Hypothetical judgment is under the relation category according to Kant. The logical form of hypothetical judgment is independent of the content and consists of a proposition and a consequence. To form a hypothetical judgment, one starts out with two propositions (P and Q). After one applies the logical form of hypothetical judgment to them, they form an implicative relationship and take on their separate roles. As a result, one (Q) of the propositions becomes a consequent, whose ground is provided by the other proposition (P), and we arrive at a hypothetical judgment (if P then Q).
A hypothetical judgment can be analytic (i.e. only using logic can determine whether its proposition, if true, directly implies the truthfulness of its consequence through the rule of contradiction). One analytic hypothetical judgment example is: If I am allergic to all animal dairies (P2), cow’s milk will cause a damaging immune response in my body (Q2). If one regards P2 as true but Q2 as false, one arrives at a contradictory position. Milk will certainly induce a damaging immune response in a person who is allergic to all animal dairies because: 1) milk is an animal dairy and 2) allergy refers to a damaging immune response. Assuming P2 is true, denying Q2 is denying that milk is not an animal dairy and/or allergy is not a damaging immune response. However, both denied concepts are regarded as true in P2, so we have determined that Q2 must be true when P2 is true in this example through the rule of contradiction. Hence, this example is an analytic hypothetical judgment.
Another example is Kant’s example: “If there is perfect justice [(P3)], then obstinate evil will be punished [(Q3)]” (B99 Kant). One cannot imagine a world where there is perfect justice and any obstinate evil goes unpunished. Otherwise, this world must have imperfect justice, logically contradicting P3. Here, we have another analytic hypothetical judgment with the rule of contradiction serving as the sufficient method for determining the truthfulness of Q3.
In contrast, a synthetic hypothetical judgment’s validity and truthfulness must rely on empirical facts because it’s a judgment regarding the reality, so determining its truthfulness requires empirical observation and logical contradiction cannot be the sole basis. For example, if someone has not paid at the restaurant (P4), the waiter must have reported him to the police (Q4). Whether Q4 is true not only depends on logic but also on an empirical fact that all restaurants report people who don’t pay, but this empirical fact is invalid when restaurants offer free food for some special occasions. The rule of contradiction is insufficient for determining whether the proposition implies its consequence in a synthetic judgment.
To Kant, the notion of <cause> is not contained in the form of hypothetical judgment and not all hypothetical judgments are causal statements. However, the form of hypothetical judgment is the clue one uses to obtain the idea of <cause>. Based on the logical form of hypothetical judgment, one can arrive at the notion of <cause> because causal statements can take the same logical form as a hypothetical judgment. To Kant, <cause> is the idea that there exists a relationship between two appearances that one of these appearances necessarily succeeds another in time.
Kant undertakes the derivation of the categories, such as <cause>, from the logical forms of judgment because he believes that one requires justifications for using non-empirical concepts like categories or fate. He refuses to base his justifications on God like Leibniz does because he wants to do it through reason. Thus, he is left with using empirical experience or logical form to derive the categories.
Kant rejects that the categories are derivable from experience. The basis of his rejection is the subjective nature of human perception that we rely on to have empirical experience and David Hume’s differentiation between correlation and causation. Kant reasons that as we receive a manifold of sensations, we can only perceive a few appearances at a time. The ordering of the perceived appearances can be arbitrary, just like when two people see the same house, they may not perceive its components in the same order. Because one’s manifold of sensations may be arbitrary and different from reality, our subjective sensations alone do not give us the ability to experience a shared world. Also, David Hume argues that experience only provides us with the idea of correlation through induction but not causation because real-life events/appearances occur one after another and only provide us with information regarding the past. Inductive rules and sensations alone don’t tell us anything about the future. If the two people both see a ship sailing downstream right now, with only the inductive rule and sensations, they cannot say the ships will necessarily sail downstream in the future because their mind only knows what has happened in the past. Therefore, one cannot derive the categories, including causality, only from experience.
The rule he has in mind is that <cause> must have a proposition followed by its necessity, which is an a priori notion. Without the a priori notion of necessity, one will purely base his thinking on past empirical experience and the inductive rule and cannot have the idea that one appearance necessarily succeeds another. With the ship example, one must say that if the ship is going downstream, it definitely (necessity) will move from a higher altitude to a lower altitude, thus asserting the causal relation between the ship’s movement direction in the past and the present/future movement. Only with the a priori notion of necessity, the person can apply the idea of causality to understand that where the ship is moving towards or will move toward in the future necessarily succeeds the ship’s movement in the past.
The observation that the idea of causality takes the logical form of hypothetical judgments and entails the idea of necessity indicates hypothetical judgments also contain the idea of necessity. Hypothetical judgments assert that the entire consequent is necessarily true under the condition that the proposition is true, so the idea and logical form of causality is compatible with the idea and logical form of hypothetical judgment. Therefore, Kant believes through the idea and logical form of hypothetical judgment, one can arrive at the idea of causality.
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