Pawe ozi skił Ł ńInformal logic
11/03/2008 1
Informal logic
Paweł Łoziński
Institute of Computer ScienceFaculty of Electronics and ITWarsaw Univ. of Technology
e-mail: [email protected]: http://www.ii.pw.edu.pl/~plozinsk
Pawe ozi skił Ł ńInformal logic
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Agenda
Historical background
Informal logic
Trials of informal logic formalization
Fallacies
Conclusions
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Logic
Questions that brought logic into being:
How do we reason?
How do we justify our convictions?
Logic was born as a study of (not necessarily effective) proper reasoning.
Focus on reasoning itself, not things we reason about.
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Foundations
Stephen Toulmin. The uses of argument. 1958
Arthur Hastings. A reformulation of the modes of reasoning in argumentation. 1963
Charles Hamblin. Fallacies. 1970
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,,Birth”
The 70s of the XXth century
Ralph H. Johnson, John A. Blair. Logical self-defense. 1977:
Reasoning that doesn’t feature certainty (e.g. analogy); it’s based on the content of thestatements being made.
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How do we reason?
Sample inferences:
„John says chances for rain are about 75%”,
„Allowing stem cell research is playing God”,
„Polish economy will develop similarly to Ireland's few years ago”.
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Informal logic - features
Uncertainty:
we cannot guaranty that claim inferred from true premises will be true,
we cannot guaranty that claims thought to be true won't be falsified when new facts arrive.
Dialogue is:
a method of verification claims truthfulness,
a context for evaluation of soundness of inferences.
Language dependant: validity of our reasoning depends on the words we use to express it.
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What is truth in informal logic?
We consider a claim truthful, if given the current state of knowledge the assumption that the claim is true
is more rational, than assumption that it's false.
How do we decide what is more rational?
Through dialogue.
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Premises
Argument structure(Stephen Toulmin, 1958)
Claim
Premises
Warrant Inference
Context
Premises
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Example
U.S.A. should ratify the Kyoto Protocol.
- Germany has reduced greenhouse gas emissions by 17.2% in years 1990-2004 as an effect of ratification of the Kyoto Protocol.
- U.S.A. didn't ratify the Kyoto Protocol.
Things that are generalyalike will be alike in
a given aspect. Inference
1. We accept arguments from analogy.
2. Reducing greenhouse gas emission is a good thing.
3. We accept causal relation in the case of Germany.
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Premises
Argument structure(Stephen Toulmin, 1958)
Claim
Premises
Warrant Inference
Context
Premises
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Claim
Claims can be contradictory on 4 different levels:
level of fact,
level of definition,
level of value,
level of policy.
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Premises
Argument structure(Stephen Toulmin, 1958)
Claim
Premises
Warrant Inference
Context
Premises
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Premises
Premise is data that critical audiences generally accept.
What can be a premise?
Objective data – statistics, experiment results, items (e.g. in a court case).
Generally accepted claims.
An opinion of a credible person (competent, trustworthy, good will, dynamic).
Claims supported by other, valid arguments.
Irrefutable premises don't exist.
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Premises
Argument structure(Stephen Toulmin, 1958)
Claim
Premises
Warrant Inference
Context
Premises
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Rules of inference (argumentation schemes – D. Walton, 1996)
Argument from generalization
Argument form causal relation
Argument from sign
Argument from analogy
.......
....
..
.
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Rules of inference,argument from sign
Warrant: X and Y are likely to coincide.
Often link phenomena from different realms:
„Avoiding eye contact is a sign of insincerely”
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Rules of inference,argument from analogy
Warrant: things that are generally alike will be alike in a given aspect.
Analogy types:
literal (e.g. „Berlin is like London because ...”),
figurative (e.g „Abandoning your studies in order to earn money is like trading an axe for a stick”).
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Premises
Argument structure(Stephen Toulmin, 1958)
Claim
Premises
Warrant Inference
Context
Premises
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Arguments context
A set of presupposed claims (cultural, ethical, social, ...)
Dialogue
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Dialogue
We use uncertain rules of inference, how do we decide whether we are right or wrong?
By testing our claims through process of questions and answers – dialogue.
Examples of dialogues:
everyday discourse,
court trials,
Plato's dialogues.
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Dialogue
Presumption and burden of proof
Commitments
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Dialogue types (D. Walton, E. Krabbe, 1995)
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Dialogue
Dialogue stages:
opening stage (specifying the type and rules of the dialogue)
locution rules
dialogue rules
commitment rules
win-loss rules
confrontation stage (specifying what's the controversy)
argumentation stage (the main part...)
closing stage (deciding what is the outcome of the dialogue)
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Terms related to informal logic
Argumentation theorymodelling argument's internal structure (e.g. Toulmin)
classifying rules of inference (argumentation schemes),
classifying fallacies.
Dialogue theory
researching general rules that govern dialogues,
researching that makes a productive dialogue.
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Formalization trials
If you can formalize something, you can implement it...
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Logic – definition
Ordered triple of:
language – {chair, red, Birds fly, ...}
semantics – horse Andiamo
inference mechanism – if ... than ...
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In case of informal logic
language – natural language,
semantics – relation between the natural language and the reality,
inference mechanism – arguments.
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What is truth in „formalized” informal logic?
We consider a claim truthful, ifthere exists a winning strategy
in a formal dialogue game where truthfulness of the claim is at stake.
This makes informal logic an instance of dialogue logic (Paul Lorenzen)
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Formal argumentation systems
Argumentation Framework (P. Dung, 1995)
, where:
is a set of arguments,
is a relation of attacking (e.g. argument a attacks b).
The main problem: What conditions does a set of arguments have to satisfy in order to be somebodies point of view?
AF=AR ,attacks
AR
attacks⊆AR×AR
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Argumentation framework
a
f
b
d
e
c
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Argumentation framework
Oriented graph G = (V, E), where:
V is a set o vertices,
E is a set o edges.
In the given example:
V = {a, b, c, d, e, f},
E = { (a,b), (a,c),
(c,a), (c,b), (c, d),
(d,e) }.
a
f
b
d
e
c
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Argumentation framework(some definitions)
A set of arguments is conflict-free if and only if there are no arguments and , such that:
Argument is acceptable with respect to if and only if every argument that attacks is attacked by an argument in .
A conflict-free set is admissible if and only if is acceptable with respect to .
Characteristic function is defined as follows:
a∈S , b∈S , a attacksb
S⊆ARba
S⊆ARaa
S
S⊆ARS
S
F AF S ={a∈AR: a is acceptable wrt S }
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Argumentation framework(some points of view)
A naive point of view is a set of arguments is a maximal acceptable set of arguments.
A sceptical point of view is a minimal set of arguments such that . F AF S =SS
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Argumentation framework(developments)
The relation of support
a
f
b
d
e
c
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Argumentation framework(developments)
More general relation of attacking
a
f
b
d
e
c
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Formal dialogue systems
Prakken's framework (H. Prakken, 2005)
Presupposes existance of a Dung's Argumentation Framework
Comprises of elements:
topic language,
communication language,
protocol,
outcome (win-loss) rules,
commitment rules.
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Prakken's framework(communication language)
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Prakken's framework(PROLOG implementation)
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Fallacies
Argumentum ad hominem (personal attack)
Argumentum ad baculum (resorting to force)
Argumentum ad verecundiam (argument from „modesty”)
bad usage of an argument from expert's opinion.
They are not always fallacies...
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Conclusions
Informal logic is supposed to describe human way of reasoning where:
arguments are inference mechanisms,
dialogue is a method for evaluating claims.
There are formalization trials, but:
its a relatively young and unexplored discipline,
its hard to create objective descriptions of it's components, and therefore hard to formalize.