Disclaimer. These brief notes do not constitute an
attempt of writing a book. Many of the issues discussed here may
have been amended, expanded, or further clarified in the class. Some
passages are adapted, perhaps even verbatim, from a variety
of published and unpublished sources.
Very generally, the doctrine of cognitive significance recognises
two classes of meaningful statements: analytic statements having
logical meaning, and statements testable by empirical means. Hempel
then emphasises the role of the notion of cognitive significance.
Among other things it helps to discard the sentences of speculative
metaphysics.
The criterion of adequacy (A) is designed to conform to the
principle of compositionality.
Example 1[See (A2)]
The sentence `Two plus two is four and God is great.' is
non-significant, since one of its conjuncts is such.
Earlier attempts at characterising empirical significance focussed
on the relation between hypotheses and observation statements. A
significant hypothesis was supposed to be either confirmed or
disconfirmed by observation sentences.
Hempel then considers two specific earlier suggestions and discusses
their defects.
Definition 1[Complete verifiability]
A sentence has empirical meaning iff it is not analytic and follows
from a finite and logically consistent set of observation sentences.
Difficulties:
The generalisation
All men are mortal
(1.1)
fails the criterion. Yet many, if not all, scientific laws have the
same general form.
The negation of (1.1) `There is one man who is
immortal' is deducible from observation sentences and hence
significant. Yet this is impossible by (A).
Let S be a significant sentence and N non-significant one.
Then S is deducible from some observation sentences. Therefore,
also S ∨N is deducible from them. Then S ∨N is
significant-a contradiction with (A).
Definition 2[Complete falsifiability]
A sentence has empirical meaning iff its negation is not analytic
and follows from a finite and logically consistent set of
observation sentences.
Difficulties:
`There exists at least one unicorn' turns to be
non-significant.
`All x are red' is significant, but `Not all x are red' is
not-again, a contradiction with (A).
S ∧N: `Obama is mad and God is great' turns out to be
significant.
Hempel concludes that there is little hope for formulating a
coherent and non-trivial criterion of meaningfulness.
1.2 Significance as dependent on constitutive terms
The alternative approach that Hempel now describes puts limitations
on the vocabulary which can be used to form significant sentences.
The admissible vocabulary contains only those terms that either are
logical terms or have empirical significance.
Empirically significant terms must be connected to observation terms
(names or predicates). But how?
Definability
Perhaps they should be defined by means of
observation terms. This creates problems, since many scientific or
even quasi-scientific terms of the ordinary discourse are not easily
definable in observation terms. Examples include `soluble',
`electric conductor', and other. (Think of your own examples!)
Consider the predicate Fx: `x is fragile'. A plausible
definition of fragility may be that if x is struck at any time,
then x breaks:
Fx ≡ ∀t(Sxt ⊃ Bxt).
But if you take an obviously non-fragile item (a piece of metal)
which was never struck since its creation, then the universal
sentence on the right will still be true. A revised suggestion is to
consider a counterfactual conditional: `if xwere struck,
it would have broken.' But there is no accepted analysis
counterfactuals available.
Instead we should consider a reduction sentence proposed by Carnap:
∀x ∀t(Sxt ⊃ (Fx ⇔ Bxt)).
The earlier difficulty is avoided, but only narrowly. For the
meaning of F is left undetermined for those objects that are never
struck. The definition given by reduction sentences is not
inadequate, but rather partial.
Reducibility
Every empirically significant term must be
introducible, on the basis of observation terms, through a chain of
reduction sentences.
But this demand runs into difficulties with many (uncontroversial)
theoretical constructs. How, for instance, we could reduce the
length of √2 cm to a length in observational terms?
Similarly, two lengths may be observationally indistinguishable, and
yet be different by one-millionth of centimetre.
The failure of both reducibility and definability approaches leads
Hempel to a new opening:
In axiomatic theories of mathematics we distinguish between
primitive and defined terms, and between primitive and derived
statements.
Scientific theories afford axiomatic treatment when empirical
interpretation is assigned to defined terms and derived statements
(and not necessarily to primitives).
Holism: meaning is assigned not to individual statements and
terms, but to theories. Individual terms and statements receive
meaning in the context of theories where they occur.
Empirical interpretation may be partial: the method of
measuring length by means of a measuring rod applies only to medium
lengths.
The meaning of an individual expression depends, therefore, on
the linguistic framework which fixes the rules of inference and the
logical relationships between statements, and on the theoretical
context in which the expression occurs.
Having thus endorsed holism, Hempel now asks how one can determine
cognitive significance of a (partially) interpreted system.
Definition 3
A sentence S is isolated in the theory T if it is neither
a logical truth or falsehood, nor it has `experiential bearing',
that is, it can be deleted from T without changing the latter's
predictive or explanatory power.
Example 2
The sentence `Action at a distance is possible' may be inserted
among the postulates of Newtonian mechanics, but it will not change
its predictive power. However, it could still increase its
explanatory power. The sentence `Space is a sensorium of God' would
change neither its predictive, nor explanatory power.
Definition 4
A theoretical system is cognitively significant iff it is partially
interpreted to at least such an extent that none of its primitive
sentences is isolated.
A difficulty: suppose that T has as its primitive sentence the
following:
∀x(P1x ⊃ (Qx ⇔ P2x))
(1.2)
(in words: for every entity x, if x is P1, then: x is Q
just in case x is P2), where P1, P2 are observational
predicates and Q is a theoretical predicate and occurs in only one
primitive sentence, namely, in (1.2). By deleting (1.2)
from T we will not alter its predictive or explanatory power.
Remark 1
To understand this, let us consider the matter in more detail.
Suppose that we wish to introduce a novel theoretical predicate Q
into T. A way to that would be to say that if such-and-such
experiment is conducted, then: if the results of the experiment are
this-and-that, x is Q. In symbols:
∀x(P1x ⊃ (P2x ⊃ Qx)).
An additional intuitive condition would go in reverse: if
such-and-such experiment is conducted, then: if the results of the
experiment are not this-and-that, x is notQ. In
symbols:
∀x(P1x ⊃ (¬P2x ⊃ ¬Qx)).
Putting the two together we obtain the bi-conditional (1.2).
Now we also see that the fact whether for any given object a we
have Qa is determined by whether P1x and P2x. (Another
requirement to be mentioned is that ∀x (¬P1x) should
not be a logical or physical necessity.)
So (1.2) appears isolated. However, it is also possible to view
it as a kind of analytic sentence.
Remark 2
The reason is as follows. (1.2) entails ∀x ¬(P1x∧P2x ∧¬P2x). The latter is a truth of logic.
Hempel elaborates the consequences of this fact. Suppose we add
another sentence to T:
∀x(P3x ⊃ (Qx ⇔ P4x)).
(1.3)
Clearly (1.3) is analytic too. But (1.2) and (1.3)
jointly entail (why?) non-analytic sentences such as:
Therefore, a sentence may be regarded analytic relative to one
system (e.g. T enriched with (1.2) alone) and synthetic
relative to another (e.g. T enriched with (1.2) and
(1.3)).
Hempel's ultimate conclusion is skeptical regarding the possibility
of defining cognitive significance. He proposes another method for
separating `rotten apples', the suspect scientifically sounding
enquiries. Rather than declaring those activities unscientific, we
may treat them as `bad science'. The division between good and bad
science is based on the following criteria:
Hempel proposes the following model of explanation:
Laws
L1, …, Ln
Conditions
C1, …, Cm
Explananda
E1, …, Ek
Explanations are arguments. The laws and the initial conditions,
both understood as statements, logically entails the explananda.
Example 3
Suppose we have a container of gas (say, a syringe). We increase the
volume of the container by one-third. The observed phenomenon is the
decrease in the gas pressure by 25%. To explain the phenomenon we
use Boyle's Law: PV = T, assuming the temperature remains
constant:
Laws
PV = T.
Conditions
The volume of the container increases by
one-third, the temperature is constant.
Explananda
The decrease in the gas pressure by 25%.
There are difficulties with this approach:
Pre-emption
Suppose that Jones drinks a poison such that there is a law
saying that anyone who drinks it will die within 24 hours. However,
shortly afterwards Jones is hit by a bus. According to Hempel, his
death is explained by drinking the poison, and this seems wrong.
Symmetry
Suppose we increase the volume of the gas in a
syringe. Then, given that the temperature is constant, Boyle's law
should explain why the pressure subsequently drops. But equally,
that later drop in pressure also explains why the volume increases,
which is clearly wrong.
Confirmation is a notion weaker than verification. A general law
cannot be verified by a finite body of evidence, yet may well be
confirmed by it.
There are problems with the theory of confirmation:
Relevance: any evidence is relevant relative to
the hypothesis under consideration.
The relation between general hypotheses and their instances.
Rules of induction: how exactly to determine that the given
body of evidence confirms or disconfirms a hypothesis.
Upon stressing the significance of the notion of confirmation Hempel
proceed with formulating Nicod's criterion of confirmation.
Consider a hypothesis governing the behaviour of objects:
∀x(Px ⊃ Qx).
Then an object a confirms our hypothesis iff Pa and Qa;
disconfirms it iff Pa and ¬Qa; is neutral iff ¬Pa.
Nicod's criterion has several obvious shortcomings:
It applies only to conditional statements.
It fails for the transposition of conditional statements.
The second shortcoming indicates the inadequacy of the Equivalence
Condition: whatever confirms (disconfirms) one of two equivalent
sentences, also (confirms) disconfirms the other.
Nicod's criterion cannot, therefore, be seen as a necessary
condition of confirmation: the existence of black ravens confirms:
∀x(Rx ⊃ Bx),
(3.1)
but it does not confirm-as it should-the equivalent sentence:
∀x(¬Bx ⊃ ¬Rx).
(3.2)
Yet Nicod's criterion may be considered a sufficient condition of
confirmation. That is, the existence of an object which confirms a
hypothesis according to Nicod's criterion will be seen as
`genuinely' confirming it.
We are led here to the paradoxes of confirmation. Since non-black
non-ravens confirm (3.2), they would also confirm (3.1).
But clearly the existence of green frogs is irrelevant to the status
of the hypothesis about ravens, hence a paradox.
Hempel appears to suggest that non-black non-ravens confirm
(3.1) to a small degree.
In §3 of the selection Goodman discusses the problems of the
hypothetico-deductive model. Let us look at one of them. At least
some statements expressing the evidence for a given hypothesis are
the consequences of that hypothesis. This is the notorious
converse consequence condition.
Remark 3
The formulation of that condition demands some care. Let H be
(3.1) as before. Let the observation report consist of the
statements `Jack is a raven' and `Jack is black'. Then we can derive
one part of the report (that Jack is black) from H combined with
the other part of the report (that Jack is a raven). Note that the
conjunction of the report statements cannot be derived from H
alone. However, we can reasonably stipulate that whatever confirms a
given hypothesis H1 would also confirm a stronger hypothesis
H2 (such that H2 entails H1).
On the other hand, we have the consequence condition, to the
effect that whatever confirms a given hypothesis confirms also a
logical consequence of that hypothesis. Putting the two conditions
together, we get a paradox: everything confirms everything else.
Example 4
Let H1 be any hypothesis (say, Newton's Second Law). Let the
observation report R consist of just the statement `Jack is a
raven'. Then R confirms the hypothesis H2 (that Jack is a
raven). But H2 is entailed by H1 ∧H2. So, by the converse
consequence condition, R also confirms H1 ∧H2. But H1
is entailed by H1 ∧H2. Therefore, by the consequence
condition, R confirms H2.
Let us move one to the central problem posed by Goodman. It is
striking that syntactic form alone does not explain the confirmation
relation. While a piece of copper conducting electricity confirms
the hypothesis that all pieces of copper conduct electricity, the
fact that that piece of copper is owned by Barack Obama does not
confirm the hypothesis that all pieces of copper in the world are
owned by Obama.
The difference between the two hypotheses is not in their logical
relation with the respective pieces of evidence, but in that one is
a lawlike generalisation, and the other is an accidental one. This
distinction does not afford a Hempel-style treatment. Further
difficulties quickly emerge.
Goodman introduces a new predicate `grue' as follows:
a is grue iff (a is examined before T and a is green) or (a is not examined before T and a is blue).
Note that there are alternative, unsatisfactory ways of defining
`grue' such as:
a is grue iff (a is green before T) and (a is blue after T).
For every `normal' predicate we can construct a `grue-like'
predicate which would defeat all efforts of projection.
Readings
Hempel[2]
Goodman[4]
1
Give one example where a causal explanation of the phenomenon
appears to work, and one example where it does not. Lewis, [1986]
2
What is the role of the equivalence condition in generating the
paradoxes of confirmation? Hempel[2]
3
Is there a way to formulate the difference between ordinary
predicates and `grue-like' predicates? Goodman[4]
4
What is the role of crucial experiments in scientific choice?
Kuhn[10]
5
How, according to Kitcher, does the analysis of Origin
improve our understanding of scientific change? Kitcher[9]
6
Name and discuss two or three reasons for making the ontological
ascent in the theory of laws. Dretske[19]
7
What are the difficulties that the cases of preemption create for an
account of causation? Discuss with regard to one or two particular
examples. Lewis[28]
8
Give one example where Lewis's account seems right and Fair's account wrong, and one example where Lewis's account seems wrong and Fair's account right. Provide detailed explanations. Fair[29], Lewis[28]