The Art of Argumentation
Course Notes
Meeting 4. The limits of logic.
Formal logic has a number of weaknesses. The basic principle of deductive argument is that there
can never be a situation where the premises are true and the conclusion false. This leads, however,
to many problems.
Tom is crazy, Tom is not crazy; therefore he can't be trusted.
or worse:
Tom is crazy, Tom is not crazy; therefore my car won't start.
Obviously, A & ¬A is always false, therefore we can say A & ¬A⊢ B since the premise will
never be true.
My car will start; therefore, Tom is crazy or Tom is not crazy.
My car will start, your car is green, bats can fly; therefore an apple is an apple.
Here, since the conclusion can never be false, because it is a logical truth, any set of
premises will lead to it. Even though the premises are clearly irrelevant.
The basic principle can be changed to: the conclusion will always be true if the premises
are, which eliminates the first problem.
Another issue:
Suppose
By simplification
By addition
By simplification
Disjunctive syllogism
A & ¬A
A
AvB
¬A
B
Tommy is a cat and tommy is not a cat.
Tommy is a cat
Tommy is a cat or a dog
Tommy is not a cat
Tommy is a dog
Does A v B really mean ¬A→B?
These problems are caused by the relationship of formal logic to natural language which can be an
awkward one. 'Therefore' in natural language suggests that the premise is somehow responsible for
the conclusion, not just that the conclusion is true. Similarly, 'or' suggests a lack of knowledge over
which is correct and cannot be used when we know one to be correct. What works logically does
not always work linguistically - and we are studying language!
The other big problem is that deductive reasoning does not cover all, or perhaps even many, cases
of real world decision making.
Informal logic: inductive, abductive and presumptive reasoning.
Informal logic is the study of real-world argumentation. The types of argument which should be
allowed are controversial. For example, John Locke wrote:
Appeals that are valid because epistemologically superior: Appeal to Evidence (Induction), Appeal to Reason
(Deduction)
Appeals that are invalid because epistemologically inferior: Appeal to the Speaker’s Authority, Appeal to the Audience’s
Ignorance
But in his own arguments:
Appeals that are dialectically superior because they do not interrupt the rational and dialogic search for truth :
Appeal to an Opponent’s Premises and Conclusions (Argument-from Commitment and Personal-Attack Varieties),
Appeal to Evidence (Induction), Appeal to Reason (Deduction)
Appeals that are dialectically inferior because they do interrupt the rational and dialogic search for truth:
Appeal to Guilt-by-Association, Appeal to the Speaker’s Authority, Appeal to the Audience’s Ignorance
(Longaker 2014)
Some definitions
'In a deductively valid inference, it is impossible for the premises to be true and the
conclusion false. In an inductively strong inference, it is improbable (to some degree) that
the conclusion is false given that the premises are true. In an abductively weighty inference,
it is implausible that the premises are true and the conclusion is false. The abductive type of
inference tends to be the weakest of the three kinds. A conclusion drawn by abductive
inference is an intelligent guess. But it is still a guess, because it is tied to an incomplete
body of evidence. As new evidence comes in, the guess could be shown to be wrong.'
(Walton, 2001)
Deductive Reasoning: Suppose a bag contains only red marbles, and you take one out. You may infer by
deductive reasoning that the marble is red.
Inductive Reasoning: Suppose you do not know the color of the marbles in the bag, and you take one out and
it is red. You may infer by inductive reasoning that all the marbles in the bag are red.
Abductive Reasoning: Suppose you find a red marble in the vicinity of a bag of red marbles. You may infer
by abductive reasoning that the marble is from the bag.
(Preyer and Mans, 1999)
Another example: Fossils are found; say, remains like those of fishes, but far in the interior of the
country. To explain the phenomenon, we suppose the sea once washed over this land. This is an
hypothesis. (Pierce 1965)
Presumptive reasoning: A presumption then is something you move ahead with, for practical
purposes, even though it is not known to be true at the present time. It is a kind of useful
assumption that can be justified on practical grounds, in order to take action, for example, even
though the evidence to support it may be insufficient or inconclusive (Walton 2001).
How can we keep control of informal argumentation? How can we know if an informal - not
logically necessary - argument is a good one or not? Aren't non-deductive arguments fallacious?
Argument schemes:
There are many different kinds of arguments that are best evaluated by standards that are neither deductive
nor inductive. These types of argumentation are often equated with traditional informal fallacies. However,
in many cases of their use, they are not fallacious. In such cases, if seen as presumptive arguments, they do
have some weight as rational arguments that could be used to support a claim. Some of the best known
examples are argument from analogy, ad hominem argument [attacking the man], argument from ignorance
[we have no evidence otherwise], argument from sign [one thing indicates another], argument from
consequences [the truth will have desireable consequences], appeal to popular opinion, appeal to pity, and
appeal to expert opinion. Each of these types of argument does appear to have a recognizable form. But that
form is not, at least in the vast range of cases, either a deductively valid form of argument or an inductively
strong form of argument. In fact, they all seem to fall into the third category of arguments having some
presumptive (or perhaps abductive) weight of plausibility.
(Walton 2001)
Walton & Reed 2002
Argument from Position to Know
Major Premise: Source a is in a position to know about things in a certain subject domain S containing proposition A.
Minor Premise: a asserts that A (in Domain S) is true (false).
Conclusion: A is true (false).
Because this is not a deductive argument we should ask critical questions:
CQ1: Is a in a position to know whether A is true (false)?
CQ2: Is a an honest (trustworthy, reliable) source?
CQ3: Did a assert that A is true (false)?
Appeal to Expert Opinion
Major Premise: Source E is an expert in subject domain S containing
proposition A.
Minor Premise: E asserts that proposition A (in domain S) is true
(false).
Conclusion: A may plausibly be taken to be true (false).
1. Expertise Question: How credible is E as an expert source?
2. Field Question: Is E an expert in the field that A is in?
3. Opinion Question: What did E assert that implies A?
4. Trustworthiness Question: Is E personally reliable as a source?
5. Consistency Question: Is A consistent with what other experts assert?
6. Backup Evidence Question: Is A’s assertion based on evidence?
Appeal to modus ponens
Appeal to Popular Opinion
If a large majority (everyone, nearly everyone, etc.) accept A as true, then there exists a (defeasible) presumption in
favour of A.
A large majority accept A as true.
Therefore, there exists a presumption in favour of A.
Modus Ponens
Premises:
As a rule, if P then Q
P
Conclusion:
Q
Modus Non Excipiens
Premises:
As a rule, if P then Q
P
It is not the case that there is an exception to the rule that
if P then Q
Conclusion:
Q
If he has a good lawyer then he will be acquitted.
He has a good lawyer.
Therefore he will be acquitted
When is such an argument complete? How many critical questions can there be?
Abductive Argumentation Scheme
F is a finding or given set of facts.
E is a satisfactory explanation of F.
No alternative explanation E' given so far is as satisfactory as E.
Therefore, E is plausible, as a hypothesis.