Entia non sunt multiplicanda praeter necessitatem.
Ockham's Razor is not an epistomological test - that is, it doesn't tell us what is true or false. It's simply a heuristic, a rule of thumb that organizes our search for knowledge and makes it more efficient. By minimizing our explanatory apparatus - trying out the simplest explanations first - we save a lot of time and energy because we don't bother with more difficult, complicated explanations unless the easy, simple ones break down when new information comes in. Just because our simple explanation fits all the facts we've heretofore observed doesn't mean it's the right one, because (a) new observations are likely to occur that violate our explanation unless we have been very lucky, and (b) if we have two explanations that differ only in their complexity, but not their predictions, then we have no objective way to determine which one is right, we only know which one is more convenient.
You would think this latter situation would be unlikely, but an excellent example is quantum mechanics, one of the most rigorously tested and successful scientific theories ever formulated. The standard mathematical formalism of quantum mechanics is statistical, or probabilistic. Quantum mechanics doesn't say "you have a particle at position x, moving at velocity y." Quantum mechanics deals with "probability waves," so the most you can say is that "there is a 90% chance the photon will be detected at position x at time y." The official interpretation of QM is that these probabilities are irreducible - it isn't that we don't have enough information about what the particle is doing while we are not observing it, it's that the existence of the particle isn't determined until we observe it - that insofar as it has any existence at all before we observe it, it is only a set of probabilities. Einstein famously found this explanation ridiculous, saying "I am convinced God does not play dice."
Now, the problem with Einstein's view is that no observation has ever contradicted quantum mechanics. No matter how weird its predictions, when we've been able to achieve the technical sophistication necessary to test them, they have been confirmed. Aha, but not so fast! An alternative view, first advanced by Louis DeBroglie, but later developed and expanded by David Bohm, is that the behavior of particles is absolutely deterministic, but that it seems probabilistic because the particle has properties that we are prevented, even in principle, from measuring. This is what's become known as a "hidden variables" theory. Rather incredibly, Bohm formulated a deterministic theory of quantum mechanics in 1952 with a hidden variable called "quantum potential." We can never observe or measure quantum potential, but if we assume it exists, we get all the same predictions as quantum mechanics without having to accept that "God plays dice." To make matters worse, Gerard T'Hooft has come up with his own experimentally consistent hidden variables theory - so it appears there are at least three ways of producing exactly the same predictions with mathematical formalisms that make very different underlying assumptions.
Ockham's Razor doesn't help us at all in this situation! We don't even have a way of determining which the "simplest" explanation is! Is it "simpler" to believe that things behave as we naively experience them to behave - that is, deterministically (which requires us to assume the existence of things we can't possibly observe) - or is it "simpler" to assume that indeterministic quantum weirdness is (somehow that we really don't understand) the mysterious reality behind our naive experience of well-behaved determinism? WTF, Nature? Thanks for the unresolvable logical dilemma!
Now, ask yourself - if this can be the case in a field that follows absolute mathematical rules, how much more wiggle room is there in areas of experience that have less rigorous formalisms? It would be nice if we had a rule that could decide for us ahead of time how to recognize Truth when we see it - but that rule doesn't exist. This just gets back to something Kurt Gödel proved in 1931 - that all true statements can't be proved with a finite number of axioms. Put another way, if you want to know the truth, you need to make an infinite number of assumptions. And man...that ruined David Hilbert's whole decade, but that's another story.
You would think this latter situation would be unlikely, but an excellent example is quantum mechanics, one of the most rigorously tested and successful scientific theories ever formulated. The standard mathematical formalism of quantum mechanics is statistical, or probabilistic. Quantum mechanics doesn't say "you have a particle at position x, moving at velocity y." Quantum mechanics deals with "probability waves," so the most you can say is that "there is a 90% chance the photon will be detected at position x at time y." The official interpretation of QM is that these probabilities are irreducible - it isn't that we don't have enough information about what the particle is doing while we are not observing it, it's that the existence of the particle isn't determined until we observe it - that insofar as it has any existence at all before we observe it, it is only a set of probabilities. Einstein famously found this explanation ridiculous, saying "I am convinced God does not play dice."
Now, the problem with Einstein's view is that no observation has ever contradicted quantum mechanics. No matter how weird its predictions, when we've been able to achieve the technical sophistication necessary to test them, they have been confirmed. Aha, but not so fast! An alternative view, first advanced by Louis DeBroglie, but later developed and expanded by David Bohm, is that the behavior of particles is absolutely deterministic, but that it seems probabilistic because the particle has properties that we are prevented, even in principle, from measuring. This is what's become known as a "hidden variables" theory. Rather incredibly, Bohm formulated a deterministic theory of quantum mechanics in 1952 with a hidden variable called "quantum potential." We can never observe or measure quantum potential, but if we assume it exists, we get all the same predictions as quantum mechanics without having to accept that "God plays dice." To make matters worse, Gerard T'Hooft has come up with his own experimentally consistent hidden variables theory - so it appears there are at least three ways of producing exactly the same predictions with mathematical formalisms that make very different underlying assumptions.
Ockham's Razor doesn't help us at all in this situation! We don't even have a way of determining which the "simplest" explanation is! Is it "simpler" to believe that things behave as we naively experience them to behave - that is, deterministically (which requires us to assume the existence of things we can't possibly observe) - or is it "simpler" to assume that indeterministic quantum weirdness is (somehow that we really don't understand) the mysterious reality behind our naive experience of well-behaved determinism? WTF, Nature? Thanks for the unresolvable logical dilemma!
Now, ask yourself - if this can be the case in a field that follows absolute mathematical rules, how much more wiggle room is there in areas of experience that have less rigorous formalisms? It would be nice if we had a rule that could decide for us ahead of time how to recognize Truth when we see it - but that rule doesn't exist. This just gets back to something Kurt Gödel proved in 1931 - that all true statements can't be proved with a finite number of axioms. Put another way, if you want to know the truth, you need to make an infinite number of assumptions. And man...that ruined David Hilbert's whole decade, but that's another story.