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.