Scalar and Vectorial Properties

Core Idea

Scalar properties have magnitude alone (mass, temperature, charge), while vectorial properties have both magnitude and direction (velocity, force, momentum). This distinction is crucial in physics and metaphysics: fundamental properties might be scalar with vectorial combinations, or vectors might be fundamental, affecting metaphysical interpretations of space, time, and causation.

Explainer

From your study of properties, you are familiar with the determinate/determinable hierarchy: *red* is a determinable, and *crimson* is one of its determinates. You also know the intrinsic/extrinsic distinction. The scalar/vectorial distinction cuts across these familiar categories and introduces a structural difference in how properties are *specified*. A scalar property is fully characterized by a single magnitude — a real number plus a unit. Temperature of 37°C, mass of 5 kg, electric charge of +1.6 × 10⁻¹⁹ C. To know the temperature of an object is to know a scalar value. There is no question of "in which direction is this hot?"

A vectorial property, by contrast, requires both a magnitude and a direction to be fully specified. Velocity of 60 km/h is incomplete — 60 km/h northward and 60 km/h southward are physically distinct states with dramatically different consequences. The same applies to force, momentum, acceleration, and electric field. This is not merely a notational convenience. Two objects can have the same speed but opposite velocities, and combining them produces rest, not double speed. The directionality is doing real physical work.

The metaphysical interest lies in what this tells us about the fundamental structure of reality. If vectorial properties are truly fundamental — if direction is as basic as magnitude — then the world has an inherent orientational structure built into its properties. This connects to debates about the nature of spacetime: vectors are defined relative to a structure that picks out directions, and it is a live question whether that structure is a genuine feature of reality or a representational artifact of our mathematical framework. Structural realists argue that the relational and vectorial structure of physics is what's real; intrinsicalist views are more comfortable with scalar properties as the fundamental base.

There is also a question about reduction. Is velocity really just a scalar (speed) plus a relation to a direction in space? Or is the directional component intrinsic to the property itself? This parallels debates about whether relational properties can ultimately be reduced to intrinsic ones. If vectorial properties are genuinely fundamental and irreducible to scalar properties plus directional relations, then the world's fundamental ontology contains a kind of built-in directedness. This matters for causal explanation: understanding why a particle moves as it does requires specifying the vector of the net force on it, not merely its magnitude. The intrinsic nature of vector quantities is one of the places where philosophy of physics and metaphysics of properties directly intersect.