CS 100 - Week 5 Lecture 1 - 9-20-12
* still in Chapter 3... (and remember, after Chapter 3 we will
be discussing Chapter 5)
* and we've discussed several tests for helping
to determine if an argument in deductive or inductive
* two exceptions to the "strict necessity" test -
* ...situations in which the conclusion
does NOT necessarily follow with strict
logical necessity from its premises,
BUT the argument should/could still be
classified as deductive (generally NOT as
a GOOD deductive argument...!)
1. the language and/or context make clear that
the arguer INTENDED to offer a logically
conclusive argument, even though it, in
fact, is NOT logically conclusive;
2. the argument has a pattern of reasoning
that is characteristically deductive,
and nothing else about the argument
indicates clearly that the argument is
meant to be inductive
***************************************
COMMON PATTERNS of DEDUCTIVE REASONING
***************************************
1. hypothetical syllogism
2. categorical syllogism
3. argument by elimination
4. argument based on mathematics
5. argument from definition
* if you study an argument, and it is following
one of these patterns, it is reasonable to categorize
that argument as deductive
(and to then go on to evaluate it on that basis)
* syllogism: a three-line argument,
with TWO premises and ONE conclusion
HYPOTHETICAL SYLLOGISM
----------------------
...is a syllogism that contains at least one hypothetical --
or if-then (conditional) premise;
* for example, here's modus ponens, ONE type
of hypothetical syllogism:
if A, then B.
(assert) A.
Therefore, B.
* AND -- there are SEVERAL kinds of hypothetical
syllogisms...
* modus ponens (as noted above)
* chain arguments
* modus tollens (denying the consequent)
* denying the antecedent [this is a FAULTY one, though!]
* affirming the consequent [this is also FAULTY]
chain argument
--------------
* has the pattern:
if A then B.
if B then C.
Therefore, if A then C.
modus tollens (denying the consequent)
-------------
* has the pattern:
if A then B.
Not B.
Therefore, not A.
denying the antecedent [FAULTY!!]
----------------------
* has the pattern:
if A then B.
Not A.
Therefore, Not B.
affirming the consequent [FAULTY!!]
------------------------
* has the pattern:
If A then B.
B.
Therefore, A.
CATEGORICAL SYLLOGISM
----------------------
* for present purposes, this may be defined as
a three-line argument in which each statement
begins with the word ALL, SOME or NO
* example:
All oaks are trees.
All trees are plants.
So, all oaks are plants.
ARGUMENT BY ELIMINATION
-----------------------
* seeks to rule out various possibilities until
only single possibility remains
ARGUMENT BASED ON MATHEMATICS
-----------------------------
* an argument in which the conclusion is claimed
to depend largely or entirely on some mathematical
principle, calculation, or measurement (perhaps
in conjunction with one or more non-mathematical
premises)
ARGUMENT FROM DEFINITION
------------------------
* the conclusion is presented as being true by
definition
***************************************
Common patterns of INDUCTIVE reasoning
***************************************
* inductive generalization
* predictive argument
* argument from authority
* causal argument
* statistical argument
* argument from analogy
INDUCTIVE GENERALIZATION
-------------------------
* generalization (in the realm of critical thinking):
a statement that attributes some characteristic to ALL or MOST
members of a given class
* inductive generalization:
an argument in which a generalization is claimed to be PROBABLY
true based on information about some members of a particular class
* example:
All dinosaur bones so far discovered have been more than 65
million years old.
Therefore, probably all dinosaur bones are more than 65 million
years old.
PREDICTIVE ARGUMENT
--------------------
* prediction: a statement about what MAY or WILL happen in the future
* predictive argument:
an argument in which a prediction is defended with reasons
* example:
It has rained in Vancouver every February since weather records
have been kept.
Therefore, it will probably rain in Vancouver next February.
* (note: while usually inductive, note that predictions *can*
be argued for deductively...)
ARGUMENT FROM AUTHORITY
------------------------
* an argument that asserts a claim, and supports it by citing
some presumed authority or witness who has said that the claim
is true
* example:
More Americans die of skin cancer each year than die in car
accidents. How do I know? My doctor told me.
* (note: while usually inductive, note that arguments from authority
*can* be argued for deductively...)
CAUSAL ARGUMENT
----------------
* an argument that asserts or denies that something is the CAUSE
of something else
* example:
I can't log on. The network must be down.
* (note: while usually inductive, note that causal arguments
*can* be argued for deductively...)
STATISTICAL ARGUMENT
---------------------
* an argument that rests on statistical evidence -- that is,
evidence that some percentage of some group or class has some
particular characteristic.
* example:
83% of St. Stephen's students are Episcopalian.
Beatrice is a St. Stephen's student.
So, Beatrice is probably Episcopalian.
* (note: while usually inductive, note that statistical arguments
*can* be argued for deductively...)
ARGUMENT FROM ANALOGY
----------------------
* analogy: a comparison of two or more things that are claimed to be
ALIKE in some RELEVANT aspect
* argument from analogy:
an argument in which the conclusion is claimed to depend on an
analogy between two or more things
* example:
Hershey Park has a thrilling roller-coaster ride.
Dorney Park, like Hershey Park, is a great amusement park.
Therefore, probably Dorney Park also has a thrilling
roller-coaster ride.
* (note: while usually inductive, note that arguments from analogy
*can* be argued for deductively...)