Hume's Problem of Induction

Scientism #

Science delivers objective and value-free knowledge about a wholly material world.

• independent of individual perspectives
• questioned — is it even possible to have purely objective information?

The Principle of Independence #

• In order to satisfy our own confidence in the accuracy of information, we require an independent check to corroborate the information.
  • ideally, this independent check would be done by ourselves
• For many cases, such a check is difficult or impossible
  • who do we trust then?

Belief-Forming Methods #

Many different ways to form beliefs about the world: examples —

• listen to parents
• read the news
• believe in superstition
• induction
• senses (can be used to justify)

Which can we be justified to use?

→ A belief forming method is reasonable if you have an independent reason to think it is reliable. (Principle of Independence)

Logically Valid Arguments #

An argument is logically valid iff it is impossible for the premise to be true and the conclusion false.

If A, then B always.

Example: All squares have 4 corners. This shape is a square → ☐ Conclusion: It has 4 corners. ← Always true ⇒ logically valid!

Ampliative Inferences #

Drawing conclusions from a premise that may not necessarily be true.

• An argument is ampliative iff it is possible for a premise to be true but a conclusion false.
  • example: A bone contains x carbon-14. Therefore, it is y years old.
    • Carbon-14 is an imperfect indicator for age, so this is ampliative
  • An ampliative argument is not necessarily a bad argument!

Most scientific inferences are ampliative

• draw conclusions based on a limited set of data

Hume’s Problem of Induction #

Induction: All observed [A] are [B]. Therefore: All [A] are [B].

• This is an ampliative inference

Use induction to justify induction: #

Since induction worked well in the past, we can expect it to work well in the future.

• NOT an independent check!! If you didn’t believe in induction in the first place, this wouldn’t be convincing! (circular reasoning)

• Induction is reliable only if the Universe is uniform, and therefore predictable

  • (Uniformity of Nature) — Can never verify — impossible to observe entire universe

Hume’s Problem: There does not exist a logically valid, independent reasoning for the validity of induction. However, induction is the basic building block of ampliative inference.

• If we assume that all ampliative inferences are inductive, this concludes that ampliative inferences are invalid!

aside:

• Basic belief-forming method: a method not justified by independent check
• Derivative belief-forming method: a method justified on the basis of another trusted method

Possible Solutions #

• Add a qualifier: weaken the conclusion using probability
  • All observed A’s are B’s
    • It is probable that an A is a B. (most A’s are B’s)
      • but how probable??
  • Still ampliative: doesn’t address biggest problem (uniformity of nature assumption)
    • Still no independent justification

(This probabilistic weakening is exactly what formal statistical inference does — see parameter estimation and hypothesis testing. The same inductive leap from a finite sample to a general rule also underwrites Machine Learning, where models generalize from a training set to unseen data.)

Inference to the Best Explanation (IBE) #

• Scientific inference is much more complex than induction

IBE assertion:

1. Make observations O
2. Hypothesis H₁ is the best explanation of O a. H₁ is good explanation (simple, elegant, unifying) b. H₁ is better than other hypotheses c. H₁ is true.

Problems: induction is merely a specific case of IBE. If induction is unjustified, IBE must also be unjustified to some extent

• Still relies on ampliative inference
• Still no independent justification — the only other basic form of inference is a logically valid explanation, which cannot be used on ampliative inferences
• Requires that entire universe is simple and elegant

Pragmatic Defense #

If the future resembles the past, induction works. If it doesn’t resemble the past, nothing works. So it is safe to believe in induction because no other method would be reliable anyways.

• Doesn’t actually justify induction

A priori Defense #

A priori knowledge: independent of individual observation; same no matter who observes it Theoretical vs empirical

If a priori knowledge does indeed exist, it would provide substantial evidence for a predictable universe.

• Lots of issues w/ unfounded theory

Hume’s Problem, Generalized #

Regardless of what we declare as the basic form of ampliative reasoning, any attempt to justify it will violate the Principle of Independence and rely on the assumption of the uniformity of nature.

Therefore, all ampliative reasoning is invalid.

Without induction, we cannot make any assumptions/predictions about the future

Hume’s response: “All inferences are effects of custom, not of reasoning”

A Clash of Epistemic Methods #

• When two parties use different, incompatible belief-forming methods, it makes it easy for them to reject each other’s conclusions

Example: Galileo vs Bellarmine #

• Galileo believed in heliocentric Solar System
• Bellarmine believed in geocentric

Their disagreement wasn’t about the model of the Solar System — it was about their different belief forming methods

• Galileo = scientific method (induction, IBE…) [Discounted by Hume!]
• Bellarmine = revelation, scripture

Who is “right”??

Equal Validity #

There are many radically different, valid belief forming methods

• Science just one of many valid methods

Responses to Hume’s Problem #

Hume #

All inferences are effects of custom, not reasoning

• Conclusions vary based on culture / past experiences
• Example: which side of the road is the most effective side to drive on?

Feldman: Uniformity of nature argument #

• PF: the future will resemble the past [Claim about Universe]

• PFR: knowing that things have been a certain way in the past is good reason to believe they will be that way in the future. p137

• PFR suggests that induction is reasonable.

• PFR is analytic: true by definition

• PMC is analytic: true by definition

• Feldman’s definition of “justified”: a method is justified if it is inductive or involves your own senses

It thus follows, by definition, that induction is justified.

• denies Principle of Independence
• Major issue: “justified” can be changed to support any belief forming methods, not just induction

Strawson: Legal Systems vs Particular Actions #

(a lawmaking body) (example: jaywalking)

Is <Particular Action> illegal? #

• Can be answered by seeing if the action conforms to the law of the land

Is <Legal System> legal? #

• Meaningless question — by definition, a legal system must be legal in its jurisdiction

Analogy for Belief-forming methods (Legal system) and Particular beliefs (Particular action): #

Is <Particular Belief> justified? #

• Can be answered by using a belief forming method you like

Is <Belief forming method> justified? #

• Meaningless question — by definition, a belief forming method must be justified in its assertions

Epistemic Relativism #

A particular belief may be justified OR unjustified depending on the belief forming method being used. All belief forming methods are equally valid.

Goodman: The New Riddle of Induction #

Example: What will be the first emerald discovered in 2025? #

• Induction says that since all observed emeralds are green, the new emerald will also be green.

• Hypothetical predicate grue: iff X is first observed before 2025 and green OR X is not observed before 2025 and blue

Then, by induction, since all observed emeralds are grue, the new emerald will also be grue.

• → We would then predict the color to be blue by induction…
• → It is possible to change ‘blue’ to any property to predict anything. Therefore, different people can all use the same method and come to completely different conclusions.

“To say that valid predictions are based on past regularities without saying which regularities is pointless” (82)

Objections to Goodman #

1. Induction should only be used with simple predicates
   • Problem: simplicity is relative. ‘green’ would be a complex predicate if explained in terms of ‘grue’ and ‘bleen’.
   • Simplicity is a feature of language, not a feature of sets themselves