As for myself, I prefer the more universal term; that is, that defined by numerous dictionaries:
To prove: “to establish the truth or genuineness of, as by evidence or argument”
The basic, fundamental level of something can change from person to person. The truth of something cannot.
Faith: According to the dictionary (and presumably numerous dictionaries), it is “belief that is not based on proof”
The definition that you provided is that of the theological virtue of faith. But the word has more than one meaning, as does love.
Both of the definitions have been retrieved from
dictionary.com
Generic dictionaires are wonderful if one is not familiar with a specific term - as a good starting point. When it comes to a specialized field, like epistemology, the generic dictionaries are often deficient. (For example, when a mathematician talks about an “irrational” number, he means that the number cannot be expressed as the “ratio” of two integers. It a layman looks up the word “irrational” in a generic dictionary, he may very well find the meaning: “against reason”. And nothing could furter from the actual meaning of an “irrational number”.) The definition as you provided is a good starting point for “prove”. However, it is quite vague.
I really prefer to reserve the use of “prove” to mathematics and other abstract sciences. One proves a
theorem. As we seemed to agree before, the proper term for the natural sciences is “verify”, or “falsify” or “substantiate” One verifies a
theory, or falsifies it, or substantiates it - if the evidence is overwhelming.
Observe the different terms of “theorem” and “theory”. The distinction is extremely important.
As I previously established, you are basing your argument on the theological virtue of faith. But there are different definitions.
Apart from the fact that I do not consider it a virtue, you are right. There are only a few words, which are used in so many connotations. But I thought it prudent to include a Biblical definition. If you wish, let’s use the word faith as “to believe something for what there is no conclusive evidence”. In extreme cases it might “degenerate” into: "to believe something which is contradicted by evidence. This latter one is blind faith. Clear and conscise definition.
If something cannot be proven, and yet is accepted as true, then it is believed to be true. You are under the mistaken notion that because something cannot be proven, then it is automatically wrong.
Sorry, I never said that, nor did I imply that.
That is why you avoid saying bluntly that such axioms are “unproven truths”.
I have no problem of agreeing that axioms are universally accepted, unproven and unprovable principles. Furthermore, they need no proof, because they are self-evident.
I have an interest in what you would say to many followers of Eastern Religions who embrace self-contradiction. You argument presumes that the laws of logic are accepted by everybody, which they are not.
I would say that they are irrational, plain and simple. If one accepts a contradiction into a system, then
anything and its negation can be “proven” to be true, and thus the concept of truth loses its meaning.
Going back to your first paragraph, you talk about the “truth” of a proposition. I am concerned that we might mean different things by the word “truth”. In an axiomatic system, a proposition is “true” if it can be shown to be a logical corollary of the axioms. In the natural (real) world a propostion is “true” if it accurately describes a feature of the world. Is this definition agreeable?
I understand everything else accept what you mean by “a sound foundation”.
I mean that the premises of a logically valid reasoning process must be founded in reality.
