P
HILOSOPHY
150:
I
NTRODUCTION TO
L
OGIC
H
ANDOUT
12:
2
M
ARCH
2010
Alison Duncan Kerr
S
ENTENTIAL
L
OGIC
Sentential Logic (also known as Propositional Logic) is a branch of Deductive Logic.
Sentential Logic is the study of the
ways to join or modify sentences, statements, or propositions to form more complicated sentences, statements, or
propositions; it studies the logical relationships that are derived from these methods of combining or modifying the
sentences, statements, or propositions.
A major difference between inductive arguments and deductive arguments is that
only in deductive arguments can one determine whether the argument is valid based on form alone (not on content or
background).
In order to evaluate a deductive argument for validity, we can translate it into a symbolic language and use truth tables to
decide whether its logical form is valid.
T
HE SYMBOLIC LANGUAGE
contains
FIVE CONNECTIVE SYMBOLS
:
•
(“dot” for conjunction)
∨
(“wedge” for disjunction)
→
(“arrow” for conditional)
↔
(“double-arrow” for biconditional)
~ (“tilde” for negation)
It also contains capital letters (e.g., A, B, C) that stand for sentences and lower-case letters (e.g., p, q, r) that are variables.
T
YPES OF SENTENCES
:
Conditionals: If p, then q
p
→
q
arrow; p: antecedent; q: consequent
Conjunctions: (both) p and q
p • q
dot; p: first conjunct; q: second conjunct
Disjunctions: (either) p or q
p
∨
q
wedge; p: first disjunct; q: second disjunct
Biconditionals: p if and only if q
p
↔
q
double arrow; p: left side of
↔
; q: right side of
↔
Negations: It is not the case that p
~ p
tilde
Atomic:
p
S
YMBOLIC
L
ANGUAGE
:
Sentential connectives:
→
, •,
∨
,
↔
, ~
2-place connectives:
→
, •,
∨
,
↔
Variables: p, q, r, …
Sentences: A, B, C, …