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  • Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt.
    Logik ist transzendental.

    - Ludwig Wittgenstein's (1921, 6.13) Tractatus Logico-Philosophicus in the original German

    Logic is not a body of doctrine, but a mirror-reflection of the world.
    Logic is transcendental.
    - Pears/McGuinness translation

    Aristotelian Square of Opposition

    1. There are 4 logical relationships in any logical square or hexagon of opposition:
    2. Contraries can both be simultaneously false, but they cannot both be true at the same time
    3. Subcontraries can both be simultaneously true, but they cannot both be false at the same time
    4. The superaltern implies the subaltern in a subalteration relation but not vice versa
    5. Where 2 statements are contradictories, the truth of one statement implies the falsity of the other

    FIG: Aristotelian square of opposition in Aristotelian syllogistic logic
    1. Each categorical proposition asserts or denies of at least some or all members of X that they are included in Y, where:
    2. X is the subject term
    3. Y is the predicate term
    1. There are 4 types of categorical propositions:
    2. A (Universal affirmative (Affirmo)): All X are Y
    3. E (Universal negative (nEgo)): All X are not Y
    4. I (Particular affirmative (affIrmo)): Some X are Y
    5. O (Particular negative (negO)): Some X are not Y
    1. A and E are contraries
    2. I and O are subcontraries
    3. A is the superaltern and I is its subaltern
    4. E is the superaltern and O is its subaltern
    5. A and O are contradictories
    6. I and E are contradictories