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Grounding and the Hierarchy of Fundamental Facts

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Grounding and FundamentalityFacts and Truthmakers+1 more→→Fundamental and Derivative Properties: Sparse and Abundant OntologiesMetaphysical Structure and Architectural Form+1 more
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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

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Factorial → Permutations → Combinations → Counting Principles: Addition and Multiplication Rules → Introduction to Graph Theory → Propositional Logic Foundations → Logical Equivalences → Boolean Algebra → Introduction to Propositional Logic → Introduction to Predicate Logic (First-Order Logic) → First-Order Logic Syntax → Terms and Atomic Formulas in FOL → Variable Binding and Scope → Open and Closed Formulas in First-Order Logic → Variable Substitution and Capture-Avoidance in First-Order Logic → Quantifier Instantiation Rules in First-Order Proof Systems → Universal Quantification: Meaning and Scope → Free Variables and Bound Variables → Substitution and Instantiation in Predicate Logic → Terms and Atomic Formulas → Formulas and Well-Formed Expressions → Structures and Interpretations → Model Interpretation and Satisfaction → Interpretation, Truth, and Satisfaction of Formulas → Logical Consequence and Entailment → Syntactic Consequence (⊢) Versus Semantic Consequence (⊨) → Logical Consequence and Validity → Grounding and Fundamentality → Truthmakers and Grounding → Truthmaker Fundamentalism and Truth-Making Relations → Grounding and the Hierarchy of Fundamental Facts

Longest path: 92 steps · 514 total prerequisite topics

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