9/15/12
To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.
Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.
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.
11/9/2007 10Software
The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
12/25/06
This video illustrates use of the downloadable application (and the symbol ∧ for 'and' and (∀x) for the universal quantifier, some systems use (x) for this). But, what the film depicts and explains is equally good if you happen to be using the web pages applets (or different symbols for 'and' and the universal quantifier).
10Software
Hausman[2007] Logic and Philosophy Chapter 7
We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
10 Software
Hausman[2007] Logic and Philosophy Chapter 8
A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.
There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.
There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,
Universe = {a,b,c}
6/6/09 10Software
To learn how to interpret simple predicate logic formulas as being true or false.
This helps in proving invalidity by the technique of displaying a counter-example.
Hausman[2007] Logic and Philosophy Chapter 8
In sentential logic, we just took it that each of the atomic sentences either is true or is false-- we did not look into the structure of the sentences.
Truth can be discussed in more detail in predicate logic.