Deck 13: Identity

Question 1

General Theory

-Determine the status of the following relations with respect to symmetry, transitivity, and reflexivity:
a) ______________ respects _ _ _ _ _ _ _ _ _
b) ______________ resembles _ _ _ _ _ _ _ _ _
c) ______________ is a child of _ _ _ _ _ _ _ _ _

Answer 1

a. nonsymmetrical, nontransitive, nonreflexive.
b. symmetrical, nontransitive, totally reflexive.
c. asymmetrical, intransitive, irreflexive.

Question 2

General Theory

-Explain why translating "s is visible to Jane" as a material conditional, such as "if s is near Jane (and the line of sight is unobstructed, etc.) then it will be seen by her," seems to be inadequate.

Answer 2

The main problem stems from the fact that a false antecedent is sufficient for the material conditional being true. In this case then something would be visible to Jane just by the fact that it was never near her. But this could be true of something that is clearly not visible to her.

Question 3

General Theory

-Use an example to explain the distinction that is made between sentences and propositions.

Answer 3

Sentences are series of ink marks on paper or sounds in that air, and thus can be seen or heard. Examples of sentences are "Mary sees John" and "John is seen by Mary." These are each tokens of different sentence types. These sentences however express the same proposition. So it seems that propositions cannot be indentified with particular sentences, and thus seem to be a different kind of thing

Question 4

General Theory

-Give two reasons why some think that universal statements cannot be adequately expressed as conjunctions.

Question 5

Proofs with identity.
Prove the validity of the following arguments:
-

Question 6

Proofs with identity.
Prove the validity of the following arguments:
-

Question 7

Proofs with identity.
Prove the validity of the following arguments:
-

Question 8

Symbolize, using the indicated letters:
-Something that is heavier than everything else is still not heavier than itself. (Hxy = "x is heavier than y ".)

Question 9

Symbolize, using the indicated letters:
-Anything that is heavier than itself is heavier than something else.

Question 10

Symbolize, using the indicated letters:
-Any sinner who sins against someone else sins against everyone else. (Sx = "x is a sinner"; Sxy = "x sins against y".)

Question 11

Symbolize, using the indicated letters:
-The sinner who sins against every sinner sins against himself.

Question 12

Symbolize, using the indicated letters:
-All sinners who sin against everyone else, sin against themselves.

Question 13

Symbolize, using the indicated letters:
-One and only one sinner sins against all sinners.

Question 14

Symbolize, using the indicated letters:
-Not all sinners are sinned against by other sinners.

Question 15

Symbolize, using the indicated letters:
-No sinner is sinned against by all other sinners.

Question 16

Symbolize, using the indicated letters:
-At most one sinner sins against everyone else who is a sinner. (Quite difficult)

Question 17

Symbolize, using the indicated letters:
-If some sinners are not sinned against by others, then for any nonsinners, they aren't sinned against by any sinners.

Question 18

Symbolize, using the indicated letters:
-The largest Great Lake is Lake Superior (Gx = "x is a Great Lake"; Lxy = "x is larger than y"; s = "Lake Superior")

Question 19

Symbolize, using the indicated letters:
-The capitol of Ohio is a river town. (Cxy = "x is a capitol of y"; Rx = "x is a river town"; o = "Ohio")

Question 20

Symbolize, using the indicated letters:
-The capitol of Ohio is Columbus. (c = "Columbus")

Question 21

Symbolize, using the indicated letters:
-The capitol of Ohio is not the largest city in Ohio. (Ixy = "x is a city in y")

Question 22

Symbolize, using the indicated letters:

-Every state has exactly two senators. (Sx = "x is a state"; Sxy = "x is a senator from y")