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STUDY GUIDE

PROOFS (page 49 & 65ff)

Axiom I

Contradictories (diagonal flip):

ASP ~OSPOSP ~ASP

ESP ~ISPISP ~ESP

Axiom IIContraries (top truth slide):

ASP ~ESP

ESP ~ASP(only workone way)

Axiom III

Simple Conversion ofE

ESP EPS

These are the only axioms that

you need to know. Every relationon the square can be proved from

these rules.

(all) A (no T & T) E (none)

(truth seeeu (truth

trickles trickles

down) down)

(some) I (no F & F) O (some not)

See p. 54

VOCAB

Take: ALK

A = quantifier

L =subject

K = predicate

is = copula

Take for example

EPR (minor)

AGP (major)

EGR

P = Middle term

Mood = EAE

Figure = 1

Name = EAE-1

(see page 75)

DISTRIBUTION(p. 71)

A Always check for two things:

1) Distributed middle term

2) If a term is distributed in

the conclusion, check that it

is also distributed in apremise. (Maybe no term is

distributed in the concl-

usion!)

If either of these are not met, then you have

a FORMAL FALLACY (p. 92). There are

only threeformal fallacies:

If (1) is broken, then it is the Fallacy of the

Undistributed Middle Term. If (2) is

broken, check whichpremise failed to

distribute the term. You will have either the

Fallacy of the Illicit Major, or oftheIllicit

Minor.

S P

A O --

E O O

I -- --

O -- O

FIGURE(p 77)

MP Fig. 1

SM

PM Fig. 2SM

MP Fig. 3MS

PM Fig. 4

MS

TO MAKE A CONCLUSION (P 91):

2 universals (A or E): universal

1 uni. / 1 particular:particular2 particulars (I or O): XXXX

2 affirmatives (A or I): affirmative

1 aff. / 1 negative: negative

2 negatives (E or O): XXXX

The non-middle term of the minor

premise is the subject of your

conclusion. The non-middle term of

the majorpremise is the predicate.

MEMORIZE THESE LATIN NAMES! (p 98)

Fig. 1 Fig. 2 Fig. 3 Fig. 4

Barbara Baroco Bocardo Camenes

Celarent Cesare Datisi Dimaris

Darii Camestres Disamis Fresison

Ferio Festino Ferison

The vowels correspond to the mood, the column to thefigure.

Contradictory: Propositions which always have the opposite truth values.

Contrary: Propositions which cannot both be true. (If one is false, its contrary is unknown!)

Sub-contrary: Propositions which cannot both be false. (If one is true, its sub-contrary is unknown!)

Sub-alternation / implication: The truth of the particular follows from the

truth of the universal. (If the universal is false, the particular is unknown!)

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Euclids Fifth Postulate (MEMORIZE!) (p 29): That, if a straight line falling on two straight lines makesthe interior angles on the same side less than two right angles, the two straight liens, if produced

indefinitely, meet on that side on which are the angles less than the two right angles.

Read and comprehend the Eratosthenes story from pages 37 48. If you want, find extra resources

online to help make any of the concepts clearer. Do your best to explain why the assumptions are

necessary. Do your best toshow your work with the math.

Read, comprehend, and memorize the list ofinformal fallacies (AKA fallacies of relevance) from

pages 18-21. Memorize that Latin!

Read and memorize Euclids stufffrom pages 27-29. Note:postulates begin with eitherto orthat.

Common notions dont mention any geometric shapes; they talk about things orwholes & parts and

four out of five have to do with equals. Memorize thepostulates and the common notions, and youshould be good.

Remember: If you know the truth-value of one corner of the square, you dont necessarily know for

certain the truth-values of every other corner. Be comfortable with leaving things blank.

Get plenty of rest, take your time, check your work, circle the distributed terms in the syllogisms, trust

your memory of the rules, and if you dont trust your memory then ask yourself if your answer makessense. Everything in logic makes sense. If you dont remember a rule (for example: simple

conversion), just think up an example and youll re-discover the rule quickly on your own.