Logic, Metaphysics, and the Natural Sociability of Mankind. Francis Hutcheson

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      And the dictum de omni et nullo is so useful in proving a true argument and detecting a false one, that by its help any intelligent person may be able to see both true syllogistic force and its fallacious semblance, according to whether one of the premisses contains the conclusion or not, even before applying the special rules of syllogisms.

      CHAPTER 7

      With regard to the remaining forms of argument, it is evident that they are imperfect syllogisms or may be reduced to imperfect syllogisms.

      1. The enthymeme¹² or rhetorical syllogism is “when one of the premisses is unspoken because it is quite obvious”; it is for this reason that an enthymematic judgment has full syllogistic force.

      2. Induction is “an inference from various examples,” of which the chief use is in physics, in politics, and in household matters. It does not generate the highest credit or exclude all fears of the contrary, unless it is clear that there are absolutely no contrary examples.

      3. An epicheirema¹³ is “a complex syllogism in which a confirmation is attached to one or both of the premisses.”

      4. Sorites is “discourse which contains several syllogisms which are connected with each other,” or where there are several middle terms which are connected with each other or with the extremes in several propositions of which if even one is negative, the conclusion will be negative, and if two are negative or any middle term is not distributed at least once, there will be no inference.

      5. A dilemma is “a kind of epicheirema, where in making a division, that which is shown about the individual parts in the premisses is concluded of the whole.”

      6. A hypothetical syllogism is “one in which one of the premisses is hypothetical”; when the minor is hypothetical, so also is the conclusion; these also serve to prove the inference in an enthymeme. More frequent are those in which the major is hypothetical, for example:

      But since a more general predicate follows from any of the corresponding kinds (for example, If it is a man, if it is a horse, etc., it will also be an animal), but from a general predicate, no one particular species will follow (for from the fact that it is an animal, it does not follow that it will be a horse or an ass), it is evident that hypothetical syllogisms rightly proceed (1) from the positing of an antecedent to the positing of a consequent, or (2) from the removal of a consequent to the removal of an antecedent.

      It is a fallacious inference from the removal of an antecedent, or the positing of a consequent:

      The positing of a negative will be a negation, and the removal of it an affirmation.

      Hypothetical [syllogisms] are reduced to categorical [syllogisms] by this general method: “every case which posits that Titius is a man, posits that he is an animal; but every case, or some case, posits that he is a man; therefore, etc.” But often it may be more easily and briefly done when there is either the same subject or the same predicate to the antecedent and the consequent; for example:

      If man is an animal, he has sensation,

      But every man is an animal, therefore he has sensation.

      Every animal has sensation.

      Every man is an animal; therefore,

      Every man has sensation.

      If every animal has sensation, every man has sensation;

      But every animal has sensation; therefore,

      Every man has sensation.