Chapter XVI: On ignorance resulting from a defective arrangement of terms in mediate propositionsEdit
- Concerning ignorance and error; firstly in the case where two terms are predicated of one another immediately.
That ignorance which results not from the simple absence of knowledge but from a faulty arrangement of terms is a logical deception which, in cases where one thing is predicable or not predicable of one another immediately, takes two forms, (1) an immediate supposition that one thing is or is not predicable of another, (2) a supposition to this effect arrived at through a syllogism. Now in the case of the simple or immediate supposition the mistake is simple, in the case of that which is produced by the syllogism it may assume several forms. Suppose it to be proved immediately that no B is A; then if one conclude, with the help of a middle term C, that B is A, one’s reasoning will have led one astray. Here it is possible for both premises to be false or else for only one. Thus if no C be A, and no B be C, and if each of these premises be transposed, both will be false. It is in fact possible for C to be so placed with regard to A and B that it is neither included in A nor is universally predicable of B. Now B cannot be true of another term distributively, since the hypothesis was that A was not immediately predicable of C, and there is no necessity why A should be universally predicable of all C, so that here both premises are false. Further one of the premises may be true, not however either of the two, but only AC; for the premise CB will be always false, because C is predicable of no part of B. The premise AC may however be true, as when both C and B are shewn to be immediately predicable of A. For when the same thing is predicated primarily of more than one term, no one of these latter will be predicable of another. Nor does it affect the case if A be shewn to be predicable of C not immediately (but by means of a term taken from a higher class). Only in the case of premises such as these and only in this manner can mistakes arise in connection with predicating one term of another, for no syllogism in another figure can prove universal predication.
Mistakes connected with the proof that one term is not predicable of another may however occur in either the first or the second figure.
We will first mention in how many ways this may happen in the first figure, and what the position of the premises must then be.
For instance suppose A to be immediately predicable of B and C. Then if one take as premises ‘No C is A,’ and ‘all B is C,’ the premises will be false. A mistake will also follow if only one of the premises, either of the two, be false. It is possible for the premise AC to be true, BC false, AC being true because A is not distributively predicable of C, BC false because it is impossible for C to be B when no A is C, for then the premise AC would no longer be true. When however both premises are true the conclusion also will be true. Further the premise BC may be true while the other is false; for instance in the case where both C and A are B; since one of these terms must be included in the other. Hence if one assert that no C is A, the premise will be false. It is clear then that the conclusion will be false if one or both of the premises be false.
In the second figure it is not possible for both the premises to be entirely false; for when all B is A no third term can be found which will be predicable of the whole of one and not predicable of any part of the other term. If one want a syllogism at all one ought to select the premises in such a way that the middle term will be affirmed of one of the other two terms and denied of the second. If then, when thus stated, the premises are false, it is clear that the contrary of them will be true. This however is impossible, though nothing prevents each of the premises from being partially false when the conclusion is false, as in the case where some of A and also of B are C, while it is asserted that all A is C and no B is C. Here the two premises are false, not however entirely but only partially false. The same thing will happen when the position of the negative premise is changed. It is also possible in the second figure, for one premise, either of the two, to be false. Suppose that what all A is, B will be also. If then it be asserted that all A is C, and no B is C, the premise AC will be true, BC false. Again that which is predicable of no B will be predicable of no A, for if a thing be true of A it will be true also of B, but the hypothesis was that it was not true of A. If then it be asserted that all A is C, and no B is C, the latter premise will be true, the former false. Similarly if the negative premise be reversed, that which is predicable of no A will be predicable of no B. If then it be asserted that no A is C and all B is C, the former premise will be true, the latter false. Again, to assert that what is predicable of all B is predicable of no A is false, for a term which is predicable of all B must be predicable of some A. If then it be asserted that all B is C and no A is C, the former premise will be true, the latter false. It is clear then that whether both the premises are false or only one of them, an atomic or elementary error will attach to the resulting conclusion.
- Because if the conclusion be false, both the premises cannot be true.
- I.e., if the negative premise be treated as the major instead of the minor.