Tutorial 3: Propositions and Truth
8/10/26
Skills to be acquired in this tutorial:
To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.
8/10/26
To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.
There is the idea of setting up a code or convention or dictionary between atomic sentences and capital letters.
There are compound sentences, each of which has a main connective which connects its components.
There are five sentential logical connectives:
'∼' which translates back to 'it is not the case that...'
'&' which translates back to '... and ...'
'∨' which translates back to '... or ...'
'⊃' which translates back to 'if... then ...'
'≡' which translates back to '... if and only if ...'
There is the idea of setting up a code or convention or dictionary between atomic propositions and capital letters.
There are compound propositions, each of which has a main connective which connects its components.
There are five propositional logical connectives:
'∼' which translates back to 'it is not the case that...'
'∧' which translates back to '... and ...'
'∨' which translates back to '... or ...'
'⊃' which translates back to 'if... then ...'
'≡' which translates back to '... if and only if ...'
8/29/06
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9/1/12
Symbolizing compound propositions. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.
It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.
8/2/08
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Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.
7/31/08 10 Software
To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic sentences.
Bergmann[2004] The Logic Book Chapter 1
The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.
For example,