Aristotle Prior Analytics I 4

8/8/2019 Aristotle Prior Analytics I 4

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PRAYER TO THE HOLY SPIRIT

Come Holy Spirit, fill the hearts of your faithful andkindle in them the fire of your love.

V. Send forth your Spirit, and they shall be created.

R.And You shall renew the face of the earth.

Let us pray.

O, God, who by the light of the Holy Spirit, did

instruct the hearts of the faithful, grant that by thesame Holy Spirit we may be truly wise and everenjoy His consolations. Through Christ Our Lord.Amen.

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Aristotles Prior Analytics I.4

PREVIOUSLY

Categories: Individual terms

or words. (human, rational,

6 feet tall, tan, standing)

On Interpretation:

Combining 2 terms into a

proposition or sentencethat is true or false. (All

humans are rational.)

NOW

PriorAnalytics: Combining

2 propositions into a

syllogism that concludes toa new proposition.

1. All humans are rational.

2. Socrates is human.

Therefore Socrates is

rational.

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Aristotles terminology X belongs to Y

Means X is predicatedof Y (X is the predicate

of the subject, Y)

Y is X

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Whenever 3 terms are

related so that the last

is contained in the

middle, and the middleeither contained in or

excluded from the first

It is a perfect syllogism

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is contained in the



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MIDDLE

LAST


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is contained in the



or = 2 possibilities

MIDDLE

LAST

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is contained in the



1st possibility: middle

contained in first

MIDDLE

LAST

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is contained in the



1st possibility: middle

contained in first

MIDDLE

LAST

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FIRST


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is contained in the



2nd possibility: middle

excluded from first

MIDDLE

LAST

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is contained in the



2nd possibility: middle

excluded from first

MIDDLE

LAST

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FIRST


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If A is predicated of all

B, and B of all C, A must

be predicated of all C

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All B is A

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All B is A

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A

B


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All B is A

All C is B

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A

B

C


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All B is A

All C is B

Therefore All C is A

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A

B

C


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Similarly also, if A is

predicated of no B, and

B of all C, it is necessary

that no C will be A

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that no C will be A

No B is A

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that no C will be A

No B is A

B

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A


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that no C will be A

No B is A

All C is B

B

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A


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that no C will be A

No B is A

All C is B

B

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A

C


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that no C will be A

No B is A

All C is B Therefore No C is A

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A

B

C


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if the first term belongs

to all the middle, but

the middle to none of

the last term, there willbe no syllogism

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FIRST

MIDDLE


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FIRST

MIDDLE

LAST


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Or it could mean this

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FIRST

MIDDLE

LAST

LAST


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The first could belong to

some or none of the

last no conclusion

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FIRST

MIDDLE

LAST

LAST


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Nor again can syllogism

be formed when

neither the first term

belongs to any of themiddle, nor the middle

to any of the last.

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be formed when



to any of the last.

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FIRST

MIDDLE


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be formed when



to any of the last.

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FIRST

MIDDLE

LAST


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be formed when



to any of the last.

Or it could mean this

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FIRST

MIDDLE

LAST

LAST


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be formed when



to any of the last.

First could belong to

some or none of last

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FIRST

MIDDLE

LAST

LAST


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But if one term isrelated universally, theother in part only, to its

subject, there must be aperfect syllogismwhenever universality isposited with reference

to the major term

Confused? Read PAST it

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I call that term the

major in which the

middle is contained and

that term the minor

which comes under the

middle.

Comes under? Still

confused? Read PAST it

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Let all B be A and some

C be B. Then if

predicated of all

means what was saidabove, it is necessary

that some C is A.

THATS understandable

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C be B. Then if

predicated of all


that some C is A.

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A

B


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C be B. Then if

predicated of all


that some C is A.

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A

B

C


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C be B. Then if

predicated of all


that some C is A.

All B is A; Some C is B

Therefore some C is A

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A

B

C


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C be B. Then if

predicated of all


that some C is A.



39

Now go back and read

again:


major in which the


that term the minor


middle.


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C be B. Then if

predicated of all


that some C is A.



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Now go back and read

again:


major in which the


that term the minor


middle.


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C be B. Then if

predicated of all


that some C is A.



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A is that in which all

of B is contained


major in which the


that term the minor


middle.


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C be B. Then if

predicated of all


that some C is A.



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So A = the major, and B

= the middle


major in which the


that term the minor


middle.


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C be B. Then if

predicated of all


that some C is A.



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So that means that the

minor must be C


major in which the


that term the minor


middle.


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C be B. Then if

predicated of all


that some C is A.



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Middle = the only term

in BOTH premises


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C be B. Then if

predicated of all


that some C is A.



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in BOTH premises

Major = the 1st letter of

the remaining two


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C be B. Then if

predicated of all


that some C is A.



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in BOTH premises

Major = the 1st letter of

the remaining two

Minor = the 2nd

letter ofthe remaining two


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C be B. Then if

predicated of all


that some C is A.



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Premise with major in it

always goes first


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C be B. Then if

predicated of all


that some C is A.



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always goes first

Premise with minor in it

always goes second


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C be B. Then if

predicated of all


that some C is A.



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always goes first

Premise with minor in it

always goes second

In the conclusion, majorpredicated of minor


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Next: And if no B is A

but some C is B, it is

necessary that some C

is not A

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is not A

No B is A

Some C is B

Therefore some C is not

A

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is not A

No B is A

Some C is B


A

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B

A

C


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is not A

No B is A

Some C is B


A

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B

A

C


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But if the universality is

posited with respect to

the minor term either

affirmatively ornegatively, a syllogism

will not be possible,

whether the major

premise is positive ornegative

Confused? Read past it.

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e.g. if some B is or is

not A, and all C is B

Thats clear. So:

Some B is or is not A

All C is B

No syllogism

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Thats clear. So:


All C is B

No syllogism

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or = 2 possibilities.

Start with some B is A


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Thats clear. So:


All C is B

No syllogism

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A

B


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Thats clear. So:


All C is B

No syllogism

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A

B

C


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Thats clear. So:


All C is B

No syllogism

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Start with some B is A.

But it can mean this too

A

B

CC


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Thats clear. So:


All C is B

No syllogism (Some or

none of C could be A)

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Start with some B is A.

But it can mean this too

A

B

CC


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Thats clear. So:


All C is B

No syllogism

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Now do 2nd possibility

some B is NOT A.


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Thats clear. So:


All C is B

No syllogism

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some B is NOT A.

A

B


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Thats clear. So:


All C is B

No syllogism

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some B is NOT A. But:

A

B

CC


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Thats clear. So:


All C is B



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some B is NOT A.

A

B

CC


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Again if no C is B, but

some B is or is not A or

not every B is A, there

cannot be a syllogism.

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No C is B


No syllogism

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Again ifno C is B, but




No C is B


No syllogism

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Note that Aristotle

states the minor

premise first this time

(the premise with C).


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Again ifno C is B, but





No C is B

No syllogism

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Note that Aristotle

states the minor

premise first this time

(the premise with C).

Always put the minor

premise second, no

matter what order

Aristotle states it


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No C is B

No syllogism

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or = 2 possibilities


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No C is B

No syllogism

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or = 2 possibilities. 1st

possibility: Some B is A.


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No C is B

No syllogism

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A

B


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No C is B

No syllogism

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A

B

C


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No C is B

No syllogism

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Or it could look like this:

A

B

CC


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No C is B



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Or it could look like this:

A

B

CC


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No C is B

No syllogism

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or = 2 possibilities. 2nd

possibility: Some B is

not A.


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No C is B

No syllogism

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not A.

A

B


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No C is B

No syllogism

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not A.

A

B

C


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No C is B

No syllogism

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not A. Or:

A

B

CC


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No C is B



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not A. Or:

A

B

CC

A i l P i A l i I 4


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An easier way to memorize these syllogisms

Aristotle lists many combinations in this

chapter some valid, and many more invalid

Of all the combinations in this chapter, he only

lists 4 that make valid syllogisms

Memorize these 4, and you know the rest are

invalid

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1st valid combination

All B is A

All C is B

Therefore All C is A

A

B

C

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2nd valid combination

No B is A

All C is B

Therefore No C is A

A

B

C

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4th valid combination

No B is A

Some C is B

Therefore Some C is not

A

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B

A

C

Prior Analytics I 4


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Prior Analytics I.4

A chart for all premise combinations

There are only 4 kinds

of premises: 1. Universal affirmative

2. Universal negative

3. Particular affirmative

4. Particular negative

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Prior Analytics I 4


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Prior Analytics I.4

A chart for all premise combinations

There are only 4 kinds

of premises:

So since there are twopremises in a syllogism,

there are a limited

number of possible

combinations

1. Universal affirmative

2. Universal negative

3. Particular affirmative

4. Particular negative

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Prior Analytics I.4

So 4 possibilities for major premise

1ST FIGUREMajor Universal

Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

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Prior Analytics I.4

Same 4 possibilities for minor premise


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

Affirmative

Minor Universal

Negative

Minor Particular

Affirmative

Minor Particular

Negative

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Prior Analytics I 4


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Prior Analytics I.4

Fill in columns for major premise


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

AffirmativeAll B is A

Minor Universal

NegativeAll B is A

Minor Particular

Affirmative

All B is A

Minor Particular

NegativeAll B is A

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Prior Analytics I.4

Fill in columns for major premise


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

AffirmativeAll B is A No B is A Some B is A Some B is not A

Minor Universal

NegativeAll B is A No B is A Some B is A Some B is not A

Minor Particular

Affirmative

All B is A No B is A Some B is A Some B is not A

Minor Particular


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Prior Analytics I 4


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Prior Analytics I.4

Then fill in rows for minor premise


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

Affirmative

All B is A

All C is B

No B is A

All C is B

Some B is A

All C is B

Some B is not A

All C is B

Minor Universal


Minor Particular

Affirmative

All B is A No B is A Some B is A Some B is not A

Minor Particular


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Prior Analytics I 4


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Prior Analytics I.4

Then fill in rows for minor premise


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

Affirmative

All B is A

All C is B

No B is A

All C is B

Some B is A

All C is B

Some B is not A

All C is B

Minor Universal

Negative

All B is A

No C is B

No B is A

No C is B

Some B is A

No C is B

Some B is not A

No C is B

Minor Particular

Affirmative

All B is A

Some C is B

No B is A

Some C is B

Some B is A

Some C is B

Some B is not A

Some C is B

Minor Particular

Negative

All B is A

Some C is not B

No B is A

Some C is not B

Some B is A

Some C is not B

Some B is not A

Some C is not B

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Prior Analytics I.4

Highlight the ones he says are valid


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

Affirmative

All B is A

All C is B

All C is A

No B is A

All C is B

No C is A

Some B is A

All C is B

Some B is not A

All C is B

Minor Universal

Negative

All B is A

No C is B

No B is A

No C is B

Some B is A

No C is B

Some B is not A

No C is B

Minor Particular

Affirmative

All B is A

Some C is B

Some C is A

No B is A

Some C is B

Some C is not A

Some B is A

Some C is B

Some B is not A

Some C is B

Minor Particular

Negative

All B is A

Some C is not B

No B is A

Some C is not B

Some B is A

Some C is not B

Some B is not A

Some C is not B

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Prior Analytics I 4


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Prior Analytics I.4

1st Figure combinations


Affirmative

Major Universal

Negative

Major Particular

Affirmative

Major Particular

Negative

Minor Universal

Affirmative

All B is A

All C is B

All C is A

No B is A

All C is B

No C is A

Some B is A

All C is B

Some B is not A

All C is B

Minor Universal

Negative

All B is A

No C is B

No B is A

No C is B

Some B is A

No C is B

Some B is not A

No C is B

Minor Particular

Affirmative

All B is A

Some C is B

Some C is A

No B is A

Some C is B

Some C is not A

Some B is A

Some C is B

Some B is not A

Some C is B

Minor Particular

Negative

All B is A

Some C is not B

No B is A

Some C is not B

Some B is A

Some C is not B

Some B is not A

Some C is not B

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Aristotle Prior Analytics I 4