The False Subtlety of the Four Syllogistic Figures

　　General conception of the Nature of Ratiocination

　　A judgment is the comparison of a subject or thing with a predicate or attribute . The comparison is made by using the copula or linking verb is or its negative is not. Therefore, a judgment is a declarative sentence, which is a categorical proposition. Example: The tiger is four-footed. A predicate can also have its own predicate. In the example, the predicate four-footed can, itself, have the further predicate animal. One of these predicates is immediately and directly connected to the subject or thing. The other predicate is mediate and indirectly connected to the subject.

　　The tiger ----------is---------- a four-footed---------- animal.

　　In order to have clear knowledge of the relation between a predicate and a subject, I can consider a predicate to be a mediate predicate. Between this mediate predicate or attribute, I can place an intermediate predicate. For example, in the judgment the sun is luminous, I attempt a clarification by inserting the predicate star, which then becomes an immediate predicate, intermediate between the subject sun and the mediate predicate luminous.

　　The sun is a star that is luminous.

　　Sun = subject

　　Is = copula

　　Star = immediate predicate

　　Luminous = remote mediate predicate

　　Kant calls this process ratiocination. It is the comparison of a remote, mediate predicate with a subject through the use of an intermediate predicate. The intermediate predicate is called the middle term of a rational inference. The comparison of a subject with a remote, mediate predicate occurs through three judgments:

　　Luminous is a predicate of star;

　　Star is a predicate of sun;

　　Luminous is a predicate of sun .

　　This can be stated as an affirmative ratiocination: Every star is luminous; the sun is a star; consequently the sun is luminous.

　　Note: Kants examples utilized obscure subjects such a Soul, Spirit, and God and their supposed predicates. These do not facilitate easy comprehension because these subjects are not encountered in everyday experience and consequently their predicates are not evident.

　　Section II - Of the Supreme Rules of all Ratiocination

　　Kant declared that the primary, universal rule of all affirmative ratiocination is: A predicate of a predicate is a predicate of the subject .

　　The primary, universal rule of all negative ratiocination is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject.

　　Because proof is possible only through ratiocination, these rules cant be proved. Such a proof would assume the truth of these rules and would therefore be circular. However, it can be shown that these rules are the primary, universal rules of all ratiocination. This can be done by showing that other rules, that were thought to be primary, are based on these rules.

　　The dictum de omni is the highest principle of affirmative syllogisms. It says: Whatever is universally affirmed of a concept is also affirmed of everything contained under it. This is grounded on the rule of affirmative ratiocination. A concept that contains other concepts has been abstracted from them and is a predicate. Whatever belongs to this concept is a predicate of other predicates and therefore a predicate of the subject.

　　The dictum de nullo says: Whatever is denied of a concept is also denied of everything that is contained under it. The concept is a predicate that has been abstracted from the concepts that are contained under it. Whatever is inconsistent with this concept is inconsistent with the subject and therefore also with the predicates of the subject. This is based on the rule of negative ratiocination.

　　Section III - Of Pure and Mixed Ratiocination

　　If one judgment can be immediately discerned from another judgment without the use of a middle term, then the inference is not a ratiocination. A direct, non-ratiocinative inference would, for example, be: from the proposition that all airplanes have wings, it immediately follows that whatever has no wings is not an airplane.

　　Pure ratiocination occurs by means of three propositions. Mixed ratiocination occurs by more than three propositions. A mixed ratiocination is still a single ratiocination. It is not compound, that is, consisting of several ratiocinations.

　　An example of a mixed ratiocination is:

　　Nothing immortal is a man,

　　Therefore, no man is immortal;

　　Socrates is a man,

　　Therefore, Socrates is not immortal.

　　A mixed ratiocination interposes an immediate inference, resulting in more than three propositions. However, a mixed ratiocination may show only three propositions if the fourth proposition is unspoken, unexpressed, and merely thought. For example, the ratiocination

　　Nothing immortal is a man,

　　Socrates is a man,

　　Therefore, Socrates is not immortal　is only valid if the fourth proposition Therefore, no man is immortal is covertly thought. This unspoken proposition should be inserted after the first proposition and is merely its negative converse.

　　Section IV

　　In the so-called First Figure only Pure Ratiocinations are possible, in the remaining Figures only mixed Ratiocinations are possible.

　　Pattern of First Figure:

　　Subject...............Predicate

　　Middle Term........Major Term........Major Premise

　　Minor Term.........Middle Term........Minor Premise

　　Minor Term........Major Term...........Conclusion

　　A ratiocination is always in the first figure when it accords with the first rule of ratiocination: A predicate B of a predicate C of a subject A is a predicate of the subject A. This is a pure ratiocination. It has three propositions:

　　C has the predicate B,

　　A has the predicate C,

　　Therefore, A has the predicate B.

　　In the Second Figure only mixed Ratiocinations are possible.

　　Pattern of Second Figure:

　　Subject...............Predicate

　　Major Term........Middle Term........Major Premise

　　Minor Term.........Middle Term........Minor Premise

　　Minor Term........Major Term...........Conclusion

　　The rule of the second figure is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject. This is a mixed ratiocination because an unexpressed proposition must be added in thought in order to arrive at the conclusion. If I say,

　　No B is C,

　　A is C,

　　Therefore, A is not B

　　My inference is valid only if I silently interpose the immediate inference No C is B after the first premise. It is merely the negative converse of the first premise. Without it, the ratiocination is invalid.

　　In the Third Figure only mixed Ratiocinations are possible.

　　General conception of the Nature of Ratiocination

　　A judgment is the comparison of a subject or thing with a predicate or attribute . The comparison is made by using the copula or linking verb is or its negative is not. Therefore, a judgment is a declarative sentence, which is a categorical proposition. Example: The tiger is four-footed. A predicate can also have its own predicate. In the example, the predicate four-footed can, itself, have the further predicate animal. One of these predicates is immediately and directly connected to the subject or thing. The other predicate is mediate and indirectly connected to the subject.

　　The tiger ----------is---------- a four-footed---------- animal.

　　In order to have clear knowledge of the relation between a predicate and a subject, I can consider a predicate to be a mediate predicate. Between this mediate predicate or attribute, I can place an intermediate predicate. For example, in the judgment the sun is luminous, I attempt a clarification by inserting the predicate star, which then becomes an immediate predicate, intermediate between the subject sun and the mediate predicate luminous.

　　The sun is a star that is luminous.

　　Sun = subject

　　Is = copula

　　Star = immediate predicate

　　Luminous = remote mediate predicate

　　Kant calls this process ratiocination. It is the comparison of a remote, mediate predicate with a subject through the use of an intermediate predicate. The intermediate predicate is called the middle term of a rational inference. The comparison of a subject with a remote, mediate predicate occurs through three judgments:

　　Luminous is a predicate of star;

　　Star is a predicate of sun;

　　Luminous is a predicate of sun .

　　This can be stated as an affirmative ratiocination: Every star is luminous; the sun is a star; consequently the sun is luminous.

　　Note: Kants examples utilized obscure subjects such a Soul, Spirit, and God and their supposed predicates. These do not facilitate easy comprehension because these subjects are not encountered in everyday experience and consequently their predicates are not evident.

　　Section II - Of the Supreme Rules of all Ratiocination

　　Kant declared that the primary, universal rule of all affirmative ratiocination is: A predicate of a predicate is a predicate of the subject .

　　The primary, universal rule of all negative ratiocination is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject.

　　Because proof is possible only through ratiocination, these rules cant be proved. Such a proof would assume the truth of these rules and would therefore be circular. However, it can be shown that these rules are the primary, universal rules of all ratiocination. This can be done by showing that other rules, that were thought to be primary, are based on these rules.

　　The dictum de omni is the highest principle of affirmative syllogisms. It says: Whatever is universally affirmed of a concept is also affirmed of everything contained under it. This is grounded on the rule of affirmative ratiocination. A concept that contains other concepts has been abstracted from them and is a predicate. Whatever belongs to this concept is a predicate of other predicates and therefore a predicate of the subject.

　　The dictum de nullo says: Whatever is denied of a concept is also denied of everything that is contained under it. The concept is a predicate that has been abstracted from the concepts that are contained under it. Whatever is inconsistent with this concept is inconsistent with the subject and therefore also with the predicates of the subject. This is based on the rule of negative ratiocination.

　　Section III - Of Pure and Mixed Ratiocination

　　If one judgment can be immediately discerned from another judgment without the use of a middle term, then the inference is not a ratiocination. A direct, non-ratiocinative inference would, for example, be: from the proposition that all airplanes have wings, it immediately follows that whatever has no wings is not an airplane.

　　Pure ratiocination occurs by means of three propositions. Mixed ratiocination occurs by more than three propositions. A mixed ratiocination is still a single ratiocination. It is not compound, that is, consisting of several ratiocinations.

　　An example of a mixed ratiocination is:

　　Nothing immortal is a man,

　　Therefore, no man is immortal;

　　Socrates is a man,

　　Therefore, Socrates is not immortal.

　　A mixed ratiocination interposes an immediate inference, resulting in more than three propositions. However, a mixed ratiocination may show only three propositions if the fourth proposition is unspoken, unexpressed, and merely thought. For example, the ratiocination

　　Nothing immortal is a man,

　　Socrates is a man,

　　Therefore, Socrates is not immortal　is only valid if the fourth proposition Therefore, no man is immortal is covertly thought. This unspoken proposition should be inserted after the first proposition and is merely its negative converse.

　　Section IV

　　In the so-called First Figure only Pure Ratiocinations are possible, in the remaining Figures only mixed Ratiocinations are possible.

　　Pattern of First Figure:

　　Subject...............Predicate

　　Middle Term........Major Term........Major Premise

　　Minor Term.........Middle Term........Minor Premise

　　Minor Term........Major Term...........Conclusion

　　A ratiocination is always in the first figure when it accords with the first rule of ratiocination: A predicate B of a predicate C of a subject A is a predicate of the subject A. This is a pure ratiocination. It has three propositions:

　　C has the predicate B,

　　A has the predicate C,

　　Therefore, A has the predicate B.

　　In the Second Figure only mixed Ratiocinations are possible.

　　Pattern of Second Figure:

　　Subject...............Predicate

　　Major Term........Middle Term........Major Premise

　　Minor Term.........Middle Term........Minor Premise

　　Minor Term........Major Term...........Conclusion

　　The rule of the second figure is: Whatever is inconsistent with the predicate of a subject is inconsistent with the subject. This is a mixed ratiocination because an unexpressed proposition must be added in thought in order to arrive at the conclusion. If I say,

　　No B is C,

　　A is C,

　　Therefore, A is not B

　　My inference is valid only if I silently interpose the immediate inference No C is B after the first premise. It is merely the negative converse of the first premise. Without it, the ratiocination is invalid.

　　In the Third Figure only mixed Ratiocinations are possible.