# Symbolic Logic - Chapter 3 - The Predicate Calculus 1

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True.

### 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.

-Gm

### How do we say that m has property F? (93)

We juxtapose the symbols 'F' and 'm' in that order, we write:
Fm

### 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.

Fx

### How do we write 'for any x'? (95)

We enclose 'x' in brackets.

(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...

(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.

(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)

Property, Relation

### 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.

Example: