Hume's Problem with Induction

In the following essay I will explain why Hume believes that there is no way to give a rational justification of the use of inductive reasoning to acquire knowledge. I will do so by showing that both a priori and a posteriori knowledge cannot be used to justify induction, which necessarily leads Hume to conclude that inductive reasoning cannot be justifiably used in acquiring knowledge.

In order to understand Hume’s problem with inductive reasoning, it is imperative to understand how knowledge can be gained. Knowledge can be gained in only two ways: either a priori, knowledge gained prior to experience, or a posteriori, knowledge gained after an experience. Since one is prior to experience, and one proceeding from experience, logically all knowledge must be gained in one of these two categories; there are no other alternatives to how one can gain knowledge.

A priori knowledge is usually associated with mathematics and geometry; writing after Hume, Kant mentions that a priori knowledge is analytic, meaning that it is true by virtue of meaning. For example, when one states that “a triangle has three sides,” the statement cannot be denied without a contradiction. If one understands the definition of a triangle, one must also understand that a triangle has three sides. Hume calls this knowledge that is known a priori and is analytic, “The Relations of Ideas” (Section 4). Relations of ideas, because they are a priori, cannot be justified in induction, using past experiences to predict the future, since they are necessarily prior to experience. If something is prior to experience, there is no experience therefore upon which one can use to further make inferences about the future. Therefore, Hume argues that induction cannot be justified by using a priori knowledge.

Hume then gets to the heart of his argument in which he states that cause and effect are “Matters of Fact”, knowledge acquired a posteriori and what Kant calls synthetic, meaning that they are true by how their meaning relates to the world (Section 4). Matters of fact differ from relations of ideas in that a matter of fact can be denied without contradiction, where as a relation of ideas cannot. For example, the statement “all dogs hate cats,” can be denied fairly easily and therefore without contradiction, since it is not hard for one to imagine at least one dog existing in the world who likes a cat. The statement “all dogs hate cats,” is therefore a matter of fact. However, consider the statement “a triangle has four sides.” Here the contradiction that arises is quite obvious. If one understands the definition of a triangle, one knows that a triangle has three sides, and that it is impossible for it to have four. Therefore, the statement, a triangle has four sides, is necessarily a relation of ideas since a contradiction arises.

Given that matters of fact can be denied without contradiction, we cannot deduce reason from it because there can never be a necessary connection between the cause and the effect (Section 4). Because the connection between cause and effect is not necessary, there is no reason to believe that the connection must hold in the future, and therefore knowledge which requires reasoning from a past experience [induction] cannot be rational. Hume then concludes that induction cannot be justified using a posteriori knowledge. If Hume’s argument is in fact sound, he has proven that induction cannot be a justified way of acquiring knowledge since it cannot be justified in either the a priori or a posteriori sense.

            A common objection to Hume would be, “what about the laws of physics? It is widely known that these laws were discovered a posteriori, for example, the law of gravity. Are we not absolutely sure that if tomorrow, we were to throw an object into the air, that it would eventually start to fall towards the ground at a rate of 9.8 meters per second per second?”

            Hume would state that in fact we cannot be absolutely sure that this would happen. Consider the following example of Pavlov’s dogs. Every day since the dog’s birth, the owner of the dog rings a bell before feeding it. In the beginning, the owner rings the bell, after which the dog sees the food and begins to salivate. However, as time goes on, the dog begins to realize that every day; he gets food after he hears the ringing of the bell. So eventually the dog associates the ringing of the bell with food, upon which he begins to salivate, but he does so prior to seeing the food. One can even imagine that the dog notices that he gets less food if the bell is rung really loud (since the owner is mad), than if the bell is rung quieter. Perhaps there is a genius dog who formulated a mathematical equation from this “cause and effect” relationship, in which he can calculate the amount of food he will be given based on the volume the bell is rung at. However, a day will come when the dog hears the ringing of a bell and no food will arrive, leaving the dog confused. After all he did have a mathematical equation proving the direct relationship between the ringing of the bell and the amount of food he would receive!

            Hume would argue that this argument is the same one presented by those who favor induction. Every time the bell rings for the dog, food is put in front of him; every time an object is thrown into the air, it falls back down. Both of these have been happening for the entire life of both the dog and say, Newton, when he identified gravity. The dog believes that this line of cause and effect is necessary since it has been that way his whole life, just as our laws of physics have existed for us until today. The dog, like Newton, has even formulated a mathematical equation which supports what he has experienced his entire life. However, it is quite clear that the bell is not the cause of the food appearing in front of the dog. Hume would argue that it is by this reasoning that we cannot know that an object will fall to the ground tomorrow because this is how nature could be for us. It is not impossible to imagine in the future, the laws of physics will no longer hold, just as expecting food to follow the ringing of a bell one day failed for the dog.

*References to An Enquiry Concerning Human Understanding