The Problem of Induction

Inductive Arguments

Inductive arguments differ from deductive arguments.
Inductive arguments have premises based on observations that support conclusions about what has not been observed.

The Sun Rising:
- Premise 1: Monday, the sun rose.
- Premise 2: Tuesday, the sun rose.
- Premise 3: Wednesday, the sun rose.
- Conclusion: Therefore, tomorrow, the sun will rise.
Iron Rods Expanding When Heated:
- Premise 1: Iron rod 1 (IR1) expanded when heated.
- Premise 2: Iron rod 2 (IR2) expanded when heated.
- Premise 3: Iron rod 3 (IR3) expanded when heated.
- Conclusion: Therefore, the next iron rod will expand when heated.

Scientists observe the behavior of iron under various conditions.
Observations lead to premises about iron rods expanding when heated.
The conclusion generalizes that iron expands when heated, applicable to future observations.

Inductive arguments represent everyday reasoning.
Example: The bus arriving at 5 PM on consecutive days suggests it will arrive at 5 PM tomorrow.
Another example: Past experiences of gripping a doorknob, twisting, and pulling opening a door suggest it will happen again.

Inductive arguments are invalid; even if the premises are true, the conclusion could be false.
It's possible the next iron rod will not expand when heated, or the sun may not rise tomorrow.
This invalidity raises the question of whether we are justified in believing the conclusions of inductive arguments.

With deductive arguments, like modus ponens, belief in true premises justifies belief in the conclusion.
Example:
- Premise 1: The bus arrives every day at 5 PM.
- Premise 2: If the bus arrives every day at 5 PM, then the bus will arrive today at 5 PM.
- Conclusion: The bus will arrive today at 5 PM.
Inductive arguments lack this certainty due to their invalidity.

Two ways to explain why we're justified in believing inductive conclusions:
- Deductively
- Non-deductively (using induction)
Neither explanation is satisfactory, leading to the problem of induction.

The problem of induction: the challenge of satisfactorily explaining why we're justified in believing the conclusions of inductive arguments.

Attempting a deductive explanation involves creating a deductive argument with the same conclusion as the inductive argument.
Example:
- Premise 1: All observed iron rods were rods that expanded when heated.
- Premise 2: If all observed iron rods were rods that expanded when heated, then the next iron rod will be a rod that expands when heated.
- Conclusion: The next iron rod will be a rod that expands when heated.
This approach aims to justify the inductive conclusion by justifying the premises of the deductive argument.
A general form is:
- Premise 1: All observed f's were g.
- Premise 2: If all observed f's were g, then the next f will be g.
- Conclusion: Therefore, the next f will be g.

Premise 1 (All observed f's were g) is justified by observations.
Premise 2 (If all observed f's were g, then the next f will be g) poses a challenge.

A priori justification: by reason and reasoning alone (e.g., mathematical proofs).
A posteriori justification: by experience (observations).
Premise 1 is justified a posteriori.
The question is whether premise 2 can be justified either a priori or a posteriori.

Philosophers believe premise 2 cannot be justified a priori.
It necessitates justifying the connection between the antecedent (all observed f's were g) and the consequent (the next f will be g).
If justified a priori, it would imply a necessary truth, such as all observed ravens being black necessitating the next raven being black, which is not the case.

A posteriori justification (by experience) is also problematic.
We can have experiences of past observations (all observed ravens were black).
However, we cannot have experiences of the future, making it impossible to justify premise 2 a posteriori.

Since premise 2 cannot be justified a priori or a posteriori, no deductive explanation works.
We can't get justification for both of the premises and, hence, can't get justification for the conclusion.

A non-deductive explanation would have to use induction.
However, this leads to a circular argument.
Explaining "why induction works" by saying "induction makes it true" is circular.

Circular explanations are inadequate.
Example: Receiving an F grade and being told it's "because I gave you an F" doesn't provide a satisfactory reason.
Since non-deductive explanations rely on induction, and circular explanations are inadequate, there's no satisfactory non-deductive explanation.

Two possible explanations for justifying belief in inductive conclusions: deductive and non-deductive.
Neither explanation works.
Therefore, there's no satisfactory way to explain why we're justified in believing inductive conclusions.
This undermines both everyday and scientific reasoning.