7 March 2001
I. New unit: Science
A. The problem of induction
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]