Arguments & sub-arguments
Philosophy and Logic
Section 4.1
Unit 4. Analyzing Inferences
• Applied at last to real-life arguments
– ex. 4.1, 4.2, & pp. 4-23 through 4-28
• Add suppressed premises
– ex. 4.3, 4.4, p. 4-22.
• Give a technical definition
– suppressed premise, weak/strong statement/
argument, principle of charity, strawman
Constructing an argument
The dollar will fall in value against the yen, and if
the dollar falls against the yen, then the trade
deficit with Japan will get worse. So the trade
deficit with Japan will get worse.
F
F⊃W
------------------------------------W
But what if your audience does not believe that the
dollar will fall in value against the yen?
The author’s burden
• You want to persuade someone that your
main conclusion, Q is true.
• To do this generally you must dig down
until you find premises P which that person
already believes or will accept, and then
show that
(P ⊃ Q)
Author’s burden (cont.)
• If they don’t believe that the dollar will fall
against the yen (F), you must give an
argument that F.
• More generally: almost any premise might
reasonably be challenged
– If it is challenged, you should be ready with a
back-up argument for that premise.
– These “subsidiary” arguments are often given
with the “main” argument itself.
Why the dollar will fall
Treasury bill rates are going down, and if they
do, then the dollar will fall against the yen.
Hence the dollar will fall against the yen.
T
T⊃F
------------------------------------F
A more complex structure
T
T⊃F
-------------------------F
F
F⊃W
-------------------------W
A more complex structure
T
T⊃F
-------------------------F
F
F⊃W
-------------------------W
Main argument
The MAIN conclusion
A more complex structure
T
T⊃F
-------------------------F
F
F⊃W
-------------------------W
A “mini” argument
Main argument
The MAIN conclusion
A more complex structure
T
T⊃F
-------------------------F
F
F⊃W
-------------------------W
A “mini” argument
Premise F is its conclusion
Main argument
The MAIN conclusion
How to put it in words
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
Our problem: to go the other way
To go
from the words in a real-life argument
to the main and subsidiary inferences that the
passage contains.
First steps
1 Underline all of the inference indicators in
the argument.
2 Identify each of the separate statements in
the argument. Put brackets around each
one.
3 Number each statement in the argument.
1. Inference indicators
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
1. Inference indicators
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
1. Inference indicators
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
1. Inference indicators
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
1. Inference indicators
The dollar will fall in value against the yen,
since T bill rates are going down, and if
they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
Note: inference indicators. Not sentential
connectives!
2. Identify statements
The dollar will fall in value against the
yen, since T bill rates are going down, and
if they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
2. Identify statements
[The dollar will fall in value against the
yen], since T bill rates are going down, and
if they do, then the dollar falls. Now if the
dollar falls against the yen, then the trade
deficit with Japan will get worse. So the
trade deficit with Japan will get worse.
2. Identify statements
[The dollar will fall in value against the
yen], since [T bill rates are going down],
and if they do, then the dollar falls. Now if
the dollar falls against the yen, then the
trade deficit with Japan will get worse. So
the trade deficit with Japan will get worse.
2. Identify statements
[The dollar will fall in value against the
yen], since [T bill rates are going down],
and [if they do, then the dollar falls]. Now
if the dollar falls against the yen, then the
trade deficit with Japan will get worse. So
the trade deficit with Japan will get worse.
2. Identify statements
[The dollar will fall in value against the
yen], since [T bill rates are going down],
and [if they do, then the dollar falls]. Now
[if the dollar falls against the yen, then the
trade deficit with Japan will get worse]. So
the trade deficit with Japan will get worse.
2. Identify statements
[The dollar will fall in value against the
yen], since [T bill rates are going down],
and [if they do, then the dollar falls]. Now
[if the dollar falls against the yen, then the
trade deficit with Japan will get worse]. So
[the trade deficit with Japan will get worse].
What’s one statement?
• One assertion made by the author
• Hence
– “if…then…” claims should not be treated as
two separate statements.
– Ditto for “either…or…”
– But conjunctions can be split apart
3. Number the claims
[The dollar will fall in value against the
yen], since [T bill rates are going down],
and [if they do, then the dollar falls]. Now
[if the dollar falls against the yen, then the
trade deficit with Japan will get worse]. So
[the trade deficit with Japan will get worse].
3. Number the claims
[(1) The dollar will fall in value against the
yen], since [(2) T bill rates are going down],
and [(3) if they do, then the dollar falls].
Now [(4) if the dollar falls against the yen,
then the trade deficit with Japan will get
worse]. So [(5) the trade deficit with Japan
will get worse].
(2) T bill rates are going down
(3) If T bill rates go down, then the dollar falls against
the yen
---------------------------------------------------(1) The dollar will fall in value against the yen
(1) The dollar will fall in value against the yen
(4) If the dollar falls against the yen, then the trade
deficit with Japan will get worse.
------------------------------------------------(5) The trade deficit with Japan will get worse.
(2) T
(3) T ⊃ F
---------------(1) F
T bill rates go down
If they do, the dollar falls
(1) F
(4) F ⊃W
---------------(5) W
The dollar falls
If it does, trade deficit gets worse
The dollar falls
The trade deficit gets worse
Our problem, in a nutshell
• At least one of the claims is both a premise
(here, of the main argument) and a
conclusion (of a mini argument).
• It links two inferences together.
• Q: how to represent this dual role.
One possibility: write it all out!
(2) T bill rates are going down
(3) If T bill rates go down, then the dollar falls against
the yen
------------------------------(1) The dollar will fall in value against the yen
(1) The dollar will fall in value against the yen
(4) If the dollar falls against the yen, then the trade deficit
with Japan will get worse.
-------------------------------(5) The trade deficit with Japan will get worse.
The crucial steps
4 Note what the explicit indicators tell you.
Make “sub diagrams”.
5 Put the main conclusion at the bottom of the
diagram.
6 Connect all the inferences together.
7 Check the result.
4. Focus on the explicit indicators
[(1) The dollar will fall in value against the
yen], since [(2) T bill rates are going down],
and [(3) if they do, then the dollar falls].
Now [(4) if the dollar falls against the yen,
then the trade deficit with Japan will get
worse]. So [(5) the trade deficit with Japan
will get worse].
4a. Write out the indicator “schema”
[(1) The dollar will fall in value against the yen],
since [(2) T bill rates are going down], and [(3) if
they do, then the dollar falls]. Now [(4) if the
dollar falls against the yen, then the trade deficit
with Japan will get worse]. So [(5) the trade
deficit with Japan will get worse].
(1), since (2) and (3). Now (4). So (5).
4b. Make “sub-diagrams”
(1), since (2) and (3). Now (4). So (5).
– Each explicit indicator is a “flag” for an
inference.
– Each “flag” dictates an ordering among some
of the circles.
– Some of the neighbors of that flag have to be
premises, and one has to be a conclusion.
4. Make sub-diagrams
“(1), since (2) and (3)” tells us that we have
at least:
(2) T bill rates are going down
(3) If T bill rates go down, then the dollar falls
against the yen
------------------------------------(1) The dollar will fall in value against the yen
4. Make sub-diagrams
• The same inference can be represented as:
(2)
(3)
(1)
• The bracket + arrow here stands for an inference.
It means that (2) and (3) are the premises from
which (1) is claimed to follow.
4. Next sub diagram, please
“Now (4). So (5).” shows that (5) must be
a conclusion from at least (4):
(4) If the dollar falls against the yen, then the
trade deficit with Japan will get worse.
------------------------------------(5) The trade deficit with Japan will get worse.
4. Sub diagrams
“Sub diagram”:
(4)
--------------(5)
Indicates that (5) is a conclusion from (4), plus,
perhaps, other stuff
5. Identify the main conclusion
• We already know that it is (5) “The trade
deficit with Japan will get worse”.
• Note that it is the very last claim in the
passage.
• Put it at the bottom of the diagram.
6. Connect the inferences
Our sub diagrams:
(2)
(3)
(1)
(4)
-----------(5)
6. Connect the inferences
There is only one plausible structure:
(2)
(3)
(1)
(4)
(5)
7. Check your results
Look at each inference (arrow) you have
drawn. Ask: is that a reasonable way to
argue?
Is there any better way to argue, using these
claims?
Sometimes you will need to try various options.
It is not always explicit!
7. Check your results
In the example, each inference is modus
ponens. There isn’t any inference better
than that one!
Some guidelines
1 Each inference made in a passage still has exactly
one conclusion, drawn from one or more premises.
The problem is that a given passage will typically
contain several inferences.
2 Typically though the passage will have just one
MAIN conclusion. This is the “headline” that you
isolated already, in “close analysis”.
Guidelines, (cont.)
3 The MAIN conclusion should always go at the
bottom of our diagrams. The main premises, from
which it is drawn, are always exactly one layer
above it.
4 Some of those main premises are more debatable
than others, and a smart author will try to back
them up. A “mini-argument” is an argument for
one of the premises in the main argument.
Guidelines
5 Each mini-argument adds another
inferential step or inferential layer to the
structure.
You should have exactly as many layers in your
diagram as there are inferences in the passage.
6 The main goal: capture all the explicit
inferences.
Worry about the inexplicit stuff later, if at all!
The explicit inferences
• A casting is acceptable if it portrays all of
the explicit inferences which are made.
– The biggest mistake is usually: adding extra
inferences.
– If you check it , you find that this extra stuff
usually represents the author as making some
crazy inference, or arguing in an utterly
implausible way.
Guidelines on inferences
a. If you can get an inference into deductively
valid form, you can stop worrying, since there
is no way to make it better.
b.Failing deductive validity, you ought to find at
least some repeated elements among premises
and conclusion. There should be some logical
connection between premises and conclusion.
Inferences, cont.
c. Arguments generally move
– from assertions which the audience already
believes or is willing to accept, to more dubious
or controversial claims which the audience is
less likely to already accept.
– Generally you should find the least
controversial claims at the top, and the most
controversial at the bottom.
Inferences, concluded.
d.Similarly, arguments often move
– from specific instances, examples, or less
general assertions to more general assertions
which those examples or instances support.
– You should find the examples near the top, and
the generalizations down below.