18 March 2001
I. Science
B. Science is deeply committed to induction.
II. Hume
A. Two types of proposition
1. Relations
of ideas: matters that can be known either intuitively or demonstratively. Logical
analysis can suffice to know their truth (a priori). They are true
or false independently of what exists in the natural world. Timeless. Example:
Pythagorean Theorem. Truths of logic, geometry, algebra and arithmetic
generally fall into this category. [What about philosophy?]
2. Matters of
fact: not intuitive or demonstrable; cannot be known simply on the basis of
logical analysis (they are a posteriori). The contrary of every matter of
fact is still logically possible (does not imply a contradiction). Example: the
sun will rise tomorrow.
B. The Principle of Cause and Effect (PCE): Similar causes produce similar effects (and similar effects are produced by similar causes). Alternatively, “the future will be like the past (in respect of cause/effect relations).”
C. Reasonability vs. justification of induction
1. I have found
that such an object has always been attended with such an effect.
2. I forsee that
other objects, which are in appearance similar, will be attended with
similar effects.
3. “I
shall allow, if you please, that the one proposition may justly be inferred from
the other: I know, in fact, that it always is inferred. But if you insist that
the inference is made by a chain of reasoning, I desire you to
produce that reasoning.” [p. 197, column 1, italics mine]
D. Skeptical solution:
Custom, Habit
E. An inductive justification
of induction?
1. Induction:
If most instances of A’s examined in a wide variety of conditions have
been B, then (probably) in the future, instances of A will be B.
2. “Defense”
of Induction: Most instances of the application of Induction have been
successful, therefore (probably) in the future, applications of Induction will
be successful.
3. Counter-Induction:
If most instances of A’s examined in a wide variety of conditions have
been B, then (probably) in the future, instances of A will not be B.
4. “Defense”
of Counter-Induction: Most instances of the application of Counter-Induction
have been unsuccessful, therefore (probably) in the future, applications of
Counter-Induction will be successful.