By P. D. Magnus
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Extra info for forall x: An Introduction to Formal Logic
However, the sentence ∀x(P x & Qx) would mean that everything in the UD is both in my pocket and a quarter: All the coins that exist are quarters in my pocket. This would be a crazy thing to say, and it means something very different than sentence 14. Sentence 15 is most naturally translated with an existential quantifier. It says that there is some coin which is both on the table and which is a dime. So we can translate it as ∃x(T x & Dx). Notice that we needed to use a conditional with the universal quantifier, but we used a conjunction with the existential quantifier.
Contingent? equivalent? consistent? valid? 2: Do you need a complete truth table or a partial truth table? It depends on what you are trying to show. You can always start working on a complete truth table. If you complete rows that show the sentence is contingent, then you can stop. If not, then complete the truth table. Even though two carefully selected rows will show that a contingent sentence is contingent, there is nothing wrong with filling in more rows. Showing that two sentences are logically equivalent requires providing a complete truth table.
11. 12. ¬A (A & B) (A ∨ B) (A → B) (A ↔ B) Chapter 4 Quantified logic This chapter introduces a logical language called QL. It is a version of quantified logic, because it allows for quantifiers like all and some. Quantified logic is also sometimes called predicate logic, because the basic units of the language are predicates and terms. 1 From sentences to predicates Consider the following argument, which is obviously valid in English: If everyone knows logic, then either noone will be confused or everyone will.