I would have felt more satisfied if Colin had engaged some more, since there were a few respondents who were sympathetic with his position.

:) — John

Although it might not seem like it, I am one of those respondents who is sympathetic with his position, because I was secretly abducted by aliens only last week, and I know that for certain, but lots of people don't believe me either. I too laugh at those people, and look down upon them.

Aliens are beautiful, and Ellen Ripley just isn't.

That's true, but what I was pointing to was the importance of sameness, as the basis of equality, as a moral principle. Sameness is an assumed absolute. Similarity is the recognition that only the perfect One is the same, and all other cases of individuals partake of difference. — Metaphysician Undercover

Are all of your views based on ancient outdated philosophy? Or just some?

Yes, categories have fuzzy bounfaries. (I don't think imaginary nymbers is anywhere near such a boundary, btw.) — Brainglitch

OK, so let's take imaginary numbers for example. I think that this is a convention which is disputable. You seem to think otherwise. Therefore it would seem that you think that my disputing them is unreasonable.

A major indicator of the categorical difference between established math, logic, and science claims on the one hand, and moral claims on the other, is that dispute about the truth or falsity of a math, logic, science claim, is readily resolvable by appeal to the clear, universally agreed-upon rules and standards, but there is no resolution, even in principle, for dispute about the truth or falsity of whether or not most actual instances of given behaviors are moral or immoral. — Brainglitch

To justify your claim, it should be the case that we can resolve our difference concerning imaginary numbers, by appealing to universally agreed upon standards. So let's see if we can. The square of 4 is 16. The square of -4 is 16. The square of i4 (imaginary 4) is -16. The mathematical principles and universal standards, which I go by, deny the possibility that there can be a square root of a negative number. That is because any time that a negative number is multiplied by a negative number, the result is a positive number. There is very simple logic behind this. You take a negative number, a negative amount of times, and you are always going to end up with a positive. Therefore it is impossible that a negative number has a square root, and the principle of imaginary numbers is contrary to universally agreed upon standards, and should be rejected.

However, for some reason unknown to me, some mathematicians allow this convention of imaginary numbers, which is contradictory to universally agreed upon conventions, to exist. Here's the issue, one mathematical, logical, or scientific convention may be contradictory to another convention, yet they are allowed to coexist, being used in different applications. Sure, we can appeal to universally accepted standards, and readily demonstrate contradictions, in such standards, from one field of study to another, but this will not convince those who maintain the contradictory conventions to resolve the differences, they will just claim some other reason why contradictory principles are allowed to coexist in different fields of study. Different applications require different conventions, and it doesn't matter if the conventions contradict, as long as the applications stay separate.

The fact that some moral prescriptions and proscriptions, such as murder and stealing, are found across many societies does not provide a way to judge whether a given instance of killing counts as "murder" or not, whether the killing was justified or not, whether there are there are mitigating factors that reduce the immorality or obviate it entirely or not, whether a preventive strike is morally warranted or not, whether a revenge murder is immoral or not, whether an instance of the taking of property counts as stealing or not, whether such taking is morally permissible or not, the cobditions under which it is morally permissable to take without permission. — Brainglitch

Well that is the way such judgements are made, we have to keep referring to further principles to determine the exact specifics of any situation. Some acts of killing might not be clear cut cases of murder or not-murder, so we have to turn to further principles. It is no different in science, with the acts of measurement. If I have a hundred grams of water, this will not indicate precisely, without possibility of error, how many molecules I have. I have to turn to a more precise form of measurement, moles. But measuring the moles won't indicate without the possibility of error, how many electrons are there. So in each case, moral judgement, and scientific measurement, there are borderline cases which cause us to seek further defining principles.

Furthermore, there is unresolved dispute about whether the remedy for such behaviors is moral or not. Is it mroal to cut off the hand of a thief? Put him in prison? For how long? Hang him? Transport him to the wilds of America or Australia? Is it moral for the murderer to surrender a daughter to the family of the victim in recompense? — Brainglitch

I think that this is a slightly different issue, it is the question of how to produce morality, the purpose of punishment. This would be similar to the question of the application of mathematical and scientific principles, the conventions by which these are applied. But contrary principles for application, in varying fields of study, would be comparable to varying punishments for the same crime.

If only monks can reproduce and confirm then that is not knowledge.
Knowledge would indicate that any person can conduct the experiment and produce the same results.
Not just monks.

according to scientific method, which is founded on excluding some domains of understanding at the outset. But then we forget what had been excluded.

My point was that there exists no method for demonstrating religious claims.

With science the reasonable skeptic can reproduce results by applying the method.

With religion the same is not true.

For example the skeptic does not necessarily have god appear before him through prayer.

It is why when you become ill or injured you go to a hospital to be treated with science rather than a monastery to be treated with prayer.

One method produces reliable results.
The other...significantly less so.

If religious methodologies were effective in reproducing results then there would be something interesting to debate.
But that this is not the case there is nothing interesting to debate.

I see your point, but I think it's incoorect. There are in those 'domains of discourse' very exacting methods of adjudicating truth-claims. Zen Buddhism is a paradigmatic example. It often incorporates martial arts training as well, where practitioners accomplishments and skills are assessed by masters. In all of these there are methods, applications and consequences. There are similar practices in many artistic and cultural forms. But Western thinking has honed in on what can be measured quantitatively and reproduced in the public domain as the sole criterion of truth. Which is pretty well the exact definition of 'scientism'.

It is why when you become ill or injured you go to a hospital to be treated with science rather than a monastery to be treated with prayer.

Of course. But hospitals were originally created by religious orders.

It disagree, it is not western thinking that has honed in on such things, it is practical necessity.

This is a problem only if you are essentialist about the mathematics of complex numbers. Or - you could treat it as a consistent formalism and give it a geometric interpretation.

And at least one of those religious orders was of fighting men who trained to kill and did kill.
As valid or invalid a point as the one you brought up.

But Western thinking has honed in on what can be measured quantitatively and reproduced in the public domain as the sole criterion of truth. Which is pretty well the exact definition of 'scientism'.

How can that be? The greatest honours go to the scientists who overthrow the most established theories. Einstein was not a heretic. Newton was not a dishonoured charlatan. Both are in the pantheon.

Give it a geometric interpretation? What do you mean by that?

Look at "Geometric interpretation" in
http://en.wikipedia.org/wiki/Imaginary_number

So the imaginary number artificially converts one dimension into another dimension?

In a formalism, the terms don't refer to anything in particular. What is important is how they relate to each other and the rules related to what sentences you can form with them. There is no "articifial" in formalisms. They just need to be consistent. They become interesting when they can be applied, like in this case to geometry. They (complex numbers) are an integral part of quantum mechanics.

This formalism relies on certain assumptions, and if the assumptions are false, the formalism is deceptive. It is a fact that one spatial dimension is mathematically incompatible with another, and this is demonstrated by the incommensurability of the two sides of a square, and the irrational nature of pi. So the geometrical demonstration of imaginary numbers relies on a falsity. Therefore I maintain my assertion that the use of imaginary numbers is dubious.

In formalisms, there are no assumptions.
What they have are axioms and postulates.

Euclidean and non-euclidean geometry are both valid formalisms.
They differ over one axiom. The versions actually contradict each other. That is why "assumption" is not the word used and "axiom"/"postulate" are used instead.

In philosophy, an axiom is a self-evident truth, and therefore cannot be wrong. In mathematics an axiom is a postulate. Since the postulate is posited for some purpose, not because it is a self-evident truth, as is the case in philosophy, the postulate may be false. That is why mathematical axioms must all be verified, they may be false. I believe it is highly probable that the axiom of imaginary numbers is a falsity, for the reasons explained.

Since the postulate is posited for some purpose, not because it is a self-evident truth, as is the case in philosophy, the postulate may be false. — Metaphysician Undercover

In the case of geometry, is the parallel postulate false?

In philosophy, an axiom is a self-evident truth, and therefore cannot be wrong. — Metaphysician Undercover

Give an example of a philosophical axiom that is not also a logical or mathematical axiom.

That is why mathematical axioms must all be verified, they may be false. — Metaphysician Undercover

Has the parallel postulate (in geometry) been verified? Or is it false?

In the case of geometry, is the parallel postulate false? — Frederick KOH

I see no reason to assume that the parallel postulate is false.

Give an example of a philosophical axiom that is not also a logical or mathematical axiom. — Frederick KOH

Not all logical axioms are mathematical axioms. The parallel postulate might be a self-evident truth, and it might be a logical axiom, but it is not mathematical, it is geometrical. Do you recognize the difference between mathematics and geometry?

What is the status then of mathematics that replace the parallel postulate with something that contradicts it?

We're speaking past each other. Do you recognize the difference between geometry and mathematics? The parallel postulate is geometry, not mathematics.

Not all logical axioms are mathematical axioms. The parallel postulate might be a self-evident truth, and it might be a logical axiom, but it is not mathematical, it is geometrical. Do you recognize the difference between mathematics and geometry? — Metaphysician Undercover

I asked for an example of a philosophical axiom that is not also a logical or mathematical axiom. Not only do I not see the example, I see the words "logical axiom" and "mathematical axiom" in your response but no mention of philosophical axioms.

The parallel postulate is geometry, not mathematics. — Metaphysician Undercover

I take my leave here.

Mathematics, geometry and logic are all forms of philosophy.

Mathematics, geometry and logic are all forms of philosophy. — Metaphysician Undercover