Arguments cannot prove their own premises

You want to test a theory using the scientific method. You "form a hypothesis" and call it "A". You then say that if A is true, then B should occur as well, and it proves true, (B occurs when A does). So, you've proved your theory "true" in a scientific way, right, i.e. you've supported your theory with evidence?

No! That actually makes absolutely no sense at all.

This is a common mistake that is sometimes made even by professional scientists, (and, sadly, this is how the scientific method is often taught in public school).

So, what's wrong?

What's wrong is that it's illogical. You've proved nothing, and here's why.

The simplest form of logical argument is composed of a premise, an inference and a conclusion. The inference is what ties the premise and conclusion together. It's literally the actual "logic" between cause and consequence. With formal logic, you're concerned mainly with form, or structure of the argument (hence formal), rather than semantics. Why? Because even the syntactical form itself, i.e. the structure, can allow you to decide if an argument is valid or not.

However, when considering logic, the "inference is assumed" (because if the inference is screwed up, you're not doing logic anyway). So with formal logic, what you consider is the relationship between the truth value of the premise and the truth value of the conclusion. Here is how it breaks down.

Premise => Conclusion

This is often expressed in what is called a "material conditional", which is an "If-Then" statement. In other words, "If x, then y", or "If (premise), then (conclusion)".

"Valid" or 'logically valid' means that "it can happen" given the conditions of the context of formal logic. To understand logical validity, it helps to think of the (presumed) inference as a perfectly well-working logic machine or computer because this is what computers really are, they are logic circuits designed with Boolean logic. Formal logical validity is itself a matter of "form" or argument structure.

Consider…

True premise, true conclusion = valid argument (also a "sound" argument).
True premise, false conclusion = INVALID argument (it can't happen).
False premise, false conclusion = valid argument
False premise, true conclusion = valid argument

So, what do we mean by the above?

It means that if we put true information into a computer, within the context of something the computer can actually handle, and the computer is working perfectly, then we should get true information out, and if we get false information out, then the computer isn't working perfectly or your premise isn't true as you think it is. In other words, putting true info in and getting false info out of a perfectly well-working computer performing computations that it can handle in context, is not possible, ergo "invalid".

"Invalid" tells you that something is wrong in Denmark.

All other scenarios are possible, ergo "valid". We can put false info into the computer and get false info out, and we may even get true info out that's true merely by accident and not because of the false premise at all. OK, so, what has this to do with the original problem? Well, notice in the matrix above where if we have a true conclusion in a valid argument we may have either a true premise or a false premise! IT'S IMPOSSIBLE FOR A LOGICAL ARGUMENT TO PROVE TRUE ITS OWN PREMISE. The attempt to do so is the problem with the flawed line of thinking in the original problem above.

Also notice that we can use a false premise and get either a true conclusion or a false conclusion, even with a perfectly well-working computer, i.e. our logic is just fine. That is, there is nothing wrong with the logic, but rather in your choice of premise (computer input). It would be irrational to blame the computer (logic) for what one gets when one uses a false premise, or if the 'input' is not something the 'computer' can handle appropriately in context. (We shouldn't blame either logic or a computer for not being able to make sense of "What is Philadelphia plus two?")


Reconsidering the original problem above, what IS an acceptable method is for your theory to be the entire argument, instead of your theory being just the "hypothesis" premise, and for your premise to be known to be true (because who cares what conclusion you get if you use an irrelevant premise, right?)

With a known true premise, if your conclusion proves true, then your theory, i.e. your argument, is valid & sound. If your conclusion is false, then your argument (theory) is invalid. So, your theory becomes "If A, then B" instead of "My hypothesis is that A is true, then I'll test my hypothesis and look for a B as supporting evidence that A is true". The former is logical and the latter isn't. As I mentioned before, even professional scientists sometimes makes this mistake. Some may see this as evidence of how logic is lacking. Far from it. There is nothing lacking in logic, but rather there is sometimes something lacking in our understanding of it.