Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Inference

The third form of reasoning is inference, through which a new judgment, bearing new knowledge, is derived from the combination of several judgments. The judgments that compose the inference and contain already known information are called premises. The judgment that concludes the inference and contains new information is the conclusion. Inferences are divided into immediate and mediate:

• Immediate inferences are those composed of a single premise and a conclusion. These are also called operations on judgments since the conclusion is a transformation of the premise (for example, in the inference "All squares are rectangles. Therefore, some rectangles are squares," there is only one premise and a conclusion, which is a transformation of the premise);
• Mediate inferences involve more than one premise and derive the conclusion based on the combination of terms from these two premise-judgments (for instance, "Squares are rectangles. Rectangles are geometric figures. Therefore, squares are geometric figures" is a mediate inference, as it combines two premise-judgments).

Immediate inferences include:

• Conversions—inferences in which the premise-judgment is transformed into a conclusion while retaining the quantity but altering the quality: affirmative judgments become negative, and negative ones become affirmative (e.g., "All squares are rectangular. Therefore, no square is non-rectangular");
• Obversion—inferences in which the premise and conclusion are reversed while preserving their quality (e.g., "All patriots love their country. Therefore, all who love their country are patriots," or "All squares are rectangles. Therefore, some rectangles are squares");
• Contraposition—combines conversion and obversion. In this operation, the premise-judgment changes both its quantitative and qualitative characteristics. Judgments can be contraposed in any sequence, meaning either conversion followed by obversion, or obversion followed by conversion. If conversion is performed first, followed by obversion, this is called contraposition to the predicate (e.g., "All squares are rectangular" is first converted to "No square is non-rectangular" and then transformed into "No non-rectangular object is a square"). If obversion is performed first, followed by conversion, it is called contraposition to the subject (e.g., "All squares are rectangular" is first transformed into "Some rectangles are squares" and then converted to "Some rectangles are not non-squares").