The propositional calculus reveals validity when this depends on propositional structure alone. (T/F)
What do lower case letters represent in the predicate calculus?
They represent proper names.
What do upper-case letters represent in the predicate calculus?
They represent property-expressions or predicates.
What are upper-case letters called in the predicate calculus?
They are called predicate letters.
What are lower-case letters called in the predicate calculus? (93)
They are called proper names.
How does one write that m does not have G? (93)
How do we say that m has property F? (93)
We juxtapose the symbols 'F' and 'm' in that order, we write:
What do we obtain from "all robins are migrants" or "every robin is a migrant"? (94)
We obtain everything with the property of being a robin has the property of being a migrant.
It can be written as:
Everything with F has G.
To what do we naturally abbreviate 'x has F'? (95)
How do we write 'for any x'? (95)
We enclose 'x' in brackets.
How do we write 'For any x, if x has F then x has G'? (95)
(x)(Fx -> Gx)
How do we write 'nothing with F has G'? (95)
(x)(Fx -> -Gx)
For any x, if x has the property of F, then it does not have the property of G.
How do we write 'nothing with F has both G and H'? (95)
(x)(Fx -> -(Gx & Hx))
The device of universal quantifier enables us to render into logical notation many sentences that contain what such words? (95)
'All', 'every', 'any', 'everything', 'no', 'none', and/or 'nothing'.
What is (3x)? (96)
It is the existential quantifier.
What does (3x) represent? (97)
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)
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)
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.