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## Contradictions, Logical Truths and Logical Possibilities

A \emph{contradiction} is a sentence that is false in all possible situations.
A \emph{logical truth} is a sentence that is true in all possible situations.
A \emph{logical possibility} is a sentence that is true in one or more possible situations.

A sentence that is false in all possible situations.

E.g.

 A A ∧ ¬A ​T F ​F F

logical truth

A sentence that is true in all possible situations.

E.g.

 A A ∨ ¬A ​T T ​F T

logical possibility

a sentence that is true in one or more possible situations.

I’ll illustrate how this works in logic-ex. Let’s say we want to construct the truth table for A or not A.
The first thing I need is more rows, so I hit the circled plus thing.
Now I’ve got a second row, and in this case two rows is enough. Time to start filling in values ...
I’m doing the reference columns first because these are always the same and I don’t need to work out what the values are.
Now I have to enter the value of A or not A when A is true. You might be able to compute this in value in your head, but that won’t always be the case. I expect that, often, before you enter a value in the table in zoxiy you will have taken a pencil and paper and worked out the truth table step by step.
So what you enter will often be something that took quite a bit of work to compute.
Or you could just guess. But this is not generally a good strategy because I take the view that a truth table is either right or wrong, and if you are really guessing you only have a 1/16 chance of being right for most truth tables.
Anyway, I think it’s true.
Now for the last truth value.
This is also true.
We’re not done yet, we now have to say whether the sentence is a contradiction. A \emph{contradiction} is a sentence that is false in all possible situations.
This sentence isn’t false in all possible situations ...
... so it isn’t a contradiction.
Next we have to specify whether ‘A or not A’ is a logical truth. A \emph{logical truth} is a sentence that is true in all possible situations.
This sentence is true in all possible situations ...
... so this sentence is a logical truth.
Finally, we’re asked whether the sentence is a logical possibility. A \emph{logical possibility} is a sentence that is true in one or more possible situations.
This sentence is true in at least one possible situation ...
... so this sentence is a logical possibility.
2.5, 2.6