory — A coherent system of concepts and propositions that explains, organizes or predicts a domain through explicit relations and standards of support.
• Transitive relation — Whenever a relation carries from a first element to a second and from that second to a third, it also carries directly from the first to the third.
• Truth value — A semantic value assigned to a proposition or formula to represent its status with respect to truth under a specified logic and interpretation.
• Unintended consequences — Outcomes caused by a purposeful action that were neither among the actor’s aims nor fully represented in the action’s decision model.
• Unit of measurement — A conventionally fixed reference magnitude that makes quantities of the same kind expressible as comparable numerical multiples.
• Utility — Represent the preference value, benefit or desirability of an outcome for a specified agent or evaluative system.
• Wishful thinking — Let the desirability of a conclusion increase its apparent truth or likelihood despite evidence that would not support the same confidence without the desire.