Philosophy of Science:
Scientific Reasoning
Kristina Rolin 2012
Scientific knowledge?
Put empirical evidence
into a large mixing
bowl. Add reasoning
and rhetorical spices.
Mix and pour the
filling into a journal
paper crust. Bake until
the pie is ready for
the social practice of
epistemic justification.
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A scientific paper or monograph
should include an argument.
An argument is not the same as the table of
contents in a paper or a monograph
(introduction, background, method, data,
discussion of data, conclusion).
What is an argument?
What is a good argument?
Argument
An argument includes premises and the
conclusion (or the main thesis).
The premises provide reasons to believe
that the conclusion is true (or likely to be
true).
An argument aims to answer the
question: Why should we believe or accept
the main thesis?
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Explanation
An explanation includes an explanandum (a
description of an event or a state of affairs
that is to be explained) and the explanans (an
account that provides an explanation).
The explanans provides an account of at least
some of the causes that have led to the event
or the state of affairs to be explained.
An explanation aims to answer the question:
Why did something happen or why does a
certain state of affairs prevail?
Esimerkki
Kumpi on argumentti, kumpi selitys? Perustele
vastaus.
(A) Liisa on rikkonut kesämökin ikkunan, koska vain hänen
jalanjälkensä näkyvät lumessa.
(B) Liisa on rikkonut kesämökin ikkunan, koska hänellä ei
ollut avainta mukana, eikä se ollut tavanomaisessa
paikassa oven päällä.
Kakkuri-Knuuttila, Marja-Liisa (toim.) 1999. Argumentti ja
Kritiikki: Lukemisen, Keskustelun ja Vakuuttamisen Taidot.
Helsinki: Gaudeamus.
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Good argument?
A good argument should fulfill the following four
criteria:
(1) Premises are true or acceptable.
(2) Premises are relevant to the main thesis.
(3) There is a link between the premises and
the main thesis.
(4) The link is not undermined by further
information.
Two categories of arguments
The link between the premises and the
conclusion can be (1) binding or (2) less
than binding.
If the link is binding, the conclusion
follows from the premises (e.g., deductive
arguments).
If the link is less than binding, the
premises support the conclusion (e.g.,
inductive arguments).
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Deductive argument: an example
Premise #1: If Riitta is a student, then Riitta is
intelligent.
Premise #2: Riitta is a student.
Conclusion: Riitta is intelligent.
A deductive argument claims that if the premises
are true, then the conclusion must be true.
A semi-formal representation of
the argument
If p, then q.
p.
Therefore, q.
The argument is valid in virtue of its logical
structure. If the premises are true, then the
conclusion must be true (and this is the case for
any proposition p and q).
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Deductive argument: an example
All human beings are mortal.
Socrates is a human being.
Therefore, Socrates is mortal.
For every x it is the case that
if x is H, then x is M.
S is H.
Therefore, S is M.
Inductive argument: an example
Premise #1: Most students at the School of
Economics are from the metropolitan area.
Premise #2: Matti is a student at the School of
Economics.
The conclusion: Matti is from the metropolitan
area.
An inductive argument claims that if the premises
are true, then the conclusion is likely to be true.
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Simple inductive reasoning:
an example
Swan #1 is white,
swan #2 is white,
swan # 3 is white….
Therefore, all swans are white.
Statistical generalization: an example
x is a sample of 1000 randomly chosen Finnish
citizens.
12 % of the persons in the sample x are lefthanded.
Therefore, 12 % of all Finnish citizens are lefthanded.
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Validity in logic
An argument is valid if and only if it is
impossible for the premises to be true and the
conclusion to be false.
A valid deductive argument is necessarily
truth-preserving.
Validity is all-or-nothing type of property; it
does not come in degrees.
We can have a valid argument with false
premises and a false conclusion.
We can also have a valid argument with false
premises and a true conclusion.
Inductive arguments
In an inductive argument it is possible that the
premises are true and the conclusion is false.
Inductive arguments are not necessarily truthpreserving.
Inductive arguments come in different degrees of
strength.
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Good argument?
An argument is sound if and only if it is valid and
its premises are true.
A good argument does not need to be sound. In a
good argument, the premises are acceptable and
they provide sufficient support to the main thesis.
What counts as ”sufficient” depends on the
context.
Examples of bad arguments
Argumentum ad hominem appeals to a premise
which concerns the person who presents the
argument and which is not relevant to the
conclusion.
Petitio principii is a circular argument (“begging
the question”).
Non sequitur is an argument which gives reasons
for another conclusion than the intended one.
False dilemma includes a false premise of the
form: we have to accept either A or B.
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Scientific reasoning
The traditional debate concerns the
question of whether scientific reasoning is
deductive, inductive or both.
If one believes that scientific reasoning
includes inductive reasoning, then one has
to deal with the problem of induction.
The problem of induction
David Hume (1711-1776)
There is no deductive justification for induction and
any inductive justification for induction is circular.
We cannot justify inductive reasoning without
appealing to inductive reasoning of the form:
inductive reasoning has been reliable in the past;
therefore, it is likely to be reliable in the future.
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The new riddle of induction
Nelson Goodman (1906-1998):
Definition: X is ”grue” = x is examined before year
2020 and is found to be green, or x is not so
examined and is found to be blue.
All emeralds examined to date have been green as
well as grue. On what grounds do we believe that
emeralds examined after 2020 are green and not
grue?
Illustration
Suppose that we have a set of data points (x,y),
and we want to find a general hypothesis by fitting
a function f(x) to the data points. There is an
infinite number of different functions that fit the
data points. Which function should we prefer and
on what grounds?
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Simplicity
Is the principle of simplicity a solution to the problem?
y
x
Karl Popper’s (1902-1994)
falsificationism
Scientific reasoning is based on deductive logic,
not on inductive logic:
A general hypothesis H implies an observation
statement E.
It is not the case that E.
Therefore, it is not the case that H.
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Modus tollens
If H, then E.
Not E.
Therefore, not H.
Validity: It is not possible for the premises to be
true and the conclusion to be false.
Truth tables
The argument is valid because it is impossible for the
premises to be true and the conclusion to be false at the
same time (no T-T-F).
P
Q
P
T
T
F
F
T
F
T
F
T
F
T
T
Q
¬Q
¬P
F
T
F
T
F
F
T
T
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Fallacy: affirming the consequent
If H, then E.
E.
Therefore, H.
It is possible for the premises to be true and the
conclusion to be false.
Counter-arguments to
falsificationism: part I
In the actual practice of science, scientists often
argue that a hypothesis is to be accepted because
relevant evidence supports it (inductive
reasoning).
Moreover, scientists do not always conclude that a
theory or a hypothesis is false when they
encounter contradictory evidence.
A theory or a hypothesis is often rejected only
when there is a plausible alternative to it (Thomas
Kuhn).
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Counter-arguments to
falsificationism: part II
The holistic nature of falsification:
If (H and B1 and B2 and B3), then E.
Not E.
Therefore, it is not the case that
(H and B1 and B2 and B3).
So, what is false? H? B1? B2? B3? All of them?
Counter-arguments to
falsificationism: part III
Popper’s falsificationism does not provide grounds
to compare different unfalsified hypotheses.
Why is it rational to prefer a hypothesis which has
survived several attempts to falsify it to another
hypothesis which has not been tested yet?
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The Hypothetico-Deductive Model
Problem
Discovery
Hypothesis is
falsified.
Hypothesis
Deduction
Observable
Consequences
No
Consequences
correspond to Yes
observations?
Hypothesis
receives
support.
Living with the problem of induction
Quantitative methods enable one to conclude
that H is probably true, or H is acceptable with
a certain probability of error.
Bayesian reasoning
Error statistics
Qualitative methods in the social sciences: the
goal is to understand social phenomena in
their context, not to make generalizations.
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Abductive reasoning?
Charles S. Peirce (1839-1914):
E.
If H, then E.
Therefore, H.
Interpretation: The inquiry begins with E, not with
H. H is not a generalization; it is an attempt to
explain why E takes place.
Abductive reasoning?
Abductive “argument” is an attempt to understand
the “logic” of scientific discovery, not the “logic” of
epistemic justification.
It is not a valid deductive argument. It may be
reconstructed as an inductive argument where the
conclusion is that H is probably true.
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Summary
Criteria for a good argument:
(1) Premises are true or acceptable.
(2) Premises are relevant to the main thesis.
(3) There is a link between the premises and the
main thesis: deductive or inductive.
(4) The link is not undermined by further information.
The most challenging part to understand is (2):
the relevance of data to a hypothesis.
The problem of relevance
All swans are white.
Therefore, the next swan I observe will be
white too.
In most cases, there is a conceptual gap
between evidence and a hypothesis. One
needs to argue that a certain body of
evidence is relevant to the hypothesis.
Contextual empiricism
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Contextual empiricism
Background assumptions are required to establish
the relevance of observation reports to a
hypothesis or a theory. In most cases an observed
state of affairs in itself does not tell for what
hypothesis or theory it can be taken as evidence.
An observed state of affairs can be taken as
evidence for quite different and even conflicting
hypotheses given appropriately conflicting
background assumptions.
Longino, Helen. 1990. Science as social
knowledge: Values and objectivity in scientific
inquiry. Princeton: Princeton University Press.
Today’s message
Scientific reasoning includes both
deductive and inductive reasoning.
The so called abductive reasoning is not a
different type of reasoning on its own
right.
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