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Pawe ozi ski łŁ ń Informal logic 11/03/2008 1 Informal logic Paweł Łoziński Institute of Computer Science Faculty of Electronics and IT Warsaw Univ. of Technology e-mail: [email protected] www: http://www.ii.pw.edu.pl/~plozinsk

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  • 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

    mailto:[email protected]

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 2

    Agenda

    Historical background

    Informal logic

    Trials of informal logic formalization

    Fallacies

    Conclusions

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 3

    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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 4

    Foundations

    Stephen Toulmin. The uses of argument. 1958

    Arthur Hastings. A reformulation of the modes of reasoning in argumentation. 1963

    Charles Hamblin. Fallacies. 1970

  • Pawe ozi skił Ł ńInformal logic

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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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 6

    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”.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 7

    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.

  • Pawe ozi skił Ł ńInformal logic

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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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 9

    Premises

    Argument structure(Stephen Toulmin, 1958)

    Claim

    Premises

    Warrant Inference

    Context

    Premises

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 10

    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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 11

    Premises

    Argument structure(Stephen Toulmin, 1958)

    Claim

    Premises

    Warrant Inference

    Context

    Premises

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 12

    Claim

    Claims can be contradictory on 4 different levels:

    level of fact,

    level of definition,

    level of value,

    level of policy.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 13

    Premises

    Argument structure(Stephen Toulmin, 1958)

    Claim

    Premises

    Warrant Inference

    Context

    Premises

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 14

    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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 15

    Premises

    Argument structure(Stephen Toulmin, 1958)

    Claim

    Premises

    Warrant Inference

    Context

    Premises

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 16

    Rules of inference (argumentation schemes – D. Walton, 1996)

    Argument from generalization

    Argument form causal relation

    Argument from sign

    Argument from analogy

    .......

    ....

    ..

    .

  • Pawe ozi skił Ł ńInformal logic

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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”

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 18

    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”).

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 19

    Premises

    Argument structure(Stephen Toulmin, 1958)

    Claim

    Premises

    Warrant Inference

    Context

    Premises

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 20

    Arguments context

    A set of presupposed claims (cultural, ethical, social, ...)

    Dialogue

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 21

    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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 22

    Dialogue

    Presumption and burden of proof

    Commitments

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 23

    Dialogue types (D. Walton, E. Krabbe, 1995)

  • Pawe ozi skił Ł ńInformal logic

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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)

  • Pawe ozi skił Ł ńInformal logic

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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.

  • Pawe ozi skił Ł ńInformal logic

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    Formalization trials

    If you can formalize something, you can implement it...

  • Pawe ozi skił Ł ńInformal logic

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    Logic – definition

    Ordered triple of:

    language – {chair, red, Birds fly, ...}

    semantics – horse Andiamo

    inference mechanism – if ... than ...

  • Pawe ozi skił Ł ńInformal logic

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    In case of informal logic

    language – natural language,

    semantics – relation between the natural language and the reality,

    inference mechanism – arguments.

  • Pawe ozi skił Ł ńInformal logic

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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)

  • Pawe ozi skił Ł ńInformal logic

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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

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 31

    Argumentation framework

    a

    f

    b

    d

    e

    c

  • Pawe ozi skił Ł ńInformal logic

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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

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 33

    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 }

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 34

    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

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 35

    Argumentation framework(developments)

    The relation of support

    a

    f

    b

    d

    e

    c

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 36

    Argumentation framework(developments)

    More general relation of attacking

    a

    f

    b

    d

    e

    c

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 37

    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.

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 38

    Prakken's framework(communication language)

  • Pawe ozi skił Ł ńInformal logic

    11/03/2008 39

    Prakken's framework(PROLOG implementation)

  • Pawe ozi skił Ł ńInformal logic

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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...

  • Pawe ozi skił Ł ńInformal logic

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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.