Spinoza on Counterpossible Inferences

As part of his geometrical method, Spinoza uses inferences involving impossibilities: what would follow if some impossibility were true. This paper examines a puzzle surrounding his use of such ‘counterpossible’ inferences. The puzzle consists of Spinoza's apparent acceptance of the following three claims: that counterpossible inferences can produce knowledge; that inference‐making produces knowledge only on the basis of a transition between ideas; and that counterpossible inferences are unthinkable. I argue for a solution to this puzzle, which interprets Spinoza's geometrical method as a form of syntactical manipulation.