2. Logic
some working definitions
The attempt to answer, critically, the
Philosophy epistemological, metaphysical, and ethical
questions.
Principle of Sufficient Reason: For any
Reasoning
claim give reason why it is true or not true.
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3. Truth
when a sentence matches what is—two forms
Subject–Predicate Form Subject–Verb–Object Form
((Subject) predicate) ((Subject)Verb(Object))
designates expresses designates expresses designates
<<Thing> property> <<Thing> relation<Thing>>
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4. Propositions as Intensions
Intensions: Things + Properties or Relations
Thing + Property
horse _____is an Equidae.
Equidae
fast things _____is four legged.
four legged things _____is bigger than_____.
land animal
animal _____is a horse. _____is fast.
mammal _____is an animal.
Seabiscuit _____is faster than_____.
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5. Concepts
As Properties
A wavelength of light
is an electromagnetic phenomenon.
more abstract
more general
A color is a wavelength of light.
more concrete
more specific
Red is a color.
The cherries are red.
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6. Sets as Propositions
Extension: An Alternate View
Element + Set
horse _____is an Equidae.
Equidae
fast things _____is four legged.
four legged things _____is bigger than_____.
land animal
animal _____is a horse. _____is fast.
mammal _____is an animal.
Seabiscuit _____is faster than_____.
Seabiscuit ∈ {Horses}
Seabiscuit ∈ {four-legged things}
Seabiscuit ∉ {cows}
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7. Sets
Are Extensions of Properties
being a vowel
Extensions as M L
V
meanings G
Y B F S Z
C
X E K
N I U T
A O
D H
R W J
Q
P
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8. Logic
The Laws of Thought Applied to Reason
Identity: any sentences about identical things will
have the same truth value.
Non-contradiction: a sentence, adequately
defined, cannot be both true and not true.
Bi-valence: a sentence, adequately defined, is
either true, or not true.
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9. Values
The Values of Reason
Truth: when the properties or relations of
proposition match the way the world is,—or isn't.
Consistency: a set of propositions free from
contradiction.
Soundness: a valid argument (such that if the
premises are true then the conclusion is true) with
true premises.
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10. THE GOAL OF SYMBOLIC
LOGIC
The goal of symbolic logic is to build a model that captures the Laws
and Values of Reason completely.
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11. Truth
some preliminaries
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
What is the difference
between the truth, an
Matters of Necessity honest mistake, and a lie?
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12. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
The ocean is prettier than the desert & the
desert is prettier than the woods.
Does this exhaust all truths?
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13. Truth
four types of truth
Matters of Taste or Opinion
Consider someone who
Matters of Convention honestly believes red means
go and green means stop. Is
his belief true, or an honest
Matters of Fact mistake?
Matters of Necessity
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14. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Steering wheels are on the left.
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15. Truth
four types of truth
Can be indexed to a register—a
Matters of Taste or Opinion convention in culture or society:
• According to the music business,
Tupac is gangsta is while My
Matters of Convention
Chemical Romance is emo.
Matters of Fact
Matters of Necessity
Does this exhaust all truths?
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16. Truth
four types of truth
Matters of Taste or Opinion
Consider a world
without people or
Matters of Convention conventions, would
water still boil at the
temperature we call
Matters of Fact ‘212º Fahrenheit’,
ceteris paribus?
Matters of Necessity
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17. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
The earth is 93 million miles from the sun.
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18. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Water boils at 212º fahrenheit.
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19. Truth
four types of truth
Such truths as often expressed ceteris
Matters of Taste or Opinion
paribus:
Matters of Convention
• The earth is about 93 million miles
from the sun on average.
Matters of Fact
• Water boils at 212º fahrenheit at
standard barometric pressure.
Matters of Necessity
Does this exhaust all truths?
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20. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
1 + 1 = 2
Matters of Fact
Matters of Necessity
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21. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
∏ = 3.141592...
Matters of Fact
Matters of Necessity
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22. Truth
four types of truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
∏ = 3.141592...
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23. Truth
some claim—true or false?
Here is Patagonia.
George W. Bush is President
Barack Obama is our President
Felipe Calderón is our President
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24. Truth
some claims are true when indexed to the the proper speaker or hearer.
Barack Obama is our President
True
Felipe Calderón is our President
True
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25. Truth
some claims are true when indexed to the the proper speaker or hearer.
Barack Obama is our President
False
Felipe Calderón is our President
False
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26. Truth
some claims are true when indexed to the proper place.
Here is Patagonia
False
Here is Patagonia
True
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27. Truth
some claims are true when indexed to the proper time.
George W. Bush is President
False
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
George W. Bush is President
True
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28. A Valid Argument
San Jose is bigger than San Francisco.
San Francisco is bigger than Milwaukee.
Therefore _______ is bigger than ______.
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29. Is this valid?
San Francisco is smaller than San Jose.
San Jose is smaller than Milwaukee.
Therefore _______ is smaller than ______.
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30. Equivocation
to equivocate is to use a term ambiguously or vaguely in an argument.
San Francisco is smaller than San JoseCalifornia.
San JoseCosta Rica is smaller than Milwaukee.
Therefore _______ is smaller than ______.
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31. Ambiguous
an ambiguous term is a term with more than one meaning.
Names (like ‘San Jose’) and many other terms can be ambiguous:
green
fire
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32. Vague
a vague term is a term with an unclear extension.
Pile Bald
How many make a pile? How many missing hairs before you are bald?
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33. Ambiguous & Vague
some terms can be both
Try to come up with some:
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34. Defining Terms
to define a term give it one clear meaning.
This will help to avoid the fallacy of equivocation.
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36. Definitions
sentences or propositions with terms as things
Subject Predicate
‘claim’ means an assertion open to challenge
term meaning
<Thing> <Property>
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37. Truth
what goes on before we get to formal logic
Discount claims about matters of taste or opinion.
Index claims to registers (cultural conventions)
including ceteris paribus conventions as well was
to to speakers, hearers, place/time.
Define terms by giving one (unambiguous) clear
(non-vague) meaning (set of properties).
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38. TRANSLATING SL
The goal of symbolic logic is to build a model that captures the Laws
and Values of Reason completely.
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39. Logical Connectives
Translating to and from SL
J : SRJC is a junior college. C : SRJC is in California.
D : Many students will be
F : SRJC will not get funding.
disappointed.
Using the abbreviations above symbolize the following as
sentences of SL:
If it is not the case that either SRJC is a junior college or SRJC is
in California then SRJC will not get funding.
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40. Logical Connectives
Translating to and from SL
J : SRJC is a junior college. C : SRJC is in California.
D : Many students will be
F : SRJC will not get funding.
disappointed.
Using the same abbreviations symbolize the following as
sentences of SL:
Many students will be disappointed if and only if it is not the case
that [either(either SRJC is a junior college or SRJC will not get
funding) or SRJC is in California].
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41. Logical Connectives
Translating to and from SL
J : SRJC is a junior college. C : SRJC is in California.
D : Many students will be
F : SRJC will not get funding.
disappointed.
Using the abbreviations above, construct idiomatic English
sentences for the following sentences of SL:
C V (A V B)
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42. Logical Connectives
Translating to and from SL
J : SRJC is a junior college. C : SRJC is in California.
D : Many students will be
F : SRJC will not get funding.
disappointed.
Using the abbreviations above, construct idiomatic English
sentences for the following sentences of SL:
(D ⊃ C) & ~(C V J)
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43. Logical Connectives
Translating to and from SL
Symbolize the following being careful to indicate the
abbreviations you are using:
If there are stuffed animals in this room then someone was
practicing taxidermy. The there are stuffed animals in this room.
So, someone was practicing taxidermy.
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44. Logical Connectives
Translating to and from SL
Symbolize the following being careful to indicate the
abbreviations you are using:
If I read the textbook and did the homework then I did well on
the first quiz. But I neither read the textbook nor did the
homework. Thus I did not do well on the first quiz.
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45. Logical Connectives
Translating to and from SL
Which of the following is a truth-functional compound:
a) It is well known that Kelly believes surfing is a sport.
b) Either Kelly Slater is injured or Pro Surfing is being ignored.
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46. Logical Connectives
Translating to and from SL
Which of the following is a sentence of SL:
c) ~(A1 V B2) V (C3 & D4)
d) (~A1 & ~B0) ⊃ (B3 = W4)
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47. Logical Connectives
Translating to and from SL
Which of the following is a sentence of the form P ⊃ Q:
e) A V (B ⊃ C)
f) A V B V C
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48. Logical Connectives
Translating to and from SL
Which of the following is a sentence of the form P & Q:
g) (A ⊃ B) & C
h) A & B & C
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