Bits and Bobs

Easy Translations

Hard Translations

Terms

Proofs

1000

What is Quantified Logic?

A mix of sentential and categorical logic; using "all" "no" "some"

1000

Sir Lancelot was a member of the Round Table.

Rs

1000

If anything is alive, then it is conscious of its environment.

(x) (Ax > Cx)

1000

What is this called:

(x)

Universal Quantifier

1000

1. (∃x)Hx

2. (x) ~Px

so, ~(x) (Hx > Px)

3. (x) (Hx > Px) AR

4. Ha 1EI

5. ~Pa 2UI

6. Ha > Pa 3UI

7. Pa 4,5 IF

8. ~(x) (Hx > Px) 3-7 RAA

2000

What is the difference between:

~(∃x) & ~(x)

~(∃x) = no, none, nothing, etc.

~(x)= not all

2000

Cabbage is an odoriferous food when cooked.

Oc

2000

Anything that is either sweet or crunchy is tasty.

(x)[(Sx v Cx) >Tx]

2000

What is this called:

(∃x)

Existential Quantifier

2000

All humans are mortal. Socrates is human. Therefore, someone is mortal

1. (x)(Hx > Mx)

2. Hs

Therefore, (∃x) Mx

Valid

3000

Which of these is a quantified statement?

1. (x) Px > Qx

2. (x) ~(Px) v Qx

3. (∃x) Px & (Qx & Zx)

4. ~(∃x)(Px & Qx)

4. ~(∃x)(Px & Qx)

3000

Cell phones are not universally admired products.

~Uc

3000

Whole numbers are even or odd.

(x)[Wx > (Ex v Ox)]

3000

What are these called:

x, y, z

Variables

3000

(x)(Bx > Ax)

(∃x)(Bx & Dx)

so, (∃x)(Ax & Dx)

3. (~∃x)(Ax & Dx) - AR

4. (X) ~(Ax & Dx) - 3QN

5. (Ba & Da) - 2 EI

6. (Ba > Aa) - 1 UI

7. ~(Aa & Da) - 4 UI

8. Ba - 5 AND

9. Da - 5 AND

10. Aa - 6, 8 IF

11. ~Aa - 7,9 IF

4000

What do each of the following receipts stand for?

QN

EI

UI

Quantifier Negation

Existential Instantiation

Universal Instantiation

4000

Only if Joe runs the mile under four minutes will he qualify for the rally.

Qj > Uj

4000

The whale is neither a killer nor a fish.

(x)[Wx > ~(Kx v Fx)]

4000

What are these called and what do they refer to:

a - u

Constants; individual subjects

4000

Some wars are just. No war of aggression is just. Accordingly, there are wars that are not wars of aggression.

1. (∃x) (Wx & Jx)

2. ~(∃x) (Ax & Jx) (∃x)(Wx & ~Ax)

3. ~(∃x)(Wx & ~Ax) - AR

4. (x) ~(Wx & ~Ax) - 3QN

5. (x) ~(Ax & Jx) - 2QN

6. (Wa & Ja) - 1EI

7. ~(Wa & ~Aa) - 4 UI

8. ~(Aa & Ja) - 5UI

9. Wa - 6 AND

10. Ja - 6 AND

11. Aa - 7, 9 NAND

12. ~Aa - 8, 10 NAND

13. (∃x)(Wx & ~Ax) - 3-13 RAA

5000

What is the special restriction that only applies to Existential Instantiation?

You must use a different constant for each instance of EI in a proof.

5000

If Bill is honest and loyal, then he will get the job

(Hb & Lb) > Jb

5000

If all humans are mortal but Socrates is not mortal, then Socrates is not human.

(x)[(Hx>Mx) & ~Ms] > ~Hs

5000

What are these called and what do they stand for:

A-Z

Predicates; represents the predicate of a statement.

5000

(x)[(Fx & Gx) > Hx]

(∃x) Fx

(∃x) Gx

Therefore (∃x)Hx

Invalid

4. ~(∃x) Hx - AR

5. (x)~Hx - 5QN

6. Fa - 2UI

7. Gb - 3UI

8. [(Fa & Ga) > Ha] - 1UI

9. [(Fb & Gb) > Hb] - 1UI

10. ~Ha - 5UI

11. ~Hb - 5UI

12. (Fa & Ga) - 8, 10 IF

13. (Fb & Gb) - 9, 11 IF

14. Fa - 12 AND

15. Ga - 12 AND

16. Fb - 13 AND

17. Gb - 13 AND