PHL246 – Midterm I Review Notes
Hume’s argument against induction
1. The theory of induction must be justified by either a deductively valid argument or
an inductively strong argument.
2. There are no deductively valid arguments to justify the theory of induction
because premises of an inductive argument involve statements about the present
or past, and the conclusion always involves the future.
3. There are no inductively strong arguments for the theory of induction, because
an inductive argument to prove the theory of induction would have to assume
that the theory of induction is true (which is a circular argument)
Hempel – The Logic of Confirmation
Aim: wants to analyze confirmation so that he can have a proper definition of
• Intuitive and logical conditions that we take confirmation to satisfy:
o Nicod’s Criterion (NC) - Hypotheses of the form x (Fx Gx) are
confirmed by instances of (Fx^Gx)
o Equivalence Condition (EC) – If E confirms H, and H and F are logically
equivalent, then E confirms F.
• Raven’s Paradox
o Results from NC and EC The paradox: it is logically valid (from NC and
EC) that an evidence E that has nothing to do with a hypothesis H can
nevertheless confirm H.
H: All ravens are black
H is logically equivalent to F: Something is not a raven or it is black.
A black notebook is an instance of F.
A black notebook confirms F.
Since F is logically equivalent to H, the black notebook also
confirms H. i.e. The black notebook is an instance that confirms that
all ravens are black. o Hempel argues that the Raven’s “paradox” is not really a paradox; it is
only seemingly so because we make background assumptions (e.g. the
relationship between black notebooks and ravens) which shouldn’t enter
the logical equation of confirmation
• “The Prediction Criterion and its shortcomings”
o The Prediction Criterion is a “second conception of confirmation” we have
(in addition to NC and EC)
o Idea: If a hypothesis predicts A, and A happens, then A is said to
confirm the hypothesis
o PR-Confirmation: (Formal definition)
Let H be a hypothesis, B an observation report
B confirms H if B can be divided into two mutually exclusive
subclasses, B1 and B2, such that B2 is not empty and every
sentence of B2 can be logically deduced from (B1^H), but not B1
B is said to disconfirm H if H logically contradicts B
B is said to be neutral with respect to H if it neither confirms nor
E.g. H: x(Mx ^ Hx Ex), B: (Ma, Ha, Ea)
• B1: (Ma ^ Ha), B2: Ea
• Ma ^ Ha Ea, because of H
• i.e. H ^ B1 B2, so B confirms H!
• E PR-confirms H iff (H^E1)E2
PR-confirmation only works for specific