Transcript Diagramming Arguments

DIAGRAMMING
ARGUMENTS
Introduction to Logic
PARAPHRASING & DIAGRAMMING

Recall the 12 strategies for paraphrasing:
1.
Use premise- and conclusion-indicators
2.
Clearly answer the question-and-answer test
3.
Use common argument forms
4.
Balance faith and charity
5.
Add important hidden argument-parts, including contextual clues
6.
Order propositions in an intuitive manner
7.
Simplify the language of the original text
8.
Eliminate irrelevant propositions
9.
Provide uniformity of terms and language
10. Identify independent and dependent premises
11. Identify arguments within arguments (intermediate conclusions)
12. Identify the different inferential roles a proposition plays
DIAGRAMMING
 Arguments can be analysed, once recognised, by paraphrasing them or
by diagramming them
 Paraphrasing involves
 Setting forth the argument in a clear and precise form in language
 Diagramming involves
 Laying out the structure of the argument in two-dimensional spatial relations
 Premise and conclusion are numbered and arranged to identify the
relations of support between propositions
COMPLEX ARGUMENTS
 Some arguments are exceedingly complex
 Involve several intertwined arguments
 To understand a complex argument
 You must examine the author’s intent and capture the flow of reasoning
 Problems of reasoning are effective ways to strengthen reasoning skills
EXERCISES IN DIAGRAMMING
 Text
 Axel probably will have heart problems in the future because his family
history indicates a high incidence of heart disease; he is overweight and
has high blood pressure, and drinks one large bottle of Vodka per day
and these characteristics have been associated with heart attacks.
 Task
 Number all the propositions in the order in which they appear and circle each
number
 Use arrows between the circled numbers to construct a diagram of the relations of
premises and conclusions without having to restate them
 A conclusion always appears in the space below the premises that give it support
NUMBERING
 1. Axel probably will have heart problems in the future
 2. Because his family has history of high incidence of heart disease
 3. He is overweight and has high blood pressure,
 4. And drinks one large bottle of Vodka per day
 5. And these characteristics have been associated with heart attacks.
DIAGRAM
2
3
5
1
4
ALTERNATE DIAGRAMME
3
4
2
5
1
EXERCISES
 Many adults wish they could have their noses fixed for research has
shown that 45% of all adult persons do not like the shape of their nose.
 Task
 Number
 Use arrows
 Place conclusion
SOLUTION
2
1
EXERCISES: MORE COMPLEX
 Slash cannot come to the Party because his motorcycle is in the shop
for repairs. Axel cannot come to the Party because he has an
appointment with a Tatoo artist. I did not invite the other members of
Guns n’ Roses to the Party. So no member of Guns n’ Roses will come
to the Party.
NUMBER
 1. Slash cannot come to the Party
 2. Because his motorcycle is in the shop for repairs
 3. Axel cannot come to the Party
 4. Because he has an appointment with a Tatoo artist
 5. I did not invite the other members of Guns n’ Roses to the Party.
 6. So no member of Guns n’ Roses will come to the Party.
SOLUTION
2
4
1
3
6
5
EXPLANATION
 1. Slash cannot come to the Party
 2. Because his motorcycle is in the shop for repairs
 The above two premises constitute an argument:
 Premise: Because his motorcycle is in the shop for repairs
 Conclusion: Slash cannot come to the Party
 The same analysis applies to Axel
 Proposition 5 is a horizontal coordinate premise that further supports
the conclusion
ARGUMENTS WITHIN ARGUMENTS
 Often the premises that justify the main conclusion of a passage are
controversial, and thus need their own justification.
 Ex. (1) Humans are inherently selfish. (2) Socialism ignores this basic fact of
human nature, and thus (3) leads to economic inefficiency and (4) civil
unrest.
 Obviously, additional arguments can provide this justification:
 (5) Few individuals would voluntarily offer their money and belongings to
aid those they do not know. (6) This is especially true of people with limited
means. Since (7) our prehistoric ancestors lived more modestly than many
of the poorest people of today, it appears that (1) selfishness is part and
parcel of human nature.
 As a result, there will be arguments within arguments.
 Since (1) determines the plausibility of (3) and (4) (the main conclusions)
and the argument involving (5)-(7) determines the plausibility of (1), it
follows that (5)-(7) determine the plausibility of (3) and (4). Thus, (1) is an
intermediate conclusion in the argument.
AN EXPANDED VERSION OF THIS
EXAMPLE
 (1) Humans are inherently selfish. (2) Socialism ignores this basic fact of human




nature, and thus (3) leads to economic inefficiency and (4) civil unrest.
(5) Few individuals would voluntarily offer their money and belongings to aid
those they do not know. (6) This is especially true of people with limited
means. Since (7) our prehistoric ancestors lived more modestly than many of
the poorest people of today, it appears that (1) selfishness is part and parcel of
human nature.
(8) Socialism is the doctrine that resources should be distributed according to
need. (9) It does not require the people possessing the resources to know the
people who need them, and (10) such a requirement is practically impossible
for any significant population. As a result (2) it takes for granted that people
can overcome their selfish impulses.
(11) Any political-economic system that ignores human nature is bound to
make people unhappy. (12) Unhappy citizens tend to cause political unrest.
[Therefore (4)].
Furthermore, (13) if a person’s earnings are going to be given to someone else,
as they would be in socialism, then there will be no incentive for her to work
her hardest. As a result, (3) socialism causes economic inefficiency.
HOW TO DIAGRAM INTERMEDIATE
CONCLUSIONS
5
6
7
Selfish human nature
1
8
9
10
Socialism ignores
13
2
11
12
Civil unrest
Inefficient
3
4
OTHER DIAGRAMMATIC RELATIONS

A proposition can serve as:
An independent premise in 2+ arguments
A dependent premise in 2+ arguments
A dependent premise in some arguments; independent premise in
others—Is this right?
4. A conclusion in 2+ arguments
5. An independent premise in some argument + a conclusion in others
(one kind of intermediate conclusion)
6. A dependent premise in some arguments + a conclusion in others
(another kind of intermediate conclusion)
1.
2.
3.


Can you diagram these?
See if you can make the proposition “Abortion is immoral” play
all of these roles.
INFERENTIAL ROLES
 If you know all of the ways in which a proposition operates as a premise
and as a conclusion, you understand its inferential roles.
 A popular view: understanding a proposition just is grasping all of its
different inferential roles.
EXERCISE 2
 Democratic laws generally tend to promote the
welfare of the greatest possible number; for they
emanate from the majority of citizens, who are subject
to error, but who cannot have an interest opposed to
their own advantage. The laws of an aristocracy tend,
on the contrary, to concentrate the wealth and power
in the hands of the minority. It may therefore be
asserted, as a general proposition, that the purpose of a
democracy in its legislation is more useful to humanity
than that of an aristocracy.
PARAPHRASE OF EXERCISE 2
Argument A
1.
Democratic laws are established by a majority of the citizens.
2.
If a law is established by the majority of the citizens, then it cannot be
opposed to their own advantage.
3.
Democratic laws cannot be opposed to the majority’s advantage.
Argument B
4.
Aristocratic laws are established by a minority.
5.
If a law is established by a minority of the citizens, then it can be opposed to
a majority of citizens’ own advantage.
6.
Aristocratic laws can be opposed to the majority’s advantage.
Argument C
3, 6
7.
If something cannot be opposed to the majority’s advantage, it is more useful
to humanity than something that can be opposed to the majority’s advantage.
8.
Democratic laws are more useful to humanity than aristocratic laws.
DIAGRAM OF EXERCISE 2
1
2
4
5
Aristocracy
Democracy
3
7
Useful to
Humanity
8
6
EXERCISE 4
 Nothing is demonstrable unless the contrary implies a contradiction.
Nothing that is distinctly conceivable implies a contradiction.Whatever
we conceive as existent, we can also conceive as nonexistent. There is
no being, therefore, whose non-existence implies a contradiction.
Consequently, there is no being whose existence is demonstrable.
PARAPHRASE OF EXERCISE 4
Argument A

(6) If something exists, then it is conceivable as existent.

(3*) If something is conceivable as existent, then it is also conceivable as nonexistent.

(7) Any non-existent conceivable thing is a conceivable thing.

(2*) If something is conceivable, then it does not imply a contradiction.

 (4*) If something exists, then its non-existence does not imply a contradiction.
Argument B

(4*) If something exists, then its non-existence does not imply a contradiction.

(8) The contrary of an existent thing is its non-existence.

(1**) If something’s contrary does not imply a contradiction, then it is not
demonstrable.

 (5*) If something exists, then its existence is not demonstrable.
DIAGRAM OF EXERCISE 4
6
3*
7
2*
Existence has a noncontradictory contrary
8
4*
1**
Existence is not
demonstrable
5*
EXERCISE 1 (ADDITIONAL)
 A question arises: whether it is better [for a prince] to be loved than
feared or feared than loved. One should wish to be both, but because it
is difficult to unite them in one person, it is much safer to be feared
than loved, when of the two, one must be dispensed with. Because this
is to be asserted in general of men, that they are ungrateful, fickle, false,
cowards, covetous…and the prince who, relying entirely on their
promises, has neglected other precautions, is ruined, because friendships
that are obtained by payments may indeed be earned but they are not
secured, and in time of need cannot be relied upon. Men have less
scruple in offending one who is beloved than one who is feared, for love
is preserved by the link of obligation which, owing to the baseness of
men, is broken at every opportunity for their advantage; but fear
preserves you by a dread of punishment which never fails.
PARAPHRASE OF EXERCISE 1
Argument A
1.
Humans are base creatures.
2.
Base creatures are more likely to break promises made
to a person they love than to a person they fear.
3.
If people are likely to break promises with a prince, and
he relies entirely on their promises, then he is ruined.
4.
 A prince who is only loved and relies entirely on the
promises of others is ruined.
Argument B
4
5.
People can rarely be both feared and loved.
6.
 If a prince can be only feared or only loved, then it is
better for him to be feared than to be loved.
DIAGRAM OF EXERCISE 1
1
2
3
4
5
6