Where does species collide?

In logic a species is a kind that falls under a broader kind, its genus, and is marked off from the other kinds under that genus by a defining difference: dog is a species of the genus animal. Aristotle set out this ordering of genus and species in his Categories and Topics (ca. 350 BCE), and Porphyry's Isagoge (ca. 270 CE) turned it into the branching classification later drawn as the Porphyrian tree. The referent here is a rung in a hierarchy of what can be predicated of things, a class fixed by its genus plus its difference, not a breeding population of organisms, a likeness carried to the mind, or a construction in combinatorics.[1][2]

Unit

One kind standing below a genus, fixed by its genus plus its defining difference

Recovery means

Not applicable

Measured by

Identified by logical division: naming the genus and the difference that separates the kind from the others under it

In medieval theories of knowing, a species is a likeness carried from a perceived thing to the mind, the intermediary by which an object becomes present to a knower without the thing itself entering the head. Thomas Aquinas, in his Summa theologica (ca. 1274), distinguished the sensible species received in perception from the intelligible species by which the intellect grasps a thing's nature, developing an account rooted in Aristotle's De anima; Leen Spruit's Species intelligibilis (1994) traces the doctrine across the later scholastics. The referent is a mental representation standing between object and knower, not a class in a logical tree, a reproductive group of living things, or a structure counted in mathematics.[3][4]

Unit

One likeness of an object present in perception or in the intellect

Recovery means

Not applicable

Measured by

Not measured empirically; argued for by analysis of how perception and understanding are possible

In biology a species is the basic unit of classification for living things, a group whose members can breed with one another and produce fertile offspring but not with the members of other such groups. John Ray, in his Historia plantarum (1686), was among the first to fix the unit by its breeding true from seed, and Ernst Mayr's Systematics and the origin of species (1942) gave the modern biological species concept, defining a species by its reproductive isolation from others; de Queiroz (2007) reviews how the many later definitions relate. The referent is a population of interbreeding organisms in nature, delimited and counted by biologists, not a logical kind, a likeness in the mind, or a combinatorial object.[5][6][7]

Unit

One interbreeding population reproductively isolated from others

Recovery means

Not applicable

Measured by

Delimited by reproductive isolation, and in practice by morphology, geography, and increasingly by genetic difference

In combinatorics a species is a rule that assigns to every finite set the collection of structures of a given type that can be built on it, in a way that respects any relabelling of the set's elements. André Joyal introduced the theory in Une théorie combinatoire des séries formelles (1981), giving a unified way to derive counting formulas and generating functions from such structure-assigning rules. The referent is a formal, functorial construction in mathematics, its instances tracked by a generating series, and it has nothing in common with a breeding population, a logical kind, or a likeness carried to the mind beyond the shared Latin word.[8]

Unit

One rule assigning labelled structures to each finite set

Recovery means

Not applicable

Measured by

Studied through its generating series, which encodes how many structures it puts on a set of each size