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Is this argument valid, or even a WFF?

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Protoman2050
 
Reply Fri 17 Oct, 2008 08:48 pm
Is this argument valid, or even a WFF:

1. A(x)(Cat(x) -> (Cute(x) ^ Eats(x, salmon)))
2. Cat(Chloe) /:. Cute(Chloe) ^ Eats(Chloe, salmon)

What about this one:

1. A(x)(E(y)(treats(x,y) -> specialist(x,y))
2. treats(Doug, cardiopulmonary diseases) /:. specalist(Doug, cardiopulmonary diseases)

How do I prove both of these?

Why do some Venn diagrams use the outside of the circle?
 
Victor Eremita
 
Reply Fri 17 Oct, 2008 10:06 pm
@Protoman2050,
I'm a bit rusty in logic, but from what I remember from 2nd year is this right?

1. A(x)(Cat(x) -> (Cute(x) ^ Eats(x, salmon)))
2. Cat(Chloe)
:. Cute(Chloe) ^ Eats(Chloe, salmon)
asm ~ ( Cute(Chloe) ^ Eats(Chloe, salmon) )

3. ~Cute(Chloe) V ~Eats(Chloe, salmon) (from asm)

4. Cat(Chloe) (from 2)

5. Cute(Chloe) ^ Eats(Chloe, salmon) (from 1 and 4)

6. Cute(Chloe) (from 5)

7. Eats(Chloe, salmon) (from 5)

8. ~Eats(Chloe, salmon) (from 3 and 6)

Contradiction in 7 and 8
:. Cute(Chloe) ^ Eats(Chloe, salmon)
 
Protoman2050
 
Reply Fri 17 Oct, 2008 10:11 pm
@Victor Eremita,
Victor Eremita wrote:
I'm a bit rusty in logic, but from what I remember from 2nd year is this right?

1. A(x)(Cat(x) -> (Cute(x) ^ Eats(x, salmon)))
2. Cat(Chloe)
:. Cute(Chloe) ^ Eats(Chloe, salmon)
asm ~ ( Cute(Chloe) ^ Eats(Chloe, salmon) )

3. ~Cute(Chloe) V ~Eats(Chloe, salmon) (from asm)

4. Cat(Chloe) (from 2)

5. Cute(Chloe) ^ Eats(Chloe, salmon) (from 1 and 4)

6. Cute(Chloe) (from 5)

7. Eats(Chloe, salmon) (from 5)

8. ~Eats(Chloe, salmon) (from 3 and 6)

Contradiction in 7 and 8
:. Cute(Chloe) ^ Eats(Chloe, salmon)


What's "asm", again?
 
Victor Eremita
 
Reply Fri 17 Oct, 2008 10:14 pm
@Protoman2050,
assume.
We assume the opposite of P and derive a contradiction in order to show that P is true.
 
Protoman2050
 
Reply Fri 17 Oct, 2008 10:29 pm
@Victor Eremita,
Victor Eremita wrote:
assume.
We assume the opposite of P and derive a contradiction in order to show that P is true.


Ah, thanks.

Is this valid:

1. A(Cat) A(x)(x E Cat v ~(x E Cat))
2. Cat(Chloe) /:. ~~(Chloe E Cat)

What about:

1. A(x)(Human(x) -> Mortal(x))
2. E(x)(Human(x) -> Philosopher(x)) /:. E(x)(Human(x) -> (Mortal(x) ^ Philosopher(x))

Is this equivalent to what would be in category logic:

All Humans are Mortal
Some Humans are Philosophers /:. Some Humans are Mortal and Philosophers
 
 

 
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