Symbolizing Atomic Propositions

Logical System


We will start with propositional logic, then move on to the more advanced predicate logic.

Starting on propositional logic ...

Indicative English sentences 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 propositions or statements. Not all pieces of English 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.

Propositions (or statements) can be atomic or compound. 'There are 35 State Governors in the U.S.A.' expresses an atomic proposition; whereas 'There are 35 State Governors in the U.S.A. and there is one President of the U.S.A. ' expresses a compound proposition composed of two atomic propositions (one false one and one true one).

Symbols are used to stand for propositions. In the systems used here we use the capital letters 'A' to 'Z' to stand for atomic propositions-- a capital letter is used as a shorthand or code for a proposition. You decide which letter you want to stand for each particular atomic proposition; then having formed a convention or Dictionary, you stick to it throughout each argument.

For example, you may decide to let 'F' stand for the proposition expressed by 'Forests are widespread' in which case when you are trying to symbolize, every time you meet 'Forests are widespread' you symbolize it to 'F' (and, if you are trying to translate back from symbols, every time you meet 'F' you translate it back to 'Forests are widespread').

It is usual to tell the world of your conventions-- the codes you use are not intended to be secret ones.

Exercises to accompany Symbolizing Atomic Propositions

Two pieces of advice if you are using an iPad on this:

Select by double tapping with your finger (so, select a particular word by double tapping then extend the selection handles out to cover the selection you want). And if the screen keyboard gets in the way, hold down on the bottom-right 'dismiss keyboard' key then split the keyboard and move it around the screen to a suitable place (turning the iPad to 'portrait' orientation also helps).

Exercise 1 (of 1):

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