Grounding and the Hierarchy of Fundamental Facts

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grounding fundamentality hierarchy structure metaphysics

Core Idea

Grounding is the 'in-virtue-of' relation: fact B holds in virtue of fact A grounding B. A full metaphysical picture specifies which facts are fundamental (ungrounded) and how all other facts are grounded in these fundamentals, forming a hierarchy that reveals what reality is fundamentally like.

Explainer

From your study of grounding and fundamentality you already know the basic idea: some facts depend on — hold *in virtue of* — other facts. The fact that the table is red holds in virtue of facts about how its surface reflects light; the fact that a symphony is beautiful holds in virtue of facts about its structure and our responses to it. Grounding is the formal name for this dependence relation. It is not the same as causation (which relates events over time) and not the same as logical entailment (which is a relation between propositions, not facts). Grounding is meant to capture the distinctively *metaphysical* sense in which some facts make other facts obtain.

The concept of a hierarchy adds structure to this picture. Imagine a vast directed graph where each node is a fact and each arrow points from a grounding fact to a grounded fact. At the bottom of the graph sit the fundamental facts — those that are not themselves grounded in anything. These are the bedrock: they explain without being explained (in the metaphysical sense). Everything above them is grounded, directly or indirectly, in the fundamental level. A complete metaphysical theory would describe what sits at the bottom and trace the grounding chains upward through chemistry, biology, psychology, and social facts, showing how each level is grounded in the levels beneath it.

Fundamentality is a comparative and absolute concept. Two things can be compared: fundamental particles are more fundamental than molecules; molecules are more fundamental than organisms. But there is also the limiting case: the absolutely fundamental, which is grounded in nothing further. Most metaphysicians assume there is a bedrock — that the grounding hierarchy does not go on forever — because an infinite regress of "what grounds what?" would leave everything unexplained. This assumption (that grounding is well-founded) is itself contested, but it structures most discussions of what the fundamental level contains.

One useful example is the physical/mental case you may have encountered through truthmakers. The fact that you are in pain seems to hold in virtue of facts about your neural states. The fact that neural states obtain may hold in virtue of facts about molecular chemistry, which hold in virtue of atomic physics, which holds in virtue of quantum field facts. Each level is grounded in the one below. The philosophical question is not just whether this chain exists (most agree it does) but what the relationship at each step looks like — is it full reduction, constitution, realization, or something else? Grounding theory is designed to remain neutral between those options while still capturing the asymmetric, explanatory dependence involved.

The hierarchy picture has significant implications. It tells us that not all facts are equally real or equally basic — there is a genuine structure to reality, and philosophy's job is to map it. It also raises the question of priority monism versus priority pluralism: does a single ultimate entity (the cosmos as a whole, perhaps) ground everything else? Or are there many fundamental items? And it raises questions about the relationship between grounding and ontology: does everything that is grounded still *exist*, or does being grounded mean being merely derivative — perhaps less than fully real? These questions, which you will pursue further in the metaphysics of structure and architecture, all flow from taking seriously the idea that "in virtue of" relations carve reality at its joints.

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Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesDefining Finite Sets RigorouslyRecursive Definitions on Finite SetsWell-Founded Relations and Transfinite RecursionThe Axiom of Choice and Equivalent FormulationsAxiom of ChoiceWell-Ordering TheoremInfinite Cardinal NumbersCantor's TheoremSet-Theoretic CardinalityUniversals and ParticularsFacts and TruthmakersGrounding and FundamentalityTruthmakers and GroundingTruthmaker Fundamentalism and Truth-Making RelationsGrounding and the Hierarchy of Fundamental Facts

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