Instructions for exercises assigned. Say whether the argument
is (deductively) valid or not. If the argument has one of the forms
discussed in the book, give its name.
Strategy: Deductive validity depends on the argument's form.
So let's learn some basic forms and their validity status.
1. Double Negation
Not Not A
A
Bob is not unhealthy.
Bob is healthy.
Some philosophers complain that is is not d.v. because Bob's health could be borderline.
So double negation only works with "un" when there is no "middle ground".
Things seem to work better with 'not' and 'it is false that'
It is false to say Bob is not healthy.
Bob is healthy.
Watch out for this:
John does not believe that Mary is not a student.
John believes Mary is a student.
2. Transposition (a.k.a. Contraposition)
If A then B = If not B then not A
Honorary Versions of Transposition:
If not A then B = If not B then A
If A then not B = If B then not A
Pattern: Switch the Sides and the Signs
Example: p. 216
"The materials of nature that remain untouched by human effort belong to no one and are not [private] property. It follows that a thing can be someone's private property only if he works on it. From this I conclude that what ever a man improves by labor belongs to him." - J. Locke
If a thing is not worked on then it is not property.
Something is property only if it is worked on.
If not W then not P.
If P then W.
P only if W.
Something is property only if it is worked on.
If something is worked on it is property.
If P then W.
If W then P. INVALID
Don't Confuse Transposition with these invalid Ones:
Converse: If A then B NOT = If B then A
If A then B NOT = If not A then not B.
If A then not B NOT = If not A
then B
"You imply that as long as the possibility of error exists, you are against the death penalty. This implies that, if the possibility of error does not exist you would approve of capital punishment. Is this the case? ... your argument lends strength to your opposition: You merely want legal standards to be impeccable. So do we all."
- M.Vos Savant writing in H. Chronicle 3/5/00
3. Modus Ponens (Affirming the Antecedent)
A
If A then C VALID
C
Affirming the Consequent
C
If A then C INVALID
A
There is Oxygen here
If there is Fire here then there is Oxygen here.
There is Fire here.
4. Modus Tollens (Denying the Consequent)
not C
If A then C VALID
not A
Denying the Antecedent
not A
If A then C INVALID
not C
There is no Fire here.
If there is Fire here then there is Oxygen here.
There is no Oxygen here.
Honorary Modus Tollens
(Honorary Denying the Consequent):
C
If A then not C VALID
not A
Honorary Denying the Antecedent:
A
If not A then C INVALID
not C
Summary:
| Antecedent | Consequent | |
| Affirm | VALID MP | INVALID |
| Deny | INVALID | VALID MT |
5. (Pure) Hypothetical Syllogism (Chain)
If A then B
If B then C
If A then C
Honorary Hypothetical Syllogism:
If A then B
If B then C
If C then D
If A then D
6. Disjunctive Syllogism
(Reasoning by Elimination of Alternatives)
Either A or B
not A
B
DON'T CONFUSE WITH:
Either A or B
B
not A
The patent needs chemo or surgery.
The patient needs surgery.
The patient does not need chemo.
Honorary Disjunctive Syllogism:
A or B or C
not A
not B
C
7. Conditionalization:
| Suppose that A
: C |
Suppose 1<affirmative action is canceled in city building contracts.>
Then 2<minority-run contractors will go out of business> and so 3<there
will be fewer contractors around>. That means 4<less competition>
which 5<will drive up the city's construction costs>, 6<which will
be payed by the public>. So7< if affirmative action is canceled
the public will pay>.
8. Reductio ad Adsurdum (Indirect Proof):
| Suppose that A
: Contradiction (B and not B) |
not A
| Suppose that not A
: Contradiction (B and not B) |
A
NOTE: the form on p. 230 is unnecessarily complex.
1<Space cannot be empty> because supposing 2<it were>, 3<there
would be nothing between two stars>. But that would mean 4<the
stars are right up against each other>, which we know 5<is not the case>.
A. The Purpose:
Use the Principle of Charity to make the argument as sound as
possible, that is adjust things in a reasonable way so that the resulting
argument is valid and has true reasons (or at least reasons the author
would accept).
B. Tactic:
If argument is invalid, add some reasonable premises that would make it valid.
C. Requirements for Suppressed Premises:
1. They must make the argument valid (either deductively valid or strong).
2. They must be widely accepted, or at least something the writer of the argument is likely to accept.
3. They should be linked to the stated premises.
4. They should not beg the question. (So avoid using
"cheap" conditionals).
1. Some Examples
Example 1:
Abortion is intentionally taking an innocent life.
So abortion is murder.
[Intentionally taking innocent life is murder.]
Abortion is intentionally taking an innocent life.
So abortion is murder.
If I then M
If A then I
If A then M
Example 2: (Missing Conclusion as well)
If Joe gets into med. school then I'll be a monkey's uncle.
[I am not a monkey's uncle.]
If Joe gets into med. school then I'll be a monkey's
uncle.
[ Joe won't get into med school.]
Modus Tollens
2. The Linkage Requirement.
No one who is interested in fame can be trusted.
Joe is a journalist.
Joe can't be trusted.
Which of the following would be the best suppressed premise for the
above argument?
A. Joe cheats at cards.
B. Journalists cannot be trusted.
C. Joe isn't trustworthy.
The answer is NONE. The correct supressed premise is:
Journalists are interested in fame
3. Begging the question. Using a reason that
is no more obvious than the argument's soundness.
Example:
[God wrote the Bible, and would not lie to us.]
The Bible says God exists.
God exists.
4. "Cheap" Conditionals (to be avoided)
[If no one who is interested in fame can be trusted and Joe is a journalist,
then Joe can't be trusted.]
No one who is interested in fame can be trusted.
Joe is a journalist.
Joe can't be trusted.
PROBLEM: Anybody who objects to the argument will object to the suppressed premise.
[If Reason 1 then Conclusion]
Reason 1
Conclusion
[If Reason 1 and Reason 2 then Conclusion]
Reason 1
Reason 2
Conclusion
[If Reason 1 and ... and Reason n then Conclusion]
Reason 1
:
Reason n
Conclusion
5. Suppressed premises for inductive arguments
[The sample is representative of the population as a whole.]
20% of those polled prefer steamed bagels.
20% of the population prefers steamed bagels.
Is this suppressed premise begging the question?
Not if there is independent evidence for it!
Typical evidence:
Size of the sample is large (enough).
The method of selection was random (not biased).
2-? Evaluating Reasons
A. Why there is less in the book on this topic:
It is your job in all college classes to learn how to evaluate
statements as true or false.
B. Two basic method for evaluating Reasons:
Deductive
Non-Deductive
C. Two Deductive methods:
1. Provide a sound argument for (or against) the reason.
2. Show that the premises of the argument lead to something
unacceptable, and so that one of the reasons must be wrong.
p. 227 Publish or Perish Argument
Only good researchers can be good teachers.
So in evaluating professors look at their research only.
Only good researchers can be good teachers.
So in evaluating professors look at their teaching.
Only GR are GT = If GT then GR
If one is a good teacher then one is a good researcher.
So in evaluating professors look at their teaching.
D. Two Non-Deductive Methods
1. Personal Experience
Worry 1: Your own experience might differ from that of
others. Broccoli tastes terrific.
Worry 2: What seems obvious to you might be wrong.
The sky is a big upside down bowl. There Earth is not moving.
2. Authorities (People, Journals, Books, Websites)
A. The authority should be well informed.
B. The authority should have no motive to mislead.
Examples:
Physicists who examined Uri Geller (the Mind-Bender)
The AMA's arguments for having more doctors.