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LOGOS |
Not all sentences are
declarative, however, but only those to which truth or falsity belongs. Thus
truth or falsity does not belong to all sentences; for example, a prayer is a
sentence but is neither true nor false. So let all sentences which are neither
true nor false be dismissed here, for their consideration is more appropriate to
rhetoric or to poetics. Our present inquiry is about declarative sentences
[i.e., propositions (Gr. apophantikos logos)]
A. ETYMOLOGY
The English term proposition is historically derived from Latin,
proponere and cognates: to put forward, to propose. In turn, proponere
translates Aristotle’s Greek expression apophantikos logos: declarative
sentence, statement, proposition.
B. GENERAL DEFINITION
Although precise formulation varies slightly with respect to theoretical
details, there is general agreement among modern logicians for the following
definition:
A proposition is ‘what is
asserted’ by means of natural language (typically a declarative or indicative
sentence) or ‘what is expressed by’ such a sentence. Any form of discourse that
conveys or expresses a proposition is either true or false (truth-value).
Examples
1. The New England Patriots
won the Super Bowl.
2. It is raining.
3. Water freezes at 32
degree F and boils at 212 degree F.
4. Either Eminem is a very
talented musical artist or he is not.
5. Rembrandt and Picasso
were masterful painters and philosophers.
6. Lewis Carroll (pseudonym
Charles Dodgson) wrote Alice’s Adventures in Wonderland and was a
logician.
7. If a deductive argument
is sound, then it is valid.
8. Some Americans are
atheists.
9. Corrupt politicians
believe that “the end justifies the means.”
10. Nobody can predict all
the future consequences of 9/11.
C. BASIC CHARACTERISTICS
1. All propositions make a factual
claim. They assert that something is true or false, that a certain
state of affairs actually exists, that p is the case (where p is a
logical variable for any proposition whatsoever). As such, they claim to refer
to (reference) or correspond to (correspondence) some specific state of
affairs, fact or reality. Consequently, propositions are referential or
descriptive.
2. Typically, propositions
are conveyed by or expressed by means of declarative
sentences, which assert (declare) that something is a fact. As such, the
grammatical structure of the declarative sentence will constitute the minimal
conditions of a proposition. This structure consists in a subject
term and predicate term. The subject tells us what the subject is or
does, whereas the predicate is the verb phrase that attributes a particular
property or trait to the subject (predication).
Example:
Hitler (subject) was a murderer (predicate).
3. All propositions are
either true or false. This strictly disjunctive nature of the
proposition is called its truth-value. They are strictly true (T,
1) or false (F, 0). Accordingly, the truth-value of the proposition reflects the
logical law of excluded middle: any proposition is either
true or false; and the logical law of contradiction: no proposition can
be both true and false.
BASIC LAWS OF LOGIC |
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Noncontradiction/ContradictionA is not non-A (~A) |
Excluded MiddleX is either A or non-A (~A) |
Identity
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Any statement is either true or false. |
If any statement is true, then it is true. |
p ● ~p = false |
p v ~p = true |
p = p |
Symbolic notation
”
= implication
4. Propositions are the
linguistic formulation or result of a critical judgment. They
advance or assert a definite position on the truth or falsity (true-value or
status) of a specific state of affairs. Propositions are critical to
the extent that they are based upon a discriminating evaluation of evidence for
the truth or falsity of X. And they express a definite judgment
about the truth-value of X based upon the evidence provided by the
preceding critical inquiry.
5. Propositions are the
ideal information, semantic content, or meaning conveyed by means
of natural language. As such, they are not identical, equivalent,
or reducible to any specific linguistic formulation, for the same
proposition (semantic content) may be expressed by linguistic expressions.
This difference may be based on the specific natural language employed (e.g.,
English, French, Spanish, etc.) or various grammatical and syntactical
variations within a particular language. Accordingly, we refer to the
identical information or same proposition expressed by various linguistic
formulations as propositional content or ideal meaning. It
is ideal because the proposition is not identical
with any real sentence or discourse utilized to express it.
Examples
A.
Different languages
It is raining. (English)
Está lloviendo. (Spanish)
Il pleut.
(French)
Es regent.
(German)
B.
Same language
The New England Patriots
won the Super Bowl. (Active Voice)
The Super Bowl was won by
the New England Patriots. (Passive Voice)
The Patriots won the Super
Bowl. (Different words)
New England did not lose
the Super Bowl. (Stated negatively)
The Pats are the Super Bowl
winners of the 2001 NFL season. (Temporal index)
6. Propositions are the basic
building blocks or constituent components of arguments.
They function in three (3) distinguishable capacities: as premise,
as conclusion, and as both premise and conclusion (subconclusion).
Example: (1) Cats
make good pets because (2) they are affectionate. So, (3) if you want a good pet, you
should get a cat.
1) Cats make good pets.
(Subconclusion: both premise and conclusion)
2) They (cats) are
affectionate. (Premise)
3) If you want a good pet,
you should get a cat. (Conclusion)
7. There are two (2)
basic types of proposition: simple and compound.
a) Simple: contains
only one subject and one predicate
Example:
Nice guys finish last. —Attributed to Leo Durocher
Symbolic notation: p
b) Compound: contains
more than one subject, predicate, or both. As such, a compound proposition
consists of two
or more component propositions. Three (3) basic
types of compound proposition are distinguishable:
b.1) Conjunctive:
formed by adding at least two (2) component propositions (called conjuncts),
usually by putting the word “and” between them.
Examples
1. Michael Jordan is very wealthy. (simple proposition)
2. Michael Jordan is very wealthy and athletic. (conjunctive proposition)
3. Michael Jordan and Bill Gates are very wealthy.
4. Michael Jordan and Bill Gates are very wealthy and Americans.
Symbolic notation:
p ● q (the dot “●” = conjunction)
b.2) Disjunctive (or
alternative): often formed by an “either-or” phrase or more simply by
inserting the word “or” between the two component propositions (called disjuncts).
There are two distinct types of disjunctive propositions: 1) Weak, Inclusive;
and 2) Strong, Exclusive.
1) Weak,
Inclusive: The inclusive “or” has the sense of “either, possibly
both.”
Example:
Your driver’s license can be rescinded for repeated DWI convictions or for
several incidents of driving without a registration.
Symbolic
notation: p v q (the wedge
“v” = disjunction)
2) Strong,
Exclusive: The exclusive “or” has the sense of “at least one and at
most one.” Accordingly, an exclusive disjunction is true when one or
the other, but not both, disjuncts are true. As such, it is
false if both disjuncts are true or both are false. This precise meaning of the
strong disjunction is occasionally made explicit in legal documents by the
phrase “but not both.”
Example
Either Mike Tyson is emotionally stable or he is not emotionally stable.
Mike Tyson is either emotionally stable or he is not.
Symbolic
notation: p v (~p) (the tilde
or curl “~” = negation)
b.3)
Hypothetical, Conditional: Most often formed by an “if-then”
statement, the hypothetical or conditional proposition combines two (2)
component propositions by placing the word “if” before the first component
(called the antecedent) and the word “then” before the second
component (called the consequent). Accordingly, its basic meaning is the claimed
relationship between the antecedent and the consequent, and precisely in
that order. More specifically, the hypothetical proposition claims a
relationship of implication: the truth of the antecedent implies
the truth of the consequent. As such, the relationship of implication is unidirectional.
It is not claimed that the consequent implies the antecedent.
Examples
1. If
my car is out of fuel, then it will not run.
2. If
Tonya Harding is an excellent ethical example for everyone to follow, I’m the
greatest philosopher who ever lived.
3. You
cannot continue to live if you stop drinking and eating.
4. Unless
I win the lottery, I’ll keep my day job.
5. If
p is true, then ~p is false.
6. You
will win the game if you score more points than the other team.
7. If
you miss class consistently your chances of success are diminished
significantly.
8. If
Hitler was a warm and caring person, then I’m an alien from outer space.
9. Life
is worth living unless you never critically examine it.
10.
If Patrick Kennedy is a bachelor, then he is unmarried.
Types
of implication:
1.
Logical
2.
Causal
3.
Definitional
4.
Decisional
5.
Material
Symbolic notation: pq
(the horseshoe “”
= implication)
8. Propositions
and Language: Various grammatical units may express a proposition. As such,
one needs to judge whether a unit of discourse meets the minimal requirements
(a factual claim containing a subject and predicate) of a proposition.
a) Declarative
Sentence
1) An inductive argument is probabilistic.
2) Nonviolence
is the answer to the crucial political and moral questions of our time.
—Martin Luther King, Jr., Nobel Prize address
b) Relative
clause: Usually, a relative clause begins with a relative pronoun
(who, whom, which, that) and, like all clauses, contains a subject and a
predicate.
Examples:
1.
The Japanese, who eat lots of fish, have fewer heart attacks.
(nonrestrictive modification of the subject)
2.
The Japanese who eat lots of fish have fewer heart attacks. (restrictive
modification of the subject)
3.
Shaquille O’Neill is tall, like most basketball players. (modification
of the predicate)
c) Noun
clause: A phrase is a noun clause when the entire clause functions like a
noun. Unlike a relative clause, it doesn’t modify anything (neither the
subject nor the predicate) in the main clause. Rather, it is itself the subject
or predicate of the main clause.
Examples:
1.
It is irrelevant whether Antoine is gay. (subject of proposition)
The fact that Antoine is gay is irrelevant.
2.
The Pope knows that God exists. (predicate of proposition)
The Pope believes that God exists.
d) Propositions
not in declarative form: Units of discourse other than declarative forms
occasionally express propositions.
1) Rhetorical question (interrogative sentence): A question may suggest,
imply, or assume a proposition when its author believes the answer is
obvious or undeniable. As such, it can be an effective rhetorical technique
since it calls upon the reader/listener to answer the question and thereby state
the implied or indirect proposition.
Examples:
a) …what penalty can frighten a person who is not afraid of death
itself?
—Arthur Schopenhauer, “On Suicide” (1851)
b) …what is misery but the desire and possession of evil?
—Plato, Meno, 78a
c)
…he that loves not his brother whom he hath seen, how can he love God whom he
hath not seen?
— 1 John 4:20
2) Imperative sentence or phrase (command, prescription, advice,
etc.)
Examples:
a) Neither a borrower nor a
lenderer be
For loan oft
loses both itself and friend,
And borrowing
dulls the edge of husbandry.
—Shakespeare, Hamlet, act 1, scene 3
b) Since you want to excel in all your endeavors, you should work hard at
everything
you do.
c) Thou shall not kill. Therefore, if a serial murderer surprises you in
your home you should under no circumstances kill him.
d) Hope empowers one in the face of adversity. Therefore, as the Rev.
Jesse Jackson says, “keep hope alive.”
I believe that Mayor Cianci is guilty of
political corruption.
I doubt that Mayor Cianci is guilty of political corruption.
I know that Mayor Cianci is guilty of political corruption.
I hope that Mayor Cianci is guilty of political corruption.
I suspect that Mayor Cianci is guilty of political corruption.
I am certain that Mayor Cianci is guilty of political corruption.
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