[Footnote 19: Aristot. Analyt. Post. I. v. p. 74, a. 27: [Greek: ou)/pô oi)=de to\ tri/gônon o(/ti du/o o)rthai=s, ei) mê\ _to\n sophistiko\n tro/pon_ ou)de\ katho/lou tri/gônon, ou)/d' ei) mêde/n e)sti para\ tau=ta tri/gônon e(/teron.] The phrase [Greek: to\n sophistiko\n tro/pon] is equivalent to [Greek: to\n sophistiko\n **tro/pon to\n kata\ sumbebêko/s], p. 71, b. 10. I see nothing in it connected with Aristotle's characteristic of a Sophist (special professional life purpose--[Greek: tou= bi/ou tê=| proaire/sei], Metaphys. [Greek: G]. p. 1004, b. 24): the phrase means nothing more than _unscientific_.] [Footnote 20: Aristot. Analyt Post I. v. p. 74, a. 32-b. 4.] In every demonstration the _principia_ or premisses must be not only true, but necessarily true; the conclusion also will then be necessarily true, by reason of the premisses, and this constitutes Demonstration. Wherever the premisses are necessarily true, the conclusion will be necessarily true; but you cannot say, _vice versâ_, that wherever the conclusion is necessarily true, the syllogistic premisses from which it follows must always be necessarily true. They may be true without being necessarily true, or they may even be false: if, then, the conclusion be necessarily true, it is not so by reason of these premisses; and the syllogistic proof is in this case no demonstration. Your syllogism may have true premisses and may lead to a conclusion which is true by reason of them; but still you have not demonstrated, since neither premisses nor conclusion are _necessarily_ true.[21] When an opponent contests your demonstration, he succeeds if he can disprove the _necessity_ of your conclusion; if he can show any single case in which it either is or may be false.[22] It is not enough to proceed upon a premiss which is either probable or simply true: it may be true, yet not appropriate to the case: you must take your departure from the first or highest universal of the genus about which you attempt to demonstrate.[23] Again, unless you can state the _why_ of your conclusion; that is to say, unless the middle term, by reason of which the conclusion is necessarily true, be itself necessarily true,--you have not demonstrated it, nor do you know it absolutely. Your middle term not being necessary may vanish, while the conclusion to which it was supposed to lead abides: in truth no conclusion was known through that middle.[24] In the complete demonstrative or scientific syllogism, the major term must be predicable essentially or _per se_ of the middle, and the middle term must be predicable essentially or _per se_ of the minor; thus alone can you be sure that the conclusion also is _per se_ or necessary. The demonstration cannot take effect through a middle term which is merely a Sign; the sign, even though it be a constant concomitant, yet being not, or at least not known to be, _per se_, will not bring out the _why_ of the conclusion, nor make the conclusion necessary. Of non-essential