HSS101 PHILOSOPHY OF SCIENCE
Induction: Is
science
derived from
facts?
RECAP: A COMMON SENSE VIEW OF
SCIENCE
„ Science is derived from facts
„ Facts are established by careful observation,
experiment and experience prior to and independent
of theories, presuppositions, and expectations
„
Problems with the commonsense idea that “science is
derived from facts”
„
Facts are not directly given to unprejudiced observers,
„
Facts are not prior to and independent of theory,
„
Facts may not constitute a firm and reliable foundation
for scientific knowledge
→The theory-ladenness of observation
RECAP
„ The commonsense idea that “science is
derived from facts” is also problematic in
another sense
„ It supposes that we establish scientific laws,
hypotheses and theories by “deriving” them
from facts
„ This is taken as a kind of scientific method
called induction
TODAY’S LECTURE
SCIENCE IS “DERIVED”
FROM FACTS
Scientific theories,
hypotheses, or
laws
↑
Facts acquired
through
observation/experi
mentation
INDUCTIVISM AS A SCIENTIFIC METHOD
„ Induction is a kind of inference
„ From singular observation statements, one derives a
universal statement (a general conclusion) about the
observed phenomenon
„ When we say “science is derived from facts”, “derive”
tends to be used in a logical sense.
„ If interpreted strongly, it is highly problematic
INDUCTIVE INFERENCE
Premises:
Swan no. 1 on occasion t1 is white (singular
observation statement)
Swan no. 2 on occasion t2 is white
Swan no. 3 on occasion t3 is white
...
_________________________
Conclusion:
All swans are white (universal statement)
SINGULAR AND UNIVERSAL
STATEMENTS
„ Singular: refer to a
specific observation
at a specific time and
location
„ Universal: refers to all
instances at any time
and location
„ Induction does not
guarantee the truth
of the derived
conclusion!
PROBLEM
DEDUCTION AND INDUCTION
DEDUCTION
INDUCTION
All humans are mortal
Swan no. 1 is white
Prof Fisher is a human
Swan no. 2 is white
Therefore Prof Fisher is mortal
… etc.
Therefore all swans are white
A logically valid deductive
argument
Not a logically valid argument
Most important feature: logically
valid arguments are truth
preserving
Inductive arguments are not truth
preserving
„
If the premises are true, then
the conclusion must be true
„
Even if the premises are true,
the conclusion can be false
THE LIMITS OF INDUCTION
Consider the following universal statement:
“All metals expand when heated”
Metal x1 expanded when heated on occasion t1
Metal x2 expanded when heated on occasion t2
Metal xn expanded when heated on occasion tn
Therefore all metals expand when heated
The conclusion is a universal statement inductively derived
from a finite number of observed facts
„
We derive a statement about all cases of metals expanding
from statements about only some cases
„
The conclusion goes beyond the content of the premises
SCIENCE IS NOT DERIVED FROM
FACTS IN A LOGICAL SENSE
„ Fundamental point: It is simply incorrect to say that
universal statements can be derived in the sense of
logically deduced from or “proved” by the fact. So
“derive” must be understood in an inductive not a
deductive sense
„ What then, makes a “good” inductive argument
since we cannot use the idea of logical validity?
SO, WHAT MAKES A “GOOD”
INDUCTIVE INFERENCE?
„ For a good inductive inference, we might expect the
following conditions to be satisfied: -
1. A large number of observations
2. The observations must be repeated under a wide variety of
conditions
3. No observation statement should conflict with the derived
universal statement (law/hypothesis)
THE PRINCIPLE OF INDUCTION
„ If a large number of A’s have been observed under a wide
variety of conditions, and if all those A’s without exception
possess the property B, then all A’s have the property B
„ The principle of induction expresses the
characteristics of a good inductive inference
PROBLEMS WITH THE PRINCIPLE
OF INDUCTION
„ How many observations?
„ What conditions are relevant?
„ Is it realistic to demand that there are no
exceptions?
THE “PROBLEM OF INDUCTION”
David Hume (1717-1776)
Enquiry Concerning Human
Understanding (1748)
How is induction justified?
3 options: 1.
Appeal to logic
2.
Appeal to the success of
induction
3.
Appeal to probability
OPTION 1: APPEAL TO LOGIC
Consider these two statements. How do we
establish their truth? : 1)
‘All bachelors are unmarried’
2)
‘All metals expand when heated’
OPTION 1 FAILS
‘ALL BACHELORS ARE
UNMARRIED’
‘ALL METALS EXPAND
WHEN HEATED’
„
Can be known a priori (before
experience)
„
Can only be known a posteriori
(after experience)
„
Logically necessary that bachelors
are unmarried men
„
Not logically necessary
„
The truth of the statement is not
guaranteed by the meanings of the
terms
„
To deny that the next metal we try
will expand when heated involves
no logical contradiction
„
„
The truth of the statement is
guaranteed by the meanings of the
terms in the sentence
To deny that bachelors are
unmarried would be a logical
contradiction
Induction was successful on occasion #1
Induction was successful on occasion #2
Induction was successful on occasion #3
…. etc.
Therefore induction always works
OPTION 2: APPEAL TO THE
SUCCESS OF INDUCTION
OPTION 2 RESPONSE: APPEALING TO THE
SUCCESS OF INDUCTION IS ILLEGITIMATE
„ We have used induction in order to justify
induction, but induction is the thing that lacks
justification!
„ This is what philosophers call a circular argument
„ The argument is invalid because one assumes what is in
need of independent reasons to support it
OPTION 3: APPEAL TO
PROBABILITY
Induction was successful on occasion #1
Induction was successful on occasion #2
Induction was successful on occasion #3
…. etc.
Therefore it is probably true that induction always
works
THE PROBABILISTIC PRINCIPLE
OF INDUCTION
„ If a large number of A’s have been observed
under a wide variety of conditions, and if all
those A’s without exception possess the property
B, then all A’s probably have the property B.
OPTION 3: RESPONSE
„ The appeal to probability does not overcome the problem
of induction
„
The idea that all A’s probably have the property B is a
universal statement based on a finite number of observations
and hence does not demonstrate the all applications of the
probabilistic principle of induction are true
„
Furthermore, even if we tried to be precise about the
probability of a universal statement derived from the facts,
what probability do we give to a universal statement, which
applies to an infinite number of cases, on the basis of a finite
number of singular statements?
THE PROBLEM OF INDUCTION
„ There appears to be no way to justify induction
without relying on experience, thereby
appealing to induction, which is illegitimate
RECAP: WE HAVE LOOKED AT…
„
Inductive reasoning and how it used to derive universal
statements (theories/laws/hypotheses) from the facts of
experience
„
The principle of induction (what might make an inductive
argument “good’?)
„
The problem of induction (can the principle of induction be
justified without circularity?)
„
Now we will look briefly at a popular idea of scientific method
that uses deduction and induction to determine how facts bear
on hypotheses
THE HYPOTHETICO-DEDUCTIVE
METHOD
Hypothesis
↓
Logical
deduction
Prediction ←---------------→ Observation
Comparison
•
•
•
One you have established or discovered a hypothesis, test its logical
consequences by deducing a prediction (or providing explanations) and
compare it to observations/experiments
Observation of predicted phenomenon = verification of the hypothesis.
Does a sufficiently great number and variety of verifications means the
hypothesis is true…?
Hypothesis verified on occasion #1
Hypothesis verified on occasion #2
Hypothesis verified on occasion #3
…. etc.
Therefore the hypothesis is verified and hence true X
OR: Therefore the hypothesis is confirmed and probably true X
DOES VERIFICATION
GUARANTEE TRUTH? NO!
„ Reject inductivism and appeal to an alternative
form of the H-D method called falsificationism
(see next lecture!)
„ (OR, retain inductivism in a different form:
appeal to conditional probabilities – the
Bayesian approach; see Chalmers 2013 chapter
12)
RESPONSE
DISCUSSION CLASS: READING AND
QUESTIONS
Required reading:
Alan Chalmers, “Deriving theories from the facts:
induction”, chapter 4 in What Is This Thing Called
Science 4th Edition.
Questions: 1.
What is induction?
2.
Why do we need a principle of induction? Can it toandgeneralize
check'
guarantee that our inductive arguments are good?it is helpful
3.
What is the problem of induction? Do you think it is
a serious problem? If so, why? If not, why not?
there could be exceptional case
lacks certainty, it has a probability
does not
guarantee the truth
of the derived
conclusion!
making generalizations based on observations, experiments, or specific instances