by naosnule » Mon Jun 24, 2013 6:38 pm Yolan wrote:naosnule wrote:If a person states that for him a fundamental is the prosperty and homogenity of his ethnic group, then there is no way to argue against it. Because the fundamental statement is not a conclusion, it is the axiom on which he draws conclusions and axioms cannot be shown to be false.
You are misunderstanding what an axiom is here.The term "axiom" has been abused in many different ways, so it is important to distinguish the proper definition from the others. The other definitions amount to calling any arbitrary postulate an 'axiom'. The famous example of this is Euclidean geometry. Euclid was a Greek mathematician who applied deductive logic to a few postulates, which he called axioms. In this sense, "axiom" was used to mean a postulate which one was sure was true. Later, though, it was shown that his postulates were sometimes false, and so the conclusions he made were equally false. The "axiom" he used was basing his geometry on a two dimensional plane. When his work was applied to the surface of a sphere, though, it broke down. A triangle's three angles add up to 180 degrees on a plane; they do not add up to 180 degrees on the surface of a sphere. The point is that Euclid's "axioms" were actually postulates.
True axioms are more solid than that. They are not statements we merely believe to be true; they are statements that we cannot deny without using them in our denial. Axioms are the foundation of all knowledge. There are only a few axioms that have been identified. These are: Existence Exists, The Law of Identity, and Consciousness.
http://www.importanceofphilosophy.com/M ... Axiom.html
I can argue with your hypothetical ethnic nationalist because I can inquire into the reasons of their beliefs and talk about those. And they do have reasons. You might tell me that their stance is 'fundamental'. That doesn't mean it appeared out of nowhere and that it is not informed by other beliefs which can be questioned in terms of truth.
"Philosophers" and their lack of understanding for mathematics and love for semantics.
Euclidean Geometry was shown to not be a suitable tool for analyzing space that is "curved", such as the surface of a sphere.
Note the difference between an "axiom being false" and a certain "axiomatic system" not being an appropiate tool in certain situations.
Surely, people have made claims that Euclidean Geometry was the geometry of "Physical Space", and those claims have later been shown false. The geometry of "Physical Space" is a curved geometry, although in certain situations it is flat enough to use Euclidean Geometry as a tool. However, this does not meant that the axioms of Euclidean Geometry were false.
To attempt to show that an axiom is false is a fruitless attempt. What you can do is to show that an axiom in an axiomatic system can be derived by the other axioms in the axiomatic system and is thus redundant; but that is not applicable in the Euclidean Geometry case.
Axiomatic systems do not need to depend on the physical laws of our universe. However, how useful they are in our universe is an entirely different question.
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As for the asking for reasons for fundamental beliefs: I'll avoid the word "belief", because it has far too many definitions as shown by http://dictionary.reference.com/browse/belief which are not the ones I've been refering to. The only one of those which would be acceptable in my eyes for what I meant would be "opinion".
So why do people have certain fundamental opinions? Well, I am guessing that it is due to a mixture of genetics, environment and their own "mind".
How do we change fundamental opinions? If those opinions are consistent with historical facts and the physical world, and several ones are (such as the fundamental opinion that one should strive for the prosperity and homogenity of one's ethnic group), the only way is through what I would consider brainwashing.
Is it wrong to brainwash? Completely depends on personal opinions about how important things are.
What is a fundamental opinion for someone, may not be fundamental for someone else. American History X show several examples of the latter case. The latter case is simpler to combat without "feeling dirty".
. (Of course most never admit this outright, but it is what it is) 