# Categorical Logic

• Nov 11th 2007, 06:59 AM
ambergarrett955
Categorical Logic
Is this right,

Translate into standard form:
The only boys who deserve cake are good ones.
• Nov 11th 2007, 07:46 AM
Soroban
Hello, Amber!

You'll have to explain what concepts you've been taught already.
To me this is a strange problem . . .

Quote:

Translate into standard form:
The only boys who deserve cake are good ones.

Answer: Some B are G . . . . . I don't agree

First of all, I'm not sure what "standard form" means in your course.

The statement itself is an unusual one to translate.

It says: Only good boys deserve cake.

We can translate this a number of ways:
. . "If a boy deserves cake, then he must be a good boy."
. . "A boy deserves cake only if he is good."
. . "Bad boys do not deserve cake."

It does not say: "If a boy is good, then he deserves cake."

It does not even say that there are any good boys.

• Nov 11th 2007, 01:31 PM
ambergarrett955
Standard form right now is just simply stating the names of the classes for example.....
Every good boy deserves cake

Only good boys deserves cake
answeer All G are C
• Nov 11th 2007, 02:12 PM
Plato
Quote:

Originally Posted by ambergarrett955
Standard form right now is just simply stating the names of the classes for example.....
Every good boy deserves cake
answer All G are C YES

Only good boys deserves cake
answeer All G are C NO

This problem has a long history. Irving Copi set of quite a discussion of a similar problem in his symbolic logic text. We were to quantify the following: Only the brave deserve the fair. The key to it turns on a simple fact. “P only if Q” is equivalent to “If P then Q”. Anyone deserving the fair must be among the brave: $\left( {\forall x} \right)\left[ {F(x) \to B(x)} \right]$.

Now you apply that bit of history to your problem.
• Nov 12th 2007, 05:02 AM
ambergarrett955
Quantifier
Could someone please explain what a quantifier of a preposition is....in categorical logic...Thank You
• Nov 12th 2007, 05:55 AM
Plato
Quote:

Originally Posted by ambergarrett955
Could someone please explain what a quantifier of a preposition is....in categorical logic...