Homework assignment 2 (due October 3, 2013)
The swan-hypothesis H is a universal if-then sentence and says that all swans are white. H is logically
equivalent to the universal if-then sentence H’ that everything that is not white is not a swan. His also
logically equivalent to the universal if-then sentence H’’ that everything that is or is not green is not a
swan or is white.
The Nicod Criterion NC says that universal if-then sentences of the form “All Fs are Gs” are confirmed by
their instances of the form “a is F and a is G.”
The Equivalence Condition EC says that if evidence E confirms one hypothesis F, then evidence E
confirms any hypothesis G that is logically equivalent to F.
Your evidence consists of three claims: E1 = “a is a swan and a is white”, E2 = “b is not white and b is not
a swan”, E3 = “(c is green or c is not green), and (c is not a swan or c is white).”
Use NC and EC to show that each of the three claims E1, E2, and E3 confirms the swan-hypothesis H.
ANSWER (note that there is more than one way to correctly answer this question):
E1 is an “instance” of H. Therefore E1 confirms H by NC.
E2 is an “instance” of H’, and so E2 confirms H’ by NC. H is logically equivalent to H’. Since E confirms H’,
and since H is logically equivalent to H’, E also confirms H by EC.
E3 is an “instance” of H’’. Hence E3 confirms H’’ by NC. H is logically equivalent to H’’. Therefore E
confirms H by EC.
The Entailment Condition EntC says that evidence E confirms hypothesis H if evidence E logically implies
The Special Consequence Condition SCC says that, if evidence E confirms a hypothesis H, and if H logically
implies some consequence G, then E also confirms the consequence G.
The Converse Consequence Condition CCC says that, if evidence E confirms a hypothesis H, and if some
theory F logically implies H, then E also confirms the theory F.
Recall that evidence, hypotheses, consequences, and theories are nothing but sentences (I just use
different words to formulate these conditions in a suggestive way). Furthermore