This chapter discusses in depth Vasil'ev's imaginary logic. Vasil'ev criticizes the uniqueness of logic and the absoluteness of logical principles, taking into consideration the conceptions of Gerardus Heymans, Carl Göring, Benno Erdmann, Edmund Husserl and John S. Mill. The key point of his criticism is the assumption of another world, different from ours, and of beings with a different intellectual structure from our own. He then proposes a novel concept of negation, which is not based on the incompatibility between predicates and is not a deduction as it is in our world. In an imaginary world, in which negations are immediate and perceptible, the law of contradiction does not hold. In this imaginary world another logic is valid, imaginary logic, which accepts a third form of judgment near affirmation and negation, namely the indifferent judgment, which asserts that both P and non-P apply to the same object simultaneously. In this new logic, the law of excluded middle does not hold, but the law of excluded fourth does. After an exposition of the different kinds of judgments (individual, universal, and particular), Vasil'ev shows how it is possible to conduct inferences containing indifferent judgments. The chapter closes with three arguments: the analogy between imaginary logic and non-Euclidean geometry, some alternative interpretations of imaginary logic (e.g., a logic that, distinguishing between absolute and relative negation, accepts degrees of falsehood), and the notion of metalogic, that is, a minimal logic which is shared by both Aristotelian logic and imaginary logic.