Answers to Exercises

1.1 | 1.2 | 2.1 | 2.2 | 3.1 | 3.2 | 3.3 | 4.0 | 5.1 | 5.2 | 6.1 | 6.2

Exercise 1.1

1	I	universal
2	J	particular
3	E	distributed
4	F	undistributed
5	E	distributed
6	H,G	h quality; g quantity
7	B	I(ab)
8	B	I(ab)
9	A	A(ab)
10	D	E(ab)
11	C	O(ab)
12	E, FF, E	e distributed; f undistributed, orf undistributed; e distributed

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Exercise 1.2

1	No c is s. E(cs)No Christian is a secularist.
2	Some c is s. I(sc)Some children are runners-to school.
3	All s is g. A(sg)All students who get A's are good students
4	All f is b. A(fb)All those who deserve the fair are brave.
5	All non-w is e. (A(w' s)All non-workers are those who may enter. (And)No w is e. E(we)No worker is one who may enter.
6	All b is f. A(bf)All those who use the back door are freshmen.
7	All w is p. A(wp)All times someone is with you are times the poor are with you.
8	All a is o. A(ao)All times you get into an argument are times you squirm out of it.
9	All non-l is v. A(l' v)All un-Godly labor is vain. (Or)No l is v. E(lv) by obversionNo Godly labor is vain.
10	All l is s. A(ls)All logic is necessary inference-science.
11	All s are l. A(sl)All sinners are transgressors-of-the-law.
12	All f is e. A(fe)All of the Fall is a bringer-of-sin-and-misery.
13	No w is e. E(we)No worthwhile thing is an easy thing.
14	All i is k. A(ik)All lovers of instruction are lovers of knowledge.
15	No j is c. E(jc)No one who is in Jesus Christ is one who is condemned.
16	All s is a. A(sa)All of the New Testament sacraments are Baptism and the Lord's Supper.
17	All m is l. A(ml)All those who say something meaningful are those who do so by virtue of the Law of Contradiction.
18	Some s is p. I(sp)Some hold that God's Sovereignty and man's responsibility are paradoxical.
19	Some q is e. I(qe)Some exercise questions are easy.
20	Some f is non-v. I(fv' )Some eligible voters are persons who do not vote.

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Exercise 2.1

1	F	proposition
2	C	immediate inference
3	I	valid
4	A	affirmative forms
5	D	negative forms
6	B	distributed term
7	G	undistributed term
8	A	affirmative forms
9	D	negative forms
10	H	universal forms

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Exercise 2.2

1	A	contraries
2	F	subcontraries
3	B	contradictories
4	B	contradictories
5	A	contraries
6	F	subcontraries
7	C, G, C	c false; g true; c false
8	G, D, D	g true; d undetermined; d undetermined
9	C, D, D	c false; d undetermined; d undetermined
10	G,C,G	g true; c false; g true
11	D	undetermined
12	H	reflexive
13	I	symmetrical
14	J	transitive

15
(1)	H	reflexive
(2)	J	transitive
(3)	I	symmetrical
(4)	J	transitive
(5)	I	symmetrical
(6)	J	transitive
(7)	J	transitive
(8)	J	transitive

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Exercise 3.1

1	K	syllogism
2	D	major term
3	G	minor term
4	E	middle term
5	C	major premise
6	F	minor term
7	J	simple conversion
8	A	conversion per accidens
9	B	first figure
10	I	second figure
11	L	third figure
12	H	fourth figure

1.1 | 1.2 | 2.1 | 2.2 | 3.1 | 3.2 | 3.3 | 4.0 | 5.1 | 5.2 | 6.1 | 6.2

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Exercise 3.2

1	All thinking beings are existing beings. I am a thinking being.Therefore, I am an existing being. AAA-1 Barbara ( A version of Cogito, ergo sum. It is questionable whether "existence" is a significant predicate.)
2	All communists are persons who practice what they preach.Some good Christians are persons who practice what they preach.Therefore, Some good Christians are communists.AII-2, Invalid by Rule 1; the middle term is undistributed.
3	All persons who are stupid are persons who swallow propaganda.No logic students are persons who are stupid.Therefore, No logic students are persons who swallow propaganda.AEE-1; Invalid, Rule 2; the major term in premise is undistributed.
4	All who know the truth are free indeed.All whom the Son makes free are those who know the truth.Therefore, All whom the Son makes free are free indeed.AAA-1; Barbara, Valid
5	No thing that is a descriptive science is a thing that can justify evaluations.All psychology-science is a descriptive science.Therefore, No psychology-science is a thing that can justify evaluations.EAE-1; Celarent, Valid.
6	All things done by God are good things.All God-predestinated-evil is a thing done by God.Therefore, All God-predestinated-evil is a good thing.AAA-1; Barbara, Valid.
7	No person who knows the truth is a slave of sin.All whom the son makes free are persons who know the truth.Therefore, No person whom the Son makes free is a slave of sin.EAE-1; Celarent, Valid
8	All theologians are former seminary students.Some former seminary students are poor scholars.Therefore, Some poor scholars are theologians.AII-4; Invalid, Rule 1; middle term is undistributed.
9	All change in our sense organs are changes that lead to deception at one time or another.All persons are persons who have changes in their sense organs.Therefore, All persons are persons who have changes that lead to deception at one time or another.AAA-1; Barbara, Valid
10	All system-starting-points, by definition, are indemonstrable axioms.All systems of philosophy (or theology) are systems that choose starting points.Therefore, All systems of thought are systems with indemonstrable axioms.AAA-1; Barbara, Valid; OR,No starting points of a system of thought are first principles that can be demonstrated.Every system of thought has starting points.Therefore, No system of thought has first principles that can be demonstrated.EAE-1; Celarent, Valid; Or, by obversion of the conclusion:Therefore, All systems of thought have indemonstrable first principles.

Exercise 3.3

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1	A	axioms
2	C	Rule I (Deduction)
3	D	Rule II (Deduction)
4	E, F	e strengthened formf weakened form
5	G	Five Rules
6	B	theorem
7	H	necessary & sufficient.

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Exercise 4.0

1	G	modus ponens
2	H	modus tollens
3	B	affirming the consequent
4	D	denying the antecedent
5	A	disjunctive syllogism
6	E	dilemma
7	J	valid
8	C	complete
9	I	interdefinable
10	F	transitive syllogism

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Exercise 5.1

Part A		Part B
1	B	1	G
2	E	2	A
3	A	3	B
4	C	4	C
5	F	5	D
6	D	6	D
7	G	7	C
		8	E
		9	F
		10	F

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Exercise 5.2

Hawk Newton is good in either science or theology, but not both. Moreover, either he is good at logic or bad at theology.

If he is not good in science, he is bad at theology. If he is bad at theology, he is good at logic.

What do these four premises imply, if anything? Is Hawk good in anything? In or at what?

1	. Hawk is good in either science or theology, but not both.	(s + t)(st)'
2	Hawk is good at logic or bad at theology.	(l + t' )
3	If he is not good in science, he is bad at theology.	(s' < t' )
4	If he is bad at theology, he is good at logic.	(t' < l)

				1st		2nd	3rd	4th
	s	l	t	(s + t)	(st)'	(l + t')	(s' < t' )	(t' < l)
1	T	T	T	T	F	T	T	T
2	T	T	F	T	T	T	T	T
3	T	F	T	T	F	F	T	T
4	T	F	F	T	T	T	T	F
5	F	T	T	T	T	T	F	T
6	F	T	F	F	T	T	T	T
7	F	F	T	T	T	F	F	T
8	F	F	F	F	T	T	T	F
	i	ii	iii	iv	v	vi	vii	viii

Row #2 is the only row that has true values in columns iv through viii. Notice the values of the propositional variables in that same row. There, Hawk is good at science and logic, but it is false that he is good at theology, at least according to this truth table analysis. One more deduction is possible from the third and fourth propositions: (s' < t' ) and (t' < l) imply (s' < l) by transitive syllogism. If Hawk is not good at science, then he is good at logic.

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Exercise 6.1

1	B	11	I
2	C	12	A
3	D	13	L
4	F	14	O
5	G	15	M
6	H	16	P false dilemma
7	P hasty generalization	17	P non sequitur
8	J	18	P weak or false analogy
9	K	19	E
10	N	20	P strawman

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Exercise 6.2

1	K	12	B
2	E	13	I
3	F	14	J
4	A	15	N
5	L	16	H
6	D	17	C
7	H	18	I
8	J	19	N
9	M	20	H
10	G	21	N
11	C	22	K

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