propositional

9/1/12

Skills to be acquired in this tutorial:

Symbolizing compound propositions. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

Why this is useful:

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

8/25/12

Not all propositions are atomic propositions. Consider the proposition asserted by 'It is not the case that in 2011 the United States had a female President'. This is a true proposition, yet it is not an atomic one. It is made up of the atomic proposition 'in 2011 the United States had a female President' (which is false) and negation (expressed by 'It is not the case that...'), and the resulting compound proposition, which is the negation of a false proposition, is true.

There are several types of compound proposition.

8/25/12

The symbolization of English statements or propositions can be done using instruments of varying degrees of logical sophistication. The presentation here is restricted to propositional and predicate logic. Researchers in linguistics, philosophical logic, advanced computer science, or artificial intelligence would likely use some more advanced form of logic. However, predicate logic, encompassing propositional logic, is not introductory and it is entirely adequate for many purposes. Being familiar with it is worthwhile intellectually (and it is non-trivial to learn).

8/25/12

In English there is usually more than one way to say the same thing. For example, the sentences 'Forests are widespread or grass is plentiful.' and 'Either forests are widespread or grass is plentiful.' assert the same compound proposition-- the new word 'either' at the beginning of the second sentence does not alter the underlying logical structure. Both these sentences should be symbolized to (F∨G).

One symbolic formula can represent the logical structure of a proposition asserted by several different English sentences (this is one reason why we symbolize).

8/25/12

We will start with propositional logic, then move on to the more advanced predicate logic.

Starting on propositional logic ...

8/2/08

Tutorial 1 Exercise 2

[This is a film-- press the 'play' symbol.]

7/31/08

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]

7/7/12

Skills to be acquired in this tutorial:

To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic propositions.

Tutorial:

The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.

For example,

If it rains, I get wet.
It rains.

Therefore,

I get wet.

7/6/12

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.

7/5/12

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.