Well, let's look at mathematics as one example. An experiment occurs when a specific set of circumstances are set up and permitted to work themselves out in order that we might observe the results. (In a few cases, such as astronomical experiments, we lack the ability to set up and control the circumstances; however, nature provides us with such a diversity of cases that we can seek out and identify conditions that match the situations we wish to study.)
Each and every mathematical proposition can be evaluated only sending data through a computational system that represents the mathematical rules in question and determining what the result is. It's irrelevant whether this system is artificial (as in electronic computers and calculators) or natural (as in the human brain).
That's the scientific method. And it's the only way the validity of mathematical statements can be determined.
Sorry, that's not exactly the scientific method. Pure mathematical computations are not empirical in the sense that the physical sciences are empirical. They are abstract; their truth does not rely on observations about natural phenomena (indeed, they do not even depend on the
existence of the natural universe). A calculation is not an experiment, as
Wittgenstein said, and he was right with respect to what
experiment signifies in the context of empirical scientific method.
What distinguishes the natural sciences from mathematics is precisely the way in which the validity of mathematical statements can be determined -
a priori, rather than by reference to empirical evidence. Any statement which cannot not be falsified by any
empirical data is not scientific, and the fields of mathematics and logic abound with such statements.
Chrystopher Nehaniv puts it concisely: "[W]hether empiricist science and engineering like it or not, mathematical results are neither physical nor subject to
Popper's notion of 'falsifiability',
viz. the possibility of disproof by experiment. Thus mathematics is a branch of metaphysics providing tools applied by science and engineering, while remaining itself outside their epistemological scope."
Melendwyr said:
If we cannot, even potentially, determine whether such statements are true or false, they're meaningless, and any claims made about their truth value are invalid.
In that case, we are compelled to conclude that the statement you just made is meaningless, and any claims made about its truth-value are invalid.
Melendwyr said:
To the extent that statements about the nature of God have meaningful content, we're within science. To the extent that contentless claims are made, we're not.
Science certainly doesn't provide a basis for any such value judgment about the meaningfulness of statements. You are essentially making a
metaphysical claim here.