An Introduction to Models of Reasoning

©2004 Edward G. Rozycki, Ed. D.

edited 4/20/14
See related article: Doing Ethics



Part A: The Toulmin Model of Argument

The Syllogism

The Enthymeme

Exercises for Part A

Part B: Enhanced Structures of Rebuttal

Questions Relating to Rebuttals


Part A: The Toulmin Model of Argument

Reasoning has both a general and a particular aspect. Reasoning about, say, ethics, rather than economics, can be understood to be not so much a matter of form as of content. To illustrate the general form of a reasoning interaction we will begin with the model developed by Stephen Toulmin. It specifies the parts of an argument in a dialogic encounter. These are: (the arrows indicate "supports" if the item is positive +, or "undermines" if the item is negative -)

a. The Claim (Proposal) Statement (with Qualifiers): C, Q.

b. Evidence (Data) supporting Claim, E.

c. Warrant(s) connecting evidence to claim, W.

d. Backing (if needed) for warrants, B. **

e. Rebuttal(s), R.


Ethical reasoning, for example, uses what discussants generally recognize as the appropriate kind of evidence, warrant and backing and is subject to the appropriate kind of rebuttal. Consider the following dialogue between John, a school principal, and Sam, a teacher, -- the parts are labeled in brackets:

John: We should suspend (Q) Johnny. [C]

Sam: Why do you think that?

John: He hit Billy [E]. You can't let anyone hit another without punishment. [W]. We don't have the resources to provide some other type of response for as many students as we have in this school [B]**.

Sam: Perhaps there are mitigating circumstances that save Johnny from punishment in this case. [R].

Now, each item might be questioned as to whether or not it is true. A false component will undermine an argument. However, it may not make the form of reasoning less valid. It is very important to distinguish between whether an argument is

a. valid; or

b. sound.

Valid arguments have the appropriate form. Sound arguments are valid arguments that contain no falsehoods. An argument may be valid and unsound; or, valid and sound; or, invalid. We will see that if the argument is invalid, it does not matter that it is composed of truths.


** For more examples of Backing, e.g. assumptions and presuppostions, click here.

The Syllogism.

This distinction is easiest to see if we strip Toulmin's model down to its more classical form, called a syllogism.A syllogism strips the inner argument out of context and reduces it to

            1. A major premise (served by the Warrant)

            2. A minor premise (served by the Evidence) and

            3. A conclusion (served by the Claim)

John's argument when converted into the form of a syllogism is thus:

Major Premise: You can't let anyone hit another without punishment.

Minor Premises: Johnny hit Billy. Suspension is a punishment. Therefore,

Conclusion: Johnny should be suspended..

A clearly unsound argument that is valid is this:

1) Johnny is a part-time circus clown, (C), since he likes to eat corned beef (E). Only part-time circus clowns like to eat corned beef (W).

Another valid but unsound argument is this:

2) Johnny either is the principal of this school, or he is President of the United States. Johnny is not the principal of this school. Therefore he is President of the United States.

But the other side of this is that an argument may be composed entirely of facts (or what is accepted as fact) and still be invalid. Consider this example:

3) George Washington was elected the first American president. He never visited China. No one who had visited China during the 18th Century was ever elected President of the United States.

Another example is this:

4) Pineapples were not eaten in colonial British frontier settlements. We have no evidence that Iroquois tribespeople during the 18th Century ate pineapples. Consequently, we can deduce that Iroquois tribespeople did not live in British frontier settlements.

For a more intensive development of the use of syllogism to examine informal argument see
Hidden Logic HiddenLogic.html
and also,
Critiquing an Argument CritiqueQ%26D.html


The Enthymeme

One last distinction. Sometimes a premise goes unspoken. So we might find argument 4 above stated merely as:

Iroquois tribespeople did not live in British frontier settlements, since we have no evidence that they ate pineapples.

What is left out is the connection between (the warrant or major premise) living in British frontier settlements, and being a member of the Iroquois.


Exercises for Part A

For each of the discussions or paragraphs below, identify 1) the parts of the argument using Toulmin's model and 2) the syllogism (or enthymeme) embedded in it.

1. ___

Sam: Al Capone was a thief and murderer.

Sharon: The only thing he was ever convicted of was income tax evasion.

Sam: Yes, but we know from confessions by his associates that he ordered such crimes.

2. In an atmosphere of unbridled hope for the future and a public committed to the belief in progress, college founding committees would not restrain their ambitions within considerations of finance and risk. So it was that hundreds of ill-fated colleges were established in antebellum 19th Century America.

3. ___

Sam: Early American colleges were violent places. Just consider the Harvard food riots.

Sharon: Yes, particularly since such things didn't make the newspapers.

Sam: What can you expect when the students were not permitted to have electives?

4. The German model of the university, de-emphasizing teaching and exaggerating scholarship, would eventually generate a form of highly articulated professionalism among the faculty that could not be cost-effective in promoting teaching excellence as it would be conceived of in the later 20th Century. Better a professor neglect teaching than publishing. It is the kiss of death at many universities in the United States for an untenured professor to receive a MacArthur Award for Excellence in Teaching.

5. ___

Sam: Making concessions to parents because they threaten a law suit is a bad practice. Look at how school budgets have expanded for often useless accommodations.

Sharon: But what about the risk of incurring higher losses by fighting such suits?

Sam: Everything has some aspect of risk. Why assume the worst possible outcome without reckoning in its probability of occurrence?

PART B: Enhanced Structures of Rebuttal

We compare the Toulmin model with the syllogism and with three models that specify more exactly the nature of the rebuttal.



Casual Discourse



CCC[2] Rebuttals

AC[3] Rebuttals

HC&B[4] Rebuttals















contradiction meaning








Reasons for:


Data (Evidence)

Minor Premise





Major Premise








Reasons against



I. Rebuttals attack (or deny) claims, recommendations or reasons. They can be constructed as negatives of Reasons For. Conversely, considering possible rebuttals and negating them may yield a useable warrant.

II. The reasoning structure is "fractal," that is, it any subpart can be analyzed on the pattern of the whole. Thus any reason supporting (opposing) a claim may be treated as a claim in its own right requiring its own evidence, warrants and bases.

III. CCC, AC and HC&B are all aimed at rebuttal but tend to focus on different structures.

Questions Relating to Rebuttals

The list of questions below can be used to generate rebuttals to arguments depending on the assumptions made. See the articles associated with each list (given in the endnotes).

List A: Cue, Concern, Control
Potential Rebuttals

1. Significance of indicator variance: What unexpected change -- or stasis -- indicates a problem?

2. Indicator relevance: What does this change (or stasis) mean?

3. Non-subversion: Might the indicator have been manipulated to deceive us? Is there any reason to believe this has happened?

4. Interest: Why is the situation indicated of concern? Whose while is it worth to intervene?

5. Non-naturalness: Can we assume that intervention will not make things worse?

6. Practicality: Will the benefits of intervention outweigh its costs? Need they?

7. Liability: Who will suffer if we forego intervention?

8. Innocence: Do the potential sufferers merit their predicament? If so, does this matter?

9. Obligation: On what principle are we obliged to act?

10. Optimality: Is this course of action the best alternative?

List B: Analyzing Controversy
Potential Rebuttals


1. Can you state the apparent controversy as a yes-no question?

2. Are there representatives for both sides of the issue?

Content Analysis: Problems of Understanding (slogans, reifications, definitions, pseudo-solutions, name-calling, presuppositions.)

3. What are the critical terms upon which this controversy hinges?

a. Give the definitions on which there seems to be consensus.

b. Are there other problems of understanding?

Content Analysis: Problems of Fact (feelings; authority, operationalizing, inquiry blockers)

4. What are the issues of fact underlying this controversy?

a. What sources of fact (authorities) are recognized by both parties?

b. Are there other issues relating to fact that need clarification?

Content Analysis: Problems of Value (fact & value, benefits & costs, responsibility)

5. What issues of value are there which relate to this controversy?

Meta-analysis: (logical errors, problems with consensus, commitments to a special theory of society, agendas maintaining conflict)

6. Are there metaproblems?

List C: Huck, Courmier & Bounds
Potential Rebuttals

1. Are the dependent and independent variables accurately described?

2. Are the procedures for measurement clearly defined?

3. Are the instruments used reliable and appropriate ?

4. Is there any interaction of history and treatment effects?

5. Are data accurately transcribed ?

6. Are appropriate statistical procedures being employed?

7. Is there any interaction of time of measurement and treatment ?

8. Does any pretest/posttest sensitization occur as a result of measurement?

9. Do "Hawthorne" effects account for any research results?

10. Has "novelty effect" contaminated research results?

11. Has the "Rosenthal" effect introduced alternative explanations?


[1] See for example, "What is the Toulmin Model?"

[2] Rozycki, Rationales for Intervention (2001) See

[3] Clabaugh & Rozycki, Analyzing Controversy (1999) See

[4] Huck, S.W., Courmier, W.H. & BoundsW.G. (1974) See