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Parts of sentences: sentential clauses and sentence-connectives

In this step we look at the kind of structure or form that we'll be focusing on.
A length of chain showing the links
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Take another look at one of our example arguments.

  • Mattie is tidying or Mattie is gaming online
  • Mattie is not tidying
  • So, Mattie is gaming online

The conclusion is (expressed by) the sentence ‘Mattie is gaming online’. This sentence also turns up as part of the first premise. Here it’s what is called a sentential clause: a sequence of words which is part of a larger sentence and which could stand as a sentence in its own right (and which functions in the larger sentence in a sentence-like way).

That first premise contains another sentential clause: ‘Mattie is tidying’. Now, does this sentential clause crop up anywhere else in the argument? Not exactly, but it’s obviously closely related to the second premise, ‘Mattie is not tidying’.

Notice that we could express the second premise using the sentence ‘It is not the case that Mattie is tidying’. (That would seem a bit stiff in ordinary conversation, but it does seem to mean the same as the original, at least in the sense that they have the same truth-conditions: they are true in the same circumstances and false in the same circumstances.) With that adjustment, the first sentential clause in the first premise crops up again as a sentential clause in the second premise.

If we mark repeated sentences/sentential clauses with letters, we get the following pattern. (We’ll use Greek letters — α, alpha, and β, beta —for this job, because we’ll want to use standard roman alphabet letters for another job soon.)

  • α or β
  • It is not the case that α
  • So, β

Looking back at our other examples, we can see that they also feature this pattern.

The pattern is made up in part from repeated sentences/sentential clauses, but it also features some other expressions: ‘or’ and ‘It is not the case that’. These aren’t sentential clauses. They couldn’t stand in their own right as sentences. Instead, they are what are called sentence connectives: a sentence connective is an expression which connects to (a specific number of) sentences/sentential clauses to form a larger sentence (or sentential clause).

As we’ve already seen, it looks like any argument which has this structure or form will be valid, and it looks like it will be valid because it has this form. It looks like these arguments are, as we’ll say, formally valid. We haven’t made this out in a fully convincing way for these arguments yet — it’s part of our project to do this — but it looks very plausible. Exploring this idea will be our focus for much of the rest of the course.

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Logic: The Language of Truth

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