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The material explained here is conceptually at a higher level than the earlier tutorials; it also covers relatively rare cases.
Hausman[2007] Logic and Philosophy Chapter 11
To understand the concepts of scope, free, bound, and free for. To learn of the restrictions on the quantificational rules
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Hausman[2007] Logic and Philosophy Chapter 9
Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective.
The circumstance that Existential Instantiation gets invoked looks like this.
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Hausman[2007] Logic and Philosophy Chapter 9
There is a rule for adding a Existential Quantifier. This permits the step illustrated by the following proof fragments.
5 Fa 6 (∃x)Fx 5 EG
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Hausman[2007] Logic and Philosophy Chapter 9
There also is a rule for adding a Universal Quantifier. This permits the step illustrated by the following proof fragments.
5 Fx 6 (x)Fx 5 UG
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Hausman[2007] Logic and Philosophy Chapter 9
To understand the concepts of scope, free, bound. To meet substitution and a simplified version of the rule for removing a Universal Quantifier.
Hausman[2007] Logic and Philosophy Chapter 8
The sentential rules of derivation carry over unchanged into Predicate Logic
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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
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You now have to tools to appraise sentential arguments.
Let us run through how these might be used with two examples.
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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Learning conditional proof, and indirect proof.
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.
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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.
Hausman[2007] Logic and Philosophy Chapter 4