Disclaimer, blue text are of my ow writing.
Impredicative Definitions
(Source)
Individuals
Traditionally, the term “individual” is used to pick out members of a certain category of existents, each member of which is said to be unique. More precisely, individuals are said to be non-repeatable (not multi-exemplifiable), which means that they can’t be in more than one place at a time. Examples include the familiar objects of sense-experience, such as chairs or tigers. A room may contain many chairs that are virtually alike in their intrinsic qualities, but each chair is nonetheless a distinct thing in one place at one time. By contrast, the universal “chair” is repeated around the room.
Mary C. MacLeod | Email: mmacleod@iup.edu | Indiana University of Pennsylvania | U.S.A.
Eric M. Rubenstein | Email: erubenst@iup.edu | Indiana University of Pennsylvania | U.S.A.
Internet Encyclopedia of Philosophy
Numerical Identity
Numerical identity requires absolute, or total, qualitative identity, and can only hold between a thing and itself. Its name implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical (Geach 1973). (source)
by Harold Noonan <Harold.Noonan@nottingham.ac.uk>
Ben Curtis <benjamin.curtis@ntu.ac.uk>
Predicative
(Source)
Qualitative Identity
Things with qualitative identity share properties, so things can be more or less qualitatively identical. Poodles and Great Danes are qualitatively identical because they share the property of being a dog, and such properties as go along with that, but two poodles will (very likely) have greater qualitative identity. (source)
by Harold Noonan <Harold.Noonan@nottingham.ac.uk>
Ben Curtis <benjamin.curtis@ntu.ac.uk>
Sortals
Qualitative sortals identify and classify the referent as a certain kind of object.
Quantitative sortals measure how much of a substance the referent contains.
https://plato.stanford.edu/entries/sortals
Universals
Universals are a class of mind-independent entities, usually contrasted with individuals (or so-called “particulars”), postulated to ground and explain relations of qualitative identity and resemblance among individuals. Individuals are said to be similar in virtue of sharing universals. An apple and a ruby are both red, for example, and their common redness results from sharing a universal. If they are both red at the same time, the universal, red, must be in two places at once. This makes universals quite different from individuals; and it makes them controversial.
Realism: Universals are real entities that exist to explain similarities among things.
Conceptualism: Universals exist only as general ideas or concepts in the mind, not independently.
Nominalism: Denies universals altogether similarities between things are just brute facts. (Includes Trope Nominalism, which explains properties as individual instances called tropes.)
Mary C. MacLeod | Email: mmacleod@iup.edu | Indiana University of Pennsylvania | U.S.A.
Eric M. Rubenstein | Email: erubenst@iup.edu | Indiana University of Pennsylvania | U.S.A.
Internet Encyclopedia of Philosophy
Stanford Encyclopedia of Philosophy Definition
Sources
Stanford Encyclopedia of Philosophy
Internet Encyclopedia of Philosophy
Routledge Encyclopedia of Philosophy
The Cambridge Dictionary of Philosophy (2nd Ed.)
The Oxford Dictionary of Philosophy