A start can be made in predicate logic by taking apart 'atomic' propositions and by re-phrasing what they have to say in a 'entity-has-property' way.
The constant terms a,b,c...h are used to denote entities, the predicates A,B,C...Z are used to denote properties that these entities have, and these are put together by writing the predicate first followed by the term, for example Gb.
10 Software
In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,
2013
To start learning how to symbolize propositions using predicate logic.
There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.
There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.
8/26/2012
Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.
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).
8/26/2012
In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,
8/26/2012
Propositional logic, while good for many purposes, is not adequate for everything. One of the central uses of logic is to judge which arguments are valid and which are not. But there are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
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]
Welcome!
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.