Philosophy
6: Logic in Practice
Los Angeles Pierce College
Department of History, Philosophy, & Sociology
Lecture Notes
Lecture Notes for
"Chapter Seven" of Porter's The
Voice of Reason
The Structure of an Argument
Premises supporting
conclusions
Warrants supporting claims
Indicator Words
Differentiating premises
from conclusions, and warrants from claims can sometimes be tricky
Indicator words make such
differentiations easier
Premise/Warrant Indicator Words
since
inasmuch as
because
for the reasons that
for
in view of the fact
whereas
as evidenced by
Conclusion/Claim Indicator Words
consequently
we can conclude that
therefore
it follows that
thus
we may infer that
so
this means that
hence
it leads us to
believe that
accordingly
this bears our the
point that
E.G. of the Difference
"Television presents
a continuous display of violence in graphically explicit and extreme
forms. It also depicts sexuality
not as a physical expression of internal love but in its most lewd forms and
obscene manifestations. We must
conclude, therefore, that television contributes to the moral corruption of
individuals exposed to it."
Claim/Conclusion: "television contributes to the
moral corruption of individuals exposed to it."
Warrant/Premise: "Television presents a continuous
display of violence in graphically explicit and extreme forms."
Warrant/Premise: Television "also depicts sexuality
not as a physical expression of internal love but in its most lewd forms and
obscene manifestations."
Judging Arguments
Analyzing arguments into
their parts facilitates our judging those arguments
Soundness "the logic is not sound," "if
the conclusion does not strictly follow from the premises"
Testing the E.G.
"Has the writer shown
that television does corrupt society?"
"Doesn't TV refine
and educate people in some of its programming?"
"Has a causal link
been shown between the depiction of gross sexuality and the deterioration of
morals?"
"Does TV promote
violence in our culture or merely reflect it?"
"And when can we say
that sex is lewd and obscene?"
Good Advice
"In writing an essay,
we should summarize our argument in the introduction and articulate the
structure so the reader is prepared for our exposition."
"Then we can develop
the argument in the body of our essay, clearly indicating what we are arguing
for and why we are arguing it."
Logical Translations / Paraphrasing
Formalizing statements
facilitates our testing for soundness
"The process of
casting sentences that we find in a text into one of these four forms is
technically called paraphrasing"
Quality / Affirmative or Negative
"in this process of
paraphrasing we designate the affirmative or negative quality of a statement
principally by using words 'no' or 'not.'"
Quantity / All of a Class or Part of a Class
"We indicate
quantity, meaning whether we are referring to the entire class or only a
portion of it, by using the words 'all' or 'some.'"
And something to memorize:
all entails some, but some does not entail all
Copula / "Is" or "Are"
"In addition, we must
render the subject and the predicate as classes of objects with the verb 'is'
or 'are' as the copula joining two halves."
Target Forms
The target in paraphrasing
is to render statements into one of our different logical forms
Logical Forms of Statements
(A) All X is Y.
(E) No X is Y.
(I) Some X is Y.
(O) Some X is not Y.
Logical Forms of Statements E.G.
(A) All unicorns are
gauche creatures.
(E) No unicorn is a gauche
creature.
(I) Some unicorns are
gauche creatures.
(O) Some unicorns are not
gauche creatures.
The Trick
"the main trick is to
translate sentences into statements covering all or some, none or not, and to
use language that designates categories or classes of objects."
Paraphrasing E.G.s
"Cats have a quiet
tread (flannel-footed)."
translates to
"All cats are
creatures with a quiet tread (flannel-footed)."
"Several houses were
damaged by the hurricane."
translates to
"Some houses are
structures damaged by the hurricane."
"All men are not
preoccupied with sports."
translates to
"Some men are people
preoccupied with sports."
"No one need fear
justice who is innocent of any crime."
translates to
"No person who is
innocent of any crime is a person who need fear justice."
Implications
Once rendered into logical
form, it becomes easier to see what does and does not follow
Conversions
Some statements' subjects
and predicates are interchangeable
(A) All unicorns are gauche creatures.
does not convert to
(A) All gauche creatures are unicorns.
*
(E) No unicorns are gauche creatures.
does convert to
(E) No gauche creatures are unicorns.
*
(I) Some unicorns are gauche creatures.
does convert to
(I) Some gauche creatures are unicorns.
*
(O) Some unicorns are not gauche creatures.
does not convert to
(O) Some gauche creatures are not unicorns.
Trying it Out
I. 1
I. 2
I. 3
IV. 2
IV. 3
V. 2
V. 3
VI. 1
VI. 2
Syllogisms
"In a syllogism we
lay out our train of reasoning in an explicit way, identifying the major
premise of the argument, the minor premise and the conclusion."
Major Premise
"The major premise
consists of the chief reason for the conclusion"
"it is the premise
that contains the term in the predicate of the conclusion."
Minor Premise
"The minor premise
supports the conclusion in an auxiliary way"
"it contains the term
that appears in the subject of the conclusion."
Syllogism E.G.
Major Premise: All single-horned creatures
are special.
Minor Premise: All narwhals are
single-horned creatures.
Conclusion: Narwhals
are special.
Enthymemes
Arguments "with an
unstated premise or conclusion" are "incomplete arguments called
enthymemes."
First Order Enthymeme
"When an argument
lacks the major premise it is called an enthymeme of the first order"
First Order Enthymeme E.G.
Major:
Minor: All narwhals are single-horned
creatures.
Conclusion: Narwhals are special.
Second Order Enthymeme
"one that lacks the
minor premise is an enthymeme of the second order"
Second Order Enthymeme E.G.
Major: All single-horned creatures are special.
Minor:
Conclusion: Narwhals are special.
Third Order Enthymeme
"one missing the
conclusion is an enthymeme of the third order"
Third Order Enthymeme E.G.
Major: All single-horned creatures are special.
Minor: All narwhals are single-horned
creatures.
Conclusion:
Validity
"an argument is
called valid if, given the premises, the conclusion is unavoidable."
"Validity ... applies
to the structure of an argument"
Invalid
"An argument ...
where the conclusion fails to follow from the premises, is consider
invalid."
Truth
"Truth ... is a
quality of statements, and we call a statement false if it fails to reflect
reality."
True & Invalid
All mammals are creatures
that breathe.
All narwhals are creatures
that breathe.
All narwhals are
mammals.
Valid & Untrue
All mammals are creatures
that lay eggs.
All cedars are
mammals.
All cedars are creatures
that lay eggs.
True & Valid / Sound
"a sound argument
must be both valid and true, that is, valid in form and with premises and a
conclusion that are true."
Trying it Out
I. 3
II. 2
II. 3
IV. 4
IV. 6