Symbolic Logic

Chapter 46

Chapter 46187 wordsPublic domain

_INTRODUCTORY._

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. Such a Proposition may be called an '=Entity=.'

[Note that, when there are _two_ letters in the expression, it does not in the least matter which stands _first_: "xy_{1}" and "yx_{1}" mean exactly the same.]

Also that "x_{0}" shall mean "No existing Things have the Attribute x", i.e. (more briefly) "No x exist"; also that "xy_{0}" shall mean "No xy exist", and so on. Such a Proposition may be called a '=Nullity='.

Also that "+" shall mean "and".

[Thus "ab_{1} + cd_{0}" means "Some ab exist and no cd exist".]

Also that "¶" shall mean "would, if true, prove".

[Thus, "x_{0} ¶ xy_{0}" means "The Proposition 'No x exist' would, if true, prove the Proposition 'No xy exist'".]

When two Letters are both of them accented, or both _not_ accented, they are said to have '=Like Signs=', or to be '=Like=': when one is accented, and the other not, they are said to have '=Unlike Signs=', or to be '=Unlike='.

pg071