problem of induction

David Hume denies the idea that we are justified in using induction.

Inductive Skepticism

Hume distinguishes between two types of knowledge:

• Relations of ideas: a priori knowledge that can be justified without experience, e.g. $1+1=2$. Note that we can obtain relations of ideas from experience and still be justified in believing them due to our ability to reason (consistency with British empiricism).
• Matters of fact: a posteriori knowledge that is obtained from the physical world, e.g. $F=ma$. One hallmark of matters of fact is that its negation is not implasible, which would never be true for relations of ideas (e.g. $1+1\ne 2$ is not sound).

Matters of fact are obtained by inferring a cause (e.g. earth’s spin) from multiple observed effects (e.g. sun rises every day). This relies on induction, since there’s no telling whether or not the next cause will be followed by a different effect. Hume argues that humans are not justified in believing induction, and as a result, matters of fact:

• If induction is valid, it has to be a matter of fact.
  • Facts are either relations of ideas or matters of fact.
  • It is conceivable for induction to be invalid, so induction has to be a matter of fact if it’s valid.
• Matters of fact can only be obtained by experience, but validity of induction cannot be proven from experience (self-referential).

What now?

Although using induction is not sound on a philosophical standpoint, Hume denies that we should stop using induction, as it is so essential in survival and daily lives. Hume gives a few reason humans may give using it:

• Custom/habit: Humans (like other organisms) are biologically programmed to expect the same effect to follow a cause. This is not necessarily irrational, since it’s just how we’re made. Reason cannot overpower habituation.
• Inductive skepticism only invalidates congruence. Although we know induction is logically unsound, that doesn’t affect us from using it by custom.

Alternatives and Hume’s Counterarguments

The denial of induction seems pretty daunting, which could motivate some alternative beliefs, namely:

• Hidden powers: Hidden powers/mechanisms in matter can explain causes and effects with reason (e.g. coffee makes us feel more alert because caffeine inhibits adenosine receptors).
• Causal connections: Objects have causal relations to each other. If a ball in motion strikes another stationary cube, the cube is bound to move.

Hume believes both ideas are invalid due to misuse of terms. By the copy principle, any idea we may have about hidden poewrs or causal connections have to be impressions of the real world, and Hume believe these impressions to be impossible due to the limited clarity of human senses:

• Sense data is particular and not universal
  • Hidden power and causal connections require a universal cause and effect that has no exception.
  • Sense data only concerns a particular case of cause and effect. As such, sense data proves neither universality (observes only an instance of A, then B) nor necessity (observes $A$ and $B$, but not whether or not it has to be the case; could it be B next time?).
• Sense data does not provide connection
  • Hidden power and causal connection requires a concrete link between cause and effect.
  • An impression does not convey a connection, otherwise a mere impression of the cause would be sufficient to infer the effect by reason, without ever seeing the effect in reality.