Toulmin's Structure of Arguments thomasalspaugh.org/pub/fnd/argument.html

Πρῶτον εἰπεῖν περὶ τί καὶ τίνος ἐστὶν ἡ σκέψις, ὅτι περὶ ἀπόδειξιν καὶ ἐπιστήμης ἀποδεικτικῆς.

As a start, we must say what this inquiry is about and to what subject it belongs; namely, that it is concerned with the way in which conclusions are to be established and belongs to the science of their establishment.

[Aristotle Prior Analytics, quoted in Toulmin1958-ua]

Terminology and context

14 (Page numbers refer to Toulmin+Rieke+Janik1984-ir.)

Argumentation: the process of making a claim, challenging another's claim, backing up claim, or rebutting a claim.
Reasoning: the process of presenting reasons supporting a claim.
Argument: a connected chain of claims and reasons. If the connected chain hangs together to support the claim, then the argument is sound.
Rational: describing someone who is open to argument, as opposed to deaf to argument.

The basic parts of a simple structured argument are 25:

a claim: The statement whose truth is asserted; the goal the argument is directed towards.
grounds: What is needed to support the claim.
warrant: Justification that this claim in fact follows from these grounds.
backing: Support for the validity of the warrant in the current context.

Roles in fruitful reasoning are 29:

the claimant who makes a well-defined claim, and
the interrogator who elicits information needed for him or her to be convinced of the claim.

If the claim is ambiguous (could be interpreted in more than one way), or otherwise unclear, the interrogator won't be able to be convinced. The claimant's first task is to make a clear, unambiguous claim 31.

An example dialogue of reasoning

The claimant makes a claim.
The interrogator questions whether this claim is true.
The claimant produces grounds for the claim (perhaps a single ground, perhaps several grounds).
The interrogator questions whether these grounds support the claim. After all, the grounds might not be relevant to the truth of the claim, or the grounds might not be sufficient to show the truth of the claim.
The claimant produces a warrant that the claim follows from the grounds.
The interrogator questions whether this warrant is valid. After all, the warrant might not be relevant to these grounds and claim, or the warrant might not be sufficient in the context of this argument.
The claimant produces backing for the warrant (a single backing, or several backings all supporting its validity).
The interrogator questions whether the backing supports this warrant. After all, the backing might not be relevant to the truth of this warrant, or the backing might not be sufficient to support the claimed strength of the warrant (see Qualifying the strength of an argument).

If the interrogator is still unconvinced, the claimant can present a secondary argument in support of the backing (or, earlier, the grounds) by chaining the two arguments together.

Figure 1. Initial argument 74

Figure 2. Sub-argument for ground (1) of initial argument 75

Chaining arguments together

The claimant can chain arguments to support the claim more convincingly 73:

by treating the grounds as a claim that needs to be supported, and then constructing an argument supporting it (with secondary grounds, warrant, and backing); or
by treating the backing as a claim that needs to be supported, and then constructing an argument supporting it (with secondary grounds, warrant, and backing);

Figure 1 shows an initial argument, and Figure 2 shows a sub-argument supporting Ground (1) of the initial argument. Figure 3 shows how the two arguments chain together. (All example arguments here are from Toulmin, Rieke, and Janik.)

Figure 3. Chaining sub-argument for
ground (1) to initial argument

Qualifying the strength of an argument

Figure 5. Argument with rebuttal

Figure 4. Argument with qualifier

Figure 6. An argument limited by a qualifier and three rebuttals 125

So far we have been considering only whether an argument is sound or not. If the required logical connections are present, the argument is sound; if not, the argument is unsound. There's no in between.

Figure 7. An argument limited by a qualifier and a rebuttal 125

But an argument may be sound and yet not be completely convincing. In this case, we are interested in the strength of the argument. This is typically expressed by a qualifier (Figure 4), which is an adverb or adverbial phrase like one of the following 81:

Necessarily
Certainly
Presumably
In all probability
So far as the evidence goes
For all that we can tell
Very likely
Very possibly
Maybe
Apparently
Plausibly
Seemingly

A second way an argument may be restricted in its strength is that it may only apply in certain contexts. A rebuttal gives a specific condition under which the argument is not valid (Figure 6) 95.

Note that typically the presence of a rebuttal is what causes a qualifier to be necessary.

Figures 6 and 7 show example arguments with qualifiers and rebuttals.

Argument as a guide to choosing among claims

So far we've looked at argumentation as a way of constructing and assessing an argument in favor of a specific claim. Now we will look at argumentation as a means of choosing among several alternative claims.

Suppose you need to take a convincing position on some question, or to choose among several possible positions. How might you go about it?

Choose the position which seems most promising; make that your claim.
Construct an argument supporting that claim.
Is the argument convincing?
1. No, the argument isn't convincing. Why not?
  1. The claim is correct, but your argument is not as convincing as it could be.
    1. Examine your argument's structure, find out where it is weak, strengthen it, and try again at step 3.
    2. If that doesn't seem to be helping, return to step 2 and try a different argument.
    Or...
  2. The claim is not correct (so no correctly-structured argument for it will be convincing). Return to step 1 and try again with a different claim.
    (You might look at the structure of your unconvincing arguments for help seeing how the claim might be made broader or more exact, so that a convincing argument could be made.)
2. The argument is only somewhat convincing. Now what?
  1. The claim is correct, but your argument is only somewhat as strong as it could be.
    Examine your argument's structure, find out where it is weak, strengthen it, and try again at step 3.
    
    Or...
  2. The claim is only somewhat correct, so no correctly-structured argument could make it completely convincing.
    Look at the structure of your only-somewhat-convincing arguments for help seeing how the claim might be made broader or more exact, so that a convincing argument could be made. Return to step 2 and try again with this improved claim.
3. Yes, thank goodness, the argument is convincing. Are you done?
  1. Not if another even more convincing argument exists for your claim.
    If so, figure out what that argument would be, and try again at step 3.
  2. Not if an even broader or more exact claim exists for which a more convincing argument can be made.
    If so, figure out what that claim would be, and try again at step 2.
  3. If your claim is the broadest and most exact and your argument for it is the most convincing, then you are done.
    There is no way you can be completely sure about this (it's like testing: testing can find bugs, but not show the absence of bugs). The best way seems to be to try several claims (as many as you have patience for), and for each claim try several arguments (see the steps above).

Argument as a guide to improving the thing about which you claim something

So far we've seen argument structure from the point of view of a claimant desiring to convince an interrogator of a specific claim. Now we will look at argument structure as a means of improving the the entity about which something is claimed, by changing that entity so it better supports the claim:

By revising the claim to something for which the entity supports a better argument;
By altering the entity to provide better grounds for the claim;
By altering the entity to provide grounds for which a better warrant exists;
By altering the entity to provide stronger backing for the warrant relating its grounds to the claim; or
By altering the entity in order to eliminate one or more rebuttals.

Haley, Moffett, Laney, and Nuseibeh take a similar approach for security requirements, in which they use argumentation to identify factors essential for security.

References

Charles B. Haley, Jonathan D. Moffett, Robin Laney, and Bashar Nuseibeh. "Arguing Security: Validating security requirements using structured argumentation." Symposium on Requirements Engineering for Information Security (SREIS), 2005.

Antony Flew. How to think straight. Prometheus Books, 1998.

George Lakoff and Mark Johnson. Metaphors We Live By. Univ. of Chicago Press, 2000.

Stephen Toulmin. The uses of argument. Cambridge, 1958.

Stephen Toulmin, Richard Rieke, and Allan Janik. An introduction to reasoning. Macmillan, second edition, 1984.