Quantity quantity, that which can be counted or measured, is not a property of things but the extension of a concept under which objects fall. a number is not a thing perceived, but the result of a logical operation upon a concept. when we say “there are three horses in the field,” we do not attribute threeness to the horses; rather, we assert that the concept “horse in the field” falls under the number three. the number three is the extension of the concept “equinumerous with the concept ‘horse in the field.’” this extension is not a physical aggregate, nor a mental image, but a logical object, determinate and independent of intuition. first, a concept must be clearly delimited. the concept “prime number less than ten” is distinct from the concept “even number less than ten,” though both have extensions. the former contains the objects 2, 3, 5, 7; the latter, 2, 4, 6, 8. the number associated with each concept is the class of all concepts equinumerous with it. two concepts are equinumerous if their objects can be put into one-to-one correspondence. this relation of correspondence is not established by counting, but by the logical structure of the concepts themselves. counting is a sign-game, a procedure for ascertaining number, not the source of number. then, number arises from the application of the principle of abstraction to the relation of equinumerosity. the concept “number” is not derived from objects, but from the equivalence classes of concepts under equinumerosity. the number zero is the extension of the concept “not identical with itself.” no object falls under this concept. thus zero is the number of this concept. the number one is the extension of the concept “identical with zero.” only zero falls under this concept. the number two is the extension of the concept “identical with zero or one,” and so on. each number is thus the extension of a concept defined recursively upon the preceding ones. but number as object must not be confused with the numeral as sign. the symbol “3” is not the number three, but a mark employed to refer to it. the reference of the sign is fixed by its sense, which is its mode of presentation within the logical structure of arithmetic. the sense of “the successor of two” is different from the sense of “the cube root of twenty-seven,” though both refer to the same number. sense determines how the number is given to thought; reference determines its identity in the domain of objects. furthermore, the identity of numbers cannot be grounded in empirical observation. no amount of gathering objects, weighing substances, or measuring lengths yields the number five as an entity. the number five is not found in the world; it is constructed in the realm of thought through the logical analysis of concepts. a line may be divided into five segments, but the number five is not in the divisions; it is in the concept “segment of this line” under the relation of equinumerosity with the concept “finger on the hand.” quantity, then, is not a property of space or time, nor a measure of magnitude. it is the logical outcome of the extension of concepts under the relation of equinumerosity. numbers are objects, but not perceptual ones. they are graspable only through the laws of logic, and they subsist in a domain independent of human cognition. the truth of “2 + 2 = 4” is not verified by counting pebbles; it is deduced from the definitions of number, addition, and identity within the system of arithmetic. but if number is not derived from experience, and yet we apply it to the world without error, what accounts for its applicability? what makes the logical structure of thought correspond to the order of things? [role=marginalia, type=clarification, author="a.husserl", status="adjunct", year="2026", length="44", targets="entry:quantity", scope="local"] The number is not a class of concepts, but the objectified result of a purely logical act of counting under a well-defined concept—its identity lies not in plurality of instances, but in the invariant structure of one-to-one correlation, independent of intuition or empirical grouping. [role=marginalia, type=clarification, author="a.spinoza", status="adjunct", year="2026", length="48", targets="entry:quantity", scope="local"] Quantity is not in things, but in the understanding’s determination of concepts. The number three is not a property of horses, but the logical equivalence-class of all concepts with three instances. Thus, number is the intellect’s freedom—measuring not objects, but the relations of concepts under which they fall. [role=marginalia, type=objection, author="Reviewer", status="adjunct", year="2026", length="42", targets="entry:quantity", scope="local"]