Duplication

“ The great law of division became clear to him—the separation for a time of the universal agent into two parts, by the separation and reuniting of which comes light and heat and the hidden force of life, and the prime rules of attractive action; all things that are accounted material. ”

“ In order to resolve this point, we may observe that all plurality is a consequence of division. Now division is twofold; one is material, and is division of the continuous; from this results number, which is a species of quantity. Number in this sense is found only in material things which have quantity. The other kind of division is called formal, and is effected by opposite or diverse forms; and this kind of division results in a multitude, which does not belong to a genus, but is transcendental in the sense in which being is divided by one and by many. ”

“ When any two Divisors with their Remainders are proposed, try the Multiplices of one of them, increased by its Remainder, and divide by the other: If you find such Remainders as are not for the purpose, and that they are repeated, the Problem is impossible. ”

“ A plurality is therefore a relation of units considered as a sum. Unity is constant only in ultimate particles. Bodies are combined, dissolved again and recombined, making variable units of plurality. ”

“ But men in society came to a division of things by agreement. Things not so divided were afterward discovered by individuals and reduced to possession. Thus things came to be subjected to individual control. A complete power of disposition was deduced from this individual control, as something logically implied therein, and this power of disposition furnished the basis for acquisition from others whose titles rested directly or indirectly upon the natural foundation of the original division by agreement or of subsequent discovery and occupation. ”

“ The truth of this strange contradiction of the multiplication table is seen in the relationship of friends. Each gives to the other, and each receives, and the fruit of the intercourse is more than either in himself possesses. Every individual relationship has contact with a universal. ”

“ What we call a division on a single basis is in reality the compressed result of a scheme of division and subdivision by dichotomy, in which a fresh principle has been introduced at every step. Thus when we divide men, on the basis of colour, into white, black, brown, red and yellow, we may be held to have first divided men into white and not-white, and then to have subdivided the men that are not-white into black and not-black, and so on. ”

“ When the number of players is reduced to two, they can, if they possess an equality of lives, as two each, or one each, divide the stake; or they may by agreement play out the game for the entire pool. ”

“ For example, division is one and the same thing, whether it be considered within him who divides, or in that which is divided; nevertheless dividing is something different from being divided. Or again, division is not one and the same thing according as it proceeds from him who divides, or as it is received by him who is divided; to divide means to cause in the divided thing another movement, which is the result of the dividing action or movement. ”

“ And is it not to be regretted that the period of courtship, which is intended to give to the parties an opportunity of judging of their fitness for each other, is usually the period in which the greatest degree of duplicity prevails? ”

“ Now if, as a universal rule, the totality of the relations of one ‘Thing’ to all the others is the reason for its appearance at a fixed place, then all the changed relations, which successively occur during the conflict of both the aforesaid reasons, must also manifest themselves in an unbroken sequence of the phenomena of the ‘Thing’ at intermediate places fixed by these reasons. ”

“ For a social relationship of the type of debtor, friend, neighbor, fellow-citizen, teacher, superior, ancestor, cousin, has the logical character illustrated by saying that if A stands in this relation to B, B may, and frequently does, stand in the same relationship to C, C to D, and so on, — the collection of social individuals A, B, C, constituting in this way an ordered series, sometimes of a very limited, but more often of a very widely extended scope. ”

“ Any declaration can be doubled and redoubled once, but not more; a player cannot double his partner's declaration, nor redouble his partner's double, but he may redouble a declaration of his partner which has been doubled by an adversary. ”

“ Chapter 7 Deception of these (paralogisms) from equivocation and (ambiguous) sentence, arises from our not being able to distinguish that which is multifariously predicated, (since it is not easy to divide some things, for instance, the one, being, and the same;) but of those from composition and division, in consequence of fancying there is no difference between a conjoined, and a divided sentence, as is the case in most things. ”

“ The one and the many are opposed in several ways, of which one is the opposition of the one and plurality as indivisible and divisible; for that which is either divided or divisible is called a plurality, and that which is indivisible or not divided is called one. ”

“ And here we must first of all observe, that (as gain and loss are terms of relation, and of a reciprocal nature) by whatever method one man gains an estate, by that same method or it's correlative some other man has lost it. ”

“ But combinations are of various sorts; there are express combinations entered into by people having the same interest for a particular purpose. Those are done by a sort of an agreement, when the interest of the individual and of the body are the same. ”

“ You know that at all events the husband must give up one-third of his share, which consists of three parts. The mother must likewise give up one-third, of which each legatee partakes according to the proportion of his legacy. Besides, she must pay to the legatee to whom one-fourth is bequeathed, and whose legacy has been imposed on her, as much as the difference between the one-fourth and his portion of the one-third, namely, nineteen one hundred and fifty-sixths of her entire share, considering her share as consisting of one hundred and fifty-six parts. ”

“ The closing paragraph becomes significant, when we reflect upon the danger which the initiates feared would accrue to those still in the heyday of manhood's passions, if they proved unworthy of the Great Secret. The expression "The secret of the combination by twos and threes" has probably a double meaning here the esoteric meaning turning upon the two kinds of marital partnership; known to the initiates; husband and wife being the "combination by two" (in the second degree) ”

“ To divide by an arbitrary line something that cannot be divided is a process that is disturbing to some. Perhaps our deductions are not as inevitable as they are logical, which suggests that they are not "logic." ”

“ If two persons, each having the same sum upon two different vessels which have sailed from the same port to the same destination, agree to divide equally all the money which may arrive, it is clear that by this agreement each of them divides equally between the two vessels the sum which {155} he expects. Indeed this kind of assurance always leaves uncertainty as to the loss which one may fear. ”

“ And if there are many subordinate divisions to any particular class, after that has been simply explained in the first arrangement of the oration, it will be more easily and conveniently arranged when we come to the subsequent explanation in the general statement of the case after the division. And this, too, concerns the subject of conciseness, that we should not undertake to prove more things than there is any occasion for ”

“ We were not born to work together and it is clear that we have come to the parting of the ways. To-morrow we will make division of our holdings, for I tell you plainly that I will have no more to do with you and your dishonest schemes. ”

“ Experience must have shown that the two events are of equally frequent occurrence. Why, in tossing up a half-penny, do we reckon it equally probable that we shall throw cross or pile? Because we know that in any great number of throws, cross and pile are thrown about equally often; and that the more throws we make, the more nearly the equality is perfect. ”

“ But that which acts in conjunction with something else, being of itself incapable of operating by itself, we describe as co-operating and concausing, and say that it becomes a cause only in virtue of its being a joint-cause, and receives the name of cause only in respect of its concurring with something else, but that it cannot by itself produce the right effect. ”

“ It may happen, from one of the companionship absenting himself, that his former share of letter remains undistributed at a time a second division is taking place; under these circumstances, he must not be included in this division. In the event of a scarcity of letter, if any man absent himself beyond a reasonable time, his undistributed matter should be divided equally among his companions, and when he returns, he may then have his share of the next division. ”

“ The general proposition thus stated, that in a joint action upon a bond against several obligors, the judgment must be joint against them all, is admitted to be true; we say the general proposition, because there are exceptions as well established as the principle itself. ”

“ They have come to know the strength of numbers, solidly phalanxed and driving onward with singleness of purpose. These purposes may be various and many, but one and all, ever discovering new mutual interests and objects, obeying a law which is beyond them, these petty aggregations draw closer together, forming greater aggregations and congeries of aggregations. ”

“ Why is a single instance, in some cases, sufficient for a complete induction, while in others, myriads of concurring instances, without a single exception known or presumed, go such a very little way toward establishing a universal proposition? ”

“ My principal reason for addressing you upon this subject is to ask you to suggest to your readers that a similar interchange of duplicates might be effected between the Society and any persons who chance to have duplicate proclamations in their possession.
It is of the very highest literary and historical importance that we should get together, in some accessible place, a collection of proclamations, which if not actually complete (a consummation hardly to be expected) , shall yet approach to completeness. ”

“ This is an excellent example of the so-called 'fallacy of division,' or predicating what is true only of a collection, of each member of the collection distributively. It no more follows that if a thousand things together cause sensation, one thing alone must cause it, than it follows that if one pound weight moves a balance, then one ounce weight must move it too, in less degree. ”

“ Hence a Proposition of Relation, beginning with “All”, is a Double Proposition, and is ‘equivalent’ to (i.e. gives the same information as) the two Propositions
(1) “Some Members of the Subject are Members of the Predicate”;
(2) “No Members of the Subject are Members of the Class whose Differentia is contradictory to that of the Predicate”.
[Thus, the Proposition “All bankers are rich men” is a Double Proposition, and is equivalent to the two Propositions
(1) “Some bankers are rich men”;
(2) “No bankers are poor men”.] ”

“ All the relations which can naturally be represented as equality in any respect, or as possession of a common property, are transitive and symmetrical—this applies, for example, to such relations as being of the same height or weight or colour. ”

“ The observation of any concomitance in agreement in presence, or agreement in absence, does not require any permanent observer, for under certain conditions of agreement there is the knowledge of the concomitance of agreement in presence, and in other conditions there is the knowledge of the concomitance in absence. ”

“ Similarly, in the case of three partners, they would have only one third of the force—in the case of four, only one fourth—and in a multitude, no force whatever. For beyond a certain point of minuteness, the interest would be so small as to elude perception, and would obtain no hold whatever on the human mind. ”

“ The negation of a categorical judgment is not a negative, but a particular judgment. Now the relations between objects are two-fold: either original ones, due to synthesis, or derived from an analysis of other relations. The process of thought which in this way derives relations from given relations is deduction. Induction creates original relations. ”

“ The method which we call short division was largely used in the middle ages, as was also the method of dividing by using the factors of the divisor. The process by long division was known, but was not so commonly used as others. ”

“ At any rate, unless it is realized that there has been no proof that all are due to similar deficiencies, we may, by stamping them all alike and by grouping them together, be misled into taking their close relationship for granted. ”

“ Appeal to lucky omens.Before the seulangké begins his task, the requisite appeal to lucky omens must be made. Long before the formal proposal, a sort of calculation is made which is supposed to show whether a blessing can rest on the union; for example the numerical value of the initial letters of the names of both are added together and divided by a certain number, and the remainder left over after this division shows whether it is wise to commence the negociations or not [5] . ”