It doesn’t help too much when dealing with real life situations. Take for example the following two contradictory statements:
- Republicans are not responsible for the government shutdown, but the Democrats are.
- Democrats are not responsible for the government shutdown, but the Republicans are.
You are going to find intelligent people who say that 1 is true and you are going to find intelligent people who say that 2 is true. Each will present compelling arguments.
There is a problem with the principle of non-contradiction because it assumes things are either black or white. but things can be gray.
First, “intelligent people” can be just wrong. Even if they offer “compelling” arguments (that is, persuasive to you).
Second, do look at what Law of Non-contradiction really says. For example, Aristotle’s “Metaphysics”, Book Γ (Commentary by St. Thomas Aquinas in
http://dhspriory.org/thomas/Metaphysics4.htm#6): “It is that the same attribute cannot both belong and not belong to the same subject at the same time and in the same respect; and let us stipulate any other qualifications that have to be laid down to meet dialectical difficulties.”.
Are you going to claim that Republicans (or Democrats) are both responsible and not responsible for government shutdown at the same time and in the same respect?
By the way, even if you are, those “intelligent people” you cited are sure to disagree.
Let’s solve the other sophisms you offered:
Take the following two propositions: They contradict each other, but both are true:
- Trump is a good ;president.
- Trump is not a good president.
Let’s note that it is not explained what is meant by “good president”. Solve this ambiguity, and it will be clear that there is no contradiction.
Here is another example:
- Lake Mead is big.
- Lake Mead is not big.
They are contradictory but they are both true.
- Is true because Lake Mead is much bigger than Beaver Lake or Lake George.
- Is true because Lake Mead is not big in comparison with Lake Superior or Lake Huron.
Again, explain what is meant by “big lake”, and contradiction will disappear.
Why do things that begin to exist need a cause? The person with whom I argued brought this up.
That seems to be the same question, as in the original post. Is there anything else that hasn’t been covered already?