derivations

Tutorial 21: Existential Elimination

Logical System

2013

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial


Existential Elimination (often called 'Existential Instantiation') permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. It is one of those rules which involves the adoption and dropping of an extra assumption (like ∼I,⊃I,∨E, and ≡I).


The circumstance that Existential Instantiation gets invoked looks like this.

Sentential Logic: Try your own derivations admin Sat, 01/11/2014 - 01:50
Logical System

Roll your own derivations

2013

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 ∼ & ∨ ⊃ ≡ ∀ ∃ ∴

Supplementary: Why are we doing all these derivations anyway? admin Sat, 01/11/2014 - 01:50
Logical System

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.

Tutorial 10: Common Inference Patterns and Rewrite Rules admin Sat, 01/11/2014 - 01:50
Logical System

2013

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