Posted: Oct 23, 2016 2:09 pm
Wortfish wrote:Pythagoras' theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. You can't have a triangle existing in one dimensional space. In the same way, you can't have laws of arithmetic in the absence of numbers. The laws of physics are derived from our observation of the behaviour of physical objects. Some of them may even be wrong and based on our own misunderstanding.
You're still hunting after a statement that is necessarily true without being self evident. That's the difference between theology and science/mathematics. If you think the notion of an 'uncaused cause' is self-evident, it's entirely because you don't want to think about the problems such a statement invokes as a result of being plucked out of thin air or someplace smellier. That is because the first theologian who came up with 'uncaused cause' plucked it out just so.
In science, nothing is necessarily true, and statements always have to be supported by evidence. In mathematics, statements that are argued to be true are based on beginning with self-evident axioms and definitions that are not obfuscated. Scientific theories are better than hypotheses, because they have been repeatedly tested.
You're right that scientific hypotheses can be wrong, but they can be corrected by making further observations. It is not to say that they must inevitably be corrected, any more than it is to say that some statement can be necessarily true without stating self-evident axioms and undisguised definitions.
You can, of course, have laws of arithmetic, but they need not be based on 'numbers'. You begin by defining a field that is closed under a pre-determined set of operations, and go from there. If you don't know how mathematics works at this basic level, you should stick to theology.
Wortfish wrote:Pythagoras' theorem is not a "physical law". It is a rule about shape, in this case of a right-angled triangle.
Don't obfuscate with imprecise terminology like 'shape'. The Pythagorean theorem is a rule about about the relations of the lengths of sides and hypotenuse. Do all triangles have at most one right angle? Then you can start talking about 'shape'.
Wortfish wrote:And irrational numbers can be physically expressed.
You mean, written symbolically. If you'd like to say the word was made flesh, let's just not go there, because it's happy horseshit.