- When a man cannot make up his mind which of two parties he will join, he is said to be "sitting on the fence"--not being able to decide on which side he will jump down.
- "Some x are y" and "no x are y'".
- A Proposition, whose Subject is a single Thing, is called 'Individual'. For example, "I am happy", "John is not at home". These are Universal Propositions, being the same as "all the I's that exist are happy", "ALL the Johns, that I am now considering, are not at home".
- Propositions beginning with "some" or "all".
- When they begin with "some" or "no". For example, "some abc are def" may be re-arranged as "some bf are acde", each being equivalent to "some abcdef exist".
- Some tigers are fierce, No tigers are not-fierce.
- Some hard-boiled eggs are unwholesome, No hard-boiled eggs are wholesome.
- Some I's are happy, No I's are unhappy.
- Some Johns are not at home, No Johns are at home.
- The Things, in each compartment of the larger Diagram, possess THREE Attributes, whose symbols will be found written at three of the CORNERS of the compartment (except in the case of m', which is not actually inserted in the Diagram, but is SUPPOSED to stand at each of its four outer corners).
- If the Universe of Things be divided with regard to three different Attributes; and if two Propositions be given, containing two different couples of these Attributes; and if from these we can prove a third Proposition, containing the two Attributes that have not yet occurred together; the given Propositions are called 'the Premisses', the third one 'the Conclusion', and the whole set 'a Syllogism'. For example, the Premisses might be "no m are x'" and "all m' are y"; and it might be possible to prove from them a Conclusion containing x and y.
- If an Attribute occurs in both Premisses, the Term containing it is called 'the Middle Term'. For example, if the Premisses are "some m are x" and "no m are y'", the class of "m-Things" is 'the Middle Term.'
If an Attribute occurs in one Premiss, and its contradictory in the other, the Terms containing them may be called 'the Middle Terms'. For example, if the Premisses are "no m are x'" and "all m' are y", the two classes of "m-Things" and "m'-Things" may be called 'the Middle Terms'.
- Because they can be marked with CERTAINTY: whereas AFFIRMATIVE Propositions (that is, those that begin with "some" or "all") sometimes require us to place a red counter 'sitting on a fence'.
- Because the only question we are concerned with is whether the Conclusion FOLLOWS LOGICALLY from the Premisses, so that, if THEY were true, IT also would be true.
- By understanding a red counter to mean "this compartment CAN be occupied", and a grey one to mean "this compartment CANNOT be occupied" or "this compartment MUST be empty".