Overview
Inductive Logic deals with reasoning from specific observations to general conclusions. Unlike deductive logic (where the conclusion must be true if premises are), inductive logic deals with probability and strength.
Core Idea
The core idea is learning from experience. If the sun has risen every day for a billion years, it is reasonable (though not logically certain) to expect it to rise tomorrow.
Formal Definition
Inductive logic attempts to formalize the relationship of “support” or “confirmation” between evidence and hypotheses. It often uses Probability Theory (specifically Bayesianism) as its calculus.
Intuition
Deduction is like math: $2+2=4$. Certainty. Induction is like detective work: “He has the motive, the weapon, and no alibi.” High probability, but not absolute certainty.
Examples
- Generalization: “Every swan I’ve seen is white. Therefore, all swans are white.” (Vulnerable to the “Black Swan”).
- Analogy: “Earth has water and life. Mars has water. Therefore, Mars might have life.”
- Bayesian Update: Adjusting the probability of a hypothesis (e.g., “I have a disease”) based on new evidence (e.g., “Positive test result”).
Common Misconceptions
- Misconception: Induction is just “guessing.”
- Correction: It is reasoned inference based on evidence. Science relies entirely on induction.
- Misconception: Induction proves things.
- Correction: Induction never proves in the mathematical sense; it only confirms or disconfirms to varying degrees.
Related Concepts
- Deductive Logic: Reasoning from general to specific.
- Abductive Reasoning: Inference to the best explanation.
- Problem of Induction: Hume’s philosophical argument that induction cannot be rationally justified (because justifying it using past success is circular).
Applications
- Science: The Scientific Method is essentially formalized inductive logic.
- Machine Learning: Algorithms “induce” patterns from training data to predict new data.
- Law: Juries decide based on “reasonable doubt” (induction), not absolute certainty.
Criticism and Limitations
- Hume’s Problem: We assume the future will resemble the past, but we have no logical proof of this.
- Goodman’s Paradox: “Grue” and “Bleen”—shows that formalizing exactly what can be projected into the future is difficult.
Further Reading
- Choice and Chance: An Introduction to Inductive Logic by Brian Skyrms
- The Logic of Scientific Discovery by Karl Popper