Are there philosophical problems for which there's only a trivial solution?

Question

I can't really think of a philosophical example, but in mathematics, it would be something like 'find the x where f(x) = 0 given that f(x) = x', and the solution would be 'x = 0', which is trivial. Is there any such "theorem" in philosophy? What are the most popular ones? Is there even an analog?

Answer 1

Short Answer

The answer is yes and no. Philosophical theory itself does not because philosophical texts are largely exercises in defeasible reason conducted in natural language which is far more syntactically and semantically complex than artificial language. However, formal logic, like problems conducted in Fitch, can have trivial solutions.

Long Answer

The question isn't quite what would be considered well-formed which means there are some usages in your language that reflect the need to explain relationships between philosophy, mathematics, and logic.

Philosophy is chiefly conducted through argumentation, and those arguments are primarily divided between formal logic and informal logic with the latter being more encompassing and more related to natural language. As such, philosophical discourse doesn't have "trivial solutions" in the same way mathematical theory might.

Philosophy, generally speaking, doesn't use theorems which by this article is a mathematical term:

In mathematics, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems.

That being said, philosophy deals almost exclusively in propositions which is a unit of meaning roughly based on a sentence, but somewhat flexible in syntax. For instance, two different sentences can represent the same proposition:

The boy is holding the blue ball.
The boy is holding the ball that is blue.

Both of these would be considered relatively identical in meaning. A mathematical theorem doesn't manifest such syntactic flexibility and therefore is not open to debate in meaning. Natural language propositions are and that's why philosophy (and law and argumentation) are seen as exercises in hair-splitting. Formal logic shares the same nature and as such, within formal logic, there are trivial solutions to formalisms. A simple example would be determining the truth condition of the statement p=p which is true by the law of identity.

So, it's fair to say that the trivial solutions of formal logic have a similarity to those of mathematics in that the problems are generally simple and reduce to the axioms of the formal system with relative ease requiring few if any inferences.

Answer 2

Yes, many. Better still there are lots of non-problems presented as problems.

Philosopy Is A Tool

Once one get too indulged in a tool he may loose the sight of reason of using the tool.

Purpose of philosophy is to understand the world. If something don't happen its pointless to study it.

The basic goes this way: If P is considered true, Q is always true. Simply put, if P happen, Q also always happen.

Do P Actually Happen

Now, if P is never found to happen its useless to give the whole proposition any thought.

What if P ever happen Q will also happen? What do that tell you when all your data suggests that P will never happen?

If P Happen Do Q Is Found To Happen

Yeah, found. All the arguments are useless if observation goes against them.

Would two objects, one heavier than the other, fall to ground in same time? You can argue about it till end of your life. What about doing a simple test. It took humanity thousands of years to do that test.

Unclear / Ambigious Terms

Terms as in P and Q in a proposition. Note that there can be many of them.

People argue about propositions a lot of times before agreeing on them. There are inbuilt biases. Incorrect associations.

Trivial solution ofcourse is to define your terms before drawings ifs and thens from them.

Proportionality Problems

A lot of people don't understand that finding one counter example falsify a proposition. Yes, that much is enough. It changes "always" to "usually".

On the reverse, people don't understand that showing that all data point to something do imply an always.

Containers Are Not The Objects In Them

This one looks obvious apparently to only non-philosophers. See Russell's paradox.

You cannot make an omellete out of the container your eggs come in. How much more trivial a solution do you want?

Absence of Proof Is Not Proof of Absence

Your knowing or not knowing about a thing has no effect on existence of the thing.

An Object Is Not The Idea Of The Object

One can think about Nothing but Nothing itself cannot exist.

Idea of an apple in your head is not same as an apple itself.

The list is ofcourse not complete.

Answer 3

A trivial solution (in philosophy) vis-à-vis negative utilitarianism which advocates the reduction of suffering is kill everybody. (with no one alive, no one will suffer).

Another trivial solution, again to do with hedonistic morality, is maximizing happiness (the greatest happiness principle) can be "achieved" by putting everyone on a morphine drip round the clock.