propositional

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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'.

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

F ∴ F . G ∼ ∨ ⊃ ≡ ∃ ∴

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

So, a selection needs to have a form similar to this

F⊃G,G⊃H∴F⊃H

10/12/26

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

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Skills to be acquired:

Learning conditional proof, and indirect proof.

The Tutorial:

There are two additional sentential rule of inference-- Conditional Proof and Indirect Proof (Reductio ad absurdum)-- which are slightly more difficult than the ones that we have met before. They are slightly more difficult in that they require you to make new assumptions, and the correct new assumptions at that.

10/12/26

Skills to be acquired

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

Reading

Hausman[2007] Logic and Philosophy Chapter 4

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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)

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Skills to be acquired in this tutorial:

a) Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

b) Learning elementary Tactics.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

10/12/26

Skills to be acquired in this tutorial:

Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

The Tutorial:

Thus far we have encountered 3 sentential rules of inference: Simplification, Conjunction, and Addition. If we write these out as forms or patterns, these are the kinds of inferences they permit.

Simplication (Simp)

Review of new material

There are the truth-tables for the connectives...

Negation

F	∼F
True	False
False	True

Conjunction

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Skills to be acquired in this tutorial:

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

Reading

Hausman[2007] Logic and Philosophy Chapter 4

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.

10/12/26

Skills to be acquired in this tutorial:

To learn how to symbolize arguments, and how to judge whether they might be invalid using truth-table methods.

Why this is useful:

We wish to appraise arguments, to do this we have to symbolize them first. Judging the invalidity of arguments by truth-table methods is not particularly important, but it does help to develop skills involving truth and lists of formulas.

Reading

Hausman[2007] Logic and Philosophy Chapter 3