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Recognizing and analyzing arguments

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									      Recognizing and analyzing arguments
            a. Read: Nolt, pp. 17-23, C&C, pp. 30-37, 21-28
            b. Assignment: Nolt, p. 19, ex. 1-10; C&C, pp. 28-30, ex. 2, 6, 8

Recognizing arguments ....................................................................................................................... 1
  Arguments vs. lengthy descriptions and lengthy instructions ................................................... 1
  Recognizing premises...................................................................................................................... 2
  Other rules of thumb for recognizing arguments ....................................................................... 3
Analyzing arguments ........................................................................................................................... 5
  What you’ve learned thus far ......................................................................................................... 5
  New stuff .......................................................................................................................................... 7
    Diagramming ............................................................................................................................... 7

When trying to ascertain the logical characteristics of an argument, it’s VERY helpful to
paraphrase. In general, paraphrasing is one of the most useful intellectual exercises you can
engage in, as it’s a great way to work on both your reading and writing skills. In this course, it
provides a crucial link between the formal and technical concepts we discuss and their more
practical, real-world applications.


Recognizing arguments
Arguments vs. lengthy descriptions and lengthy instructions
Paraphrasing is an effective way of recognizing and (especially) analyzing an argument. Let’s
begin with recognition. The first thing you need to make sure of is that you’re dealing with
an argument rather than some other collection of statements. As you know, an argument
must have no more than one (ultimate) conclusion and at least one premise. Thus, if any
passage does not contain a conclusion or a premise, it cannot be an argument. One thing to
look out for is confusing lengthy descriptions with arguments, e.g.,

            When you press a key, the plunger moves down in the cylinder, compressing the
            spring. This spring is already holding the toggle away from the matrix. As the
            pressure increases, the spring becomes "unstable" and bends rapidly to form a loose
            "U" shape. This action is felt (and heard) as the "break" of the key. When the key
            breaks, the direction of the pressure on the toggle is reversed, causing it to swing
            down about 1.5mm closer to the matrix. This is detected by the keyboard logic
            circuitry as a change in capacitive potential and the appropriate scan code is sent to
            the 8088 bus, to be processed.

There is a lengthy description here, and one that even has a “sequence” to it that may seem
awfully similar to the flow from premises to conclusion, but there is no argument here.
Similarly, arguments should not be confused with lengthy instructions, e.g.,

            Place the bow tie around your neck, situating it so that end "A" is about two inches
            longer than end "B". Cross end "A" over end "B". Bring end "A" up and under the
            loop. Now double end "B" over itself to form the front base loop of the bow tie.
            Loop end "A" over the center of the loop you just formed. Holding everything in
        place, double end "A" back on itself and poke it through the loop behind the bow tie.
        Adjust the bow tie by tugging at the ends of it and straightening the center knot.

As before, there is a sequence that should not be equated with the flow from premise to
conclusion.

So what’s missing in these lengthy descriptions and instructions? The first telltale sign is that
there is no conclusion. How do we know this? There is no magic formula, but here are some
good rules of thumb:
          (A) No conclusion indicators: Certain words, like “then,” “so,” “thus,” and “therefore”
               are signposts that tell you where the conclusion is. Note that these words are
               absent from the lengthy non-arguments.
                    a. Note that it’s not enough to simply know which words are conclusion-
                        indicators—as these words often have other uses than indicating
                        conclusions. For example, if we say that, “Place the bow tie around your
                        neck, situating it so that end "A" is about two inches longer than end "B",
                        then cross end "A" over end "B",” we don’t intend “then” to be a
                        conclusion-indicator but simply a marker of temporal ordering.
          (B) The question-and-answer test: All arguments arise in response to some issue. An issue
               can always be expressed as a yes-or-no question. The conclusion is an answer to that
               question. There is no yes-or-no question that the lengthy descriptions and
               lengthy instructions would provide good answers to. (Of course, they do provide
               potential answers to other kinds of questions like “How does a keyboard work?”
               or “How do you tie a bowtie?”

One familiar consequence that follows from these remarks is that (by themselves), conditional
statements are not arguments! For example:
         If a keyboard works, then there is a change in capacitive potential.
Note that “then” is often a conclusion-indicator, but that, in this case, it is not because it is
nested in an “if…then” structure. However, conditionals like this fail miserably at the
question-and-answer test. What is the yes-or-no question that this answers? It can’t be “Is
the keyboard working?” because this conditional statement can’t tell you yes, the keyboard is
working, or no, it’s not. Ditto for “Is there a change in capacitive potential?”


Recognizing premises
So you’ve identified the issue and the conclusion of the argument. Obviously, something’s
missing—the premises! For example, here’s an argument I heard this morning:
        As an elite institution of higher learning, Columbia University should be committed
        to pursuing the truth. So they never should have invited Mahmoud Ahmedinejad to
        speak.
“So” is a conclusion-indicator. This leaves you with a pretty crude but semi-effective means
of identifying the premises—they’re everything else in the passage. This works smashingly in
this particular example, since it’s very compact and doesn’t have extraneous information.
However, look what happens with the inclusion of one more sentence:
         As an elite institution of higher learning, Columbia University should be committed
         to pursuing the truth. Mahmoud Ahmedinejad has ambitions of waging a nuclear
         Jihad on the U.S. and its allies. So Columbia never should have invited him to speak.
The key problem with this second passage is that Ahmedinejad’s nuclear ambitions are not
inherently at odds with Columbia’s pursuit of truth—indeed, it might be the case that
Columbia wants to further its pursuit of the truth by uncovering the reasons and/or causes
of his nuclear ambitions. In other words, the new information doesn’t appear to have a clear
role as a premise. Worse yet, it really obscures the role of the initial premise—should
Columbia not invite Ahmedinejad because he is antithetical to their pursuit of truth or
because of his nuclear ambitions or both?

Thus, you need to decide what to do with this new information in the second passage.
There’s no hard and fast rule here, but there are a few guidelines:
         (A) Try to be as faithful to the author’s intentions as possible. Did he/she intend this
             as a premise or was this merely an aside or tangent?
         (B) Try to be as charitable to the author as possible, i.e., try to interpret his/her
             argument that is as compelling (i.e., close to being valid) as possible without
             massively violating the faithfulness guideline.
Depending on the context, you may need to weigh one of these guidelines more heavily than
the other. For example, if you’re doing textual exegesis, faithfulness becomes paramount.
Often, however, the real issue isn’t about getting Mr. So-And-So “right,” but about what the
best position is (Mr. So-And-So may be a representative or even an exemplar of this
position, but he may also be a very clumsy proponent of that position, so you’ll need to be
VERY charitable in this case). This suggests two possible strategies:
         (1) Treat the “nuclear” proposition as a premise.
         (2) Dismiss the “nuclear” proposition as extraneous information.
Since (2) is more intuitive, let’s look at how you might pursue (1) in a legitimate manner:
         As an elite institution of higher learning, Columbia University has an obligation to
         both pursue the truth and to respect certain ethical norms, including the promotion
         of international peace. As a Holocaust denier and a person who has threatened to
         use nuclear arms against the U.S. and its allies, Ahmedinejad would appear
         antithetical to both of these norms. Therefore, Columbia University should not have
         invited him to speak.
To be sure, this isn’t a water-tight argument (e.g., would this rule out inviting any U.S.
politician who has been in favor of any war?), but as an interpretation of the arguer’s
intentions, it’s fairly charitable.


Other rules of thumb for recognizing arguments
    1) As with conclusions, there are certain words that serve as premise-indicators. In this
       example, “as” is a premise indicator. Thus, more generally, we can say that you
       should search for argument-indicators. In addition to those inference-indicators listed in
       C&C, p.31, here are some more:
             ADDITIONAL CONCLUSION-INDICATORS                          ADDITIONAL PREMISE-INDICATORS
                                in short                                                  in light of
                         which indicates that                                       as is made clear by
                      which makes it clear that                                   we may deduce from
                         we may deduce that                                  as is made highly probable by
                 which makes it highly probable that                                as is supported by
                              in summary                                             as is suggested by
                                  ergo                                            as is demonstrated by
                              we see then                                         as is made obvious by
                    which supports the view that                                          being that
                  which suggests very strongly that                                        being as
                  which leads me/us to believe that                        in the first place/first…second1
                   which bears out (the point) that                                       given that
                      which demonstrates that                                         supposing that
                      in this way, one sees that                                         seeing that
                             clearly, then                                  on the correct supposition that
                           obviously, then                                             assuming that
                        my conclusion is that                                   may be concluded from
                                                                                        as a result of
                                                                                        for example

       2) Some elements of an argument (i.e, premises or conclusions) may be implicit. Note
          that in reconstructing the second argument, I added the bit about ethical norms and
          international peace, as well as Holocaust denial. These bits of information help to
          provide a more charitable argument. An argument containing an implicit premise is
          called an enthymeme.
       3) Some elements of an argument may not be stated as declarative sentences. In the
          Columbia example, two key propositions are that Columbia is an elite institution of
          higher learning and that Ahmedinejad is a Holocaust denier and a person who
          threatens the U.S. and its allies. However, these are stated as phrases, e.g., “As an
          elite institution of higher learning, Columbia…” in the passage. We can also do the
          same thing with conclusions, e.g., “Columbia’s highly questionable invitation to
          Ahmedinejad…” Here are some variations on this theme:
               a. Rhetorical and/or loaded questions: All questions contain presuppositions. For
                   example, asking “How many Intro to Logic students did their homework on
                   Tuesday?” presupposes that there is an Intro to Logic class with students in it
                   and that some homework was due in Intro to Logic. Of course, some
                   questions make stronger presuppositions than others. To choose a famous
                   example from the law, “Have you beaten your wife recently?” presupposes
                   that the answerer has beaten his wife. (Consider that if the person answered
                   “No,” this would not imply that he had not beaten his wife, only that he has
                   not beaten his wife recently).
               b. Commands/imperatives: Commands are of the form, “Do action A.” Note that
                   it makes very little sense to say that, “It is true that do action A.” (Nor can
                   you say, “It is false that do action A.”) Thus, it cannot be a proposition.
                   However, there is a very simple formula for translating commands into
                   propositions. Simply take the imperative, “Do action A” and replace it with
                   “Person S should do action A.” Depending on the context, person S may be
                   a specific person, e.g., “Khalifa should challenge his students” or it may be a
                   general claim, e.g., “Everyone should be rational,” or somewhere in between,

1
    These typically arise in contexts where the author is listing independent reasons/arguments.
               “Every teacher should challenge his/her students.” The point is, all of these
               translated sentences are easily understood as propositions, e.g., “It is true [or
               false] that person S should do action A.”
          c. Phrases: Some phrases, particularly when nested in a complex sentence, are
               propositions. For example, “Given Bush’s growing unpopularity, Republican
               candidates’ distancing themselves from the White House is understandable”
               contains two propositions, expressed in the phrases, “Bush’s growing
               unpopularity” and “Republican candidates’ distancing themselves from the
               White House.” As before, it’s nonsensical to say, “It is true [or false] that
               Bush’s growing unpopularity,” etc. Thus, the phrases must be translated:
               Bush’s unpopularity is growing, and Republican candidates are distancing themselves from
               the White House.
   4) Use context and background information to identify the issue, conclusion, and premise(s). Often
      there are no inference-indicators, but context helps to identify the premises and
      conclusions, helping especially to:
          a. Make vague terms, elliptical terms, and pronouns more transparent and
               precise; and
          b. Using connotations and additional information to indicate what is at issue.


Analyzing arguments
So, you’ve discerned whether or not the passage you’re dealing with is an argument, and in
the process, have identified the issue, conclusion, and premises. Next, you should figure out
how the premises support the conclusion, i.e., what kind of argument the author is
presenting. This constitutes the analysis of the argument.


What you’ve learned thus far
You’ve already armed yourself with a nice arsenal of tools for analyzing arguments. Here
they are in all their glory.
    A) Obey Weston’s Rules. Especially important to any analysis are:
             1) Distinguish premises from conclusions
             2) Present your ideas in a natural order
             3) Be concrete and concise
             4) Avoid loaded language
             5) Use consistent terms
             6) Stick to one meaning for each term
    These rules help to make your analysis as clean as possible, and facilitate any subsequent
    criticism of the argument.

   B) It’s useful to present arguments in standard form, i.e.,
      Premise 1
      Premise 2
      …
      Premise n.
       Conclusion
This helps to make the reasoning of the argument more transparent than it would be
otherwise.

C) Look for your old friends. Additionally, you know that the argument can take one of the
     following forms:
              1) Argument by example
              2) Argument by analogy
              3) Argument by authority
              4) Causal argument
              5) Deductive argument
                       i. Modus ponens
                      ii. Modus tollens
                     iii. Disjunctive syllogism
                     iv. Hypothetical syllogism
                      v. Dilemma
                     vi. Reductio ad absurdum
While there are other forms of good argument, many arguments fit it into one of these
cubbyholes. (Several of the other forms of good argument are just complex
combinations or more specialized cases of these ten types of arguments). For this reason,
it’s a really good idea to look at my handout on Types of Arguments and memorize
those argument forms, making sure you can identify these forms in different contexts.

D) Look for your old enemies. Given the principle of charity mentioned above, it’s a good
   idea to try to interpret the passage as an example of a good argument. However, the
   principle of faithfulness also requires that you capture the author’s reasoning as
   closely as possible, and there’s always the possibility that the author is not reasoning
   well. You’ve also learned some of the most common mistakes or fallacies that people
   succumb to:
       (1) Generalizing from incomplete information
       (2) Ad hominem
       (3) Appeal to ignorance
       (4) Appeal to pity
       (5) Appeal to popularity
       (6) Affirming the consequent
       (7) Begging the question
       (8) Complex question
       (9) Denying the antecedent
       (10) Equivocation
       (11) False cause
       (12) False dilemma
       (13) Loaded language
       (14) Non sequitur
       (15) “Person who” argument
       (16) Persuasive definition
       (17) Poisoning the well
       (18) Post hoc, ergo propter hoc
       (19) Straw man
        Keep an eye out for these guys as well. But remember, charity dictates that if you can
        interpret someone’s argument as a good argument rather than a fallacy, go for
        goodness. This is especially true when there’s a separate Criticism stage in your
        reading process. As you might guess, it’s also a good idea to internalize the ideas on
        my Fallacies handout.


New stuff
Diagramming
There’s also a few new tricks that emerge from diagramming arguments. Here they are:
   A) Independent versus dependent premises. Sometimes, there is one, tightly interconnected
        argument for a conclusion, in which any individual premise by itself would not
        provide a good reason to accept the conclusion, but when that premise is combined
        with all of the other premises in the argument, the combination is quite compelling.
        We call these dependent premises. For example:
                        (1) Anyone under 18 is not allowed on the premises.
                        (2) Sally is under 18.
                        (3)  Sally is not allowed on the premises.
        Now if it were the case that (1) is true and (2) is false, i.e., anyone under 18 is not
        allowed on the premises but Sally is over 18, then this would be a bad argument.
        Similarly, if (1) were false and (2) were true, i.e., people under 18 are allowed on the
        premises and Sally is under 18, then this would also be a bad argument. Thus, (1) and
        (2) depend on each other if they are to support (3). Pictorially, we represent dependent
        premises in the following manner:
                                                  |(1)(2)|

                                                   (3)
        In contrast, our earlier argument might run as follows.
               ARGUMENT A:
               (1) Columbia is an elite institution of higher learning.
               (2) Elite institutions of higher learning should pursue the truth.
               (3) If someone is a Holocaust denier, then he is opposed to the pursuit of
                    truth.
               (4) Ahmedinejad is a Holocaust denier.
               (5)  Columbia should not invite Ahmedinejad to speak.

                ARGUMENT B:
                (1) Columbia is an elite institution of higher learning.
                (6) Elite institutions of higher learning should promote international peace.
                (7) If someone threatens nuclear attacks on the U.S. and its allies, then he
                    does not promote international peace.
                (8) Ahmedinejad threatened nuclear attacks on the U.S. and its allies.
                (5)  Columbia should not invite Ahmedinejad to speak.
        Premises (2)-(4) and (6)-(8) provide independent reasons for accepting (5) as a
        conclusion, since regardless of whether or not Columbia is committed to promoting
        international peace, if it is committed to pursuing truth, ARGUMENT A would be
       an argument for (5). Analogously, if Columbia is not committed to pursuing truth,
       ARGUMENT B would be an argument for (5). We represent independent premises
       in the following manner:
                                              (1)    (2)

                                                     (3)

       For the Columbia argument, we diagram it as follows:
                                |(1)(2)(3)(4)| |(1)(6)(7)(8)|


                                                 (5)
       Here, the left cluster of number propositions corresponds to ARGUMENT A while
       the right corresponds to ARGUMENT B.

   B) Intermediate and ultimate conclusions. Earlier, we said that there should be no more than
      one (ultimate) conclusion and at least one premise in any argument. What do we
      mean by an ultimate conclusion? Certain propositions may be conclusions to one
      argument but then serve as premises in a larger or subsequent argument, these are
      often called intermediate conclusions. It’s important that you recognize the larger
      argument of which they’re a part or else you’ll lose the forest for the trees. For
      example, we might break apart ARGUMENT A above in the following manner:

       ARGUMENT C:
       1) All elite institutions of higher learning are committed to the pursuit of truth.
       2) Columbia University is an elite institution of higher learning.
        3) Columbia University is committed to the pursuit of truth.

       ARGUMENT D:
       4) If someone is a Holocaust denier, then he is not committed to the pursuit of truth.
       5) Ahmedinejad is a Holocaust denier.
        6) Ahmedinejad is not committed to the pursuit of truth.

       ARGUMENT E:
       7) If an institution is committed to the pursuit of truth, then it should not invite
       anyone not committed to the pursuit of truth to speak.
       2) Columbia University is committed to the pursuit of truth.
       6) Ahmedinejad is not committed to the pursuit of truth.
        8) Columbia should not invite Ahmedinejad to speak.

Thus, (3) is the conclusion of ARGUMENT C, (6) is the conclusion of ARGUMENT D,
and both are premises of ARGUMENT E. Therefore, (3) and (6) are intermediate conclusions
and 8), the conclusion of ARGUMENT E, is the ultimate conclusion. A simple intermediate
conclusion structure might look like this:
                                               (1)

                                               (2)

                                              (3)
Where (2) is an intermediate, and (3) an ultimate conclusion. Our own monster, involving
ARGUMENTS C, D, and E, looks like this.

                                    |(1)(2)|         |(4)(5)|

                                      |(3)     (7)     (6)|

                                               (8)


RAC-ing it up: Six Magic Questions, Ten Rules of Thumb, and
Other Curiosities
Combining the various ideas from the semester thus far, there is a set of SIX QUESTIONS
that will help you in reading, writing, and thinking in a wide variety of contexts. Whenever
you read or hear something, ask yourself the following:
A) Recognizing an argument
             1) What is the issue? What is the main question that the author is attempting
                 to answer? Make sure that the question is of the yes-or-no variety, i.e., it
                 should not be a why-, how-, when-, where-, or what-question.
                       i. This isn’t to say that no reasoning or argumentation goes into these
                           other kinds of questions, only that framing the question in yes-or-no
                           terms facilitates paraphrasing, and thus understanding the passage.
                      ii. SAMPLE ISSUE: Should Columbia University invite Mahmoud
                           Ahmedinejad to speak?
             2) What is the conclusion? How does the author answer the question he/she
                 raises as the issue? While identifying the issue involves identifying a question,
                 identifying the conclusion involves identifying and being able to state a
                 proposition, in the form of a declarative sentence. While the answer to the
                 issue/question can be most directly stated in yes or no terms, spell out the
                 whole sentence. Here you should look for the ultimate conclusion, the
                 intermediate conclusion(s) will arise when you analyze the argument.
                       i. ISSUE: Should Columbia University invite Mahmoud Ahmedinejad
                           to speak?
                      ii. CONCLUSION: Columbia should not invite Mahmoud
                           Ahmedinejad to speak.
             3) What are the premises? How does the author support the conclusion she
                 asserts? At this point, it suffices to list the premises, though you can take
                 certain preemptive steps to facilitate analysis and criticism, e.g., inserting
                 implicit premises, simplifying language, and imposing uniformity upon your
                 terminology.
B. Analyzing an argument
          4) How do the premises support the conclusion? At this point, you’ve got
              all the raw data—the premises and the conclusion—but you’ve still got to
              figure out how it all hangs together. If you’re asked to diagram, it comes
              here; the heart of the paraphrase also comes here. Assembling our list of
              slogans from above, we get the following 10 RULES OF THUMB for a
              good paraphrase:
                     i. A good paraphrase should be faithful to the author’s intentions;
                    ii. A good paraphrase should be charitable to the argument being offered,
                        trying its best to make the argument valid or at least inductively
                        strong, and, wherever possible, trying its best to not render the
                        reasoning fallacious;
                   iii. A good paraphrase should list the premises in an order which makes
                        the structure of the argument clear, minimally in standard form;
                   iv. A good paraphrase should simplify the language of the original text, by
                        trading out more elliptical and counterintuitive language for more
                        concrete and concise language;
                    v. A good paraphrase should eliminate irrelevant propositions. A proposition
                        is irrelevant if it is neither a premise nor a conclusion of an argument;
                   vi. A good paraphrase should provide uniformity of terms and language;
                  vii. A good paraphrase should state hidden premises (enthymemes);
                 viii. A good paraphrase should use conclusion- and premise-indicators in
                        abundance. See above for a list of these indicators;
                   ix. A good paraphrase should identify intermediate conclusions wherever
                        they are to be found;
                    x. A good paraphrase should differentiate independent and dependent
                        premises wherever they are to be found.
              You should definitely paraphrase before your diagram.

C. Criticizing an argument
            5) Is the argument valid? If you’ve done a good job paraphrasing, then you
               should put yourself in a good position to see whether or not the argument is
               valid. Recall the single most important concept in the class:
                     i. Deductive validity is the property of an argument such that if all
                        of the premises are true, then the conclusion is necessarily true.
               Thus, an argument is invalid if it is possible that its premises are true and its
               conclusion is false. This is where you would construct a counterexample,
               which you will recall has three conditions:
                    ii. A counterexample must affirm the premises of the argument.
                   iii. A counterexample must deny the conclusion of the argument.
                   iv. A counterexample should explain how the premises can be true when
                        the conclusion is false. I then provided you with three rules of
                        thumb for constructing an effective explanation for a
                        counterexample:
                            1. The explanation need not true; only conceivable, i.e., not
                                yielding in a contradiction.
                            2. An explanation that is closer to reality is usually more
                                effective than one that requires big leaps in imagination.
                            3. An explanation that is closer to the premises is usually more
                                effective than one that requires a long detour from the
                                premises.
                I also provided you with a general schema for framing a counterexample in
                plain English:
                     v. Suppose that [INSERT ANSWER TO HOW POSSIBLE
                        QUESTION HERE]. Then it could still be the case that [AFFIRM
                        PREMISES HERE], but nevertheless [DENY CONCLUSION HERE].


               Finally, you have general strategies for generating counterexamples for the
               most common kinds of invalid arguments there are:
                   vi. Bad inductive arguments: search for “Defeaters” as specified in the
                        “Types of Arguments” handout I gave you;
                  vii. Fallacies: use the “Tips for Rebutting” in the “Fallacies” handout I
                        gave you.
            6) Are the premises true? At long last, we come to our last magic question,
               fledgling logicians. As I’ve said before, logic can’t help you as much with this,
               as there are empirical issues that go beyond logic alone. That being said,
               sometimes the best way to illustrate that a premise is false is either:
                     i. To provide an argument for its contrary; or
                           1. Ex. Apply the following to our earlier argument:
                                If elite institutions of higher learning were obligated to
                                promote peace, then they should not have played an active
                                role in the development of nuclear weapons.
                                Elite institutions played an active role in the development of
                                nuclear weapons.
                                 Elite institutions of higher learning are not obligated to
                                promote peace.
                    ii. To show that the best argument that supports it is invalid.
                           1. Ex. Apply the following to our earlier argument:
                                An institution should not contradict its commitments with its
                                actions.
                                 If an institution is committed to the pursuit of truth, it
                                should not invite someone who is not so committed to speak.
                                Counterexample: Suppose that an institution is committed to
                                pursuing the truth by discovering the true motivations of a
                                person’s false beliefs, and that the only way to do so is to see
                                what he says and how he responds to certain questions. Then
                                it could still be the case that the institution does not
                                contradict its commitments with its actions, as it remains
                                committed to pursuing the truth even though it should invite
                                a speaker who is not so committed.

Assignment:
Nolt, p. 19, ex. 1-10;
    1. Uranium is heavier than iron, because gold is heavier than iron and uranium
        is heavier than gold.
Gold is heavier than iron.
If uranium is heavier than gold, uranium is heavier than iron.
Uranium is heavier than gold.
 Uranium is heavier than iron.

    2. Since anyone under 18 is a juvenile and juveniles are not allowed on the
         premises, Sally is not allowed on the premises.
Anyone under 18 is a juvenile.
No juveniles are allowed on the premises.
Sally is under 18.
 Sally is not allowed on the premises.

     3. If there is a storm warning, the siren sounds. So there is no storm warning,
        since the siren is not sounding.
If there is a storm warning, the siren sounds.
The siren is not sounding.
 There is no storm warning.

    4. Savage could not have been the thief. The thief was over six feet tall. But
        Savage is only 5’8”.
If someone is the thief, then he/she is over six feet tall.
Savage is only 5’8”.
If someone is only 5’8”, then he/she is not over six feet tall.
 Savage could not have been the thief.

  5. We went to Indianapolis; then we went to Chicago.
NOT AN ARGUMENT.

    6. The water froze, and when water freezes the temperature must be at or below
        zero degrees Celsius.
If water freezes, then the temperature must be at or below zero degrees Celsius.
The water froze.
 The temperature must be at or below zero degrees Celsius.
NB: This one might be interpreted as a non-argument.

     7. Different cultures have different conceptions of rationality. Hence rationality
         itself takes many forms, for what a culture conceives as rational is rational for
         that culture.
Different cultures have different conceptions of rationality.
If a culture has a conception of rationality, then the form of rationality, so-conceived, exists.
 There are many different forms of rationality.

    8. Alice has a National Rifle Association sticker on her windshield. It is likely
       therefore, that she opposes gun control.
If someone has an NRA sticker on his/her windshield, then it is likely that he/she opposes
gun control.
Alice has an NRA sticker on her windshield.
 It is likely that Alice opposes gun control.

    9. Because all things other than pleasure are valued only for the pleasure they
        produce, but pleasure is valued for its own sake, only pleasure is intrinsically
        valuable. For a thing is intrinsically valuable if and only if it is valued for its
        own sake.
A thing is intrinsically valuable if and only if it is valued for its own sake.
All things other than pleasure are valued only for the pleasure they produce.
Pleasure is valued for its own sake.
 Only pleasure is intrinsically valuable.

     10. I lied because I was afraid you would hate me if I told the truth.
If I do not tell the truth, then I lie.
If I tell the truth, then I should be afraid that you will hate me.
I should not be afraid that you will hate me.
 I lied.

NB: This one might also be construed as a non-argument or an exceedingly bad argument.

C&C, pp. 28-30, ex. 2, 6, 8
  2) Why decry the wealth gap? First, inequality is correlated with political
       instability. Second, inequality is correlated with violent crime. Third,
       economic inequality is correlated with reduced life expectancy. A fourth
       reason? Simple justice. There is no moral justification for chief executives
       being paid hundreds of times more than ordinary employees.
What is the issue? Should the wealth gap be decried?
What is the conclusion? (1) The wealth gap should be decried.
What are the premises?
  (2) A wealth gap is correlated with political instability.
  (3) If a wealth gap is correlated with political instability, then it should be decried.
  (4) A wealth gap is correlated with violent crime.
  (5) If a wealth gap is correlated with violent crime, then it should be decried.
  (6) A wealth gap is correlated with reduced life expectancy.
  (7) If a wealth gap is correlated with reduced life expectancy, then it should be decried.
  (8) A wealth gap is unjust.
  (9) If a wealth gap is unjust, it should be decried.
  (10)          If there is no moral justification for something, then it is unjust.
  (11)          There is no moral justification for a wealth gap.
How do the premises support the conclusion?
       Argument A:
       (2)
       (3)
        (1)
        Argument B
        (4)
        (5)
         (1)

        Argument C
        (6)
        (7)
         (1)

        Argument D
        (8)
        (9)
         (1)

        Argument E
        (10)
        (11)
         (8)

                                           Diagram:
                                                           |(10)(11)|

                    |(2)(3)|        |(4)(5)|         |(6)(7)|       |(8)(9)|



                                               (1)

6) Our entire tax system depends upon the vast majority of taxpayers who attempt to
pay the taxes they owe having confidence that they’re being treated fairly and that
their competitors and neighbors are also paying what is due. If the public concludes
that the IRS cannot meet these basic expectations, the risk to the tax system will
become very high, and the effects very difficult to reverse.
What is the issue? Should the IRS treat taxpayers fairly and consistently?
What is the conclusion? (1) The IRS should treat taxpayers fairly and consistently.
What are the premises?
        (2) If the IRS does not treat taxpayers fairly and consistently, then the vast majority
        of taxpayers will not have confidence that the tax system is fair and consistent.
        (3) If the vast majority of taxpayers do not have confidence that the tax system is fair
        and consistent, then the risks to the tax system will be very high and the effects very
        difficult to reverse.
        (4) Intermediate conclusion: If the IRS does not treat taxpayers fairly and consistently,
        then the risks to the tax system will be very high and the effects very difficult to
        reverse.
        (5) The tax system should not be subject to high risks or negative effects that are
        difficult to reverse.
How do the premises support the conclusion?
      ARGUMENT A:
      (2)
      (3)
      (4)

       ARGUMENT B:
       (4)
       (5)
       (1)
                                          Diagram:
                                          |(2)(3)|

                                               |(4) (5)|

                                                  (1)


8) Twenty-eight children in the United States were killed by falling television sets
between 1990 and 1997. That is four times as many people as were killed by great
white shark attacks in the twentieth century. Loosely speaking, that means watching
“Jaws” is more dangerous than swimming in the Pacific.

What is the issue? Is watching television or a shark attack more dangerous?
What is the conclusion? (1) Watching television is more dangerous than a shark attack.
What are the premises?
       (3) In between 1990 and 1997, 28 children were killed by falling television sets.
       (4) Throughout the entire twentieth century, only 7 people were killed by great white
           shark attacks.
       (5) Thus falling television sets killed more people in a significantly shorter period of
           time than great white shark attacks.
       (6) If X kills a greater number of people in a significantly shorter period of time than
           Y, then X is more dangerous than Y.
How do the premises support the conclusion?
Argument A
       (3)
       (4)
       (5)

Argument B
      (6)
      (5)
      (1)
Diagram:
|(3)(4)|

   |(5)(6)|

      (1)

								
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