propositional

Roll your own derivations

6/21/07 10 Software

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴ (or use the palette to produce them)

Roll your own derivations

6/21/07 10 Software

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'.

[Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴

6/14/07

You now have to tools to appraise sentential arguments.

Let us run through how these might be used with two examples.

Example 1.

Consider the argument

If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.

First it should be symbolized

6/3/09 10 Software

Skills to be acquired

Becoming familiar with common inference patterns and being able to use them via three new rules of inference and via rewrite rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.

Reading

Bergmann[2008] The Logic Book Section 5.5

5/2/09 10 Software

Quiz 6 Example of a difficult derivation

6/1/09

6/2/09

Negation Introduction, Simple Reductio

Advanced Reductio via Negation Elimination

6/2/09 10Software

Skills to be acquired:

Learning the Rules Or Elimination and the Introduction of the Biconditional.

Reading

Bergmann[2008] The Logic Book Section 5.1 and 5.4

The Tutorial:

Or Elimination, in the guise of Dilemma, also is a form of inference dating from antiquity.

3/16/06

So that we can show certain arguments to be valid.

The focus of the course lies with the validity and invalidity of arguments. Now, invalidity can be established by counter-example (by producing an interpretation under which all the premises are true and the conclusion false, at the same time). But validity is a different matter. And the usual approach is to have rules of inference and to do derivations.

6/2/09 10 Software

Skills to be acquired:

Learning reductio proof, both as plain Negation Introduction and via (double) Negation Elimination (to prove some formulas that do not have negation as their main connective).

Reading

Bergmann[2004] The Logic Book Section 5.1 and 5.4

The Tutorial:

Reductio ad Absurdum is the second of the classical forms of inference.