Dichotomous Division

Dichotomous Division

 

division of the extension of a concept (division of a class, set) into two subordinate (derivative) classes according to the principle of the excluded middle: “A or not-A.” In other words, only that division into two will be dichotomous in which derivative classes are defined by a pair of logically contradictory properties (terms), one of which is used as a basis for the division. Thus, the division of the set of all human beings into males and not-males (on the basis of the attribute of “being a male”) is dichotomous. But the division of such a set into the class of males and the class of females (on the basis of the attribute of sex) is not a dichotomous division. In such a case the bases for division are different, and the property “being a male” does not logically contradict the property “being a female.”;

The last type of division (as an analogy of “division into two”) is sometimes called pseudodichotomous. The results of both types of division may coincide. In this sense, the classification of a certain “division into two” as a dichotomous division (if it is not such “absolutely,” by definition) depends in a number of cases on which assumptions are accepted. Thus, within the framework of the principle of bivalence, pseudodichotomous division of statements into true and false (the basis for division being the truth value of a proposition) is equivalent to their dichotomous division into a class of true and a class of not-true propositions (the basis for division being the property of the proposition “to be true”). But if the principle of bivalence is not accepted, then it is evident that from the point of view of their results these two divisions are clearly different—among the not-true statements may also be those which we have no basis to consider false.

Any pseudodichotomous division may be converted into a dichotomous division, but the converse is not true. This results specifically from the fact that in dichotomous division one of the derivative classes—the complementary class— is always defined negatively (by means of a negative term), while in pseudodichotomous division both classes are defined positively. It is not always possible to replace a negative definition with a positive one. For example, since there is no positive definition of the concept “transcendental function,” there is no pseudodichotomous division corresponding to the dichotomous division of functions into algebraic and transcendental (nonalgebraic).

M. M. NOVOSELOV

Mentioned in ?
References in periodicals archive ?
By rejecting dichotomous division, Aristotle need not accept that every kind is divisible by two.
The use of ROC curves is based on a dichotomous division of the data, whereas numerical changes over the entire concentration range will not be picked up by such analyses.
In the first book of the Parts of Animals Aristotle lays out his objections to the system of dichotomous division.
The great strength of the older, strict form of dichotomous division is that it prevents the kinds of slipshod divisions we find in Plato's Sophist, divisions in which the successive differentiae bear no essential relationship to their predecessors; that is, dichotomous division prevents the definiendum from falling into a heap of unrelated features having no conceptual unity.
In dichotomous division the sub-genera become more and more distantly removed from one another with each successive division, and since the sub-differentiae of each sub-genus are unique, the sub-groups have less and less to do with one another.
Vladimir Kompanichenko's paper, "Origin of Planetary Systems Due to Dichotomous Division of Ejected Superheat Mass," is interesting.
The dichotomous division of giant stars to smaller stars could be possible and logical.
It is still premature to suggest a strictly dichotomous division of specific activities'.
Outcomes were thus determined directly by partial evaluations of cost, reward and control, rather than through a shared mission of improvement to end insecurity, or according to a dichotomous division determined by skill and standing.
In one notable article, "Origin of Planetary Systems due to Dichotomous Division of the Ejected Superheat Mass," author Vladimir Kompanichenko brings to light the dichotomous conception and explains main regularities of the solar system structure, including angular momentum distribution, position of the asteroid belt between the orbits of Mars and Jupiter, and opposite rotation of Venus and Uranus around their axes.
After the terminal bronchiole, the following seven generations of dichotomous divisions are called respiratory bronchioles and serve the gas-exchanging parenchyma consisting of budding alveoli.
The taxonomy is constructed through a series of dichotomous divisions, the broadest of which is between descriptive and non-descriptive ethical theories.