1. Introduction to Deductive Logic

Question 1

Truth-preservation.

Answer 1

Never takes one from truths to a falsehood. The premises do not lead to false conclusions.

Question 2

Valid reasoning.

Answer 2

Reasoning that is truth-preserving: the premises do not lead to false conclusions.

Question 3

List (7) examples of systems of deductive logic:

Answer 3

(1) Euclid’s axiomatization of plane geometry (300 BCE; classical Greece); 5 fundamental assumptions/axioms;
(2) Giuseppe Peano; successfully axiomatized arithmetic (1889);
(3) Aristotle (350 BCE); developed “categorical” or “syllogistic” logic;
(4) Gottlob Frege; invented axiomatic predicate logic;
(5) David Hilbert; Hilbert-style deductive system; most suited for first-order logic;
(6) Bertrand Russell; axiomatic predicate logic;
(7) other logicians in the late nineteenth and early twentieth centuries.

Question 4

What is the difference between “Roberta will pass if she completes all of her homework” and “Roberta will pass only if she completes all of her homework”?

Answer 4

If “Roberta will pass if she completes all of her homework” is true, then Roberta can still pass even if she does not complete her homework. Completing all of her homework may not be the only pathway for Roberta to pass. This is unless “Roberta will pass only if she completes all of her homework”.

Question 5

What kinds of sentences have a truth value?

Answer 5

Sentences that assert something.

Question 6

What truth values can a sentence have?

Answer 6

True, false, and indeterminate.

Question 7

Argument.

Answer 7

A set of two or more sentences, one of which is designated as the conclusion and the others as the premises.

Question 8

Sets.

Answer 8

Abstract objects that have members (zero or more).

Question 9

Argument in standard form.

Answer 9

Lists premises with a horizontal line under the last premise, followed by a conclusion.

p1.
p2.
- - - - -
c.

Question 10

Logically valid argument.

Answer 10

An argument is logically valid if and only if it is not possible for all the premises to be true and the conclusion false. An argument is logically invalid if and only if it is not logically valid.

Question 11

A logical valid argument, by definition, is _____.

Answer 11

…truth preserving.

Question 12

Logically sound argument.

Answer 12

An argument is logically sound if and only if it is logically valid and all of its premises are true. An argument is logically unsound if and only if it is not logically sound.

Question 13

Provide an example of an argument that is logically valid but not logically sound:

Answer 13

p1. Italy is a country that is located in North America.
p2. Every country that is located in North America uses the United States dollar as its currency.
- - - - -
c. Italy uses the United States dollar as its currency.

Question 14

Provide an example of an argument that is logically valid and logically sound:

Answer 14

p1. The United States is a country that is located in North America.
p2. No country that is located in North America uses the euro as its currency.
- - - - -
c. The United States doe not use the euro as its currency.

Question 15

Provide (7) examples of conclusion indicator expressions:

Answer 15

(1) therefore,
(2) thus,
(3) it follows that,
(4) so,
(5) hence,
(6) consequently, and
(7) as a result,

Question 16

Provide (6) examples of premise indicator expressions:

Answer 16

(1) since,
(2) for,
(3) because,
(4) on account of,
(5) inasmuch as, and
(6) for the reason that.

Question 17

Does the formal definition of ‘argument’ allow for arguments in which the premise(s) provide no support whatsoever for the conclusion?

Answer 17

Yes, but it will be invalid if it is possible for the premise to be true and the conclusion false.

Question 18

Logically true sentence.

Answer 18

A sentence is logically true if and only if it is not possible for the sentence to be false.
- All sentences of the form p or not p, where p has a truth-value and not p is a denial of p.

Question 19

Logically false sentence.

Answer 19

A sentence is logically false if and only if it is not possible for the sentence to be true.
- All sentences of the form p and not p, where p has a truth-value and not p is a denial of p.

Question 20

Logically indeterminate sentence.

Answer 20

A sentence is logically indeterminate if and only if it is neither logically true nor logically false.
- Whether the truth value is true or false, it depends upon how the world in fact is.

Question 21

Provide an example of a logically true sentence:

Answer 21

Either June will pass Chemistry 101 or June will not pass Chemistry 101.

Question 22

Provide an example of a logically false sentence:

Answer 22

Both June will pass Chemistry 101 and June will not pass Chemistry 101.

Question 23

Provide an example of a logically indeterminate sentence:

Answer 23

It rained on July 6, 1309 in what is now San Francisco.

Question 24

Logically equivalent sentences.

Answer 24

Sentences p and q are logically equivalent if and only if it is not possible for one of these sentences to be true while the other sentence is false.

Question 25

Provide an example of logically equivalent sentences:

Answer 25

‘Jake loves Henry’ and ‘Henry is loved by Jake’.

Question 26

Logical consistency.

Answer 26

A set of sentences is logically consistent if and only if it is possible for all members of that set to be tyrue. A set of sentences is logically inconsistent if and only if it is not logically consistent.

Question 27

Provide an example of a logically consistent set:

Answer 27

{Tom is left-handed, Carol is left-handed, Mona is left-handed}

Question 28

Provide an example of a logically inconsistent set:

Answer 28

{Everyone in the room is left-handed, Mona is in the room, Mona is not left-handed}

Question 29

Entailment.

Answer 29

A set of sentences logically entails a sentence if and only if is impossible for the members of the set to be true and that sentence false.

Question 30

Provide an example of a sentence that this set entails:

{Henry and Joan will both receive their law degrees in June}

Answer 30

Joan will receive her law degree in June.

Question 31

Provide an example of a sentence that is entailed by:

{Andrew plays soccer, Siri Plays tennis}

Answer 31

Andrew does not play tennis and Siri does not play soccer.