Valid Moods

Question 1

What is the form of 1st figure syllogisms?

Answer 1

PM, MS, PS

Question 2

What is the form of 2nd figure moods?

Answer 2

MP, MS, PS

Question 3

What is the form of 3rd figure moods?

Answer 3

PM, SM, PS

Question 4

What is the form of 4th figure moods?

Answer 4

MP,SM, PS

Question 5

Which moods are 1st figure?

Answer 5

Barbara,Celarent, Darii, Ferio, Barbari, Celaront

Question 6

Which moods are 2nd figure?

Answer 6

Cesare, Camestres, Festino, Baroco, Cesaro, Camestrop

Question 7

Which moods are third figure?

Answer 7

Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison

Question 8

Which moods are fourth figure?

Answer 8

Bramantip, Camenes, Dimaris, Fesapo, Fresison, Camenop

Question 9

What does the first letter of the mood’s name mean?

Answer 9

That the mood must be reduced to the perfect syllogism which starts with the corresponding letter

Question 10

What are the four perfect moods?

Answer 10

Barbara, Celarent, Darii, Ferio

Question 11

What does the letter “s” after a vowel indicate?

Answer 11

The proposition with that vowel as a copula must be simply converted

Question 12

What does the letter “p” after a vowel indicate?

Answer 12

Either that the proposition with that vowel as a copula has to be accidentally converted, or that accidents conversion will be used on another proposition in order to general the proposition with that vowel as a copula

Question 13

What does the letter “c” after the first or second vowel indicate?

Answer 13

The mood has to be proved indirectly by proving the contradictory of the corresponding premise by the use of reductio ad absurdum

Question 14

What does the letter “m” indicate?

Answer 14

The premises have to change order (either via reiteration or other rules)

Question 15

Give a summary of the transformation rules:

Answer 15

• a claims can only be converted accidentally
  -e claims can be converted both simply and accidentally
  -i claims can be converted only simply
• o claims cannot be converted (accidental conversion can take place from e to o but not from o to e claims)

Question 16

Prove that simple conversion is truth preserving

Answer 16

We show that s.c. of an e-claim is truth preserving. Let I be an interpretation that makes t1 e t2 true but such that it makes t2 e t1 false. For t2 e t1 to be false, its contradictory, t2 i t1, must be true. That is, I must be such that there is some object, call it x, where:

x is an element of (use symbol) I(t2)
x is an element of I(t1)

But any such interpretation will make t1 e t2 false as well, since there is an overlap between I(t1) and I(t2).

Question 17

Prove that accidental conversion is truth preserving

Answer 17

We show that a.c. of an a-claim is truth preserving. Let I be an interpretation that makes t1 a t2 true. Then we know that there is at least one object, call it x, that is in I(t2) given our interpretation of the terms be non-empty:

x is an element of (use symbol) I(t2)

For this interpretation to make t1 a t2 true, any object in I(t2) must also be in I(t1):

If x is an element of I(t2)
Then x is an element of I(t1)

But then it follows that I is valid (use single turnstile) to t2 i t1, since there is something that is in both I(t2) and I(t1), namely x, so I(t2) intersects (use symbol) with I(t1) and is not equal to an empty set

Question 18

Give the theorems concerning the validity possibilities of syllogisms

Answer 18

• no conclusion can be proven from two negative premises (none of the perfect mood have two negative premises)
  -no conclusion can be proven from two partial premises (none of the perfect moods have two partial premises)
  -no affirmative conclusion can be proven from a negative premise (Celarent and Ferio have negative conclusions and at least one affirmative premise)
  -no negative conclusion can be proven from two affirmative premises (Barbara and Darii have an affirmative conclusion)
• no universal conclusion can be proven from a partial premise (Darii and Ferio have a partial conclusion)

None of reiteration, simple conversion, or accidental conversion can be brought in to change the nature of the conclusion . Even accidental conclusion does not change the quality of the proposition. Accidental conversion cannot be applied to partial claims.

Question 19

Why can RAA not be used to change the rules of the validity rules for syllogisms?

Answer 19

• a premise has to be reiterated into the subproof so that it can be used alongside the proposition assumed at the start of the subproof in the application of an axiom
  -the other premise will be reiterated into the subproof as the contradiction of the prop. resulting from the application of the axiom in step 1
  -if both premises are negative, then in order to apply an axiom in the subproof, the assumed prop must be affirmative (since no axiom can be applied to two negative claims)
  -if a premise is negative and the other positive, only Celarent or Ferio can be used, both of which result in a negative conclusion
• this conclusion would have to be contradicted by the other premise, but two negative props can’t contradict
  -same story with partial claims