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Updated: July 21, 2025
All the other concepts of which experience suggests the idea to me are only in part constructible a priori; the definition of them is therefore imperfect, and the deductions into which these concepts enter, however closely the conclusion is linked to the premisses, participate in this imperfection.
To ordinary lookers-on it naturally seemed that a shattering and decisive blow had been struck at the Tractarian party and their cause; struck, indeed, formally and officially, only at its extravagances, but struck, none the less, virtually, at the premisses which led to these extravagances, and at the party, which, while disapproving them, shrank, with whatever motives, policy, generosity, or secret sympathy, from joining in the condemnation of them.
But if, instead of concluding straight to the particular case, we place before ourselves an entire class of facts—the whole contents of a general proposition, every tittle of which is legitimately inferrible from our premisses, if that one particular conclusion is so; there is then a considerable likelihood that if the premisses are insufficient, and the general inference, therefore, groundless, it will comprise within it some fact or facts the reverse of which we already know to be true; and we shall thus discover the error in our generalization by what the schoolmen termed a reductio ad impossibile.
It has been argued that, at any rate, definitions are premisses of science, provided they give such meanings to terms as suit existing things: but even so, the inference would obviously be from the existence, not of the name which means, but of the thing which has the properties.
It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclusion, and another called the middleterm, which must be found in both premisses, since it is by means of it that the other two terms are to be connected together.
By dropping the use of diagrams, and substituting, in the demonstrations, general phrases for the letters of the alphabet, we might prove the general theorem directly, that is, we might demonstrate all the cases at once; and to do this we must, of course, employ as our premisses, the axioms and definitions in their general form.
From these premisses we have two modes of ascertaining what passes during vinous fermentation: either by determining the nature of, and the elements which compose, the fermentable substances; or by accurately examining the products resulting from fermentation; and it is evident that the knowledge of either of these must lead to accurate conclusions concerning the nature and composition of the other.
Also that euery one of the fiue partners shall foorthwith call vpon their partners to supply towards this new rigging and victualling, 29 li. 10s. 6d. for euery 100. li. value. Also that euery one of the fiue partners shall foorthwith bring in 50 li. towards the furniture of the premisses.
But, if we understand by spirituality a progress to ever new creations, to conclusions incommensurable with the premisses and indeterminable by relation to them, we must say of an idea that moves among relations of necessary determination, through premisses which contain their conclusion in advance, that it follows the inverse direction, that of materiality.
If Knowledge then is such as we have described it, the Knowledge produced by demonstrative reasoning must be drawn from premisses true and first, and incapable of syllogistic proof, and better known, and prior in order of time, and causes of the conclusion, for so the principles will be akin to the conclusion demonstrated. True, they must be, because it is impossible to know that which is not.
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