study guide for exam 1
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7/29/2019 Study Guide for Exam 1
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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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7/29/2019 Study Guide for Exam 1
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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.
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