Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Modal Judgments

Beyond quantity and quality, simple judgments are categorized by modality, which refers to the degree of necessity in the relationship between the subject and the predicate of the judgment. Modal judgments are divided into the following types:

• Apodictic Judgment: This is a judgment where the connection between the subject and the predicate is necessary (e.g., "It is necessary that humans are living beings," "A rectangle necessarily has right angles"). Apodictic judgments are denoted by the operator "□"; the formula "□P" is read as "it is necessary that P."
• Assertoric Judgment: This is a judgment in which the connection between the subject and the predicate is actual but not necessary (e.g., "Paris is the capital of France").
• Problematic Judgment: This is a judgment in which the predicate expresses a characteristic that may belong to the subject but is not necessarily the case or has not been proven (e.g., "There may be life on Mars" expresses a hypothesis that does not contradict the laws of nature and is therefore possible, though unproven). Problematic judgments are denoted by the operator "◊"; thus, the formula "◊P" is read as "it is possible that P."

The relationships between apodictic, assertoric, and problematic judgments are governed by three fundamental logical principles:

• All necessary things are actual, but not vice versa.
• All actual things are possible, but not vice versa.
• All necessary things are possible, but not vice versa.