1. No. Consider the following argument:
All bats are mammals.
All bats fly.
Therefore, all bats are blind.
The premises and conclusion are true, but the argument is invalid, since the premises don't support the conclusion.
2. Yes, since it is one of the expressions you can get by substituting a statement constant for each statement variable in the expression.
3. A quantifier statement must begin with a quantifier and the scope of that quantifier must be the entire formula. A truth functional compound of quantifier statements is the result of constructing larger expressions from these statements using only the the five truth functional operators.
4. [Again, this was translated into quantifier logic notation rather than propositional, but you can still see how the propositional translation would work from this.]
Notation:
m = the mind.
b = the brain.
Ixy = x is identical to y.
Px = x is physical.
Tx = x is a thought.
Mx = x is material.
Translation:
1. Imb -> (Pb <-> Pm).
2. Pm -> (x)(Tx -> Mx).
3. ~(Ex)(Tx & Mx) & Pb.
4. Therefore, ~Imb.
It is equally acceptable to treat "the mind and the brain are identical" as a single unit and thereby have a translation that is the same as above, but with Imb replaced by, say, the letter A.
5. notation:
Px = x is a person
Bx = x is beautiful
Rx = x is rich.
Fx = x is famous
Ax = x is appreciated.
Translation: ~(x)((Px & (Bx & Rx)) -> (Fx & Ax))
6.
| S | T | U | ~S | ~T | ~U | ~S v ~T | ~S -> ~U | (~S v ~T) & (~S -> ~U) | T & U | S v (T&U) | S v (T&U) <-> [(~S v ~T)&(~S -> ~U)] |
| T | T | T | F | F | F | F | T | F | F | T | F |
| T | T | F | F | F | T | F | T | F | F | T | F |
| T | F | T | F | T | F | T | T | T | F | T | T |
| T | F | F | F | T | T | T | T | T | T | T | T |
| F | T | T | T | F | F | T | F | F | F | F | T |
| F | T | F | T | F | T | T | T | T | F | F | F |
| F | F | T | T | T | F | T | F | F | F | F | T |
| F | F | F | T | T | T | T | T | T | F | F | F |
The statement is a contingency, as one can see from the second and third rows.
7.
01. C -> (D -> ~C)
02. C <-> D / .: ~C & ~D
03. |-> C AIP
04. | D 2, 3, BE, SIMP, MP
05. | D -> ~C 1, 3 MP
06. | ~C 4, 5 MP
07. | C & ~C 3, 6 CONJ
08. |- ~C 3-7 IP
09. |-> D AIP
10. | C 2, 9 BE, SIMP, MP
11. | D -> ~C 1, 10 MP
12. | ~D 10, 11 MT
13. | D & ~D 9, 12 CONJ
14. |- ~D 9-13 IP
15. ~C & ~D 8, 14 CONJ
8.
01. (Ex)~Hx -> (x)(Fx -> Gx)
02. ~(x)(Hx v Gx) / .: ~(x)Fx
03. (Ex)~(Hx v Gx) 2, QN
04. ~(Ha v Ga) 3, EI
05. ~Ha & ~Ga 4, DEM
06. ~Ha 5 SIMP
07. ~Ga 5 SIMP
08. (Ex)~Hx 6 EG
09. (x)(Fx -> Gx) 1, 8 MP
10. Fa->Ga 9 UI
11. ~Fa 7, 10 MT
12. (Ex)~Fx 11 EG
13. ~(x)Fx 12 QN
9.
01. (Ex)Ax -> (Ex)(Bx & Cx)
02. (Ex)Cx -> (x)(Dx & Ex) / .: (x)(Ax -> Ex)
03. |-> flag a FSUG
04. | |-> Aa ACP
05. | | (Ex)Ax 4, EG
06. | | (Ex)(Bx & Cx) 1, 5 MP
07. | | Bc & Cc 6 EI, flag c
08. | | Cc 7 SIMP
09. | | (Ex)Cx 8, EG
10. | | (x)(Dx & Ex) 2, 9 MP
11. | | Da & Ea 10 UI
12. | | Ea 11 SIMP
13. | |- Aa->Ea 4-12 CP
14. |- (x)(Ax -> Ex) 3-13 UG
10.
01. |-> ~(Ex)(Fx & Gx) ACP
02. | |-> (x)Fx ACP
03. | | |-> flag a FSUG
04. | | | Fa 2 UI
05. | | | (x)(Fx -> ~Gx) 1 CQN
06. | | | Fa -> ~Ga 5 UI
07. | | | ~Ga 4, 6 mp
08. | |- (x)(~Gx) 3-7 UG
09. | | ~(Ex)(Gx) 8 QN
10. | |- (x)Fx -> ~(Ex)(Gx) 2-9 CP
11. |- ~(Ex)(Fx & Gx) -> ((x)Fx -> ~(Ex)(Gx)) 1-10 CP
11. ad hominem tu quoque. Daugher tries to defeat mother's argument against marriage at seventeen by pointing out that mother married at seventeen.
12. ad hominem abusive. Wife threatens to abuse husband's credit cards. The threatening circumstances don't support the conclusion that she deserves to go somewhere nice.
13. strawman. Arguer distorts the views of those who don't fight communism, in saying that they must be communists themselves.
14. ad populum. Appeal to the majority for why you should own a chevy.
15. weak analogy. How criminals are treated in a work of fiction is not an appropriate analogy for how we should treat criminals in real life.