Symbolic Logic

1. The Univ. is "persons." The Individual "I" may be regarded as a Class, of persons, whose peculiar Attribute is "represented by the Name 'I'", and may be called the Class of "...

17. No one, who exercises self-control, fails to keep his temper; Some judges lose their tempers. pg102 18. All pigs are fat; Nothing that is fed on barley-water is fat.

It may be well to explain what I mean by the _complete_ Conclusion of a Syllogism or a Sorites. I distinguish their Terms as being of two kinds----those which _can_ be eliminate...

21. No goods in this shop, that are still on sale, may be carried away. pg133 22. No acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus.

We will limit ourselves, at present, to Problems which can be worked by the Formulæ of Fig. I. (See p. 75.) Those, that require _other_ Formulæ, are rather too hard for beginners.

We already know how to represent each of the three Propositions of a Syllogism in subscript form. When that is done, all we need, besides, is to write the three expressions in a...

To translate a Proposition from concrete into abstract form, we fix on a Univ., and regard each Term as a _Species_ of it, and we choose a letter to represent its _Differentia_.

Henceforwards, in stating such Propositions as "Some x-Things exist" or "No x-Things are y-Things", I shall omit the word "Things", which the Reader can supply for himself, and...

[Note that, though its Sign of Quantity tells us _how many_ Members of its Subject are _also_ Members of its Predicate, it does not tell us the _exact_ number: in fact, it only...

Buy "THE WONDERLAND CASE FOR POSTAGE-STAMPS," invented by LEWIS CARROL, Oct. 29, 1888, size 4 inches by 3, containing 12 separate pockets for stamps of different values, 2 Colou...

First, let us suppose that the above Diagram is an enclosure assigned to a certain Class of Things, which we have selected as our 'Universe of Discourse.' or, more briefly, as o...

This tells us that there is at least _one_ Thing in the Inner portion of the North Half; that is, that this Compartment is _occupied_. And this we can evidently represent by pla...

The Reader had better now begin to draw little Diagrams for himself, and to mark them with the Digits "I" and "O", instead of using the Board and Counters: he may put a "I" to r...

First, let us suppose that the above _left_-hand Diagram is the Biliteral Diagram that we have been using in Book III., and that we change it into a _Triliteral_ Diagram by draw...

the Trio is called a '=Syllogism='; the Genus, of which each of the six Terms is a Species, is called its ='Universe of Discourse=', or, more briefly, its '=Univ.='; the first t...

A Proposition of Relation, beginning with "Some", is henceforward to be understood as asserting that there are _some existing Things_, which, being Members of the Subject, are a...

The best plan, for a _beginner_, is to draw a _Biliteral_ Diagram alongside of it, and to transfer, from the one to the other, all the information he can. He can then read off,...

'Classification,' or the formation of Classes, is a Mental Process, in which we imagine that we have put together, in a group, certain Things. Such a group is called a '=Class=.'

[Thus, we might think of the Class "books," and imagine that we had divided it into the two smaller Classes "bound books" and "unbound books," or into the three Classes, "books...

Similarly we may interpret a _Grey_ Counter, when placed in the North-East, or South-West, or South-East Cell. pg037 Next, let us suppose that we find a _Red_ Counter placed on...

Such words as "oh!" or "never!", and such phrases as "fetch me that book!" "which book do you mean?" do not seem, at first sight, to convey any _information_; but they can easil...

The word "Thing", which conveys the idea of a Thing, _without_ any idea of an Adjunct, represents _any_ single Thing. Any other word (or phrase), which conveys the idea of a Thi...

"No x are y'" = "No y' are x", "No x' are y" = "No y are x'", "No x' are y'" = "No y' are x'". pg072 Let us take, next, the Proposition "All x are y".

When a Set of three or more Biliteral Propositions are such that all their Terms are Species of the same Genus, and are also so related that two of them, taken together, yield a...

It is evident that every Member of a _Species_ is _also_ a Member of the _Genus_ out of which that Species has been picked, and that it possesses the _Differentia_ of that Speci...

[Note that, though its Sign of Quantity tells us _how many_ existing Things are Members of its Predicate, it does _not_ tell us the _exact_ number: in fact, it only deals with _...

Let us agree that "x_{1}" shall mean "Some existing Things have the Attribute x", i.e. (more briefly) "Some x exist"; also that "xy_{1}" shall mean "Some xy exist", and so on. S...

Let us also agree that a _Red_ Counter, placed on the partition between two Cells, shall mean "The Compartment, made up of these two Cells, is _occupied_; but it is not known _w...

A =Proposition of Relation=, of the kind to be here discussed, has, for its Terms, two Specieses of the same Genus, such that each of the two Names conveys the idea of some Attr...

Thus, we may say that a rose has the Attribute "red" (or the Adjunct "red," whichever we prefer); or we may say that it has the Adjunct "red, scented and full-blown."]

_Given a Pair of Propositions of Relation, which contain between them a Pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any,...