Sentential Logic Introduced
Sentences may be true or false as in the real world. Whilst we should not be tempted to always 'translate' from the logic of language to another as we do with foreign spoken languages, this comparison between languages can still be made and we will need to do this to a limited extent in order to understand the language whilst learning.
Sentential is composed of sentences, and these are of the form X1 to Xn, where n is indefinitely large number. So it follows that there are an infinite number of potential sentences that can be formed in sentential. Note that in text books the '1' etc are always written as subscript.
As opposed to spoken languages that are geared to, well, being spoken and communicated, sentential is a structural language and it is used by the professionals (the philosophers and logicians, that is) in order to look clearly at arguments and their validity, as this is what it is particularly suited to do without the vagaries of scope and looseness of the English language when it comes to the form of arguments and the connectives therein and their semantics.
One important thing to note is that X1 or Q1 or whatever the sentence is, is not fixed. So on one occasion X1 might be 'I am smiling' and on another occasion it could mean 'It is snowing outside'.
So, the most basic sentence is something like 'Q1'. Sentences that contain more than this are compound or 'non-basic' as they are sometimes called in the jargon. Connectives such as '&' are used, so you may see something like 'A & B'. Brackets will sometimes be used to make scope clear, that is, to avoid ambiguity of how to interpret the sentence.
For instance, these say very different things:
¬A1 v A2
¬(A1 v A2)
in the first case, only A1 is negated; in case two it affects the whole sentence - that is A1 v A2.
If this is the first you are reading about sentential logic, the actual meaning of those symbols will not be clear to you yet; more information is given on these in the following article 'sentential connectives and truth tables'.
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