An Alternative Version of Categorical Logic

Logicians have a very specialized definition of the word ‘some’: in logic it means ‘at least one’. But that is not how people outside of logic use the term at all. In other contexts ‘some’ means ‘at least one but not all’, or ‘not all and not none’. In this work I explore how categorical logic is transformed with this new definition, which is more in harmony with how the word ‘some’ is used outside of formal logic. This results in a more intuitive, and, I believe, more accurate version of categorical logic.

Topics discussed: The proper definition of ‘some’, Aristotle’s Square of Opposition, the Modern Square of Opposition, the ‘Boolean interpretation’, existential import, the Triangle of Opposition, categorical syllogisms, sorites arguments, conversion obversion and contraposition, modal logic (including the Modal Triangle of Opposition), the connection to propositional logic, and the connection to predicate logic.