Scientific reasoning: A philosophical toolkit
(OL350)
Tiago de Lima
2nd semester 2007/2008
Organizational details
Scientific
reasoning
Eight two-hours lectures.
Course
overview
Material: slides (http://home.tm.tue.nl/tlima) and
copies.
Evaluation: written exam.
Lectures on Wednesdays at 13:30, MA1.43.
Class of 16 April will be replaced with 11 June at 13:30.
Presence not compulsory, but slides are not made for
self-study.
Consultation by appointment: IPO 2.05.
Contact by e-mail: [email protected].
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Theme
Scientific
reasoning
Course
overview
This course is about tools to evaluate arguments in
everyday life and in science.
Example 1:
If a man has a son, he is a father. This man is
a father, so he has a son.
Example 2:
The human-induced greenhouse effect exists,
because climate data show a sharp increase in
average temperature after 1900.
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Topics
Scientific
reasoning
Course
overview
1
Argumentation theory.
1
2
3
2
Formal logic.
1
2
3
3
The structure of arguments.
Types of arguments and critical questions.
Fallacies.
Propositional logic: paraphrases.
Propositional logic: control.
Predicate logic and beyond.
Scientific reasoning.
1
2
Deduction, induction and traditional methodology.
A contemporary approach: Bayesianism.
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The toolkit
Scientific
reasoning
Course
overview
Why so many different topics?
This course is best compared to a toolkit containing
different devices.
Some serves different purposes, such as a hammer and
a screwdriver.
Some differ in precision, such as a chain saw and a
hand saw.
Which tool you must choose depends on the goal and
precision you want to attain: you can choose more or
less wisely.
The same goes for these critical tools: nothing serves all
purposes, everything serves some purpose, and there
are some purposes for which there are no tools yet.
You only master the tools if you can apply them and
know when (not) to apply them.
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Example of precision
Scientific
reasoning
Course
overview
Some fish have lungs, because if all fish would
have gills and a heart, no fish would have lungs;
and some whales have a heart but no gills.
Argumentation scheme:
P1 + P2
C
Propositional logic:
(G ∧ H) → ¬L, Q |= L
Predicate logic:
∀x((Fx ∧ ∃y∃z(Gxy ∧ Hxz)) → ¬∃x(Fx ∧ ∃yLxy))
∃x(W x ∧ ∃y(Hxy ∧ ¬∃zGxz))
∃x(Fx ∧ ∃yLxy)
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Scientific
reasoning
The structure
of arguments
Part I
Argumentation theory
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Outline
Scientific
reasoning
The structure
of arguments
We start with a coarse, but generally usable tool:
constructing argumentation schemes.
By means of these schemes, you can make clear “how
an argument fits together.”
This is a first, often crucial step for evaluation.
It is also a small step beyond your intuitions.
All tools covered in this course support or extend your
intuitions. Only very few have counterintuitive results –
and those are mostly bad for the tool.
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What is an argument?
Scientific
reasoning
The structure
of arguments
Arguments, opinions, and explanations.
Opinions: can be formed with or without evidence.
Explanations: attempt to show how it came to be that a
fact is the way it is.
Argument: a set of claims put forward as offering
support for a further claim.
Example of explanation:
The window had been shut all summer and the
weather was hot and damp. So the room smelled
awfully musty when he returned.
Example of argument:
There are no international police. It takes police to
thoroughly enforce the law. Therefore, international
law cannot be thoroughly enforced.
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What is an argument?
Scientific
reasoning
The structure
of arguments
The backbone of every argumentative text is that a
couple of (sets of) statements are given in support of a
statement, or set of statements.
The supporting statements are called “premises”; the
supported statement is called the “conclusion”.
The support relation is (sometimes) indicated with
words like “so”, “because”, “therefore”, etc.
This basic structure allows many variations, such as:
chains of premises,
multiple conclusions from the same premises,
multiple premises for one conclusion,
refutation of the denial of the conclusion.
Argumentation schemes map these structural elements.
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Truth, validity, and soundness
Scientific
reasoning
The structure
of arguments
In a good argument, the premises “support” the
conclusion. But this can mean two things:
The premises entail the conclusion.
The premises are true.
Many tools (logic!) only concern the first meaning:
validity.
An argument is logically valid if and only if, when the
premises are true, the conclusion cannot be false. This
does not say that the premises are true!
A valid argument with true premises is called “sound”.
N.B.: Statements can be true or false, arguments
cannot.
Exercise: give an example of a valid argument with a
false conclusion. What do you know about the
premises?
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Simple argumentations
Scientific
reasoning
The structure
of arguments
In (the most) simple arguments, one premise is given
for one conclusion.
Example:
The number 987654321 is divisible by 3 (C)
because the sum of the digits is divisible by 3
(P).
Notation:
P
C
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Chain arguments
Scientific
reasoning
The structure
of arguments
Many texts contain chains of simple arguments.
Example:
I cannot help you (C) because I need to go to
my mother (P1), because my washing machine
is broken (P2).
Notation:
P1
P2
C
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Parallel arguments
Scientific
reasoning
The structure
of arguments
In other texts, premises are given that independently
support a conclusion.
Signal words: “moreover”, “also”.
Example:
You cannot have seen Peter in class yesterday
(C), because Peter was at his girlfriend’s (P1)
and yesterday was a Sunday (P2).
Notation:
P1, P2
C
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Combination arguments
Scientific
reasoning
The structure
of arguments
Slightly more complex (and frequent) are arguments in
which the premises together support the conclusion.
N.B.: There are no typical signal words to indicate
combination.
Example:
We had to eat out (C), because we had no food
at home (P1) and the shops were closed (P2).
Notation:
P1 + P2
C
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How to construct a scheme?
Scientific
reasoning
The structure
of arguments
Some general rules for constructing argumentation schemes
are:
1
Start by identifying the conclusion.
2
Search for signal words (“so”, “furthermore”, “in
addition”, “firstly ... secondly...”).
3
Find the premises by backtracking from the conclusion.
4
Try to represent the text as faithfully as possible.
5
Be complete, but do not add (hidden) premises unless
you really think you should.
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If-then statements
Scientific
reasoning
The structure
of arguments
Constructing argumentation schemes seems simple,
but there are many pitfalls and ambiguities.
One common mistake (especially if you know some
logic) is to represent if-then statements as a simple
argument.
In general, this is incorrect: an if-then statement is a
single statement, not a conclusion supported by a
premise.
The speaker/writer does not state the antecedent
(if-clause) as a statement!
Example:
If I want to catch my train, I need to leave now.
So I will leave now.
This is actually a combination argument, with a hidden
premise: “I want to catch my train”.
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Exercise 1
Scientific
reasoning
The structure
of arguments
A good team player is able to cooperate with others
(P1). Someone who wants all the credit himself
cannot cooperate with others (P2). A very
competitive person will not be a good team player
(P3). So we see that the quality of team sports is
not increased by promoting a competitive attitude
(C).
How are P1, P2 and P3 related to the conclusion? Do they
form a chain, a combination, or a parallel argument? And
how do you decide on the “correct” representation?
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Exercise 2
Scientific
reasoning
The structure
of arguments
Construct a scheme for the following argument by Gorgias
(a sophist living around 400 b.C.):
Nothing exists. For if there would be anything, it
would either be eternal, or it would have come into
existence. But it cannot have come into existence,
because it cannot have come from being, nor from
non-being. And it cannot be eternal, because if it
would be eternal, it would have to be infinite. But
the infinite is impossible, because it could be
neither in itself nor in something else. So it would
have to be nowhere, and what is nowhere is
nothing.
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