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Please find a more recent version at:

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

Michael H.G. Hoffmann

March 31, 2007

  • 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

foundational problems i ontology
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
foundational problems ii epistemology
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?
tools for a solution i semiotics
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
tools for a solution ii pragmatism
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

tools for a solution iii semiotic pragmatism
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)
tools for a solution iv boundary critique
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)
tools for a solution iv boundary critique9
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)
tools for a solution iv boundary critique10
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.)
problems of boundary critique
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” is—like “framing,” or “sensemaking”—a 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 regress—there is no way to look at systems of selectivity from the outside
problems of problems
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
what can we do logical argument mapping lam
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 fulfilled—since 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
lam its functions
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)
lam theoretical background
LAM: Theoretical background
  • Peirce’s concept of “diagrammatic reasoning” (Hoffmann 2004, in press)
  • Vygotsky’s 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 <1958>)
  • Application-oriented approaches to logic (e.g. Luckhardt & Bechtel 1994)
  • Computer-Supported Argument Visualization (CSAV; Kirschner, Buckingham Shum, and Carr 2003)
lam the procedure
LAM: The procedure
  • Formulate a claim: the central goal of your argument, a central thesis

All maps are created with IHMC Cmap tools:

The example is based on Economist 2006

lam the procedure17
LAM: The procedure
  • Provide a reason for your claim
lam the procedure18
LAM: The procedure
  • Justify the relation between reason and claim by means of a warrant
lam the procedure19
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
lam the procedure20
LAM: The procedure

5.a) Provide further reasons for your reason

lam three essential ideas
LAM: Three essential ideas
  • By providing a justification for the relation between reason and claim in the 3. step, a crucial part of the arguer’s boundary judgments and constraints becomes visible
    • Because: A reason is a reason for a claim only if one acknowledges—at least implicitly—the 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
lam other logical forms modus tollens
LAM: Other logical forms: modus tollens

The whole example is available online. Click here

lam forms of warrants
LAM: Forms of warrants
  • The validity of those argument forms depends on the following truth-table definitions of the warrants
lam notation for its ontology
LAM: Notation for its ontology

“Ontology” refers to the content that can be represented in a map. LAM’s ontology contains the following elements:

lam evaluation criteria
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?
lam examples on the web
LAM: Examples on the web
  • Analysis of an argument about the importance of jihad (October 23, 2007, 877 KB)
  • 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)

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 <1981>). 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), 305–335.

—— (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.

Toulmin, S. E. (2003 <1958>). 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.