Could we fix it?
We continue with our search to fill in the blanks of the statement: If an object is all black and all white at the same time, then its color is …
Attempt 1: Could we get more information about the object? No, the object is completely black and also completely white, and that’s all we know about the object. So there’s no way to know which of the colors the true one is.
Attempt 2: Or, could we introduce a second object? Then at least the colors on the object would not contradict. But then we have another problem.
Where is it wrong?
Attempt 1: Logic tells us that we need to use only the given data. Through using specific rules, together with these data, we arrive at a logical conclusion. If however two statements – or premises as they are called – say something is true and something is also not true, then we have a problem. Aristotle says: “Contradicting premises cannot both be true at the same time.” So we haven’t got a clue as to which color we can exclude.
Attempt 2: We would make 2 mistakes:
1. Having added new data, we would not have used solely the given data.
2. The rule for a logical proof is that it has a certain form. The premises are part of the form, and they have a subject and a predicate – both called terms – that connect to each other in a certain way. And the terms of the conclusion connect back to the terms of the premises.
So then, instead of having it repaired to avoid the contradiction, we would have created 2 unconnected statements, from which we can’t ever draw a conclusion, because they don’t form a coherent argument. Having only one premise, we can’t prove a thing.
What is the solution?
What’s left? The only thing we can determine is that we can’t conclude anything that is logical, because there’s no logic in this statement to begin with.
Actually, it’s even worse.
A logical rule states that from a contradiction we can conclude anything. To understand this fully, we need to be trained in propositional logic.
Not only can we not exclude any of the given data in this statement, but the logic also adds to this, that since no exclusions can be made, any conclusion is possible. When the number of ‘solutions’ is limitless, we say nothing (distinguishable).