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

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Cabbage is an odoriferous food when cooked.

Oc

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Anything that is either sweet or crunchy is tasty.

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

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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)

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Cell phones are not universally admired products.

~Uc

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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

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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

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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