There is an x such that.. An object x can be found which...
How do we write 'some felons are German'?
(3x)(Fx & Gx)
If F means felon and G means German, how do we read: (3x)(Fx & Gx)? (97)
There exists some object that is both a felon and a German.
How can one write 'something with F has not G', such as 'some Frenchmen are not generous'? (97)
(3x)(Fx & -Gx)
How might we summarize the task of translation into the quantifier-notation? (97)
1) Render into a sentence about properties, and employ predicate-letters for these properties. 2) Introduce variables 3) Introduce propositional calculus connectives and quantifiers.
A predicate-letter followed by one name expresses a ___________. A predicate-letter followed by two names expresses a ___________. (98)
If we give 'Pmn' the interpretation 'm is a parent of n', how can we express 'Prince Charles has a parent', where n is Prince Charles? (98)
(3x)Pxn This translates to: "There exists an 'x', that is a parent of Prince Charles." (I'm a bit confused as to why the book does not use 'm', but rather 'x'.)
If we give 'Pmn' the interpretation of 'm is a parent of n', and Prince Philip is represented by m, how can we write 'Prince Philip has a child'? (99)
(3x)(Pmx) This translates to: "There exists an 'x' of which Prince Philip is a parent."
If Pmn reads as 'm is a parent of n', what is the difference in reading (3x)Pnx in contrast with (3x)Pxn if 'n' represents Prince Charles? (99)
The first reads: there exists an 'x' of which Prince Charles is a parent. The second reads: there exists an 'x' of which Prince Charles is a son, or there exists an 'x' of which 'x' is a parent of Prince Charles.