AJ

>>I take it then, George, that you cannot defend your claim?<<

I do not know what claim you are talking about that needs defending. It was you who made the claim that I was “falsely equating atheism with religion” because I wrote something about different world views. It is like claiming that by writing something about white and black horses, one is EQUATING the COLOURS white and black.

I thought this was rather obvious so I preferred just to thank you off since we have been through this confusion many times.

Dear Jardine,

You can observe for yourself that people are irrational. Just watch their numerous addictions and the nonsensical activities that they perform and watch despite having a brain.

1. This example, "All birds have feathers", is obviously irrational because some birds have no feathers (if nothing else, you could catch a bird and pluck its feathers, it would still be a bird, or would it?). As an axiom it would be irrational, but as a common practical assumption, it is relatively more rational than many other statements. Abandoning rationality, rather than recognising its limitedness, would be a serious mistake.

2. Axioms are not "arrived at", but accepted as in "take it or leave it". Please distinguish between the reason(s) why an axiom is correct and the reason(s) (if any) that people choose to accept them.

3. The fact that the mind cannot arrive at the truth/reality through a rational process does not imply that there is no truth or reality. Nevertheless, reason can detect inconsistencies and often detect when other people's ideas are derived from axioms that are different than yours.

Take "man acts": In some systems of axioms this is a conclusion/theorem, in others it is an axiom, yet in others still, it is a contradiction. What Gödel discovered in his incompleteness-theorem, however, is that in most systems of axioms, "man acts" is neither of the above.

That ethical propositions follow from this axiom and/or theorem, is yet to be shown and I sincerely cannot see or believe how this can be done without introducing further axioms regarding the nature of good and/or evil.

Posted by George, Sunday, 2 April 2017 7:13:29 AM p15.

"Pogi, Thanks for illustrating why your personal attacks and insults do not deserve a dignified response."

Simple logic and reasonig leaves little room for a cogent reply. Thay's why you failed to provide one.

Nevertheless, you're welcome.

Yuyutsu

1.
“All birds have feathers” is rational in the sense that it posits a relation between A and B that is based in reason. That doesn’t necessarily mean it’s true. Rational doesn’t mean true. And the fact that it’s untrue doesn’t automatically prove that it’s irrational. A syllogism can be logically valid but nevertheless factually false and logically unsound.

"All swans are white." Lots of things thought to be axioms, and rationally based, and factually true, turned out later to be axioms, and rationally based, and factually false.

Therefore it is not true that an axiom cannot be rational.

2.
Even if an axiom must be accepted on a take-it-or-leave-it basis, that doesn’t mean it can’t be rational, it doesn’t mean it can’t posit relations between x and y that have a basis in reason.

So all you have done is repeatedly asserted that an axiom cannot be rational, but have given no reason to prove it. All the reasons you have given simply resolve back to the assertion that it can't be done, when obviously, it is and can be done.

Therefore you have not provided any cogent reason why an axiom cannot be rational.

3. It means that as soon as one embarked on a rational process, the first thing one would have to do is abandon rationality by definition of an axiom, according to you.

“Take "man acts": In some systems of axioms this is a conclusion/theorem, in others it is an axiom, yet in others still, it is a contradiction.”

Then so far as it is both an axiom and a conclusion/theorem, it can be both an axiom and rational.

In what, pray, is it a contradiction?

“That ethical propositions follow from this axiom and/or theorem, is yet to be shown”

That’s because I haven’t attempted to show it, unless you are interested, and open to the possibility that it might be true. But if you aren’t, then there’s no point me showing you, is there?

Dear Jardine,

1. Correct: "rational" does not imply true (nor vice-versa).

When "All birds have feathers" is derived from thinking about earlier assumptions, then it is likely to be rational (whether true or otherwise), but not otherwise. These can co-exist because they're two separate instances of the same claim.

«Lots of things thought to be axioms, and rationally based [and X] turned out to be axioms and rationally based [and Y]... Therefore it is not true that an axiom cannot be rational".

Logically, this construct sounds as: "Lots of creatures thought to be blue flying fairies, turned out to be red flying fairies, therefore it is not true that fairies cannot fly.

2. An axiom is, by definition, primitive or underived. It's like an atom of thought as opposed to molecules of thought. If you break down any assertion down to its primitive building blocks, you get axioms. Any assertion that can still be broken down, is not an axiom. Assuming that a person can think only a finite number of thoughts per lifetime, it follows that any idea can be broken down into its constituent axioms.

3. «Then so far as it is both an axiom and a conclusion/theorem»

These would be different instances of the same claim. A tyre cannot be both a car's front-tyre and back-tyre, but two, practically identical tyres can be placed one in front, the other in the back.

«That’s because I haven’t attempted to show it, unless you are interested, and open to the possibility that it might be true. But if you aren’t, then there’s no point me showing you, is there?»

I have not doubt that you are capable of creating ethical systems.
And they may possibly even be true, in the sense of correctly predicting: "this act is good, it ought to be done; that act is bad, it ought to be avoided".

What I cannot believe to be possible, in order for the proposed system to be a system of ethics, is to do so without introducing any new axioms (or theorems) regarding the nature of good and evil.

Yuyutsu

1.
Isn’t that a contradiction?

Here:
“This example, "All birds have feathers", is obviously irrational because some birds have no feathers”
you seem to be saying that the proposition is irrational because factually false.

Then later you say: “"rational" does not imply true”.

Given ‘rational’ does not imply true, therefore it is not “obviously irrational” to say that ‘all birds have feathers’.

Therefore you have not established that, as an example of an axiom, it is irrational.

And even if you had, you would not have established that an axiom cannot be rational.

“When "All birds have feathers" is derived from thinking about earlier assumptions, then it is likely to be rational (whether true or otherwise), but not otherwise.”

Then aren’t you saying that an axiom can be rational in certain circumstances?

“Lots of things thought to be axioms, and rationally based [and X] turned out to be axioms and rationally based [and Y]”
Not sure what you’re getting at there.

“Logically, this construct sounds as: "Lots of creatures thought to be blue flying fairies, turned out to be red flying fairies, therefore it is not true that fairies cannot fly.”

No it doesn’t. People thought all swans were white, until they discovered black swans as well. This did not change the characteristics of the original swans (they didn’t go from being X to being Y).

Therefore you have not proved that an axiom cannot be rational.

And you have given no reason, that I can see, for saying that an axiom cannot be rational, other than repeatedly insisting that it cannot be *by definition*.

2.
“An axiom is, by definition, primitive or underived.”

No it ain’t.

Or at least, I have never seen that as part of the definition.

Here’s the definition I get from typing “axiom definition” into bing:
“a statement or proposition that is regarded as being established, accepted, or self-evidently true”
“a statement or proposition on which an abstractly defined structure is based”

That does not say or require that it cannot be rational.

Here’s another from dictionary.com:
“a self-evident truth that requires no proof.”