The practical syllogism of the customary type, “desire, belief /∴ action”, which we may also formulate as “W_I (q), B_I (p→q) /∴ p”, is the main topic of the following discussions. This syllogism is not valid, viewed at the level of rigid, symbolic logic. That is the initial claim made in this article (§2). Kant may save us from this dead end (§1); but his logic of the imperative is never always provided for our ordinary lives (§3.1). Contrasting the two, Kant’s logic and the customary syllogism, we look into where the invalidity of the latter resides in: individuality of the belief (§1.4), a fallacy of affirming the consequent (§2.1), propositional attitudes (§2.3), irrationality (§3.2), concretely. Although the validity is finally given up, we find another dimension of understanding in the formulation of utilitarianism; this point has been passed over by former thinkers (§4). Before jumping to this conclusion, we look through the landscape of their discussions as well, especially those held under the name of Humeanism. Readers who wonder how this article relates to the main stream of modern debates are recommended to see those parts (§3.3-3.4) first.

Keywords: practical syllogisms; logical validity; causation; utilitarianism; Humeanism.