Re: ... Fundamentalist are those who refuse to acknowledge evidence...
Kof writes:
The knowledge is not axiomatic, but the field of the inquiry that presents a fact as knowledge is always axiomatic.
So all methods of knowledge acquisition are axiomatic as far as you are concerned?
Kof writes:
All knowledge is contingent upon the axiom(s) inherent in the particular discipline wherein there is evidence to support that knowledge.
How does one select one's axioms? Are all axioms equal or are some more equal than others?
Kof writes:
For instance, the evidence of an Algebraic solution depends upon the Twelve Field POSTULATES.
I don't think anyone is arguing that mathematics is anything but axiomatic.
Kof writes:
The eight basic axioms of Geometry must be agreed to as, assumed they are true, before the Proof of a geometric fact (knowledge) can be established.
Are there any limits on what we can assume as our axioms?
If two different sets of axioms result in two mutually exclusive conclusions regarding reality how do you decide which conclusion best reflects reality?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
I can accept "Cogito ergo sum" as a starting point for inquiry. I don't however think it should be immune from critical analysis or unquestioningly accepted as axiomatic (both Hume and Nietzsche to name but two found it wanting).
But if for pragmatic purposes of starting inquiry somewhere that you want to call that an "axiom" I am not going to overly object.
So is "Cogito ergo sum" the only axiom you are putting forward? The one axiom that you think underpins all methods of knowledge acquisition?
Or are you suggesting that every proposed method of knowledge acquisition has it's onw specific axioms?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
Kof writes:
With that clear, we can understand that a Postulate or an Axiom is always constructed and inherent in every academic discipline.
If two different academic disciplines based on different axioms result in two mutually exclusive conclusions regarding reality how do you decide which conclusion best reflects reality?
Are all axioms equal or are some more equal than others?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
Kof writes:
An example would be the idea that Euclidean Geometry explains the real world.
That Euclidian geometry describes the real world was never an axiom. And Euclidian geometry is no less axiomatically or mathematically true/proven for not being an accurate description of the real world is it?
Kof writes:
Usually when in the course of scientific investigation we find the paradox of conflicting theories, we return to those axioms which were assumed true, and revise, alter, change, or study them with the suspicion that one or he other, or both are actually not true at all.
Can you give a non-mathematical example of axioms used in scientific investigation?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
On one hand you are asserting that we use axioms to discern that which is true. On the other hand you seem to be suggesting that we can reject some axioms because they turn out to result in conclusions that are demonstrably not true.
This seems somewhat contradictory doesn't it?
Kof writes:
Our theories are all based upon the axiom that there is always a Cause for every effect.
But cause and effect is itself derived from observation. It's not necessary to treat it as an axiom. Indeed both relativity and QM have asked serious questions of our notions of causality.
I don't think you have thought this through sufficiently.
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
But cause and effect as perceived is, according to modern physics, the result of entropy at macroscopic scales. At quantum scales interactions are time reversible and it makes no sense to talk of causes and effects. Instead we can only talk of causality as a form of consistency when considering time reversible interactions.
According to modern physics cause and effect as perceived by us is an explicable property of our physical universe rather than some sort of metaphysical underpinning that must be assumed to be true. And at the quantum scale common notions of cause and effect get thrown out of the window anyway.
If you are treating common notions of cause and effect is an axiom then I would suggest that it is one of those axioms that should be discarded as having been found to be wanting as compared to reality.
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
Kof writes:
An axiom is something which seems true but has never been proven, and appears unprovable.
On that basis one can call pretty much any old nonsense an "axiom" can't they?. It amounts to "whatever seems subjectively obvious to me"......
How does one select one's axioms? Are there any limits on what we can assume as our axioms?
Kof writes:
So people can agree to accept that unproven idea as the basis for developing other ideas which WOULD be true if and only if the prime axioms are ACTUALLY true.
If I axiomatically assume that my role in the universe is too important for it to allow me death or serious harm I can logically conclude that if I leap out of a tenth story window I will land alive and unharmed.
It's entirely internally consistent. But pointlessly wrong.
Kof writes:
When you digest that definition, you will be able to see how it could turn out that the initial belief in that basic axiom was misplaced.
If this axiomatic method of knowledge acquisition is so unreliable then the obvious question to ask is why bother with these axioms at all?
Kof writes:
But Galileo demonstrated the axiom was false.
So why not use the method Galileo used to overturn this axiom as a method of knowledge acquisition rather than messing around with axioms in the first place?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
kof writes:
Galileo used the axiom that "Seeing is believing," (i.e.; empiricism).
So why did Galileo’s axiomatic conclusion trump Ptolemy’s axiomatic conclusion...?
Kof writes:
Seeing is believing
That would be nave empiricism.
If we take a more sceptical approach to seeing is believing then we arrive at a number of epistemologically derived techniques designed to improve the accuracy and reliability of our conclusions. Experimentation. Falsification. Peer review. Randomised subject selection. Double blind trials. Control groups. Hypothesis testing. Verification by means of prediction. Tentativity. Occam’s razor. The null hypothesis.
And so on and so forth.
Do you think the inclusion of such devices would add anything to the rather nave seeing is believing approach you have put forward as trumping all other axioms? How are you going to include these techniques in your axiomatic approach? Is it worth considering whether or not the whole idea of axioms has much of a role to play here at all?
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
Kof writes:
The very heart of modern physics is this threat to the initial science axiom, of Cause/Effect.
As I have already partially explained quantum mechanics has already done away with the notion that the sort of cause and effect that one arrives at from everyday experience applies universally.
And it doesn't make sense to say that science has invalidated the axioms science itself is dervied from does it?
All of which suggests that such assumptions aren't really axioms at all. The things you are calling axioms sound more like hypotheses - Assumptions to be tested against observed reality.
Re: ... Fundamentalist are those who refuse to acknowledge evidence...
You actually said "seeing is believing".....
Which would be naive empiricism.
And you still haven't explained how the more reliable (and still developing) approach to empiricism I outlined could all be incorporated into an axiom (or few) have you?
Russell ignored the necessity incumbent upon himself, to agree to some axiomatic discipline wherein his scepticism could be put to the test of a Proof.
Why are you so obsessed with axiomatic disciplines?
As you yourself have pointed out calling one’s assumptions axioms has absolutely no bearing on whether they, or the conclusions derived from them, remotely conform or even particularly relate to reality. In fact most of the axioms you have put forward would be better described as failed hypotheses (Ptolemy’s model, everyday notions of cause and effect etc. etc.) So why bother obsessing over these axioms at all?
Furthermore your attempts to show that science is axiomatic have fallen flat. Thus providing grounds for significant scepticism towards your assertion.
Kof writes:
Yes, it is paradoxical that Russell would suggest he is sceptical while ignoring the reason we have developed disciplines exactly for the purpose of showing people like him how reasoning can establish truth.
I don't think you have understood what he is saying. Here is another Bertie quote:
quote:"To my mind the essential thing is that one should base one's arguments upon the kind of grounds that are accepted in science, and one should not regard anything that one accepts as quite certain, but only as probable in a greater or a less degree. Not to be absolutely certain is, I think, one of the essential things in rationality".
But with regard to safegaurding my children's brains I am not interested in mere opinion. I want to take the safest rational course of action as per my stated criteria:
[1] I want to safeguard my children from suffering brain damage. [2] I want to act in a manner that is rational.
So - What is the safest rational course of action according to your approach? This is what I want to know.
RAZ writes:
Without a determinable risk there is no rational choice but to wait for more information.
Just waiting to see if my children become brain damaged is not a sensible approach to the predicament at hand. If this is the only rational course of action according to your approach then your approach is practically useless for any situation where the potential consequences of inaction are dire.
Straggler writes:
Opinion 1: Brain damage due to the inaudible trumpeting of ethereal elephants congregating in the garden is a realistic proposition and action should be taken to avoid damage to my children's brains (i.e. I should evacuate my children to a gardenless place)
Opinion 2: Brain damage due to the inaudible trumpeting of ethereal elephants congregating in the garden is not a realistic proposition and there is no need to take any practical action to avoid it.
Does your open-minded approach allow us to distinguish between opinion 1 and opinion 2 in terms of either one being any more or less rational than the other?
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