Q&A: Deduction and Induction
Deduction and Induction
Question
1. Seemingly, in order to arrive at general principles and infer conclusions about particular cases from them, you first have to observe the particulars. For example, I saw many inscribed angles in a circle that are 90 degrees and subtend a diameter, so I establish a rule that all inscribed angles subtending a diameter are right angles. So according to this, the root of everything is induction. Where am I going wrong?
2. Are water not being wet, fire not being hot, fire not burning (as in the example of the burning bush), contradictions that are physical rather than logical?
Answer
What exactly was asked here? Who says it isn’t true that the root of everything is induction?
As for the matter itself, that’s not correct. You do not necessarily arrive at the fact that an inscribed angle subtending a diameter is 90 degrees from examples. It is proven in a general way. It is fairly clear that some of the theorems in geometry were a surprise even to those who proved them, and did not come from looking at examples.
Discussion on Answer
I didn’t understand the question. These are simple concepts on the definitional level. As for their philosophical understanding, I don’t know of a source that explains it. I’ve addressed this in several places, but not in a systematic discussion from the beginning on these topics. A logical analysis and a mathematical model can be found in my pair of articles in Bedad:
מידות הדרש ההגיוניות כאבני הבסיס להיסקים לא דדוקטיביים – חלק א’
מידות הדרש ההגיוניות כאבני הבסיס להיסקים לא דדוקטיביים – חלק ב’
You once said—regarding Popper, I think—that a scientific theory is not deduction, and that you can call it deduction only if you say it does not describe reality, which in your view is not correct. So what exactly was gained by Popper defining theory as deduction? After all, it comes from induction, doesn’t it?
Is there a particular book that explains these basic concepts (deduction, induction) from A to Z? Or maybe an article you wrote?