Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Simple Judgments

Simple judgments can either assert or deny (e.g., "Ukrainians are Europeans," "Chinese are not Africans"). They can also express properties of all members of a class (e.g., "All students study") or only some members of the class (e.g., "Some students study"). Combining these two criteria (quality and quantity) allows us to classify all simple judgments into four types:

• Universal Affirmative: Denoted by the formula "All S are P" (e.g., "All Ukrainians are Europeans," "All squares have right angles"), abbreviated as "A," the first vowel of the Latin word "affirmo" (I affirm).
• Universal Negative: Denoted by the formula "No S is P" (e.g., "No Ukrainian is an African," "No square has obtuse angles"), abbreviated as "E," the first vowel of the Latin word "nego" (I deny).
• Particular Affirmative: Denoted by the formula "Some S are P" (e.g., "Some Ukrainians are Galicians," "Some triangles have right angles"), abbreviated as "I," the second vowel of the Latin word "affirmo" (I affirm).
• Particular Negative: Denoted by the formula "Some S are not P" (e.g., "Some Ukrainians are not Kyivans," "Some triangles do not have equal sides"), abbreviated as "O," the second vowel of the Latin word "nego" (I deny).

Simple judgments are interrelated in terms of their truth values, which can be depicted using a visual schema known as the "logical square." This schema is designed to illustrate the relationships between judgments with the same terms but differing in quantitative and qualitative characteristics. The relationships between judgments are as follows:

• Universal Affirmative and Universal Negative judgments are contraries, meaning they cannot both be true simultaneously; if one is true, the other must be false (e.g., if "All Ukrainians are Europeans" is true, then the contrary universal negative "No Ukrainian is a European" is false).
• Universal Affirmative and Particular Affirmative judgments are in a hierarchical relationship; if the universal affirmative is true, then the particular affirmative must also be true (e.g., if "All Ukrainians are Europeans" is true, then "Some Ukrainians are Europeans" must also be true); however, a particular affirmative is only subordinate to a universal affirmative when the universal affirmative is true, meaning a false universal affirmative does not imply a false particular affirmative ("All Swiss speak German" may be false, while "Some Swiss speak German" may still be true).
• Particular Affirmative and Particular Negative judgments are known as subcontraries; if the particular affirmative is true, the particular negative may be false and vice versa (e.g., "Some continents are washed by the ocean" may be true, while "Some continents are not washed by the ocean" may be false). Subcontraries can both be true when universal affirmatives and negatives are false (e.g., "Some citizens of Ukraine are men" and "Some citizens of Ukraine are women" can both be true). However, subcontraries cannot both be false.
• Contradictory judgments cannot both be true or both be false; if one is true, the other must be false (e.g., if "All Ukrainians are Europeans" is true, then the particular negative "Some Ukrainians are not Europeans" must be false).

Another important feature of a judgment is the distribution of terms. A term is considered distributed when the entire extent of that term is considered within the judgment. For instance, in the judgment "Dogs are animals," the subject "dogs" is distributed because it refers to all dogs, while the predicate "animals" is undistributed, as it refers only to those animals that are dogs.