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To learn the rule for adding a Universal Quantifier.
Bergmann[2004] The Logic Book Section 10.1.
There also is a rule for adding a Universal Quantifier (often called 'Universal Generalization'). This permits the step illustrated by the following proof fragments.
The rule is
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To understand the concepts of scope, free, bound. To meet substitution and the rule for removing a Universal Quantifier.
Bergmann[2004] The Logic Book Section 10.1.
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The sentential rules of derivation carry over unchanged into Predicate Logic
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Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.
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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'.
[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 ∼ & ∨ ⊃ ≡ ∀ ∃ ∴
And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).
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.
6/21/07
Rewrite Rules
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This video uses '&' as the logical symbol for 'and'.
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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.
Bergmann[2008] The Logic Book Section 5.5
10/23/06
2/27/06