Falsification, Induction, and the Popperian Method

Induction moves from specific observations to general claims; foundational to science but cannot guarantee certainty.
Inductive reasoning yields high probability, not absolute truth.

Replace induction with deduction via falsification: science aims to falsify theories, not confirm them.
Key idea: if A → B and ¬B, then ¬A (logical deduction).
Observation can disprove a universal claim with a single counterexample.
Falsification provides deductive certainty about what is false; positive observations only increase probability, not certainty.
Distinction:
- Confirmation/verification (inductive): increases probability but is not certain.
- Corroboration (deductive): survives falsification but is not proven; tentative.
Popper’s aim: use falsification to separate science from pseudoscience; if unfalsifiable, it’s pseudoscience.

Universal claim and counterexample:
- Premise: $\forall x\,(Swan(x)\rightarrow White(x))$
- Counterexample: $\exists x\,(Swan(x) \land \neg White(x))$
- Conclusion: the universal claim is falsified by the counterexample.
Induction vs deduction intuition:
- If $A\rightarrow B$ and $\neg B$ , then $\neg A$ (deductive certainty).
- Inductive pattern: observing many swans being white increases belief but does not guarantee that all swans are white.
Example of logical invalidity vs validity:
- If all observed swans are white, it does not guarantee all swans are white (induction).
- If the rules are: $A\rightarrow B$ , $B\rightarrow C$ , but we also have $\neg A$ , the conclusion about C depends on the structure; valid arguments require true premises to guarantee true conclusions.

All metals conduct electricity → counterexample suffices: a metal that does not conduct electricity falsifies the claim.
All mammals give live birth → platypus is a counterexample; the universal is falsified.
In induction, even a billion white swans do not prove all swans are white; a single non-white swan falsifies.
In deduction, if A → B and ¬B, then ¬A must be true; this yields logical certainty about falsity, not probabilistic support.

General relativity posits curved spacetime; light bends in the presence of mass/energy.
Newtonian gravity predicted no such curvature; testing via a solar eclipse showed starlight bending as GR predicted.
Popper’s view: the eclipse test did not prove GR; it disconfirmed Newtonian gravity, thereby corroborating GR as the surviving theory.
This is an example of disconfirming a competing theory through deductive reasoning and observation.

Popper’s testing in isolation is problematic: real tests rely on many auxiliary assumptions (optics, instruments, brain, etc).
A failed test does not pinpoint where the fault lies in a complex setup.
This challenges the idea that a single hypothesis can be falsified in complete isolation.

Falsifiability as a criterion for science; unfalsifiable theories (e.g., certain pseudosciences) are not scientific.
Examples discussed: Freudian psychology, astrology, Marxist historiography (historical claims can be reframed to accommodate any outcome), etc.
Popper’s view emphasizes demarcation through the potential for falsification, not through verification.

Induction cannot guarantee truth; science seeks falsifiable, deductive testing.
Falsification (not confirmation) is the engine of scientific progress.
Corroboration = survived falsification, not proven truth.
Logical forms: use of $A\rightarrow B$ with $\neg B$ leading to $\neg A$ for deductive falsification.
Key historical example: Eddington’s solar eclipse test as a disconfirmation of Newtonian gravity and support for general relativity.
Testing holism: real experiments rely on many auxiliary assumptions; failures don’t identify the exact faulty component.
Demarcation criterion: science = what can be falsified; pseudoscience = unfalsifiable claims.

Four issues with falsification as a methodology and demarcation criterion will be discussed; the first is testing holism (isolation of hypotheses in testing).