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.
Let us check:
Mathematics.
a.
(of a number) not capable of being expressed exactly as a ratio of two integers.
b.
(of a function) not capable of being expressed exactly as a ratio of two polynomials.
This was found under the fifth definition of “irrational” in
dictionary.com. And this is from a layman’s dictionary. The point is, you cannot take a definition and say “this is how it will be” unless you want me to accept it as arbitrary which would greatly undermine your position.
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.
Sometimes it is important to be clear about words; some words may be better than others. However, in this case, I can only find it to be a problem of semantics, nothing else. Some scientists say that theories are proven others say that they are verified. It really does not matter as long as the meaning is understood.
Observe the different terms of “theorem” and “theory”. The distinction is extremely important.
I am very well aware of the distinction, although I thank you kindly for the clarification.
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.
By saying it was a virtue, I was referring to the source from which you obtained your definition which says that it is. Note that what you pulled up is only one aspect of what the Bible considers “faith” to be. If you follow “my wish” that faith is “to believe something for which there is no conclusive evidence”, then you must deal with the fact that there is “no conclusive evidence” for various axioms that are accepted as true. Try arguing with various Eastern philosophers about these axioms and you might understand what I’m trying to say.
Sorry, I never said that, nor did I imply that.
I will direct post #15 where you most explicitly said this. Hopefully, with utmost kindness, we don’t have to argue about words, which are so clearly expressed:
R Daneel:
The other incorrect (but frequently claimed) assertion is: “absence of evidence is not an evidence of absence”. It is an evidence of absence and a very strong evidence it is. The correct form would be: “absence of proof is not a proof of absence”. But then again I (and many others) have pointed that one out before - and I am willing to bet dollars to cents, that it will come back again.
Not ignoring the “correct form” of the assertion, no physical thing or event can be
proven without evidence.
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.
The problem is that they are NOT universally accepted. Try talking to an Eastern Philosopher who does not accept what is known as the law of noncontradiction in Western Philosophy. You might say “Well, I don’t have time for such people”, but that doesn’t prove your case.
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.
You might say they are “irrational”, but that’s really all you can do. You have no
proof that they are. And this brings us back to what has been said all along. Axioms and logic are accepted because they are
believed to be reasonable and true and no other reason whatsoever. Try as you might, there is no way around this fact. You might say that surety comes from this belief in reason, but that’s something very different.
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?
An even simpler definition is that something is to be considered true if it “is” and something is to be consider false if it “is not” (does not exist).
I mean that the premises of a logically valid reasoning process must be founded in reality.
Your reality is much more limited than mine. How do you go about demonstrating that your reality is true and mine false? Or will you finally admit that your reality is what you believe to be true and mine is what I believe to be true? That is not to say that there is no such thing as objective reality. But that we arrive at such a reality by believing the right things.
:thumbsup:
