Final answer:
Philosophical and scientific methodologies demonstrate that established beliefs can indeed be shown to be false if they contradict evidence or lack justification. Scientific laws and theories are constantly tested and are not immune to reassessment or rejection upon the discovery of counterexamples.
Step-by-step explanation:
The assertion that our established beliefs can never be shown to be false is not supported by philosophical inquiry or scientific practice. In the realm of logic and science, beliefs must be open to refutation. For instance, in logic, while one cannot generally prove a negative claim, those that assert the affirmative do carry the burden of proof. Moreover, knowledge, which is differentiated from belief, must be based on what is true; one cannot 'know' something that is factually incorrect, even if it is a dearly held belief.
In scientific methods, theories and laws are continuously tested against the real world through experiments and observations. If verifiable experiments contradict a theory, then it must be re-evaluated or discarded, regardless of how established it may be. This notion underscores that no belief or scientific law is beyond falsification if evidence to the contrary is robust. Additionally, philosophical discussions on truth and belief suggest there are objective truths about the world that aren't merely 'personal truths,' refuting the idea that what's true for one might not be true for others.
The idea that one's beliefs can never be proven false is further undermined by the discrepancy between belief and knowledge. Just because a belief is strongly held does not mean it equates to knowledge. Belief requires truth and justification to become knowledge, as exemplified by Plato’s JTB (Justified True Belief) account. Claims without 'checkable' statements, like those of certain religious experiences, cannot serve as proof for one’s belief due to their non-veridical nature.