4DQSAR
Bluelighter
- Joined
- Feb 3, 2025
- Messages
- 793
In 1934 Karl Popper in his book 'The Science of Discovery' asserted that no experiment can prove a hypothesis or theory. All we may do is to alter the weight of evidence supporting said hypothesis or theory. In fact, it's the resistance to experments intended to DISPROVE a statment that is key to increasing that weight of evidence.
But in the end doubt must always exist.
He went on to provide a simple tool that has become the bedrock ot the scientific method. If an assertian is unfalsifiable, it is a belief. If anyone makes a claim to which they cannot provide a methodology to prove it UNTRUE, it is an irrational belief.
Gödel formalized the fact that given any set of axioms, there will always be logical statements that are classed as 'undecidable'. If one adds more axioms, two things happen. Suddenly there will be logical statements that could previously be resolved that become undecidable and there will be new statements that are undecidable.
In essence, however far science progresses, we can be certain that there are questions that cannot be answered. Even statments judged true of false are subject to new axioms being introduced.
It is quite scary to realize that in fact nothing is certain. We can only ever provide a weight of evidence that may allow us to proceed on the provisional basis that they are in fact true.
A few people have suggested that Gödel's work only applies to rare cases in the field of mathmatics but there is no way of knowing in advance if adding an axiom will undermine previously decidable statement. Mathmaticians have occasionally been able to show that certain unsolved problems can be considered to be true if they are proven true or proven undecidable. But again, who is to say that futher axioms will not change that position.
But in the end doubt must always exist.
He went on to provide a simple tool that has become the bedrock ot the scientific method. If an assertian is unfalsifiable, it is a belief. If anyone makes a claim to which they cannot provide a methodology to prove it UNTRUE, it is an irrational belief.
Gödel formalized the fact that given any set of axioms, there will always be logical statements that are classed as 'undecidable'. If one adds more axioms, two things happen. Suddenly there will be logical statements that could previously be resolved that become undecidable and there will be new statements that are undecidable.
In essence, however far science progresses, we can be certain that there are questions that cannot be answered. Even statments judged true of false are subject to new axioms being introduced.
It is quite scary to realize that in fact nothing is certain. We can only ever provide a weight of evidence that may allow us to proceed on the provisional basis that they are in fact true.
A few people have suggested that Gödel's work only applies to rare cases in the field of mathmatics but there is no way of knowing in advance if adding an axiom will undermine previously decidable statement. Mathmaticians have occasionally been able to show that certain unsolved problems can be considered to be true if they are proven true or proven undecidable. But again, who is to say that futher axioms will not change that position.
