Skills to be acquired in this tutorial:
To start learning how to symbolize sentences using predicate logic.
To symbolize at predicate logic level, entities like Beryl are symbolized by constant terms which are lower case letters from the beginning of the alphabet ('b' would be fine for Beryl) and properties are symbolized by upper case letters ('W' would be fine for '..is wise'); and the two are put together by writing the property first followed by the individual it applies to. The result, using the conventions mentioned here, is
There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.
The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. [CS Peirce, How to make our ideas clear]
These web pages provide an introduction to logic to the level of Propositional and Predicate Calculus.
The focus of the program is on arguments and the question of whether they are valid. Arguments have the form <list of premises> ∴<conclusion>. An argument is valid if and only if it is not possible for all its premises to be true and its conclusion false at one and the same time; an argument which is not valid is invalid.
Tutorial 16 Symbolization using the quantifiers.
Skill to be acquired in this tutorial:
To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.
In Predicate Logic there are two new logical connectives, the Universal Quantifier (∀x) and the Existential Quantifier (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).