bergmann

Help with Reading a Counter Example [Generic]

Topic
trees
Logical System
bergmann

1/25/09

Reading a counter example from an open branch

[This is a Quicktime Movie, click the Play button to view it. The logical symbols you see in use may be different to the ones you are familiar with (sorry about that, but it is not practical to produce different movies for all the minor variations in symbols). Any differences will not affect the principles being explained here.]

Supplementary: Alternative Indicator Words

Logical System
bergmann

Alternative Indicator Words

2/2/06

The examples of arguments in English that have been given thus far have had the form

All men are mortal.
Socrates is a man.

Therefore,

Socrates is mortal.

This form is definitely something of an ideal case. In practice we rarely use the word 'therefore', and there are plenty of arguments that do not have exactly two premises, and, indeed, there are real world arguments where the conclusion comes first and the premises come later.

Tutorial 5: Valid arguments, searching for a proof

Topic
derivations
propositional
Logical System
bergmann

5/18/09 10Software

Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Simple sentential derivations using some of the Rules of Inference.

Reading

Bergmann[2004] The Logic Book Section 5.1.

The Tutorial:

If you suspect that an symbolized argument might be valid, you should attempt to give a derivation of it.

A derivation is a proof of validity.

Reading a Counter Example from the Tree

Topic
trees
Logical System
bergmann

5/18/09 09 Software

A central use for Trees is to produce a counter example to an invalid argument. To do this, you construct a tree with a complete open branch. You will be able to do this for invalid arguments (but not valid ones). Then you run up that branch assigning all atomic formulas True and all negations of atomic formulas False.

This applet will let you try a few.

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