propositional

6/20/12

You need to know some propositional logic to be able to understand the tree tutorials to come. In particular, you need to know about the symbols used in propositional logic, truth tables, satisfiability, consistency, and semantic invalidity (by counter example). You do not need to know propositional rules of inference and derivations.

Howson [1997] will give you enough background.

Alternatively you could look at the first five propositional tutorials in Easy Deriver

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)

9/4/06

Tutorial 5 Example: Doing a derivation

This movie shows the downloadable application being used, but the manipulations are so similar to those of the web page applet that it really covers both.

This video is also using a different logical system, but it is close enough for now to illustrate the important points. [The video will be revised and replaced.]

11/27/11 10Software

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

11/27/11 10Software

2/4/08

Indirect Proof

12/21/06

Modus Ponens (MP)

p⊃q,
p
∴
q

Modus Tollens (MT)

p⊃q,
~q
∴
~p

Disjunctive Syllogism(DS)

p∨q,
~p
∴
q

or, if desired,

p∨q,
~q
∴
p

Simplication (Simp)

p.q
∴
p

or, if desired,

p.q
∴
q

Conjunction (Conj)