Polythetic classes
(for Dave, if he reads this journal still)
adj. relating to classification in which the members of a class share a large number of constituent characteristics. First described by Wittgenstein in 1953.
A regular class (known as monothetic) is one in which all members share a defined set of characteristics {A,B,C,D,E,F}. If it has all of these characteristics, a thing is a member of the class, but otherwise, it is not.
A polythetic class is more complex in that to be a member of a class, you need to have some (ideally many or all) of the characteristics, but not all. So, for example, take four things, 1,2, 3 and 4, which are members of a polythetic class having the defining traits {A,B,C,D,E,F}.
1: A, B, C
2: B, C, D
3: A, E, F
4: D, E, F
All four are members of the class. In theory, even something only with trait F would be a member of the class. Moreover, even though there is no overlap between the traits of 1 and those of 4, they are still both members, because each member of the class need only share at least one characteristic with at least one other member of the class. This is quite distinct from fuzzy set theory as I understand it, though, because each characteristic is still two-valued (present/absent), not probabilistic.
Polythetic classification is used in biological taxonomy, psychological diagnosis, the definition of archaeological cultures, and all sorts of other fun things. Wittgenstein's classic example is that the class "game" is polythetic, in that there is no one criterion that makes something a 'game' or 'not a game', but rather a set of criteria exists, of which all games will have some. Any gamer who has tried to explain role-playing to a 'norm' knows this to be true.
So, when I state that "sciences" constitute a polythetic class, I mean that they need not all fulfil any one criterion, but hang together more loosely. Sciences have some but usually not all of a set of characteristics such as "reliance on logical proof", "use of experiment/reproducibility", "use of diachronic data set", "rejection of subjective elements", and others I haven't thought of.
adj. relating to classification in which the members of a class share a large number of constituent characteristics. First described by Wittgenstein in 1953.
A regular class (known as monothetic) is one in which all members share a defined set of characteristics {A,B,C,D,E,F}. If it has all of these characteristics, a thing is a member of the class, but otherwise, it is not.
A polythetic class is more complex in that to be a member of a class, you need to have some (ideally many or all) of the characteristics, but not all. So, for example, take four things, 1,2, 3 and 4, which are members of a polythetic class having the defining traits {A,B,C,D,E,F}.
1: A, B, C
2: B, C, D
3: A, E, F
4: D, E, F
All four are members of the class. In theory, even something only with trait F would be a member of the class. Moreover, even though there is no overlap between the traits of 1 and those of 4, they are still both members, because each member of the class need only share at least one characteristic with at least one other member of the class. This is quite distinct from fuzzy set theory as I understand it, though, because each characteristic is still two-valued (present/absent), not probabilistic.
Polythetic classification is used in biological taxonomy, psychological diagnosis, the definition of archaeological cultures, and all sorts of other fun things. Wittgenstein's classic example is that the class "game" is polythetic, in that there is no one criterion that makes something a 'game' or 'not a game', but rather a set of criteria exists, of which all games will have some. Any gamer who has tried to explain role-playing to a 'norm' knows this to be true.
So, when I state that "sciences" constitute a polythetic class, I mean that they need not all fulfil any one criterion, but hang together more loosely. Sciences have some but usually not all of a set of characteristics such as "reliance on logical proof", "use of experiment/reproducibility", "use of diachronic data set", "rejection of subjective elements", and others I haven't thought of.