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IntroductionPhil 4: Logic
Philosophy
Thales, 620 — 546 BCE
How do you know?
mythos/logos
Philosophy
How do you know?
Anaximander, 610—546 BCE
What is real?
the Boundless
Philosophy
How do you know?
What is real?
Heraclitus, 500 BCE
How to live?
All humans are bound by one law
Philosophy
How do you know?
What is real?
How to live?
Epistemology
Philosophy
How do you know?
What is real?
How to live?
Epistemology
Metaphysics
Philosophy
How do you know?
What is real?
How to live?
Epistemology
Metaphysics
Ethics
How do you know?
What is real?
How to live?
Epistemology
Metaphysics
Ethics
Philosophybegins in wonder
Philosophy
The attempt to answer, critically, the epistemological, metaphysical, and
ethical questions.Philosophy
a working definition
Reasoning
Leibniz, 1646 – 1716
Principle of Sufficient Reason:
For any claim give reason why it is true or not true.
Reasoning
Generally, we express our reasoning in sentences.
Logica rough distinction
Logica rough distinction
Empirical Sciences investigate the truth values of propositions about the sensible world;
Formal Sciences, such as Logic, investigate the relations between such propositions.
Briefly: Empirical Sciences are about content, Formal Sciences are about relations.
Logica rough distinction
Empirical Sciences investigate the truth values of propositions about the sensible world;
Formal Sciences, such as Logic, investigate the relations between such propositions.
Briefly: Empirical Sciences are about content, Formal Sciences are about relations.
Logica rough distinction
Empirical Sciences investigate the truth values of propositions about the sensible world;
Formal Sciences, such as Logic, investigate the relations between such propositions.
Briefly: Empirical Sciences are about content, Formal Sciences are about relations.
Truthwhat makes a claim true?
?
?
?
Subject–Predicate Form Subject–Verb–Object Form
<<<<ThingThing> > propertyproperty>>
((((subjectsubject) ) PredicatePredicate))
expressesexpressesdesignatesdesignates
<<<<ThingThing> > relationrelation<<ThingThing>>>>
((((subjectsubject))VerbVerb((ObjectObject))))
expressesexpressesdesignatesdesignates designatesdesignates
Truthwhen a sentence matches what is—two forms
The Claim What is: reality
The sun’s gravity well bends light.
when a sentence matches what is—two forms
Truth
The Claim What is: reality
((((The sun’s gravity wellThe sun’s gravity well) ) bends bends light.light.))
((((subjectsubject) ) PredicatePredicate))
The sun’s gravity well bends light.
Truthwhen a sentence matches what is—two forms
<<<<ThingThing> > propertyproperty>>
The Claim What is: reality
expressesexpressesdesignatesdesignates<<the sun’s the sun’s
gravity wellgravity well>>
<<bending bending lightlight>>
Truth
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
when a sentence matches what is—two forms
The Claim What is: reality
Truth
The remora is on the shark.
when a sentence matches what is—two forms
The Claim What is: reality
Truth
((((The remoraThe remora) ) is on is on ((the sharkthe shark..))))((((subjectsubject) ) VerbVerb ( (objectobject))))
The remora is on the shark.
when a sentence matches what is—two forms
The Claim What is: reality
<<remoraremora>>
<<sharkshark>>
expressesexpressesdesignatesdesignates
<<<<ThingThing> > relationrelation<<ThingThing>>>>
designatesdesignates<<being onbeing on>>{
Truth
((((The remoraThe remora) ) is on is on ((the sharkthe shark..))))((((subjectsubject) ) VerbVerb ( (objectobject))))
The remora is on the shark.
when a sentence matches what is—two forms
Thing–Property Form Thing–Relation–Thing Form
<<<<ThingThing> > propertyproperty>>
((((subjectsubject) ) PredicatePredicate))
expressesexpressesdesignatesdesignates
<<<<ThingThing> > relationrelation<<ThingThing>>>>
((((subjectsubject))VerbVerb((ObjectObject))))
expressesexpressesdesignatesdesignates designatesdesignates
Propositions (sometimes considered as intensions or meanings)
PropositionsThings + Properties or Relations
Thing Property+
horse
Seabiscuit
animal
Equidae
mammal
land animal
fast things
four legged things
_____is four legged.
_____is an animal.
_____is a horse.
_____is faster than_____.
_____is fast.
_____is an Equidae.
_____is bigger than_____.
Propositions as IntensionsIntensions: Things + Properties or Relations
Red is a color.Red is a color.
A color is a wavelength of light.A color is a wavelength of light.
The cherries are red.The cherries are red.
A wavelength of light A wavelength of light is an electromagnetic is an electromagnetic
phenomenon.phenomenon.
ConceptsAs Properties
Red is a color.Red is a color.
A color is a wavelength of light.A color is a wavelength of light.
The cherries are red.The cherries are red.
A wavelength of light A wavelength of light is an electromagnetic is an electromagnetic
phenomenon.phenomenon.
Red as a concept.
Red as a thing.
ConceptsAs Properties
Red is a color.Red is a color.
A color is a wavelength of light.A color is a wavelength of light.
The cherries are red.The cherries are red.
A wavelength of light A wavelength of light is an electromagnetic is an electromagnetic
phenomenon.phenomenon.
Color as a thing.
Color as a concept.
ConceptsAs Properties
Red is a color.Red is a color.
A color is a wavelength of light.A color is a wavelength of light.
The cherries are red.The cherries are red.
A wavelength of light A wavelength of light is an electromagnetic is an electromagnetic
phenomenon.phenomenon.
more
genera
lm
ore
genera
l
more
specifi
cm
ore
specifi
c
more
ab
stra
ctm
ore
ab
stra
ct
more
concre
tem
ore
concre
te
ConceptsAs Properties
Element Set+
horse
Seabiscuit
animal
Equidae
mammal
land animal
fast things
four legged things
_____is four legged.
_____is an animal.
_____is a horse.
_____is faster than_____.
_____is fast.
_____is an Equidae.
_____is bigger than_____.
Sets as PropositionsExtension: An Alternate View
Seabiscuit ∉ {cows}
Seabiscuit ∈ {four-legged things}
Seabiscuit ∈ {Horses}
A
BC
D
E
F G
H
I
J
K
LM
NO
PQ
R
S
TU
V
W
X
Y Z
being a vowel
Extensions as meanings
SetsAre Extensions of Properties
being divisible by two without a remainder
22
9
11
32
27
21
1366
3
14
1445
77
Extensions as meanings
SetsAre Extensions of Relations
The Sentence The Abbreviation
Symbolism
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
how English is translated into logic
((The sun’s gravity well) Bends light.)((subject) Predicate)
sB((subject) Predicate)
Bs((Predicate) subject)
The Sentence The Abbreviation
Symbolism
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
how English is translated into logic
((The sun’s gravity well) Bends light.)((subject) Predicate)
sB((subject) Predicate)
Bs((Predicate) subject)
find the subject & predicate
The Sentence The Abbreviation
Symbolism
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
how English is translated into logic
((The sun’s gravity well) Bends light.)((subject) Predicate)
sB((subject) Predicate)
Bs((Predicate) subject)
abbreviate the subject abbreviate the Predicate
The Sentence The Abbreviation
Symbolism
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
how English is translated into logic
((The sun’s gravity well) Bends light.)((subject) Predicate)
sB((subject) Predicate)
Bs((Predicate) subject)
with an upper case letterwith a lower case letter
The Sentence The Abbreviation
Symbolism
((The sun’s gravity well) bends light.)((subject) Predicate)
The sun’s gravity well bends light.
how English is translated into logic
((The sun’s gravity well) Bends light.)((subject) Predicate)
sB((subject) Predicate)
Bs((Predicate) subject)reverse them
The Sentence The Abbreviation
Symbolism
((The remora) is on (the shark.))((subject) Verb (object))
The remora is on the shark.
how English is translated into logic
((The remora) is on (the shark.))((subject) Verb (object))
rOs((subject) Predicate)
Osr((Predicate) subject)
The Sentence The Abbreviation
Symbolism
((The remora) is on (the shark.))((subject) Verb (object))
The remora is on the shark.
how English is translated into logic
((The remora) is on (the shark.))((subject) Verb (object))
rOs((subject) Predicate)
Osr((Predicate) subject)
find the subject, Verb, & object
The Sentence The Abbreviation
Symbolism
((The remora) is on (the shark.))((subject) Verb (object))
The remora is on the shark.
how English is translated into logic
((The remora) is on (the shark.))((subject) Verb (object))
rOs((subject) Predicate)
Osr((Predicate) subject)
abbreviate the subject & object
abbreviate the Verb
The Sentence The Abbreviation
Symbolism
((The remora) is on (the shark.))((subject) Verb (object))
The remora is on the shark.
how English is translated into logic
((The remora) is on (the shark.))((subject) Verb (object))
rOs((subject) Predicate)
Osr((Predicate) subject)
with an upper case letterwith lower case letters
The Sentence The Abbreviation
Symbolism
((The remora) is on (the shark.))((subject) Verb (object))
The remora is on the shark.
how English is translated into logic
((The remora) is on (the shark.))((subject) Verb (object))
rOs((subject) Predicate)
Osr((Predicate) subject)order them, Verb first
Symbolismtry these
Red is a color.Red is a color.
A color is a wavelength of light.A color is a wavelength of light.
The cherries are red.The cherries are red.
A wavelength of light A wavelength of light is an electromagnetic is an electromagnetic
phenomenon.phenomenon.
Light is faster than Sea BiscuitLight is faster than Sea Biscuit
55 is divisible by 555 is divisible by 5
LogicThe Laws of Thought
Identity: a relation each thing bears to itself and to nothing else.
Non-contradiction: nothing can simultaneously both have and not have the identical property or relation.
Bi-valence: a thing either is, or isn't.
LogicThe Laws of Thought
Identity: a relation each thing bears to itself and to nothing else.
Non-contradiction: nothing can simultaneously both have and not have the identical property or relation.
Bi-valence: a thing either is, or isn't.
LogicThe Laws of Thought
Identity: a relation each thing bears to itself and to nothing else.
Non-contradiction: nothing can simultaneously both have and not have the identical property or relation.
Bi-valence: a thing either is, or isn't.
LogicThe 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.
ValuesThe 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.
ValuesThe 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.
ValuesThe 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.
The goal of Symbolic Logic
The goal of symbolic logic is to build a model that captures the Laws and Values of Reason completely.