S
Spock
Guest
There is no therefore here. The fact that physival sciences use mathematics does not change the fact that the physical sciences are inductive (based upon a few basic principles) and mathematics is deductive (based upon axioms). We could create a different set of axioms, and have a different kind of mathematics. See the different types of geometry. You seem to think that mathematics is the only abstract system. Not so. Chess - for exanple - is another abstract system, and the movements of the pieces is arbitrary. All the games belong to this category. And the rules of every game are arbitrary.Considering that the scientific method has mathematics underlying it, it would not explicitly or implicitly exclude mathematics in anyway shape or form. The basic axioms defined in mathematics to construct models to interpret physical realities is through the scientific method, therefore it’s innately a part of the scientific method and therefore a part of how we interpret the reality present before us. Therefore your statement is erroneous.
I already mentioned them.What unprovable principles are these?
And that is the strength of the scientific method. It is able to correct its own mistakes. The basic principles are accepted to be true, until one counter-example shows that they are not.This is rather vague and could also be fallacious depending on how one interprets these statements.
- Innumerable observations do not imply a truth or a basic principle. I’m not even too sure what you mean by “basic principle” - what I instantly thought of here was the black swan argument, whereby all swans a few centuries ago were thought to be white because a black swan had never been seen, therefore the reality of the situation by innumerable observation was that there were no black swans, which is of course incorrect. As far as abstraction goes, all you need is one counter-example to disprove a supposed generality for a scenario, so your first statement is either incomplete or completely incorrect
Above I already showed why this is incorrect. Axiomatic systems are simply mind-games. If they can be used for some other purpose, that is fine. However, there is no requirement that they should be useful.
- Axioms are not “arbitrarily” selected for a system, if they are selected it’s by necessity to validate something.
Not ambiguous at all. You hypothesize that acid is nutritious, you drink some, and your hypothesis is refuted by reality.
- This is similar to your first point, and is ambiguous.
The propositions within an axiomatic system are only applicable within that system. Whether they can be applied outside the system, is irrelecant.
- The problem with this of course is axioms are for a given system, therefore if the axioms no longer apply to something, then it’s likely that whatever the corollaries imply don’t either, not always, but likely.
Nonsense. Science cannot be formalized. There are only principles and not axioms in the inductive systems. The distinction serves to clarify the difference. Science is constantly changing due to the self-correcting feedback nature of the scientific method.Furthermore, perceptions of reality is one thing, but to make propositions based on innumerable observations in a scientific way requires one to adopt a system which is formalized, for which we have formed axioms and corollaries to do so, therefore your first point is actually a subset of your first and seemingly redundant.
Funny stuff: I keep asking to introduce an alternate method to gain knowledge about the physical reality, and there are no takers. I wonder why?