27 November, 2013
Logically True: A sentence P is logically true if and only if P is true on every interpretation
Logically False: A sentence P is a contradiction if and only if P is false on every
interpretation
Contingent sentence: A sentence P is conti
16 October, 2013
MEANING & TRUTH
How are they related?
If you don't know what someone means by their words, you don't what they are saying
about the world.
But, if you don't know what somebody is saying about the world, you don't know what
their words mea
21 October 2013
Unit 4
What can truth tables tell us about sentences?
Validity: no TVA on which all premises are T and the conclusion is F.
Tautological implication: cfw_x, y, implies z. No TVA on which all sentences cfw_x, y,
are T and z is F
Logical e
23 October, 2013
Symbolization for Predicate Logic
is good
Ga (Aristotle is good)
~Ga (Aristotle is not good)
xGx (Something is good)
~xGx (Nothing Is good)
xGx (All things are good)
Working with the Universal Quantifier
"All Cats are mammals"
All things
4 November, 2013
New Derivation Rules
UI Universal Instantiation
EI Existential Instantiation
EG Existential Generalization
And a new derived Rule - QN Quantifier Negation
Universal Instantiation
This rule allows us to derive a substitution instance from
28 October, 2013
Two and Three Place Predicates
Dyadic (2) and Triadic Predicates (3)
Examples:
Fcfw_1 a is a person
Dcfw_1 a is a present
Lcfw_2 a loves b
G cfw_2 a gives b to c
a: Archie
b: Betty
c: Veronica
Archie loves Veronica L(ac)
Veronica Loves Ar
CONDITIONAL DERIVATION
you are going to begin a CD
on the next line, write the antecedent
Justification: ASS CD
New Goal: Show Consequent
box and cancel
BICONDITIONAL
you probably want to derive each of the two conditionals separately
then use CB to build
16 September, 2013
Basic Symbols
Capital Letters Represent propositions
Truth- functional connectives (~, ->, V, <->, ^)
organizational symbols () cfw_ Brackets
If you take a complex sentence with lots of connectives you can always determine
the truth or
30 September, 2013
Start with your show line
Write "show" then the sentence you need to prove
analyze your show line
can you directly derive it? DD
use the premises
use the derivation rules
use the lines you derive
Is the show line a conditional? CD
write
Monday 9 September, 2013
Logic HIstory
Aristotle- Aristotelian or syllogistic logic
Leibniz- father of symbolic logic. Developed logical calculi
George Boole- Boolean Logic (basis of modern computers) - bivalent algebraic
logic
Gottlob Frege- laid foundat
Wednesday 11 September, 2013
Bi-valent Logic- Either True or False. A sentence that is true or false has truth value
Deductively Valid and Sound
An argument is valid if it is impossible for the premises to be true and the
conclusion to be false
An argumen
18 September, 2013
Negation
P
T
F
~P
F
T
If P is true, not P is not true
If P is not true, not P is true
Material Conditional
P
T
T
F
F
Q
T
F
T
F
P->Q
T
F
T
T
P->Q
Antecedent (P is the antecedent, it comes before the arrow)
Consequent (Q is the consequent
25 September, 2013
Double Negation dn
Repetition r (X to X)
Modus Ponens mp
Modus Tollens mt
Direct Derivation
you begin with show one
and you prove it using the premises and your derivation rules
Available Lines:
Some lines are "available" in that the se
23 September, 2013
Neither NOR
Neither Karl Popper nor W.V.O. Quine is still living
~(PVQ) - Not either one of them
~P^~Q - Not the first and not the second
Not Both (OR)
Popper and Quine were not both british
~(P^Q)
(~PV~Q)
Exclusive OR - exactly on of t
6 November, 2013
How do you make sure you are choosing the right variable for Existential Instantiation?
1. Use EI as soon as possible
as soon as you have a sentence which is in the scope of an existential, you
want to use EI
2. Always choose an entirely