by Albert Major

Critical and Scientific Thinking

1. The Problem of Induction

What is Induction?

Induction is the process of moving from specific observations to general conclusions - like watching several pieces of cesium explode in water and concluding that all cesium must explode in water.

The Logical Problems

Two key attempts to formalize induction reveal its weaknesses:

1. First Logical Structure:
   • If Hypothesis (H) is true, then we'll observe Evidence (E)
   • We observe E
   • Therefore H must be true
   • Problem: Other explanations could cause E
2. Second Logical Structure:
   • If we observe E, then H must be true
   • We observe E
   • Therefore H is true
   • Problem: We can't justify universal claims from limited observations

Hume's Problem

• Core Issue: We assume the future will resemble the past, but can't prove this
• Classic Example: The Sun Rising
  • We've seen it rise every day in the past
  • But we have no logical guarantee it will rise tomorrow
• The Chicken Story:
  • A chicken is fed by a farmer every day
  • It develops complete trust in the farmer
  • One day, instead of food, it meets its end
  • Shows how inductive reasoning can fail dramatically

2. Popper's Falsification Theory

Popper's falsification theory states that instead of trying to prove scientific theories true through repeated observations (induction), scientists should try to prove theories false through experiments - if a theory survives repeated attempts to disprove it, we can tentatively accept it while remaining open to future evidence that might prove it wrong.

Key Points:

• Focus on disproving theories rather than proving them
• One counter-example can disprove a theory
• Accept theories until proven false