Species #1

Difference 2

Species #2

Difference 1

Genus

Logical Division of a

A genus is divided into species by adding differences.

Substance

Substance having life = Organism

Having life

GENUS

GENUS+ DIFFERENCE = SPECIES

DIFFERENCE

A difference must exclude some individual members of the genus.

EXCLUDES

COPPER, IRON, SALT, ET AL.

Substance

Substance having life = Organism

Having life

?

Something that excludes nothing is not a difference, and so it does not divide the genus,

nor does it make a species.

EXCLUDES

No organismEvery organism

Being cellular

Organism

NOT A DIFFERENCE

Something that includes nothing is not a difference, and so it does not divide the genus,

nor does it make a species.

EXCLUDES

Every animal

Animal

No animal

Having leaves

NOT A DIFFERENCE

Each part in a genus requires its own difference.

havingTwo Legs

BipedQuadruped

havingFour Legs

Animal

Not all differences make good divisions.Is this a good division of the genus?

Species #1

havingWebbed Feet

e.g. a dog e.g. a duck

Species #2

havingFour Legs

Animal

To which species does a snake belong?

A good division is exhaustive.

DEFINITION: An exhaustive division of a genus is one in whichevery individual of the genus falls into a species.

Species #1

havingWebbed Feet

Species #2

havingFour Legs

The division is no good because it is not exhaustive.

Animal

To which species does a frog belong?

Animal

A good division is exclusive.

DEFINITION: An exclusive division of a genus is one in whichno individual of the genus falls into two species.

Species #1

havingWebbed Feet

Species #2

havingFour Legs

The division is no good because it is not exclusive.

neither

What counter example proves this division is not exhaustive?

A division is EXHAUSTIVE when every individual of that genus has a species to which it belongs.

What counter example proves this division is not exclusive?

havingWebbed Feet

havingFour Legs both

Animal

Species #1 Species #2

A division is EXCLUSIVE when no individual of that genus falls into more than one species.

Summary

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

Summary

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

• A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species.

• A difference must include some individual in the genus and exclude some individual in the genus.

• A perfect division has two qualities: it must be exhaustive and it must be exclusive.

• Imperfect divisions fail to be exhaustive, or exclusive, or both.

What counter example proves this division is not exhaustive?

Give two differences that make a division which isEXCLUSIVE but NOT EXHAUSTIVE.Why is this division exclusive?

??

Animal

Species #1 Species #2

Having exactly four legs

Having exactly two legs

What counter example proves this division is not exclusive?

Give two differences that make a division which isEXHAUSTIVE but NOT EXCLUSIVE.Why is this division exhaustive?

??

Animal

Species #1 Species #2

Water-breathing Air-breathing

What counter example proves this division is not exhaustive?

Give two differences that make a division which isNEITHER EXCLUSIVE NOR EXHAUSTIVE.

What counter example proves this division is not exclusive?

??

Animal

Species #1 Species #2

Four-footed Web-footed

Why is this division exhaustive?

Give two differences that make a division which isBOTH EXCLUSIVE and EXHAUSTIVE.

??

Animal

Species #1 Species #2

Why is this division exclusive?

Species #1

Not havingfeathers

Species #2

Havingfeathers

To guarantee that a division is both exhaustive and exclusive, logicians divide using contradictory differences.

Such a division is bothexhaustive

(an individual animal either has feathers or it doesn’t)and exclusive

(an individual animal can’t have feathers and not have them at the same time.)

Animal

HomeworkSelect four different genera. Divide each one as follows:

•Divide genus #1 so the division is exclusive but not exhaustive.•Divide genus #2 so the division is exhaustive but not exclusive .•Divide genus #3 so the division is neither exclusive nor exhaustive.•Divide genus #4 so the division is both exclusive and exhaustive.

Give reasons for each, using complete sentences, of the following form:Division is exhaustive b/c every _______(genus) falls under one of the differences.Division isn’t exhaustive b/c ________(counter-ex.) doesn’t fall under one of the differences.Division is exclusive b/c no _______(genus) falls under two differences.Division isn’t exclusive b/c ________(c-example) does fall under two differences.

Division by contradictory differencesis called logical dichotomy

YUM“What is the essence of a

banana?”

Man

Not having thecapacity to reason

Brute

Having thecapacity to reason

Animal

Man Brute

“What is the meaning of

life?” EAT!

Man

Non-rational

Brute

Rational

In division by contradictory differences,one difference is called possession,

the other privation.

Animal

Man is a rational animal. A brute is an irrational animal.

Positive Difference

Privative Difference

One problem with logical dichotomy is that the definition of one species says not WHAT IT IS,

but WHAT IT ISN’T.

“What is the nature of

happiness?”

Abstract thinking – OH YEAH!

Abstract thinking – NOT!

For more complex divisions, differences can be combined in a

matrix.

SPECIES #1 SPECIES #2

SPECIES #3 SPECIES #4

Possession Privation

DIFFERENCE #1

Poss

essi

onPr

ivati

onDIF

FERE

NCE

#2

GENUS

SQUARE OBLONG

RHOMBUS

Quadrilateral with an

unequal side and oblique

angle.

Possession Privation

WITH ALL SIDES EQUAL

Poss

essi

onPr

ivati

on

WIT

H A

LL A

NG

LES

RIG

HT

QUADRILATERAL

Quadrilaterals can be divided using a matrix.

NB: Species is unnamed, so we

must use circumlocution to

identify it.

Rhomboids & Trapezia

SQUARE OBLONG

RHOMBUS

Divide a genus of your choosing using a matrix.

Possession PrivationPo

sses

sion

Priv

ation

Homework

Select four different genera. Divide each using a matrix:

• Do not give examples of the species, but name the species in the matrix.

• If a species does not have a name, identify it using circumlocution.

FINIS.

FINIS

© 2009 Peter Orlowski. All rights reserved. © 2009 Peter Orlowski. All rights reserved.