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actual admit adopted already answer application assertion assigned attributes Boole called chapter class terms combination common compartments complete conclusion condition considered corresponding course described determine diagram direct discussion distinct doubt elements employed entirely equal equation equivalent example exclusive existence explanation expression extension fact familiar figures former formula four give given ground Hence identical implies important included indefinite indicated instance interpretation involve kind language latter limits Logic mathematics means merely mutually nature negative notation notice once operation ordinary particular positive possible predicate premises present problem propositions question reader reason reference regards relation remarked represent respect restriction result rule scheme seems seen simple stand statement Suppose symbolic things tion true universe various whole write yield
Page 70 - Tr"1 is defined. Thus it is the office of the inverse symbol to propose a question, not to describe an operation. It is, in its primary meaning, interrogative, not directive. Suppose the given equation to be Then on the above principle of notation we should have...
Page 107 - ... w but are no part of z). It must be admitted that such a diagram is not quite so simple to draw as one might wish it to be; but then consider what the alternative is if one undertakes to deal with five terms and all their combinations; — nothing short of th'e disagreeable task of writing out, or in some way putting before us, all the 32 combinations involved.
Page 120 - In this respect logical calculations stand in marked contrast with those of mathematics, where economical devices of any kind may subserve a really valuable purpose by enabling us to avoid otherwise inevitable labour. Moreover, in the second place, it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines. It is but a very small part of the entire process, which goes to form a piece of reasoning, which they are capable of...
Page 121 - It then becomes a question of judgment which of these is the simplest and best. For instance, in the last example but one, there are a quantity of alternative ways of reading off our conclusion ; and until this is done the problem cannot be said to be solved. I cannot see that any machine can hope to help us except in the third of these steps ; so that it seems very doubtful whether any thing of this sort really deserves the name of a logical engine.
Page 429 - Ji & ff so as to coincide with DE. This seems to me to constitute the essential characteristic of his scheme, which is worked out in a variety of figures of a more or less complicated kind. It is decidedly cumbrous, and not entirely effective as regards this its main aim, but it deserves recognition as an attempt to remedy a real defect in the ordinary scheme. Hamilton who, as we know, never could succeed in grasping the nature of a triangle, entirely misconceived all this; and seeing that Maass...
Page 427 - I have seen no attempt to extend diagrammatic notation to the results of four terms, and it is only quite recently that really adequate figures have been proposed for those of three terms : — for instance both Drobisch and Schroder have used what we may call the three-circle diagram1.