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Welcome to Week 3

Watch Professor Tom Stoneham's overview of what you'll be exploring this week.
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Welcome to Week 3 of ‘Logic: the Language of Truth’. Last week, we introduced you to the idea of a truth functional sentence connective, taking ampersand as our example. We saw how the meaning of ampersand can be specified clearly using truth tables. We saw how it looks as if a lot, but not all, uses of ‘and’ in English can be captured pretty accurately in terms of ampersand. We also introduced the semantics-pragmatics distinction and the corresponding distinction between strict or literal word and sentence meaning, on the one hand, and occasional-speaker meaning on the other. This week, we’re going to look at two more
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sentence connectives: ‘Tilda’ corresponding to ‘not’ or ‘it’s not the case that’ in English and ‘vel’, corresponding to ‘or’ in English. In the case of vel, we will see that there’s some interesting debate as to whether the meaning will specify for it really is that close to the meaning of ‘or’ in English. The uncarity here comes from the imprecision of natural languages like English and gives us another reason to use the precise language of formal logic. Well also look further at truth tables; we’ll see that truth tables can be used for a number of logically important tasks.
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We’ll see how truth tables can be used to establish when two claims are logically equivalent, that is, their meanings are such that they’re true in exactly the same circumstances, and correspondingly false in exactly the same circumstances. We’ll see how truth tables can be used to establish when a collection of claims is consistent; when there’s a way for them to be true all together and we’ll see how truth tables can be used to establish when a collection of claims is inconsistent, when is no way for them to be true all together and we’ll see how truth tables can be used to establish when a claim is necessary or a ‘tautology’, that is, when it’s true, no matter what.
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With all that logical machinery in place, we’ll be in a position to test whether arguments are formally valid or not, but that will have to wait until Week 4.

In this video, Professor Tom Stoneham gives a preview of what we’ll be exploring this week.

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Logic: The Language of Truth

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