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Welcome to Week 4

In this video, Dr Barry Lee gives a preview of this week's work on conditionals and on testing for formal validity with truth-tables.
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Welcome to Week 4 of ‘Logic: the Language of Truth. Last week, we introduced two more sentence connectives to our logical
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language: tilda and vel. We saw how useful truth tables could be and we looked at a debate over the relation between our formal logical language and English, considering the case of ‘or’ and the idea that it sometimes expresses so-called ‘exclusive or’. This week, we’re going to do
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two main things: first, we’ll look at our final and most
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controversial sentence connective: ‘arrow’, sometimes called ‘material implication’. It’s controversial because while we can specify exactly what arrow means and what its logical powers are, just like the other sentence connectives in our former logical language, there is a debate about whether it really does relate in any straightforward way to the English expression that logicians most often connect it
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with: ‘if, then’. It’s possible that this connective of our formal language doesn’t translate directly into any natural language. The second thing we’ll do is return to the main objective of this course - to work out a way to test arguments to see if they’re deductively valid or not. There’s a key challenge here. When we first looked at validity in Week one, we tested for validity largely by using our imaginations in a pretty unsystematic way. We looked at arguments and asked ourselves if there was a way for all of the premises to be true, but the conclusion false; a counterexample. if we couldn’t see one that gave us some kind of reason to think the argument was valid.
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This week, we’ll look at a way of doing this systemically, using the truth tables of formal logic. If the truth of the premises is inconsistent with the falsity of the conclusion then the argument is valid. Truth tables will allow us to check all the possible ways that the premises could be true and whether any of those are consistent with the the conclusion being false, and thus test conclusively for formal validity. Finally, we’ll look ahead to where you might take your investigation of logic next, by looking briefly at some arguments which look like they’re formerly valid, but not valid because of the sentence connectives we’ve defined in terms of truth tables.

In this video, Dr Barry Lee introduces this week’s work on conditionals and on testing for formal validity with truth-tables.

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Logic: The Language of Truth

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