The Relations Between Simple Judgments on "a Logical Square": Relations of a Contradiction, Submission, Contrast and Subcontrast

1. The relations between simple judgments on "a logical square": relations of a contradiction, submission, contrast and subcontrast.

We will consider the possible relations between simple judgments. In different life situations we state different judgments. One of them are comparable among themselves as identical subjects and predicates have. In judgments with different subjects and predicates different concrete contents is thought. Such judgments are called incomparable. Say about such judgments that they are various and the logical relations between them are absent. Comparable judgments can also be compatible and incompatible. The compatibility happens triple: full (coincidence, equivalence), partial (crossing) and subordinating (inclusion). The incompatibility also happens various. At clarification of the logical relations between judgments the greatest value have two appearance of incompatibility: contrast (counterarity) and discrepancy (kontradiktornost).

In general the logic establishes four types of the logical relations between comparable categorical judgments:

- submission;

- contradictions (kontradiktornost);

- contrasts (counterarity);

- subcontrasts (subcounterarity).

Each of these types of the relations sets quite certain semantic relations between judgments of A, E, I, O. However at first it is necessary to establish what of these judgments are connected by the called logical relations.

For descriptive reasons in logic the concept of "a logical square" on which corners judgments of A, E, I, O settle down is used, and his parties and diagonals are symbolical expression of the main logical relations between judgments.

 The relation of submission has connected judgments of A and I, E and O. The general judgments (And, E) are subordinating, and private (I, O) – subordinates. For the judgments which are in the submission relation the following condition of the validity matters: if it is true And, then also I is true; if it is true E, then is also true and Oh, but not on the contrary. Really, if truly that "All students pass test logically" (And), the same is faithful also rather some of them (I) "Some students pass test logically", but not on the contrary. Doesn't follow at all from the fact that "Some days of the week are non-working" (I) that "All days of the week are non-working" (And). If judgment "Is true any month doesn't contain the thirty second" (Е), then the chastnootritsatelny judgment which is also subordinated to him "In some months will be true there is no thirty second" (About). The return isn't right. From the validity of chastnootritsatelny judgment "Some fruits aren't edible" (0) doesn't follow, as "Any of fruits isn't eaten" (Е).

 Concerning a contradiction there are judgments of E and I, and And yes the Lake. According to laws of logic, two contradictory judgments can't be at the same time neither true, nor false. Means, in two-digit logic they will accept different logical values:

if And – it is true, then About – it is false or And ≡ ┐О,

if And – it is false, then About – it is true or ┐A ≡ O,

if About – it is true, then And – is false or O ≡ ┐A,

if About – it is false, then And – is true or ┐O ≡ A,

if E – is true, then I – is false or E ≡ ┐I,