Oct 30-Nov 3 - Induction
 
1. Induction (TTT pp.167-79)
 
• Induction =
    1. (i)in general, any legitimate non-deductive inference
    2. (ii)more specifically, reasoning from ‘some’ to ‘all’
 
2. Newton’s Inductive Method
 
• Book III of the Principia (‘The Mathematical Principles of Natural Philosophy’) Newton argues from observations of the motions of the planets and their moons, and of the bodies falling at the Earth’s surface (i.e., from ‘some’ instances of gravity) to the law of universal gravitation – that between any two bodies is a force of the form f ∝ mM/r2 (i.e., to ‘all’ instances of gravity.) Let’s see how (in part).
 
  1. (a)Data
    1. (i)visible planets satisfy period2 ∝ (radius of orbit)2
    2. (ii)Jupiter and Saturn’s moons satisfy period2 ∝ (radius of orbit)2
    3. (iii)moon’s acceleration towards Earth ÷ acceleration of bodies at Earth’s surface = (Earth’s radius/radius of moon’s orbit)2
  2. (b)Deductive Reasoning – mathematical results
    1. (iv)from (i), the forces on the planets are approximately ∝ m/r2
    2. (v)from (ii), the forces on the moons are approximately ∝ m/r2
    3. (vi)from (iii), the forces on the moons and at the Earth’s surface are approximately ∝ m/r2
  3. (c)Inductive Reasoning – apply Rule 2 (p.175) to conclude the cause of all these forces is the same.
    1. (vii) The force everywhere towards the sun is ∝ m/r2
    2. (viii) The forces everywhere towards the planets are ∝ m/r2
    3. (ix)The force towards any particle of matter is ∝ m/r2
 
3. Inductive Skepticism
 
• Suppose F ∝ mM/r2 is true universally. Does Newton’s argument provide us with the knowledge that it is? How? The premises do not necessitate the conclusion – there are worlds in which (i)-(iii) are all true (and, hence, so are (iv)-(vi)) but (vii)-(ix) are false. I.e., inductive reasoning is not deductively valid – which is why we need something like Bayesian updating to understand inductive reasoning.
 
• Glymour’s argument: however much data is taken into account, it is always logically possible that the next piece of data will be incompatible with a universal hypothesis – there is a possible world which is just like ours up to the present, but differs after.
 
• Answer Q1 p.179.