CS 100 - Week 11 Lecture 2 - 11-1-12
continuing Chapter 7,
talking more about summarizing arguments by writing
them in standard logical form
(which is called standardization)
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review: what do we mean by standard logical form?
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An argument is said to be in this form when:
* each step/statement in the paraphrased argument
is numbered consecutively.
1. Blah
2. Blah
...
* premises are stated above the conclusions
they are claimed to support -- for example,
1. Premise
2. Conclusion
1. Premise
2. Premise
3. sub-conclusion
4. Premise
5. Conclusion
* justifications are provided for each conclusion
in the argument, and at least a main overall conclusion is
included
* if a premise or conclusion is implied but not explicitly
stated, include it in the standard logical form,
surrounded by square brackets
1. Premise
2. [Implied premise]
3. Premise
4. Conclusion
1. Premise
2. Premise
3. [Implied conclusion]
* for each conclusion or subconclusion, indicate in
parentheses which previous parts of the argument
the conclusion or subconclusion is claimed to
follow from
1. Premise
2. Conclusion (from 1)
1. Premise
2. Premise
3. sub-conclusion (from 1, 2)
4. Premise
5. Conclusion (from 2, 3, 4)
1. Premise
2. Premise
3. Blah, blah (from 1, 2)
1. Premise
2. [Implied premise]
3. Premise
4. Conclusion (from 1, 2, 3)
1. Premise
2. Premise
3. [Implied conclusion] (from 1, 2)
* in summarizing an argument in standard logical
form, you can and should paraphrase, omit
non-statements and irrelevant statements, and
provide missing premises and conclusions;
suggested steps for standardizing an argument
(summarizing an argument by converting it into
standard logical form)
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1. Read through the argument carefully and try to identify
its main conclusion (it may only be implied)
Once you have identified the main conclusion, go through
and try to identify major premises and subconclusions
offered in support of the main conclusion.
Paraphrase as needed to clarify meaning.
...notice that this means trying to achieve accuracy, clarity,
conciseness, and charity as discussed earlier,
can mean "converting" hard-to-tell-are-statements statements
(like rhetorical questions, ought imperatives) as
more straightforward statements
2. Omit any unnecessary or irrelevant material.
Focus only on the key points of the argument;
omit non-statements,
omit statements that provide little or no direct support to the
main conclusion (or to a sub-conclusion that is trying to
support the main conclusion)
3. Order the steps you've come up, in "correct" logical order
(premises before the conclusion they are supporting), and
then number them,
being sure to state the main conclusion last
4. Fill in any key (implied) missing premises or conclusions.
(You might have found these earlier... but double-check one
more time.)
Don't worry about everything that may be implied --
concentrate on missing premises or conclusions in understanding
and evaluating that central argument.
...and whenever you find such implied premises or conclusions,
place square brackets around them.
5. add parenthetical justifications for each conclusion in the
argument
(from num, num, ... )
(that is, in parentheses, after each conclusion or subconclusion,
put the number(s) of the previous lines in the argument that
this conclusion or subconclusion is claimed to directly follow from
EXAMPLE...
"We can see something only after it has happened. Y'know what I mean? Future
events, however, have not yet happened. So, seeing a future event seems to
imply both that it has and has not happened, and that's logically impossible."
X. We can see something only after it has happened.
X. Future events have not yet happened.
X. So, seeing a future events seems to imply both that it has and has not
happened.
X. It is logically impossible for an event to both have happened and not
to have happened.
...but as you look over this, there is an implied conclusion missing --
X. [Therefore, it is logically impossible to see a future event.]
...add in the parenthesized support bits, and the result is this
argument in standard logical form:
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1. We can see something only after it has happened.
2. Future events have not yet happened.
3. So, seeing a future events seems to imply both that it has and has not
happened. (from 1,2)
4. It is logically impossible for an event to both have happened and not
to have happened.
5. [Therefore, it is logically impossible to see a future event.] (from 3, 4)
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So, the clicker question example argument:
Stop smoking! Don't you know it is bad for your health?
...could be reasonably expressed in standard logical form as:
1. Smoking is bad for your health.
2. Therefore, you should stop smoking. (from 1)
Common mistakes to avoid in standardizing arguments:
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1. Don't write in incomplete sentences.
for the above argument, you wouldn't want:
<avoid this!>>>> 1. Because smoking is bad for your health.
<instead, use a complete sentence> 1. Smoking is bad for your health.
2. Don't include more than one statement per line.
<avoid this!>>>> 1. Stop smoking, because it is bad for your health.
...this is 2 statements, so should be 2 numbered items
(remember that a conditional statement is a single statement,
as is an either-or statement)
3. Don't include anything that is not a statement,
and don't be afraid to paraphrase something into more-obviously-a-statement
form
4. Don't include anything that is not a premise or a conclusion.
(that is, don't include irrelevant statements,
don't include statements that are not relevant to the main
conclusion or one of its supported sub-conclusions)
argument:
Greetings, members of the community and esteemed visitors. Let's cut
right to the chase here. The president should resign, since he no
longer enjoys the confidence of the board of trustees.
1. The president no longer has the confidence of the board of trustees.
2. So, the president should resign. (from 1)