Deck 8: Predicate Logic Semantics

Question 1

General Theory

-If there are no unicorns, what is the truth value of the sentence , where Ux = x is a unicorn, and Mx = x is mortal?

Answer 1

The sentence will be true. To see this, consider the expansion of this sentence for larger and larger universes of discourse. First, in a two-individual universe of discourse, its expansion is , which will be true since each conditional will have a false antecedent. Then for larger universes, each new conjunction added will have a false antecedent and thus be true (on the assumption nothing is a unicorn).

Question 2

General Theory
-What about the truth value of the sentence ?

Answer 2

The sentence will be true also. Again, consider its expansion for a two-individual universe, namely , which will be true because each conditional will have a false antecedent. And obviously, it will be true in larger universes, since adding more disjunctions to a true sentence can't make it false.

Question 3

Proving invalidity
Prove that the following arguments are invalid by either the interpretation method or by the expansion method:
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Answer 3

Let domain be unrestricted, Ax = x is tall, and Bx = x is identical with itself.

Question 4

Proving invalidity
Prove that the following arguments are invalid by either the interpretation method or by the expansion method:
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Question 5

Proving invalidity
Prove that the following arguments are invalid by either the interpretation method or by the expansion method:
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Question 6

Proving invalidity
Prove that the following arguments are invalid by either the interpretation method or by the expansion method:
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Question 7

Proving invalidity
Prove that the following arguments are invalid by either the interpretation method or by the expansion method:
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Question 8

Proving consistency
Show that the premises of the arguments below are consistent.
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Question 9

Proving consistency
Show that the premises of the arguments below are consistent.

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