1
Lecture: Philosophy of Science (Schurz) Ss 2015 Wed 10.30-12 24.91/U1.61
Part I: General introduction and philosophical foundations
1) 04-15 Tasks and aims of Philosophy of Science. The method of rational reconstruction
2) 04-22 Common epistemological assumptions and methodological features of the
sciences
3) 04-29 Classification of scientific disciplines and the demarcation problem: The
requirement of value neutrality
4) 05-06 Scientific inference: Deduction, induction and abduction
Part II: Logical foundations
5) 05-13 Kinds of concepts
6) 05-20 Kinds of sentences
7) 05-27 Degrees of generality. Logical relations between sentences
Part III: Law hypotheses and their empirical testing
8) 06-03 Testing for Truth and Relevance 1: the deterministic case
9) 06-10 Testing for Truth and Relevance 2: the statistical case
10) 06-17 Correlation and causality
Part IV: Scientific theories
11) 06-24 Observation concepts, empirical disposition concepts and theoretical concepts
12) 07-01 Structure and methodological features of scientific theories
Example 1: Newtonian physics
13) 07-08 Example 2: Piaget's cognitive psychology. Theory evaluation and theory
progress
14) 07-15 Exam
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Book to the lecture: Gerhard Schurz: Philosophy of Science: A Unified Approach,
Routledge, New York 2013.
Further literature (in red: recommended):
Bird, A. (1998): Philosophy of Science, McGill-Queen's University Press, Montreal
& Kingston.
Bunge, M.: Scientific Research, Springer, Berlin 1967.
Carnap, R.: Philosophical Foundations of Physics, Basic Books, New York 1966.
Curd, M., and Cover, J.A. (1998, ed.): Philosophy of Science, Norton, New York.
Feyerabend, P.: Against Method, New Left Books 1975.
Godfrey-Smith. P. (2003): Theory and Reality: An Introduction to the Philosophy of
Science, University of Chicago Press, Chicago.
Hempel, C. G.: Philosophy of Natural Science, Englewood Cliffs, Prentice Hall 1966.
Kuhn, T.: The Structure of Scientific Revolutions, 2nd ed., Univ. of Chicago Press
1975 (orig. 1962).
Ladyman, J. (2002): Understanding Science, Routledge, London.
Lakatos, I., Musgrave, A.: Criticism and the Growth of Knowledge, Cambridge
University Press 1970.
Losee, J. (2001): A Historical Introduction to the Philosophy of Science, Oxford
Univ. Press, Oxford (Orig. 1972).
Popper, K.: The Logic of Scientific Discovery, Basic Books, New York 1959.
Psillos, S. (1999): Scientific Realism. How Science Tracks Truth, Routledge, London
and New York.
Reichenbach, H.: The Rise of Scientific Philosophy, Univ. of California Press, Berkeley and Los Angeles 1951.
Van Fraassen, B.: The Scientific Image, Clarendon Press, Oxford 1980.
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Questions of the General Philosophy of Science
General versus special characteristics of the sciences  including the natural sciences, social sciences and the humanities.
the objects
What are
the methods
of the sciences ?
the goals and limitations
a scientific language
correct scientific argument
What is
a scientific observation, fact or measurement
?
a scientific law, a theory?
a prediction, explanation, causal relation ?
How are
laws or theories empirically tested?
What are
criteria for theory progress in science
What is objectivity and truth ?
Philosophy of science
epistemology
Values in science versus value-neutrality? Philosophy of science
(meta-)ethics
•
Applications internal to sciences:
 Methodological advice and decision support on controversial questions in sciences
 Interdiscplinary relations and transdisciplinary discoveries
 Pioneer function for new sciences
•
Applications external to sciences:
 Demarcation problem (example: controversy surrounding creationism)
 Critical function: critique of political or economical abuse of the sciences
(example: systematic biases in pharmaceutical research)
3
4
4
The method of the philosophy of science
•
The normative view (earlier): Karl Popper, Vienna circle (logical empiricism)
•
The descriptive view: Thomas Kuhn ('historical turn'), W. Stegmüller, L. Laudan
R. Giere ()
Argument of the normativists: Context of discovery (genesis)
versus
context of justification ( confirmation)
The method of rational reconstruction (Lakatos 1971, Stegmueller 1979):
NORMATIVE CORRECTIVE
Supreme epistemic goal
(Revision?)
(Minimal) epistemological model
(Justification)
(Revision?)
RATIONAL RECONSTRUCTION
Philosophy of Science develops models of:
Observation, experiment, law, theory, confirmation, disconfirmation
falsification, explanation, causality, theory progress ....
(empirical support)
(application)
Real (factual) sciences
Real sciences vs. pseudo-sciences
positive and negative paradigm cases
Controversial cases
DESKRIPTIVE CORRECTIVE
Unsolved problems
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Supreme Goal: (G) Finding true and content-rich statements
relating to the given domain of investigation
 tension between probability of truth and richness of content
Minimal epistemological modell  five assumptions:
(E1) Minimal realism (correspondence theory of truth)
(E2) Fallibilism (critical attitude)
(E3) Objectivity & Intersubjectivity (criterion)
(E4) Minimal empiricism (empirical testability)
(E5) Logic in the broad sence (concepts, statements, arguments)
5
6
6
Minimal methodology  four methodological features:
(M1)
(M2)
(M3)
(M4)
Search of general and content-rich laws and theories
Search of actual observation statements
Attempt to explain the actual observation statements
and to predict potential observation statements,
with help of the laws or theories conjectured in (M1)
Attempt to test laws and theories by comparing the
predicted (potential) observation statements with the
actual observation statements.
Agreement:
Confirmation
Disagreement:
Falsification or Disconfirmation
Three levels:
Scientific theories
Prediction explanation
Confirmation disconfirmation
Empirical laws
Prediction
explanation
Confirmation disconfirmation
(Actual) observation statements
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Classification of scientific disciplines, according to their domain of objects:
SCIENCES 
1) of nature: physics, chemistry, biology, geology, medicine (astronomy, cosmology,
geography, paleontology, history of biological evolution)
2) of technology: mechanical and electrical engineering …, also: computer science
3) of human beings: psychology (also: education, medicine, cognitive science)
4) of (human) society: sociology, economics, political science (also: anthropology,
ethnology, geography)
5) of (human) history: history (also: anthropology, ethnology)
6) of cultural (mental, social) artifacts: legal sciences, linguistics, literary science,
sciences of fine arts and music, media studies (also: education, religious studies)
7) of formal structures (formal sciences): mathematics (logic, statistics, theoretical
computer science, system theory…), formal methodology and philosophy of science
8) of the general foundations of human ideas: philosophy (epistemology, philosophy of science and theoretical philosophy; ethics, aesthetics and practical philosophy)
9) of God: theology (also: religious studies)
Natural sciences: only 1?, +2?, +7? +3?
Humanities: 5,6, 8 Why not 7? Or 3?
Human and social sciences: 3, 4 (5?, 6?)
[Cultural sciences]
Factual sciences (as opposed to structural sciences): 1, 2, 3, 4, 5, 6 8?, 9??
Exceptional case of formal sciences 7: G; E1-E3, E5 (not E4); M1 (not M2-M4)
Demarcation: "Science" comprises all empirical sciences (satisfying G, E1-E5, M1M4, plus their associated formal and methodological auxiliary sciences (7).
Limitations of science:
 where evaluative statements enter the discipline ( 6, 8, 9 )
  where assumptions of faith (religios creed) enter the discipline (9)
7
8
8
Example: Value judgement in jurisprudence (the science of legal judgment).
(Is a billboard advertising underwear still in accord with "common decency" or
is it already a legal offense?)
Eike von Savigny et al. (1976)
E. Hilgendorf and L. Kuhlen (eds., 2000)
Max Weber (1864-1920): Postulate of value-freedom
 because: Values are not properties inherent to objects themselves, but based on subjective interpretations by us humans. Ultimately, the decision for or against certain
values is a question of personal freedom.
However, the scientist qua scientist
(1.) can study the factual presence of value and norm systems,
(2.) can discover logical relationships among value or norm sentences (test them for
inconsistencies), and
(3.) ( most importantly for practical sciences): can infer derived norms from given
fundamental norms and descriptive knowledge, by means of the so-called
Means-end inference:
Descriptive means-end hypothesis: M is in the given circumstances C a necessary
 or alternatively an optimal  means for the realization of end E.
Thus: Given (fundamental norm:) end E is to be realized,
then (derived norm:) means M should also be realized.
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The requirement of value-neutrality (VN) in sciences:
EV
IV
external values (all values except those in IV)
internal values (supreme goal (G) and all values
following from (G) by means-end inferences)
CD
CJ
CA
context of discovery
context of justification
context of application
EV & IV
CD
only IV
CJ
EV & IV
CA
(VN): A specific realm of scientific activity, namely their context of justification, should be free from fundamental scienceexternal value assumptions.
( A normative recommendation. Not a generally followed practice)
The selection of the investigated objects and parameters in (CD) is
not epistemologically neutral, but places limits on the results of
the scientific investigation.
Therefore the selection in (CD) must be accessible to subsequent
correction by results in (CJ) (even when this goes against the external goals of the research project).
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Selection of relevant variables
Example: causal theories of psychological depression
•
Hippocrates: surplus of black bile
•
Middle Ages: devil and demons; punishment for laziness
•
Astrology: star constellation
•
Freud: child development, lack of satisfaction in oral phase
•
Beck: cognitive defects
•
Seligman: uncontrolled fear
•
Genetics: genetic dispositions
•
Neurophysiology: low level of neurotransmitters
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Further classifications of disciplines:
Classification of factual sciences:
Speculation
Empirical sciences
Experimental sciences
Dissecting sciences
Graduated division of scientific methodologies by increasing degree ()
of logical-mathematical and quantitative precision
logical-mathematical language
"quantitative"
Logic
Statistics and measurement theory
Technology
natural language
"qualitative"
Hermeneutics
Content analysis
Field research
What is the characteristics of "(natural) science":
empirical?
experimental?
dissecting?
quantitative?
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12
12
+ yes - no
n naïve
Position
? between + and - ?+ tends towards +
?- tends towards -
VN
A1
A2
A3
A4
A5
M1
M2
M3
M4
Plato
-
n+
-
+
?
-
+
-
-
-
Aristotle
?-
n+
-
+
+
?-
+
-
+
?-
Alexandria
+
n+
-
+
+
n+
+
+
+
n+
MA ≤ 12th century
-
n+
-
+
?
-
+
-
+
-
Late scholasticism
?+
+
?+
+
?+
n+
+
+
+
n+
?+
n+
-
+
-
n+
+
+
+
n+
-
+
+
-
+
+
+
+
+
?+
+
-
+
+
n+
+
+
+
Descartes, Leibniz ?-
+
-
+
+
-
+
-
+
-
Kant
-
+
-
+
+
?
+
+
+
?
Pre-modern History
Modern Times
Empiricism
Bacon, Locke
Hume
+
Mill
+
Rationalism
Contemporary Phil of Sci
Logical Empiricism
+
?
+
+
+
n+
+
+
+
+
Post-Positivism
+
+
+
+
+
+
+
+
+
+
Pragmati(ci)sm
?
-
+
+
+
+
+
+
+
+
?
+/-
+
-
-
-
+
?
+
-
+/- moderate/radical
?
+/-
?
+/-
+/-
+/?
+
+/-
+
+/-
Hermeneutics
?-
?+
+
+
-
?+
-
+
-
?
Critical theory
-
-
+
-
-
-
?+
?+
+
?+
Contemporary criticisms:
Relativism
+/- moderate/radical
Constructivism
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The inductive –
deductive schema:
The general (laws and theories)
inductive ascent
deductive descent
(Aristotle)
The particular (observations)
Induction in the broad sense: Induction (i.n.s.) + abduction
Three kinds of scientific inference and argumentation:
Deduction - certain: Logic in the narrow sense
All As are Bs, this is an A / therefore: this is a B
(Other kinds of ded. inference: from general to general, from particular to particular)
Induction - uncertain:
Inductive generalization:
All As observed so far were Bs // therefore (probably): all As are Bs
[Statistical version: r% of observed As were Bs // therefore: r(% of As are Bs]
Inductive prediction:
All As observed so far were Bs // therefore: the next A will be a B
Abduction - very uncertain: Inference to the best explanation, or inference to
an unobserved cause (theoretical concept)
This is an A. Can be explained (in given background knowledge) by the
assumption that this is a B //(Conjecture:) this is a B
Controversial: is abduction a scientifically legitimate form of inference?
Popper: No: abduction  discovery of hypotheses by trial and error
 But oh! Popper and his students even doubt the scientific legitimacy of induction
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Three Kinds of Induction:
1. Methodological induction
Induction as a method of "extracting" laws and theories from observations
Example: All As observed so far were Bs  therefore all As are Bs
Major criticism of Popper:
Confusion of context of discovery and context of justification
Theories are not  or better: not only  discovered by induction
2. Logical Induction (Carnap, Reichenbach, Bayesianismus):
Induction as a method of justification: determining the conditional probability of
scientific hypotheses H given the observational data O:
Probability(H / O) = so-and-so (e.g., 0.9)
Major criticism of Popper: The space of all possible alternative theories is unlimited
and cannot be probabilistically measured.
3. Epistemic Induction (or meta-induction):
Induction as a merely comparative evaluation of the probability of scientific
hypotheses (laws or theories):
Theory T1 has been empirically
We believe that T1 will be empirically
more successful than theory T2
more succesful than T2 in the future
current state of observational knowledge
the degree of confirmation of a
theory is always doubly relative:
current state of alternative theories.
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Abduction to theories - example:
Planets move around the sun in elliptic orbits.
This can be explained by Newton's force laws (2nd law & gravitational law & cp).
// Abductive conjecture: Newtons' force laws are approximately true
Interaction of epistemic induction and abduction
(1) Evidence: Tk is among the alternative theories T1,,Tn so far the empirically
most successful.
epistemic inductive inference
(2) Instrumentalist conclusion: Tk is among T1,,Tn the most empirically adequate
(therefore also in future the most empirically successful)
abductive inference to the best theory
(3) Realistic conclusion: Tk is among T1,,Tn the closest to the truth.
 Empiricist instrumentalism versus
realism
in the philosophy of science
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KINDS OF CONCEPTS --- Classifications:
According to the logical type: (shorted presentation)
Singular concepts or terms (designate a single individual,
spatiotemporal location or situation)
Non-logical
(individual constants: a, b, …)
concepts
General concepts
predicates
one-place: express properties
or kinds (F, G, …)
n-place: express (n-ary) relations (R, …)
function symbols: express functions (f, g, …)
Logical
concepts
Truthfunctional sentence operators not (), and (),
inclusive or (), if-then (), 
Quantifiers "for all" (), "exists" ()
(prop. logic)
(pred. logic)
Intensional sentence operators necessary (), possible ()
probable
(modal logic)
Variables (for individuals x, y,…; for predicates ,  ,…)
Mathematical concepts  (set theory), +, (arithmetics), …
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According to the content type:
(logical concepts)
observation concepts
empirical
concepts
descriptive concepts
empirical disposition concepts
theoretical concepts
(non-logical
concepts)
prescriptive
norm concepts
concepts
value concepts
 criterion for observability: ostensive learnability
observable in the narrow sense versus empirically measurable in the wide sense
According to the gradation (scale) type:
classificatory concepts
nominal (categorial) scales
qualitative concepts
comparative concepts
ordinal (ranking) scales
interval (difference) scales
quantitative concepts
ratio scales
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KINDS OF SENTENCES --- Classifications:
According to the content type:
logically determined
analytic
determined by definition
observation sentences ()
empirical
general emp. sentences (...)
descriptive
synthetic
theoretical
purely theoretical
mixed-theoretical
normative
purely prescriptive
evaluative
mixed-prescriptive
(Simplified) definitions:
Observation sentence: a singular sentence (*), which contains (apart from logical
concepts) only observation concepts. Example: "this raven is black".
(*: or a localized-quantified sentence: e.g., "all apples in this basket are red")
Empirical sentence: a (possibly quantified) sentence, which contains (apart from logical concepts) only empirical concepts. Example: all raven are black.
Theoretical sentence: a sentence that contains theoretical concepts (besides logical
concepts and possibly empirical concepts). Example: "atoms consist of protons, neutrons and electrons", or "in the center of our galaxy there is a black hole".
(T-theoretical concept, T-theoretical sentence)
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A sentence is purely descriptive iff it
(it either contains no prescriptive concept, or if)
every prescriptive concept occurring in it lies in the scope of a subjective
attitude operator
A sentence is purely prescriptive iff all of its descriptive components (subsentence
or subformulas) lie within the scope of a prescriptive operator.
(In other words, iff all of its elementary subsentences/subformulas are elementary
prescriptive sentences.)
A sentence is mixed otherwise (it has descriptive and prescriptive elementary subsentences/subformulas).
Examples:
Peter believes that stealing is bad.
Stealing is bad.
Stealing is allowed for a person, if this person is suffering from hunger.
Peter believes that stealing is bad, although he is a thief himself.
If stealing is permitted, then there exists no right to private property.
Peter's car has good breaks.
Peter has a good character.
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A sentence is logically true iff every sentence of the same logical form is true.
 in other words: iff its truth depends only on its syntactic structure and on the
meaning of its logical concepts.
Logical form of a sentence:
Replace all nonlogical symbols by variables (dummy letters).
Example of a logically true sentence:
If all men are mortal, then there exists no man who is immortal.
Logical form: If all F are G, then there exists no F which is not a G
Formalization: x(FxGx)  x(FxGx)
Example of a synthetically true sentence:
All men are mortal. (All F are G)
An argument (inference) is logically valid iff for every argument which has the
same logical form the following holds: if all premises are true, the conclusion is
true.
Example:

Premise 1: All humans are mortal.
Premise 2: You are a human.
Conclusion: Therefore your are mortal.
Logical Form:
All F are G
Formalization:
x(Fx Gx)
This a is an F
Fa
Therefore this a is a G
Ga
Example of an invalid argument:
All humans are mortal.
All F are G
This living being is mortal
This a is a G
Therefore this living being is human.
Therefore this a is an F
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A sentence is definitorially (or: extralogically-analytically) true iff its truth is
determined by certain conventions of meaning for its non-logical concepts (that
are entrenchend in the underlying language or linguistic community)
Example:
All bachelors are unmarried
(Logical form: All F are G)
The length of the standard measure in Paris is one meter
Example of synthetical sentences:
All polar bears are white
(Same logical form)
The length of this rod is one meter.
(Definiendum)
"
(Definiens)
Explicit definitions: x: x is a bachelor defx is a hitherto unmarried man
Meaning postulates: If something is red, then it has a color.
Derived definitorially true sentences: If somebody is a bachelor, then he is male.
Requirements on definitions:
They must not be circular.
They must neither have empirical content, nor create new empirical content in
combination with the given system S of accepted background beliefs beliefs.
Hence: No concept may be defined in two different ways.
Example:
1 Meter = the length of the platin-iridium-bar in Paris.
(1)
1 Meter = the length of a pendulum at sea level with
(2)
an oscillation frequency of one second.
(1) + (2) imply the following synthetical (empirical) consequence:
The length of the platin-iridium-bar in Paris = the length of a pendulum at sea level
with an oscillation frequency of one second.
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Classification of sentences
according to their generality (logical strength):
Strict (or deterministic) generalizations
Purely universal sentences
e.g.: For all x: if x is A, then x is C
x(AxCx))
'A' for 'antecedent', 'C' for 'consequent'
(spatiotemporally) unrestricted
(spatiotemporally) restricted
Mixed-quantified generalizations; e.g. universal-existential (etc.).
General sentences
Non-strict generalizations
Statistical generalizations
e.g.: q % of all As are Cs p(C|A) = r (with: 0r1; q = 100r)
(spatiotemporally) unrestricted
(spatiotemporally) restricted
Normic and ceteris paribus generalizations
e.g.: As are normally Cs
and: C.P. As are Cs
Singular sentences e.g. This is an A, and it is (or is not) a C.
Aa(Ca
Existential sentences e .g. There exists an A that is (or is not) a C. x(Ax(Cx)
(Mixed sentences)
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Interlude: Two kinds of probability:
•
1. Statistical (objective) probability: Always refers to classes, never to individu-
al cases. "80% of all Italians are brown-eyed"
•
2. Epistemic (subjective) probability: Rational degree of belief. Refers to indi-
vidual cases. "With high probability Vicenco (from Italy) is brown-eyed"
Principle of narrowest reference class (Hans Reichenbach)
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24
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Important logical relations
Notation: "X  Y" stands for "Y follows logically from X",
and "X  Y" for "X and Y are logically equivalent".
(1)
Universal sentence  singular sentence
All As are Cs  if a is A, then a is C
(2)
Universal sentence & singular sentence singular sentence
(D-N explanation scheme)
(3)
All As are Cs, and a is A  a is C
Singular sentence falsifies strictly universal sentence (falsification scheme I)
Singular sentence  negation of a universal sentence
a is A and not C  not all As are Cs
(4)
Existential sentence falsifies strictly universal sentence (falsification scheme II)
There is an A that is not a C not all As are Cs 
(5)
Universal sentence is logically equivalent to the negation of an existential sentence.
(6)
All As are Cs  there is no A that is not a C
Singular sentence Existential sentence
a is an A  there exists an x that is an A
(7)
There are no logical consequence relations between non-strict generalizations
and singular sentences, only relations of statistical and epistemic probability.
25
Spatiotemporally unrestricted strict generalizations:
are prima facie candidates for proper laws of nature.
Examples::
(1) All physical entities attract each other
For all x and y: if x and y are physical particles, then x attracts y and y attracts x
(2) For all ideal gases x:
pressure(x)volume(x) = constant  mol-number(x)  absolute-Temperature(x).
 The problem of lawlikeness: not every sentence that is a spatiotemporally unrestricted strict generalization (according to its logical type) is a lawlike generalization!
Compare: "No lump of radioactive uranium has a diameter of more than one mile".
versus: "No lump of gold has a diameter of more than one mile".
Spatiotemporally restricted strict generalizations:
Their lawlikeness is graded: it depends (among others) on the size of their spatiotemporal region of application
Examples:
(1) All bodies close to the surface of the Earth fall downwards with a constant acceleration of 10 m/sec2 (Galileo’s law of gravity)
(2) All mammals in polar regions have a more rounded form than their conspecifics
in warm countries (Bergmann’s law)
(3) Until approximately 10,000 B.C. all humans lived from hunting and gathering
(4) In the middle ages, all agriculture was based on the feudal fief principle
(5) All apples in this basket are red (Goodman's counterexample)
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Statistical generalizations - important distinction
(1.) If spatiotemporally unrestricted (1.1) objective indeterminism versus
(1.2) epistemic indeterminism
(2.) If spatiotemporally unrestricted  lawlikeness is graded
(1) 50% of all cesium137 atoms (for any amount of the substance) will have decayed
within 30 years
(2) 80% of all lung cancer sufferers were heavy smokers
(3) 70% of all bedwetting children have parents with a disturbed relationship
(4) 70% of all Swedish peope are protestants
(5) 60% of all apples in this basket are red
Qualitative statistical generalizations:
•
•
Most bedwetting children have parents with a disturbed relationship
p(DistParents(x) | Bedwetter(x) ) = high.
Normic generalizations: Normally birds can fly
Comparative statistical generalizations:
•
•
Bedwetting children are more likely to have parents with a disturbed relationship.
p(DistParents(x) | Bedwetter(x) ) > p(DistParents(x) | not Bedwetter(x) ) .
There exists a significant positive correlation between bedwetting of children
and having parents with a disturbed relationship
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Classification of sentences according to their epistemic & methodological status:
Observation sentences
actual
singular empirical sentences
potential
Empirical laws
strict
universal empirical sentences
statistical
Theoretical laws
universal theoretical sentences
Theories
systems of theoretical and empirical laws
Hypotheses
versus
evidences (already tested and accepted sentences)
Verification, Falsification, Confirmation and Disconfirmation:
A hypothesis is ....
 verifiable iff it follows logically from a finite consistent set B of (potential) observation
sentences
 confirmable iff it is made probable by the assumption of B
 falsifiable iff its negation follows logically from a finite consistent set B of (potential)
observation sentences, and
 disconfirmable iff its negation is made probable by the assumption of B
Empirical law hypotheses
Spatio-
Spatiotemporally unrestricted
tempor.
(in principle)
Theories
Strict
with
Statistical
restricted Univ. Univ.-existence (normic, c.p.)
without
empir.
empir.
content content
Verifiable
+





Falsifiable
+
+




Confirmable
+
+
+
+
+

Disconfirmable
+
+
+
+
+

Popper-Asymmetry
28
28
Part III: (Empirical) Law Hypotheses and Their Testing
1. TRUTH
versus
2. RELEVANCE (DEPENDENCE)
The strict (deterministic) case  example:
For all x: if x is A1 and A2,
•
•
then x is C.
x((A1x A2x)
Cx)
All men who take birth controll pills do not get pregnant
If a deadly nightshade is picked at midnight during full moon, it has hallucinative
powers.
Is A1 (A2) relevant for C?
A1 is relevant for C iff
it is not already true that for all x: if A2x, then Cx.
A1 is a necessary (conjunctive) part of a sufficient
antecedent condition (or cause) of C
The statistical case  example:
95% of all A's are C's
•
p(C/A) = 0.95
95% of all persons having a cold, who regularly take high doses of vitamin C (A),
make a full recovery within a week (C).
A is (statistically) relevant for C
iff
p(C|A)  p(C).
A is irrelevant for C
iff
p(C|A) = p(C).
A is positively relevant for C
iff
A raises C's probability, p(C|A) > p(C).
A is negatively relevant for C
iff
A lowers C's probability, p(C|A) < p(C).
Simple correlation measure for binary properties: corr(A,C) =def p(C|A)  p(C).
A is
positively relevant for C
negatively relevant for C
irrelevant for C
iff
corr(A,C) =
positive
negative
zero
29
Generalization to p(C/A1A2)
r% of all those x, that are A1 and A2, are Cs:
positively relevant for C
A1 is negatively
irrelevant
p(C/A1A2) > p(C/A2)
p(C/A1A2) < p(C/A2)
p(C/A1A2) = p(C/A2)
iff
Conditional correlation measure: corr(A1,C/A2) = p(C/A1A2)  p(C/A2)
Testing of Strict Law Hypotheses
For all x: if x is A1 and A2, then x is C.
For all chemical substances x: if x is solid and x gets heated, then x expands.
John Stuart Mill: The methods of agreement and difference
Test for truth  method of agreement:
Is the law hypothesistrue?
Take an A-sample (A = A1A2)
("the experimental group")
no: law is falsified
Are all C?
yes: law is confirmed
Testing for relevance - method of difference:
Is A1 (or A2) relevant for C?
Makes only sense if law has been confirmed
Take a representative A1-control sample
("the control group")
This is a sample of individuals, which
possess all antecedent factors except A1.
no: A1 is relevant (relevance is conditionally verified)
Are all (still) C?
yes: A1 ist not relevant (irrelevance is confirmed)
Representativitity of samples: For strict generalizations: maximal variation of circumstances
 the importance of experiments
Example: the discovery of puerperal fever by Semmelweiß
29
30
30
Testing Statistical Laws
p(Cx|Ax) = 0.8
80% of all trees beside motorways (A) are sick (C)
Testing for truth  method of acceptance and confidence intervals
Take an A-sample
For example: 100 As. Found: 75 Cs.
Choose the acceptance coefficient: e.g., 95%.
From sample size (n=100) and acceptance coefficient (95%) calculate the
acceptance interval: in our case: 72 - 88 Cs out of 100 As.
Is the A-sample frequency of C
No: law is strongly disconfirmed
within the acceptance interval?
Yes: law is weakly confirmed
(In our example: yes)
What has been strongly confirmed is the (weaker) confidence interval law,
which for the given sample result is: 67% ≤ p(C|A) ≤ 83%.
Testing for relevance  method of significant difference:
Take an A-control sample
For example: 100 non-As. Found: e.g. 60 Cs.
Choose the significance coefficient: e.g. 5%.
From the sample size (n=100) and significance coefficient (5%) calculate the
significant difference: in our case 13 out of 100.
Is the actual difference between the
No: Relevance of A for C
A- sample frequency of C and the
is (strongly) disconfirmed
A- control sample frequency of C
Yes: Relevance of A for C
larger than the significant difference?
is strongly confirmed:
significant correlation
positive
In our example: 75-60 = 15 > 13
negative
signifikant positive correlation
31
Acceptance interval :=
the (centro-symmetrical) interval of the most probable sample frequencies,
in which the sample frequency is located
with a probability equal to the acceptance coefficient,
given that the law hypothesis being tested is true.
Probability of sample results
given p(C|A) = 0.8
0.1
acceptance interval (grey) = 95%
of the entire area under the curve
0.05
rejection interval (white) = 5% of
the entire area under the curve
0.01
0
20
40
60
Absolute frequency of C in 100 A
70 80 90 100
72
88 (=acceptance interval)
Acceptance interval for p(C|A) = 0.8 (computed with MatLab).
31
32
32
Probability of sample result given p(C|A) = r
1
confidence interval r [0.67, 0.83]
r% = 67 75 83
actual sample result: 75 out of 100
0
0
Absolute sample freq. of C in 100 A's
100
Acceptance intervals for r = 67 75 83
Relationship between acceptance and confidence interval.
33
Significant difference :=
that threshold,
which is exceeded by the difference between the A-sample frequency and the A-control sample frequency of C
with a probability equal to the significance coefficient,
[or: which is not exceeded  with a probability equal to 1  significance coefficient],
given the null hypothesis is true (i.e. there is no statistical relationship between A and C in the population).
Probability, given the truth of the
null hypothesis p(C|A) = p(C|A)
acceptance interval of
the null hypothesis (grey)
Significant
acceptance interval of
difference = 13
-100
the alternative hypothesis (white)
-40 -13 0 +13 40
Absolute Frequencydifference between A- and
100 A-sample (n = 100)
Probability distribution of sample differences and significant difference
 Sources of error in statistical methods
33
34
34
CORRELATION AND CAUSALITY
1. Hidden variables:
1.1. Hidden common causes:
A
B
spurious causality
"spurious correlation"
C
Example:
(direct) causation
correlation
A = Drop of the barometer (reading)
(Grünbaum)
B = Coming of a storm
C = Drop of atmospheric pressure
Example of Lazarsfeld:
A = Positive/negative attitude to the employer
B = mental health of worker
C = Stress in the work place
Statistical criterion for detection of a hidden variable C: Screening-off condition of
Reichenbach:
corr(A,B/C) = 0 , but corr(A,C/B) > 0, corr(B,C/A) > 0

 but applies also to:
 

1.2 Hidden intermediate causes ('intervening variables')
A
B
Indirect causation
C = intermediate cause
C
Example:
A = marital status :
married/single
(Zeisel)
B = frequency of absence from work
(population: women)
C = amount of extra housework to be done
Not always possible to discriminate between 1.1 and 1.2 by statistical information:
A = Drinking coffee
??
B = heart disease
C = smoking
35
Even if no hidden variables are involved:
2. Problem of the causal direction:
A
B
correlations are always symmetric
Beispiele:
(1)
Height of IQ
(2)
being
(3)
Social status
frequently watching
aggressive
violent films
Interest in
Disinterest in
computers
social relations
Criteria for the causal direction of correlations:
 Between temporally successive events: causal direction is forward directed
 Between temporally coexistent properties: Which is independent vs. dependent
variable? Background knowledge, e.g., about mechanisms, or effects of intervention.
(4)
(5)
•
Air pollution
Gender
frequency of respiratory illness
gender specific features
Historical example of the banker John Law:
correlation between paper-money in circulation and wealth of the nation.
Unjustified causal interpretations of correlations (with "sensational value") are frequently found in popular media.  Some examples 
35
36
36
Part IV: SCIENTIFIC THEORIES
Theoretical concepts
electric field
social structure
atom
authoritarian charakter
mass, force
intelligence
solvable in water
fast reaction time
length time
result of interview
table, red, greater than
test score
empirical
disposition concepts
observation concepts
(Carnap 1936/7): An observation concept can be observed by every person under
normal conditions of observation.  Problem: perception or interpretation?
Criteria for observability:
• Intersubjectivity
• Theory-, culture- and value-independence
• Language-independence
• → Ostensive learnability
B is a theory-neutral observation concept iff almost all humans can acquire this concept in an ostensive learning experiment, under normal observation conditions, independently of their background information, language and culture.
Empirical disposition concepts
(Carnap 1936/7, 1956)
One law of correspondence (a "partial/conditional definition", analytically true):
If: x is given then: x is water-soluble if and only if
into water
Tx
test condition
(Dx
disposition predicate
x dissolves
Rx)
test result
37
Differences between empirical disposition concepts and theoretical concepts:
1) Disposition concepts designate functional properties (solubilty, elasticity), while
theoretical concepts designate categorial properties (molecular structure, force).
So [contra Quine, Bird, Mumford]: empirical dispostions are not equivalent with
unobservable structures, but, rather, are caused by them.
2) One theoretical property causes many empirical dispositions [Carnap 1966].
So theoretical concepts are characterized by many laws of corresponence.
Example:
Theoretical property
Empirical Dispositions
Molecules of
x is soluble in water 
substance x
x is soluble in all polar solvents (Water, Ammonia)
have dipolar
x is not soluble in all nonpolar solvents (Oil, Benzene,)
structure
x has a high melting point (D5)
x-solutions conduct electricity (D6)
x absorbs and emits radiation of certain wavelength
etc. 
Each empirical disposition provides a law of correspondence for the theoretical concept "dipolar molecular structure"
 but they cannot all be analytically true together they entail empirical predictions,
e.g.: If a substance has been dissolved in in water, then it won't dissolve in oil
Meaning of "dipolar structure" is not explicated by chemical laws of correspondence,
but by theory of electrostatics (a different and more general theory).
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38
38
Meaning of fundamental theoretical concepts is explicated by fundamental
laws of correspondence: Example: laws of correspondence of "mass"
C1: weight as disposition of "heavy" mass  gravitational force:
•
T1x
Object x is placed
on spring scale
( Mx
R1x
mass of x = k
)
Spring is stretched or compressed by k units of length
C2 – weight as disposition of "heavy" mass: actio=reactio balance)
•
T2x
Object x is
placed on beam
(Mx
mass of x = k
R2x)
x is balanced out by
k units of mass
 Compare C1 vs. C2 – earth versus moon
•
C3: Inertia as disposition of "inertial mass": laws of momemtum
 works without any gravitational field, in outer space (space shuttle)
Various more specific laws of correspondence, for example:
•
...
C4: Sinking velocity of small particles in a liquid
Taken together, C1 & C2 have empirical content:
If: T1 x & R1x & T2x, then: R2x
(etc.)
Therefore, laws of correspondence are not analytically true postulates,
but are synthetic in nature  they possess empirical content.
Holism of meaning: The meaning of a theoretical concept is not given
by a single definition, but is rather determined by the (core of the)
background theory, to which this concept belongs.
(the "error of operationalism")
Consequence: Theory change  meaning change (!?)
39
LAWS OF CORRESPONDENCE IN HUMANITIES AND SOCIAL SCIENCE:
Theoretical concept:
Indicator:
• Level of intelligence
Score in certain cognitive tests
• Character traits (e.g. aggres-
Behavior in certain experimental
sion, authoritarian character)
• Attitude (e.g. political)
situations; or results of personality tests
Answers to interview questions
Methodological rules:
•
Avoid distortion because of biased indicators (example: self-assessment)
•
Test the theory with several different (plausible) indicators (example: Piaget)
THE STRUCTURE OF SCIENTIFIC THEORIES:
Language:
Sentences (according to their T-E-status):
Total (theoretical) language
Purely theoretical laws (mostly axioms)
Laws of correspondence (axioms or theorems)
Empirical sublanguage
Empirical content (usually theorems)
= set of all empirical consequences
 Axioms versus consequences (theorems)
39
40
40
Axiomatic (non-derived) sentences (according to their importance):
[after Lakatos]
core:
theoretical axioms and central laws of correspondence
they define the identity of the theory
periphery:
special laws of correspondence & assumptions about particular
applications = auxiliary hypotheses
they define particular versions of the theory
METHODOLOGICAL CHARACTERISTICS OF (GOOD) SCIENTIFIC THEORIES:
•
System character or "holism"
•
Empirical creativity
Holismus of meaning
of empirical content
of theory testing / falsification
•
•
Global unification power
qualitatively novel predictions
(cross-sectoral predictions)
41
Example 1: Newtonian Physics
C1:
Total_force(x)
=
Mass(x)Acceleration(x)
C2:
Force (x,y) =
(–) Counterforce(y,x)
S1:
Gravitational_force (x,y) = Mass(x)Mass(y) / Distance(x,y)2
A1:
These and these gravitational forces are acting upon planet x (nothing else)
E: (Therefore:) The orbit (path or trajectory) of planet x is this-and-this function of
the time and of x's initial position and velocity.
Deviations from the predictions
and
Ad hoc hypotheses:
1846: Adams and Le Verrier detected:
Postulated a perturbing planet:
deviation of Orbit of Uranus
 Neptune
(A1')
(was independently confirmed)
1856: Le Verrier recognized
Postulated again a perturbing planet
deviation of Orbit of Mercury
 Vulcan (was never confirmed)
 General relativity theory S1*, K1*
•
Holism of theory testing ("falsification"): [after Pierre Duhem 1908]
There exists no "experimentum crucis"
New periphery
---> new version of the same theory
New core
---> new theory
•
Lakatos against Popper's "naive" falsification model:
Theories can always be protected from a conflict with experience by the introduction
of ad hoc auxiliary hypotheses which proclaim the existence of disturbing factors.
Methodological requirement [Lakatos]: ad hoc hypotheses are legitimate as long as
they do not decrease the empirical content of the theory (are not degenerate).
Moreover, after some time they must increase the empirical content (become empirically progressive), in order to be independently testable.
41
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Example 2: Piaget's theory of cognitive development
C1: The development of intelligence in children rests (primarily) on the step-like
formation of generally applicable logical-structural abilities.
C2-4: The concrete-operational stage is characterized by the formation of the following competences:
 C2) change of perspective
 (C3) recognition of the reversibility of operations, and
 (C4) recognition of invariance.
S1: At the age of 6-7 years, children have reached the concrete-operational stage
S2-4: Typical examples of C2-4 are:
 for change of perspective: (S2) coordination of different visual perspectives
 for reversibility & invariance: (S3) invariance of number wr.t. different orderings
(S4) invariance of amount of substance w.r.t. to changes in shape
I1-3: Selective tests (indicators) for the abilities in (S2-4) are:
(I1) for visual changes in perspective, Piaget’s mountain test
(I2) for invariance of number, Piaget’s number test
(I3) for invariance in the amount of a substance, Piaget’s clay ball test
P: Empirical prediction: Nearly all children fail Piaget’s tests before reaching their
sixth year, but successfully complete Piaget’s tests upon reaching their seventh year.
Predictions were confirmed when using Piaget's indicators.
Predictions were disconfirmed in replication studies using alternative indicators
43
•
(1.) Visual perception test with a 4-coloured box: mastered by 3-4 years old
children
•
(2.) Nonverbal number test: mastered by 4-5 years old children
Hypothesis of additional hidden variables/difficulties:
 Change of periphery: I1*, I2*, I3* and S1*.
•
(3.) Propositional logic: Some rules (e.g. Modus Ponens) are mastered already
with 3 years, other rules (e.g. Modus Tollens) are mastered not earlier than with 15
years, or are never fully mastered.
•
(4.) Invariance of the object: Some instances of this principle (e.g. hiding visual
objects behind a wall) are mastered already with 2 years, while other instances (e.g.
disolving sugar in water) are not mastered before an age of 8 years.
 Change of theory-core:
(C1*) The depelopment of intelligence is based on the generation of content-specific
abilities, which are first mastered only within specific domains of application, and are
then transferred to further domains of application by the operations of differentiation
and generalization (Ausubel 1978; Novak 1980).
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Theory evaluation and theory progress
Theory-history 2 
Theory history 1
( normal phase)
C1
(revol. phase)
C1
(normal phase)
C2
C2

C1V1
•
C1V2

C2V1
C2V2
A theory version TiVj is falsified if some of its empirical consequences are falsi-
fied by observation. Normally this leads to the construction of a successor theory version CiVj+1 with the same theory core.
•
A success of a theory version CiVj is an empirically well established phenomenon
which is correctly explained or predicted by CiVj.
•
A failure of CiVj is an empirically well established phenomenon P which
(a) either contradicts CiVj (in the logical or at least high-probability sense)
(b) or which contradicted the predecessor version CiVj1 of CiVj, and CiVj resulted
from CiVj1 by adding an auxiliary hypothesis H which prevents falsification of CjVi
by P and is ad hoc in historical stage CiVj (i.e., apart from avoiding the consequence
not-P, H has no independent empirical support).
•
A nonfalsified theory version TiVj is the more confirmed, the more successes
and the less failures it has.
•
It is the more disconfirmed, the less successes and the more failures it has.
45
•
A theory (core) is the more confirmed,
-- the more confirmed its actual version is,
-- the more empirical content its actual version has, and
-- the less its earlier versions had been falsified (rejected).
•
A theory (core) is the more disconfirmed,
-- the more disconfirmed its actual version is
-- the less empirical content its actual version has
-- the more earlier versions had been falsified (rejected).
Intertheoretical theory comparison and theory progress:
•
Theory version C1V1 is empirically more successful than C2V2 iff
either C1V1 has more successes than C2V2 without producing new failures,
or C1V1 has less failures than C2V2 without losing some successes,
(where the "more" and "less" is understood in the sense of set-inclusion).
•
Otherwise the comparison of C1V1 and C2V2 is ambiguous.
The transition from C1V1 to C2V2 is an empirical theory progress, iff C1V1 is
empirically more successful than C2V2.
Theory progress:
C2V2
versus
Theory complementarity:
C2V2
C1V1
successes
successes
failures
failures
C1V1
45
46
•
46
1. A theory (core) is rationally acceptable as long as it is sufficiently confirmed
and no alternative theory core is available that is significantly more confirmed.
•
2. A theory (core) is to be rationally rejected iff it is either strongly disconfimed
or there exists an alternative theory core that is significantly more confirmed.
 Allows for coexistence of competing theory cores.
 Intermediate stages possible (2 stronger than negation of 1)
Recapitulate: the confirmation of theories is (twofold) relative to:
 the current stage of observational evidence
 the current stage of alternative theories