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Title: Logical Argument Mapping (LAM): A tool for problem solving, argumentation, deliberation, and conflict management


1
Logical Argument Mapping (LAM)A tool for
problem solving, argumentation, deliberation, and
conflict management
Please find a more recent version
at http//www.prism.gatech.edu/mh327/argument-ma
pping_111.ppt
  • Michael H.G. Hoffmann

michael.hoffmann_at_pubpolicy.gatech.edu
March 31, 2007
2
Overview
  • Foundational Problems Ontology and epistemology
  • Tools for a solution Semiotics, pragmatism, and
    boundary critique
  • Problems of boundary critique
  • Problems of problems
  • What can we do? Logical Argument Mapping (LAM)
  • LAM Its functions
  • LAM Theoretical background
  • LAM The procedure
  • LAM Three essential ideas
  • LAM Other logical forms
  • LAM Summary of important, valid argument forms
  • LAM Notation for its ontology
  • LAM Evaluation criteria
  • LAM Examples on the web
  • References

michael.hoffmann_at_pubpolicy.gatech.edu
3
Foundational Problems I Ontology
  • Whatever we are talking or thinking about, it is
    about something (to on the being in Greek)
  • Two fundamental problems of ontology
  • how to grasp a world in flux that is full of
    complexity, interdependencies, and without clear
    boundaries and structure?
  • how to bridge the gap between what exists and
    the languages, both natural and artificial, for
    talking and reasoning about what exists? (Sowa
    2001)
  • Since we can comprehend what exists only so far
    as our cognitive abilities go, there is no
    ontology without epistemology

4
Foundational Problems II Epistemology
  • Epistemology focuses on three questions
  • How to justify knowledge claims?
  • How to explain the creation of knowledge?
  • What are the conditions for the possibility of
    knowledge and the creation of knowledge?
  • Its fundamental problem is Since everything can
    be represented in an infinite number of different
    ways, what is an adequate representation?

5
Tools for a solution I Semiotics
  • Semiotics is the theory of signs and
    representation systems
  • Since there is no knowledge, no thinking, no
    communication without signs and representation
    systems, there is no ontology and epistemology
    without a semiotic foundation

6
Tools for a solution II Pragmatism
  • Pragmatism is, first of all, a theory of meaning
  • While traditional approaches to meaning define
    the meaning of a sign either by
  • its extension (the set of objects signified by
    a sign) or
  • by its intension (i.e. a definition that refers
    to other signs),
  • pragmatism defines it by its usage

7
Tools for a solution III Semiotic pragmatism
  • Semiotic pragmatism in the tradition of Charles
    S. Peirce claims that defining the meaning of a
    sign by its usage depends on interpretation
  • The set of acceptable interpretations is
    constrained by a community of sign users
  • Therefore,
  • the meaning of signs is relative to social and
    cultural communities, and evolves over time
  • also epistemology and ontology are always
    relative to time and lifeworlds (Habermas)

8
Tools for a solution IV Boundary critique
  • Boundary critique is a concept developed by
    Werner Ulrich
  • It refers to the epistemological relevance of
    boundary judgments
  • The idea is that both the meaning and the
    validity of practical propositions (eg solution
    proposals or evaluations) depend on assumptions
    about what facts (observations) and norms
    (valuations) are to be considered relevant and
    what others are to be ignored or considered less
    important. I call these assumptions boundary
    judgements, for they define the boundaries of
    the reference system to which a proposition
    refers and for which it is valid. (Ulrich 2003,
    p. 333)

9
Tools for a solution IV Boundary critique
  • No argument can be completely rational in the
    sense of justifying all the assumptions on which
    it depends as well as all the consequences it may
    have. What ought to count as knowledge, that is,
    as relevant circumstances, facts and evidence
    that should be considered? And what counts as
    relevant concerns, that is, value judgments
    concerning purposes, measures of success and
    other criteria of evaluation (norms)? Whose
    facts and whose concerns should they represent?
    Ultimately, there is no single right way to
    decide such questions. Yet at some point
    argumentation has to end and practical action has
    to begin. Boundary judgments define the
    boundaries of argumentation (Ulrich 2001, p. 91)

10
Tools for a solution IV Boundary critique
  • analyzes how any claim about facts or values is
    conditioned by boundary judgments
  • shows how facts and values change when boundary
    judgments are modified
  • assumes that observations, evaluations, and
    boundary judgments form an interdependent system
    of selectivity
  • analyzes the practical implications of
    selectivity how it may affect all the parties
    concerned (Ulrich 2003, p. 333f.)

11
Problems of boundary critique
  • Boundary judgments are not always explicit
  • From an epistemological point of view, boundary
    judgments are mostly implicit judgments, i.e.
    they are invisible and unconscious
  • From a cognitive point of view, bounding
    islike framing, or sensemakinga basic
    cognitive process it determines how we interpret
    the world around us
  • All this means Any attempt to critique
    boundary judgments is itself determined by the
    same mechanisms it analyzes
  • This leads to an infinite regressthere is no way
    to look at systems of selectivity from the
    outside

12
Problems of problems
  • Remember Whenever we are talking about
    something, we are facing the two ontological
    problems
  • how to capture a world in flux that is full of
    complexity, interdependencies, and without clear
    boundaries and structure?
  • how to bridge the gap between what exists and
    the languages for talking and reasoning about
    what exists? (Sowa 2001)
  • Since any talk about something is additionally
    constrained by the selectivity of boundary
    setting, we get problems of problems

13
What can we do? Logical Argument Mapping (LAM)
  • The infinite regress, and the fact that bounding
    determines our thinking on each level of
    analysis, is problematic only if we try to
    describe what is going on in these processes
  • Any description carries with it a pretense of
    objectivity that can never be fulfilledsince
    bounding selectivity is inevitable
  • The solution Not description, but a step-by-step
    process of visualizing bounding conditions that
    must be performed by the involved parties
    themselves

14
LAM Its functions
  • Heuristic function
  • visualizing boundary judgments and constraints
  • clarifying vague thinking and implicit
    assumptions
  • stimulating creativity, the discovery of
    alternative perspectives, and experimenting with
    representations
  • visualizing implications and problems of our
    assumptions and possible contradictions among
    them
  • challenging critical thinking and
    self-reflexivity
  • Social function
  • coordinating different problem representations
    and boundary judgments
  • stimulating negotiation of meanings and
    argumentation
  • connecting expertise
  • promoting mutual understanding by visualizing
    implicit assumptions and boundary constraints
    (Hoffmann 2005)

15
LAM Theoretical background
  • Peirces concept of diagrammatic reasoning
    (Hoffmann 2004, in press)
  • Vygotskys idea of semiotic mediation the main
    function of signs is to regulate both social
    interaction and our own thinking (Seeger 2005)
  • Toulmin-model of argumentation argumentation as
    procedure working with graphs (Toulmin 2003
    lt1958gt)
  • Application-oriented approaches to logic (e.g.
    Luckhardt Bechtel 1994)
  • Computer-Supported Argument Visualization (CSAV
    Kirschner, Buckingham Shum, and Carr 2003)

16
LAM The procedure
  1. Formulate a claim the central goal of your
    argument, a central thesis

All maps are created with IHMC Cmap tools
http//cmap.ihmc.us/
The example is based on Economist 2006
17
LAM The procedure
  1. Provide a reason for your claim

18
LAM The procedure
  1. Justify the relation between reason and claim by
    means of a warrant

19
LAM The procedure
  • Try to refute your reason and the proposition by
    which you justified the relation between your
    reason and your claim ( warrant)
  • If necessary,
  • provide further reason(s) for your original
    reason and/or the warrant this way, your
    argument becomes an argumentation or
  • provide alternative reasons for your original
    claim, or
  • reformulate your claim and start again with step 1

20
LAM The procedure
  • 5.a) Provide further reasons for your reason

21
LAM Three essential ideas
  • By providing a justification for the relation
    between reason and claim in the 3. step, a
    crucial part of the arguers boundary judgments
    and constraints becomes visible
  • Because A reason is a reason for a claim only if
    one acknowledgesat least implicitlythe
    justifying statement
  • Therefore LAM makes boundary judgments, bounding
    constraints, and implicit assumptions visible
  • LAM motivates an ongoing process of argumentation
  • The third step transforms the argument into a
    logically valid argument (here modus ponens)
  • However, it is only a sound argument if both
    the premises are true
  • That means you have to defend two very different
    things
  • your primary reason
  • the statement that justifies the relation between
    reason and claim
  • Since everything can be doubted, you are
    challenged to provide further reasons, or to
    modify the argument
  • LAM allows to check the consistency and
    completeness of argumentations based on a
    visualization of all its elements

22
LAM Other logical forms alternative syllogism
23
LAM Other logical forms modus tollens
The whole example is available online. Click here
24
LAM Summary of important, valid argument forms
alternative syllogism
Either A or B not A (not B) ?B (A)
modus ponens
If A, then B (A, only if B A implies B) A ?B

A if and only if B A (B) (not A) (not B) ?B (A) (not B) (not A)
disjunctive syllogism
Not both A and B A (B) ? not B (not A)
conditional syllogism
If A, then B If B, then C ? If A, then C
modus tollens
If A, then B (A, only if B A implies B) not B ?not A
25
LAM Forms of warrants
  • The validity of those argument forms depends on
    the following truth-table definitions of the
    warrants

A B If A then B
T T F F T F T F T F T T
A B Not both A and B
T T F F T F T F F T T T
A B Either A or B
T T F F T F T F T T T F
A B A if and only if B
T T F F T F T F T F F T
26
LAM Notation for its ontology
Ontology refers to the content that can be
represented in a map. LAMs ontology contains the
following elements
Ontology Characteristics Function to represent
can be doubted can be refuted by one counter-example claims, data, imperatives, etc. what somebody presupposes in order to justify a certain reason for a certain claim

27
LAM Evaluation criteria
  • any relation between elements must be clearly
    specified both by connector terms (therefore,
    objects to, but, refutes, includes,
    means, supports, e.g., makes unlikely,
    defined as, etc.) and by directed arrows
  • arguments must be logically valid
  • argumentations must be as complete as possible
    if there is any element that can reasonably be
    doubted, it has to be justified by further
    reasons
  • argumentations must be consistent (i.e. no
    contradictions within your map) if you add an
    objection to any part of an argument, you have to
    indicate how to deal with it Are there further
    objections to refute the objection? Should the
    objection lead to a qualification, or
    reformulation, of the argument? Is there a
    problem you do not know how to deal with?

28
LAM Examples on the web
  • Analysis of an argument about the importance of
    jihad (October 23, 2007, 877 KB)
  • http//tinyurl.com/yuqop7
  • Searching for common ground on Hamas (March 31,
    2007 279 KB)
  • Hume on causality (March 12, 2007 2.0 MB!)
  • Regulating kidney supply (Feb 27, 2007 618 KB)
  • Middle East conflict. An Argumentation on the
    sovereignty over al-Haram al-Sharif/Temple Mount
    in Jerusalem (May 30, 2006 763 KB)

29
References
  • Economist. (2006). Organ transplants. Your part
    or mine? Iran's example, and the broader case for
    making it worthwhile to give kidneys. The
    Economist, Nov 16th.
  • Habermas, J. (1984, 1987 lt1981gt). The Theory of
    Communicative Action. Boston Beacon Press.
  • Hoffmann, M. H. G. (2004). How to Get It.
    Diagrammatic Reasoning as a Tool of Knowledge
    Development and its Pragmatic Dimension.
    Foundations of Science, 9(3), 285-305.
  • (2005). Logical argument mapping A method for
    overcoming cognitive problems of conflict
    management. International Journal of Conflict
    Management, 16(4), 305335.
  • (in press). Cognitive conditions of
    diagrammatic reasoning. Semiotica (special issue
    on "Peircean diagrammatical logic," ed. by J.
    Queiroz and F. Stjernfelt).
  • Kirschner, P. A., Shum, S. J. B., Carr, C. S.
    (Eds.). (2003). Visualizing Argumentation
    Software Tools for Collaborative and Educational
    Sense-making. London Springer.
  • Klein, M. (2003). The Jerusalem problem. The
    struggle for permanent status (H. Watzman,
    Trans.). Gainesville University Press of Florida.
  • Luckhardt, C. G., Bechtel, W. (1994). How to Do
    Things with Logic. Hillsday, NJ Lawrence Erlbaum
    Associates.
  • Peirce. (CP). Collected Papers of Charles Sanders
    Peirce. Cambridge, Mass. Harvard UP.
  • Seeger, F. (2005). Notes on a semiotically
    inspired theory of teaching and learning. In M.
    H. G. Hoffmann, J. Lenhard F. Seeger (Eds.),
    Activity and Sign - Grounding Mathematics
    Education (pp. 67-76). New York Springer.
  • Sowa, J. F. (2001). Signs, Processes, and
    Language Games. Foundations for Ontology.
    http//www.jfsowa.com/pubs/signproc.htm.
  • Toulmin, S. E. (2003 lt1958gt). The Layout of
    Arguments. In The uses of argument (Updated ed.,
    pp. 87-134). Cambridge, U.K. New York Cambridge
    University Press.
  • Ulrich, W. (2001). Critically systemic discourse
    a discursive approach to reflective practice in
    ISD (Part 2). JITTA, Journal of Information
    Technology Theory and Application, 3(3), 85-106.
  • (2003). Beyond methodology choice critical
    systems thinking as critically systemic
    discourse. Journal of the Operational Research
    Society, 54(4), 325-342.
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