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Consider:

All ‘A’s are ‘B’s

No ‘B’s are ‘C’s

Is it not the case that the conclusion to this could either be:

No ‘A’s are ‘C’s

or

No ‘C’s are ‘A’s

?

Is it not also the case that the minor term of a syllogism is the subject of the conclusion and the major term is the predicate of the conclusion?

If so, then which of ‘A’ and ‘C’ is the major term and which is the minor term? Or does it depend on the form of the conclusion, such that ‘A’ is the minor term in the former and major term in the latter?

  • The swapping of the premises should ONLY be applied to valid syllogisms. It is not a good idea to think you are free to just swap things around whenever you like & when you like. Secondly, you should be aware of an inference rule named CONVERSION. This means one CERTAIN propositions you can swap the subject & predicate terms without losing meaning or truth value. For instance you can't convert an O type proposition. You CAN convert E type & I type propositions & keep the same truth values. So NO S IS P is the same truth value as NO P IS S. No change in truth value. – Logikal Jul 31 at 18:40
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Is it not also the case that the minor term of a syllogism is the subject of the conclusion and the major term is the predicate of the conclusion?

Yes.

If so, then which of ‘A’ and ‘C’ is the major term and which is the minor term?

It depends.

Or does it depend on the form of the conclusion, such that ‘A’ is the minor term in the former [No ‘A’s are ‘C’s] and major term in the latter [No ‘C’s are ‘A’s]?

This is correct.

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See Syllogism : Basic structure :

A categorical syllogism consists of three parts:

Major premise

Minor premise

Conclusion

Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion).

The third term, that is not present in the conclusion, is the middle term.

A syllogism is of the first figure when the middle term is subject of major premise and predicate of minor one.

In conclusion, the syllogism :

No B's are C's.

All A's are B's.

Therefore : No A's are C's.

is of first figure (the middle term : B is subject in major premise) and is of from Celarent.

The major premise is "No B’s are C’s", that is C is predicated of no B's.

Thus C, the predicate in major premise, will be the predicate in the conclusion.

The minor premise is "All A’s are B’s", that is B is predicated of all A's.

Thus A, the subject in minor premise, will be the subject in the conclusion : "No A's are C's", i.e. C is predicated of no A's.


If you exchange the two premises, you get a Camenes syllogism in the fourth figure (added in the Middle Ages but already known to Aristotle) :

All A are B; no B is C. Therefore : no C is A.

The fourth figure is defined again through the middle term : a syllogism is in the fourth figure when the middle term is the predicate of the major and subject of the minor premise.

  • So, in order to change the conclusion from “No A’s are C’s” to “No C’s are A’s”, is it a requirement to switch the order of the premises from “No B’s are C’s; All A’s are B’s” to “All A’s are B’s; No B’s are C’s”? – o c Jul 28 at 7:48
  • @oc - as you can see, the definitions are about the "formal structure" of the argument. The major-minor-middle terms terminology is linked to the major-minor premise nomenclature: if we switch thme, the "roles" change (also if the conclusion is still valid). – Mauro ALLEGRANZA Jul 28 at 7:50

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