THE ANATOMY OF ARGUMENTS I

1
THE ANATOMY OF ARGUMENTS I

• An argument consists of premises and a
  conclusion.
  
• The premises of an argument df. The claims
  offered in support of the conclusion. (Recall
  that a claim is a statement with a truth value
  true or false.)
• The conclusion of an argument df. The claim for
  which a person is arguing.
  
• For instance, Every student passed the test.
  (premise). No one can pass the test unless his
  or her score is 60 or above. (premise).
  Therefore, every student in the class scored 60
  or above on the test. (conclusion)

2
THE ANATOMY OF ARGUMENTS II

• MP Sometimes the conclusion of one argument
  can serve as the premise of another.
  
• For instance, Argument 1 Every student passed
  the test. (premise). No one can pass the test
  unless his or her score is 60 or above.
  (premise). Therefore, every student in the class
  scored 60 or above on the test. (conclusion 1)
• Argument 2 No student who scores 60 or above on
  the test has to retake the test. (premise)
  Every student in the class scored 60 or above on
  the test. (premise which is the conclusion of
  argument 1) Thus it follows that no student in
  the class has to retake the test. (conclusion 2)

3
THE ANATOMY OF ARGUMENTS III

• An argument can have an unstated premise.
• For instance, You cant pass the test if you
  dont study. (premise) Accordingly, John will
  not pass the test. (conclusion) What is the
  missing, implicit, or unstated premise?
• An argument can have an unstated conclusion.
• For instance, Anyone who studies hard will pass
  the test. (premise) John studies as hard as
  anyone I know. (premise) What is the missing,
  implicit, or unstated conclusion?

4
INDEPENDENT PREMISES

• Premises are independent of one another when the
  falsity of one would not cancel the support the
  other provides for the conclusion.
  
• For instance, Sex education will decrease the
  rate of teenage pregnancy. (premise) Also, sex
  education will help to lower the rate of sexually
  transmitted diseases. (premise) Thus we should
  have sex education. (conclusion)
• An argument with two independent premises can
  also be thought of as two arguments for the same
  conclusion. Thus the preceding argument can
  either be seen as a single argument with two
  independent premises, or as individual arguments
  each of which support the same conclusion.

5
DEPENDENT PREMISES

• In an argument which contains dependent premises,
  neither premise can be false without canceling
  the support that the other premise provides for
  the conclusion.
• For instance, Raising the prices of our products
  will decrease sales. (premise) Our operating
  budget cannot tolerate a decrease in sales.
  (premise) Accordingly, prices should not be
  raised. (conclusion)
• That is, in an argument with dependent premises,
  the premises are so linked that, if either
  premise is false, then the conclusion cannot
  follow from them, whereas, in an argument with
  independent premises, either premise could be
  false, and the conclusion would still follow from
  the remaining true premise.

6
GOOD AND BAD ARGUMENTS

• A good argument df. An argument which gives us
  grounds for accepting its conclusion.
  
• A bad argument df. An argument which fails to
  provide grounds for accepting its conclusion.
  
• MP Good and bad are relative terms
  Arguments can be better or worse depending on the
  degree to which they furnish support for their
  conclusions.
• In addition, There is more than one way in which
  an argument might qualify as good.

7
VALID ARGUMENTS I

• A valid argument df. An argument whose premises
  provide absolutely conclusive support for its
  conclusion.
  
• In a valid argument it cannot be the case that
  the premises are true and the conclusion false.
  Or, the conclusion is necessarily true if the
  premises are true.
• For instance, All persons are mortal. (premise)
  Jane is a person. (premise) Therefore, Jane is
  mortal. (conclusion)
  
• MP The premises of a valid argument, if true,
  absolutely guarantee a true conclusion.
  
• In the above example, it cannot be false that
  Jane is mortal if it is true that Jane is a
  person, and it is also true that all people are
  mortal.

8
VALID ARGUMENTS II

• However, an argument is still valid even if,
  although its premises are not true as a matter of
  fact, if they were true then the conclusion would
  have to be true.
• For instance, All people are beautiful,
  intelligent, and kind. (premise) Max is a
  person. (premise) Therefore, Max is beautiful,
  intelligent, and kind. (conclusion)
• The first premise of the foregoing argument is
  false as a matter of fact, and so is the second
  premise if Max is not a person. However, the
  argument is still valid since, the validity of an
  argument only depends on the truth of the
  conclusion following necessarily from the truth
  of the premises.

9
VALID ARGUMENTS III

• MP An arguments being valid does not depend
  on its premises being true.
  
• MP What determines whether an argument is
  valid is whether the conclusion absolutely
  follows from the premises.
  
• For instance, All cats understand calculus.
  (premise) Max is a cat. (premise) Max
  understands calculus. (conclusion)
  
• The foregoing argument is valid because the
  conclusion follows logically from the premises,
  or if the premises were true which they are
  not, the conclusion would have to be true as
  well.
• The preceding argument also shows that an
  argument can be valid without necessarily being a
  good argument. It is not a good argument because
  it is false (as far as we can tell) that cats do
  not understand calculus.

10
INVALID ARGUMENTS

• An invalid argument df. An argument whose
  conclusion does not follow necessarily from its
  premises.
  
• For instance, If I had all of Bertrand Russells
  knowledge I would be happy. (premise) I do not
  have all of Bertrand Russells knowledge.
  (premise) Therefore I am not happy.
  (conclusion)
• This argument is invalid because the truth of its
  premises do not guarantee the truth of its
  conclusion, as is the case with a valid
  argument.
• Remember that the premises of a valid argument
  cannot be true while its conclusion is false.
  However, in this argument, the premises can be
  and in fact are true while the conclusion can be
  and is in fact false.

11
SOUND ARGUMENTS I

• A sound argument df. A valid argument whose
  premises are true.
  
• For instance, All persons depend on oxygen for
  life. (premise) George Bush is a person.
  (premise) Therefore, George Bush depends on
  oxygen for his life. (conclusion)
• The preceding argument is valid because, if its
  premises are true, then the conclusion which
  follows absolutely from them must also be true.
  But the argument is also sound because the
  premises are true.

12
SOUND ARGUMENTS II

• An unsound argument df. A valid argument at
  least one premise of which is false.
  
• For instance, All persons depend on peanut
  butter for life. (premise) George Bush is a
  person. (premise) Therefore, George Bush
  depends on peanut butter for his life.
  (conclusion)
• The preceding argument is valid because, if its
  premises are true, then the conclusion which
  follows absolutely from them must also be true.
  However, the argument is not sound or is unsound
  because the premise that all persons depend on
  peanut butter for life is false.

13
SOUND ARGUMENTS III

• A valid argument which is unsound can have a
  false premise or premises and a false conclusion,
  or it can have a false premise or premises and a
  true conclusion.
• Examples
• 1. Every person is a scientist. F.
  Stephen Hawking is a person. T.
  Stephen Hawking is a
  scientist. T.
• 2. All two-legged animals are persons. F.
  All cats have two legs. F.
  All cats
  are persons. F.
• 3. Every person has wings in addition to legs.
  F. Pegasus is a person. F.
  Pegasus has wings in
  addition to legs. T.

14
SOUND ARGUMENTS IV

• What a valid argument which is unsound cannot
  have is true premises and a false conclusion,
  since having a conclusion which cannot be false
  if its premises are true is the mark of
  validity.
• When the premises of a valid argument are true,
  then the argument is sound.
  
• Valid arguments which are not sound are for that
  reason not good or we are not justified in
  accepting the conclusion of a valid argument with
  a false premise or premises.
• On the other hand, because the premises of a
  sound argument are true, when we understand that
  they are true we are justified in accepting the
  conclusion.

15
SOUND ARGUMENTS V

• However, whether or not a claim made in the
  premise of an argument is true may be a matter of
  dispute, and an argument containing one or more
  controversial claims as premises might be thought
  to be question begging.
• For instance, Abortion is the deliberate killing
  of an innocent being. (premise) The deliberate
  killing of an innocent being is always
  wrong.(premise) Therefore, abortion is wrong.
  (conclusion.)
• In addition, a sound argument might not be
  thought good because it is not understood that a
  premise or premises of the argument is true. (See
  the example on page 268.)

16
STRONG ARGUMENTS I

• A strong argument df. An argument whose
  conclusion is unlikely to be false on the
  assumption that the premises are true.
  
• For instance, Every semester for every class,
  the final grade average for the class has been a
  C. (premise) Therefore, next semester the
  final grade average will be C for all of the
  classes. (conclusion)
• Such an argument is strong even though it is not
  valid. It is not valid because the premise could
  be true but the conclusion false, or the truth of
  the premise does not necessitate the truth of the
  conclusion. Rather, the truth of the conclusion
  is probable only, not certain. (This is an
  example of an inductive argument.)

17
STRONG ARGUMENTS II

• An argument can be strong even if its premises
  turn out not to be true.
  
• This is because, for an argument to be strong, it
  does not have to be the case that a premise or
  premises on which the arguments conclusion rests
  is true as a matter of fact. Rather, an argument
  is strong if its conclusion is likely to be true
  on the assumption that its premise or premises
  are true.
• Perhaps it is false that past grade averages have
  consistently been C. However, on the assumption
  that they have been, then concluding that future
  class averages will also be C is a strong
  argument.
• Strong arguments are good arguments since we are
  justified in accepting the conclusion as likely
  to be true based on the assumption of the truth
  of any premise supporting the conclusion.

18
WEAK ARGUMENTS

• Recall that a strong argument is an argument
  whose conclusion is unlikely to be false on the
  assumption that the premises are true.
  
• A weak argument is an argument which is not
  strong.
  
• Thus, a weak argument df. An argument whose
  conclusion is not unlikely to be false, even on
  the assumption that the premises are true.
  
• For instance, Every year that the NFC wins the
  Super Bowl, the stock market goes up for the
  year. (premise) The NFC won the Super Bowl
  today. (premise) Therefore, the stock market
  will go up this year. (conclusion)
• Even if the premises of the argument are true,
  still it is hardly unlikely for the conclusion to
  be false given the number and complexity of the
  causes of the stock markets losing or gaining
  for a particular year.

19
VALID, INVALID, STRONG AND WEAK

• Both the terms valid and invalid are
  absolute.
  
• That is, either an argument is valid or it is
  not.
  
• If an arguments conclusion follows necessarily
  from its premises then it is valid. Or, on the
  assumption that an argument has true premises,
  its conclusion must be true.
• If an arguments conclusion does not follow
  necessarily from its premises then it is invalid
  (not valid given the definition of validity as
  indicated).
• The terms strong and weak are relative. MP
  Arguments can be evaluated as stronger or weaker
  depending on how likely the premises show the
  conclusion to be true.

20
SUMMARY OF ARGUMENTS I

• An argument is good when it provides grounds for
  accepting its conclusion.
  
• An argument is valid when its conclusion must be
  true if its premises are true. Or, an argument is
  valid when, on the assumption that its premises
  are true, its conclusion cannot be false.
• An argument is invalid when the truth of its
  premises does not necessitate the truth of its
  conclusion.

21
SUMMARY OF ARGUMENTS II

• Valid arguments are either sound or unsound.
• A sound argument is a valid argument with true
  premises.
  
• An unsound argument is a valid argument with at
  least one false premise.
  
• An argument is strong when it is unlikely that
  the conclusion is false given the assumption that
  its premises are true.
  
• An argument is weak whose conclusion is not
  unlikely to be false, even on the assumption that
  the premises are true.
  

22
UNSTATED PREMISES I

• Consider the argument Max is a cat, therefore
  she is skillful at catching mice.
  
• For this argument to be valid, the implicit or
  unstated assumption or premise that all cats are
  skillful at catching mice must be added to the
  argument.
• Remember that a valid argument is one whose
  conclusion cannot be false if its premises are
  true.
  
• Also remember that a valid argument cannot be
  sound if a premise of the argument is false and,
  unless a valid argument is sound, it is not a
  good argument (not one which justifies our
  accepting its conclusion).

23
UNSTATED PREMISES II

• The argument All cats are skillful at catching
  mice, Max is a cat, therefore Max is skillful at
  catching mice is valid, since the conclusion
  cannot be false if the premises are true, but is
  it sound?
• For this argument to be sound, it would have to
  be true both that all cats are skillful at
  catching mice and that Max is a cat. But is the
  added premise, all cats are skillful at catching
  mice true?
• Remember, if a premise of a valid argument is
  false then, even though the argument remains
  valid, it is not sound, and, if it is unsound,
  then it is not a good argument. Or, we are not
  justified in accepting the conclusion of an
  argument with a premise which we know or have
  good reason to suspect is false.

24
UNSTATED PREMISES III

• If the argument All cats are skillful at
  catching mice, Max is a cat, therefore Max is
  skillful at catching mice is unsound, and so not
  a good argument, is there a way in which we could
  make the argument a good argument?
• A more plausible assumption than the one which
  maintains that all cats are good at catching
  mice could make the argument strong rather than
  an unsound valid argument.
• Remember that an argument is strong when it is
  unlikely that the conclusion is false on the
  assumption that the premises are true, and a
  strong argument can be a good argument, depending
  on how strong it is, or on how plausible its
  premises are.
• The more plausible a premise is, the more likely
  that the conclusion which the premise supports is
  true.
  

25
UNSTATED PREMISES IV

• The premise most cats are skillful at catching
  mice is more plausible than the premise all
  cats are skillful at catching mice, since it
  seems likely that some cats are not particularly
  good at catching mice.
• The argument becomes Most cats are skillful at
  catching mice. (premise) Max is a cat.
  (premise) Therefore Max is skillful at catching
  mice. (conclusion)
• This argument is now invalid since its premises
  do not necessitate its conclusion Max might not
  be good at catching mice. But notice that it has
  been strengthened by changing all to most,
  and so it is now a strong argument, since if it
  is true that most cats are good at catching mice,
  it is likely that Max is one of those cats, and
  so it is unlikely that the conclusion is false on
  the assumption that the premises are true.

26
UNSTATED PREMISES V

• One might also strengthen the preceding argument
  by adding the term probably to its conclusion.
  The argument is now Most cats are skillful at
  catching mice. Max is a cat. Therefore Max is
  probably skillful at catching mice. (This is an
  inductive argument.)
• Linking probably in the conclusion to most in
  the first premise makes the truth of the
  conclusion more likely since, if most cats are
  good at catching mice, and Max is a cat, it is
  more likely than not that Max is a member of the
  class of cats good at catching mice. Accordingly,
  we are more justified in accepting the argument,
  and this is true even though that Max is skillful
  at catching mice can still turn out to be false.

27
UNSTATED PREMISES VI

• Note, though, that if we change most to many,
  so that the unstated premise in our argument is
  now many cats are skillful at catching mice,
  then the argument is not as strong. The argument
  is now Many cats are skillful at catching mice.
  Max is a cat. Therefore Max is skillful at
  catching mice.
• Since the class of cats good at catching mice is
  smaller with many than it is with most, it is
  now not as likely as before that Max is a member
  of the class of good mousers. Since it is not now
  as likely as before that the conclusion is true,
  the argument is not as strong.

28
UNSTATED PREMISES VII

• The conclusion in the argument Many cats are
  skillful at catching mice. Max is a cat.
  Therefore Max is skillful at catching mice can
  be weakened further to reflect the change in the
  premise, so that it reads Max may be skillful
  at catching mice.
• Linking may be in the conclusion to many in
  the first premise makes the truth of the
  conclusion better fit the premise since, if many
  rather than most cats are good at catching mice,
  it is less likely that Max is a member of the
  class of cats good at catching mice than if most
  cats are good mousers.
• Even though we are more justified in accepting
  the argument after adjusting the conclusion to
  fit the change in the premise, the argument is
  considerably weakened, since we have less reason
  to believe than before that Max is a good mouser.
  

29
A POSSIBLE CONFUSION

• On page 273 MP say If a plausible assumption
  suffices to make an argument valid, then it is a
  good argument.
  
• However, earlier on page 267 they say an
  argument can be valid without necessarily being a
  good argument, and they point out that a valid
  argument with a false premise is not a good
  argument.
• Thus these two points seem to be in conflict. The
  remedy would be to change the first quote to If
  a plausible assumption suffices to make a valid
  argument sound, then it is a good argument.

30
SUMMARY OF UNSTATED PREMISES I

• To make an argument with a missing premise valid,
  add a premise which, if true, and on the
  assumption of the truth of the arguments other
  premise, will guarantee the truth of the
  conclusion.
• If the premise added to an argument to ensure its
  validity is true, then the argument is not only
  valid, but is sound.
  
• A valid argument is not a good argument unless it
  is sound, that is, unless it contains premises
  which are true. Or, we are not justified in
  accepting the conclusion of a valid argument with
  a false premise.
• If the premises of a valid argument are not known
  to be true, then a valid argument cannot be known
  to be sound in addition to being valid.

31
SUMMARY OF UNSTATED PREMISES II

• A strong argument is an argument whose conclusion
  is unlikely to be false on the assumption that
  its premises are true.
  
• An argument with a missing premise which cannot
  be made sound might nevertheless be made strong
  by substituting a premise which is likely to be
  true. And if that is the case, then the
  conclusion is less likely to be false.
• To make an argument more plausible, and hence
  more critically acceptable, substitute a premise
  which seems more likely to be true for a premise
  which is not known to be true, sounds
  implausible, and so which is likely false.

32
GOOD ARGUMENTS

• MP A good argument provides justification for
  accepting its conclusion.
  
• Such justification means that the premises must
  both be reasonable and they must support the
  conclusion.
  
• To say that premises of an argument are
  reasonable means that it is likely that they are
  true.
  
• To say that premises of an argument support the
  conclusion of the argument means that the
  argument is either valid or strong.

33
EVALUATING ARGUMENTS I

• To evaluate an argument we have to ask
• 1. Are the premises reasonable? That is, is it
  likely that they are true?
  
• 2. Do the premises support the conclusion? That
  is, is the argument either valid or strong?
  
• A person must be able to understand an argument
  before he or she can evaluate it.

34
UNDERSTANDING ARGUMENTS

• To understand an argument, the first thing to do
  is find the conclusion.
  
• This may be a single sentence in a shorter
  argument, or may be a paragraph or more in an
  argumentative essay. Here the conclusion states
  the main point or thesis of the essay.
• Next locate the premises, or the reasons which
  are meant to support the conclusion.
  
• In addition, in an essay there may be reasons
  offered in favor of the premises which support
  the conclusion. If so, they must be identified in
  order to determine the plausibility of the
  premises.
• Understanding the relation between claims is
  identifying the structure of the argument.

35
EVALUATING ARGUMENTS II

• Determine if the premises of an argument support
  its conclusion, and determine if the premises are
  reasonable.
  
• It is reasonable to accept a premise if it comes
  from a credible source, does not conflict with
  your observations, your background knowledge, or
  other credible claims.
• Dont accept a premise that conflicts with your
  observations or background information unless
  you have a very good reason for doing so for
  instance, a claim which comes from an expert.

36
EVALUATING ARGUMENTS III

• Dont accept a premise that conflicts with the
  claims of another credible source, unless the
  question of which source to believe has been
  resolved.
• Before a premise is accepted which is vague or
  ambiguous or otherwise unclear, it should be
  clarified.
  
• One argument a might be better than another
  argument b because the premises of a are more
  likely to be true. And this can be the case even
  if the premises of b might both be reasonable.

37
EVALUATING ARGUMENTS IV

• Determining which premises of an argument are
  likely to be true requires knowledge, experience,
  and good judgment.
  
• MP One argument a might be better than another
  argument b, not because the premises of a are
  more likely to be true, but because they produce
  a stronger argument. (See the example on page
  284.)