Ok I did not ASSERT that an axiom is true , factual and demonstratable, in and of itself. The definition of an axiom and the dictionary did it for me. If an axiom is not what it says it is then what is it?. Again I have demonstrated and proved the validity of these propositions numerous times. D Bertot.
Well, on this you are just plain wrong as far as the common definition and use of the word is concerned as I point out above.
So now we know that you and some of the rest of us are not talking about the same concept when we use the word "axiom". That means that it does us no good to continue to use it or discuss it with just that word. So let's have a couple of new words to sort out what we are saying:
1) assumed-axiom. - the way most of us use the word. It is something that is an assumed (for now ) to be true for the sake of further logical argument or discussion.
and 2) true-axiom. - a "self-evident" statment which is not just assumed to be true but actually is. This is your version of the word.
From now on no one is allowed to use axiom by itself. It is either an A-axiom or a T-axiom. Ok?
No I did not say the only way to establish facts is from logic, only that it is another possible way through the application of an axiom that correspondes (sic) to the physical world., (sic) ie the only three possible explanations of things in existence.
An axiom is a premise that is assumed to be true, and neither in the study of the abstract forms of logic structure (the formal science of logic), nor in the application of logical structures (which are then assumed to be valid when properly applied) to the study of natural sciences, is the axiom validated by the evidence.
If you are testing axioms against evidence of reality then you are missing several logical steps -- a logical fallacy, shown to be an invalid structure by the science of logic. What you are actually testing is a theory that {something} arrived at by the (hopefully proper) application of (assumed to be valid logical structure) is true. You are testing a theory that you have not stated (the logical fallacy part). The theory can be as simple as "this axiom is true" - but testing that theory will not change the validity of the logical structure even if the theory turns out to be false.
This structure is valid even though the results - tested against further evidence - is shown to be false. Nor are the premises all necessarily false - "the sun rises in the east and sets in the west" can still be an assumed to be ("self evident) truth, and the diameter of the earth measured by the greeks was fairly accurate as a first approximation.
True (sic) the test is that it has to have application to the physical world.
What you are talking about is a theory (derived by the application of learned logical structures from the science of logic), and testing it against evidence of reality -- the scientific method, natural science. This does not test the logical structure nor the abstractions of structure that are studied in the (formal) science of logic, just the theory that was formulated according to (hopefully properly) learned methodology.
In other words, you have not bridged between the validity of logical structure to application of that in the real world.
And all axioms (true axioms) of course apply to the real world.
And this is absolutely false: all axioms are abstract theoretical assumptions, and you have assumed they are true without any evidence that this is the case.
You will remember that I said axioms require no PROOF, or in this case , no further testing.
Because they are assumed to be true without it, for the sake of the argument.
Ie 'DEAD MEN TELL NO TALES". Can you test this axiom, yes?.
Ah, finally? An example of a "self-evident" truth ... supposedly. But is it always absolutely and positively true - that is the question - what are the assumptions that make it seem true based on our experience?
Certainly Poe and Shakespeare tell lots of tales, though they are (to the best of my knowledge) dead. There are also recordings of all kinds of dead people telling tales, and thus there is ample evidence of dead people telling tales. Furthermore, we can do (and have done) tests on dead people, tests that tell tales about how the people lived, lingered and died. Certainly "Otzi the Iceman" has told us tales - see —tzi the Iceman.
Certainly, in the common usage of this phrase, we can all agree to assume that this is true in order to see where the argument goes, but that is all you can do with any axiom - agree to assume they are true for the sake of the argument. Such agreement does not mean that it is true.
No. I also agree with you that what I am describing is the Natural science of testing and observation. Its (sic) just that the axiom, is step aoutside (sic) you (sic) methods, that is valid as well.
We've already assumed the axiom is valid. That is not what is tested.
Now would you agree with these statements about logic: 1) The conclusion can only be valid if it flows with correct logic from the premises. (This is using valid as Chiroptera has taught me to. i.e., correctly tied to the premises but not for sure right) 2) A conclusion can be valid but wrong if the premises are wrong.
Yes.
Good start. Now see if you can condense your 5 paragraph rambling, muddled thinking labeled "premise 1" in Message 117 into an actual premise. Or show that it is a conclusion based on other premises (which is closer to the truth eh?).
Kudos to NosyNed for this question, yet the question remains unanswered - what is your first premise?
Re: No, no! Backward! One Step Forward, Two Steps Backward!
The definition of an axiom and the dictionary did it for me.
In your view, why is it written that way in the dictionary? In your view how do you think the writers of dictionaries know what that word means?
You seem to think that the dictionary represents some kind of authoritative source for the real meaning of words, but that's not true. Dictionaries are simply descriptions, and often, for technical or academic subjects (like formal logic) those descriptions are not accurate.
The dictionary is wrong. Why wouldn't it be?
If an axiom is not what it says it is then what is it?
It's what I've been telling you all along. An axiom is something assumed to be true for purposes of argument, but that doesn't mean other people have to make the same assumption. Often, they don't. Because the axiom is not defended there's no reason to assume its truth, other than for purposes of argument.
So answer the question. Is Euclid's fifth postulate self-evidently true, false, or not self-evident at all? If it's self-evidently true then how do you explain the existence of non-Euclidian geometry?
Re: No, no! Backward! One Step Forward, Two Steps Backward!
RAZD says{qs}Testing concepts against evidence of the real world on the other hand involves the scientific method.[/qs]
One of the other things I wanted to say in message 222 was that the above sentence describes the heart of the issue. Most of the very eloquent rehtoric about definitions of course is helpful but they do not demonstrate the fact, that it is immposible to demonstrate or validate a fact becuse it involves what you call ABSTRACT METHODOLOGY. Your assuming this because of the stance and definion you ascribe to the scientific method. Explaining all the terms and definitions again, simply does not establish your case. You must of course show why, for example a Fact derived from a sylogism or axiom are not actually facts and that they dont apply or have truth in the real world. D Bertot
Re: No, no! Backward! One Step Forward, Two Steps Backward!
So answer the question. Is Euclid's fifth postulate self-evidently true, false, or not self-evident at all? If it's self-evidently true then how do you explain the existence of non-Euclidian geometry?
Explain what this is and I will explained it in context of what I am saying. Thanks
In your view, why is it written that way in the dictionary? In your view how do you think the writers of dictionaries know what that word means?
You seem to think that the dictionary represents some kind of authoritative source for the real meaning of words, but that's not true. Dictionaries are simply descriptions, and often, for technical or academic subjects (like formal logic) those descriptions are not accurate.
The dictionary is wrong. Why wouldn't it be?
Wait just a minute here, all I have been hearing is how I have been equivocating here based on the definitions of terms and now you are saying the dictionary is invalided. What?
Further I only quoted the dictionary because the dictionary gives the most accurate discription of what an axiom is and what it does. If you have a problem with it talk to the people that wrote it. It should be clear that I also said the axiom defines and describes itself, without any verbage from the dictionary, it is self evident. Lets try it this way for yopu. Is an axiomm that an axiom, is an axiom. Get the point. In other words an axiom doesnt even need the dictionary to describe it for it to be true. D Bertot
I guess I worded that poorly. I did not mean to imply that you said that only logic can establish facts but rather I wanted to say that you are saying that logic alone, that is, by itself (just logic) can establish facts.
Try this: "I did not mean to imply that you said that only logic can establish facts, but rather that you can establish facts through logic alone(just logic)."
This is what I believe he is asserting.
Is this what premise 1 is about? Stay tuned folks.
Re: No, no! Backward! One Step Forward, Two Steps Backward!
An axiom is something assumed to be true for purposes of argument
One more thing, before I go. The above statement is exacally False. An axiom is SELF-EVIDENT and true on its own accord. It does not need your approval or assunption. Further, the writers of the dictionary gave it its definition because that is the exact thing that describes it. D Bertot
Re: No, no! Backward! One Step Forward, Two Steps Backward!
Wait just a minute here, all I have been hearing is how I have been equivocating here based on the definitions of terms and now you are saying the dictionary is invalided. What?
What what? Surely it's occurred to you before that a dictionary might be wrong? Why couldn't it?
Explain what this is and I will explained it in context of what I am saying.
Euclid's fifth? You're presuming to speak to us about logic and you're not even aware of the most famous axiom in mathematical history?
Surely you jest. Certainly this indicates that you didn't even bother to read message 209 before you replied to it.
Why did you reply to the message if you hadn't read all of it? Is that why you ignored nearly all my arguments?
Further I only quoted the dictionary because the dictionary gives the most accurate discription of what an axiom is and what it does.
Except that it's abundantly obvious that your dictionary is wrong. Why wouldn't it be, when it defines words in a way much different than how they are actually used?
It should be clear that I also said the axiom defines and describes itself, without any verbage from the dictionary, it is self evident.
So is Euclid's fifth axiom self-evident, or not? If it's self-evident, is it true or not?
Lets try it this way for yopu. Is an axiomm that an axiom, is an axiom. Get the point.
No. It would help, somewhat, if you phrased your replies in readable English.
Crash, it is clear that we and DB are using different meanings for the word. It is also clear that DB is not going to change on this. So why bother? The exact word doesn't matter.
I have suggested A-axioms and T-axioms above. How about we all use those and carry on discussing Dawn's T-axioms now?
One of the other things I wanted to say in message 222 was that the above sentence describes the heart of the issue. Most of the very eloquent rehtoric (sic) about definitions of course is helpful but they do not demonstrate the fact, that it is immposible (sic) to demonstrate or validate a fact becuse (sic) it involves what you call ABSTRACT METHODOLOGY.
Correct. We start with a couple of basic assumptions - that there is an objective reality, and that what we experience directly, observe, measure, etc, is evidence of that objective reality. Then we try -- through the use of theory and testing and more theory and more testing -- to eliminate the wrong ideas, the ones that don't match the evidence that we assume is true. By this process of elimination, through testing with the scientific method, we gradually arrive at a better understanding of reality ... if it is reality.
Your assuming this because of the stance and definion (sic) you ascribe to the scientific method. Explaining all the terms and definitions again, simply does not establish your case.
But it does establish what common usage is and that you are operating with definitions that are NOT common usage. That means we are not talking about the same things. So are you unwilling or unable to use common usages?
You must of course show why, for example a Fact derived from a sylogism (sic) or axiom are not actually facts and that they dont (sic) apply or have truth in the real world.
Because they can be false. You haven't derived a fact, but a conclusion - a theory. You need to test that conclusion against reality before you can know if it is a valid conclusion, but what you are using for the test is the fact, not the conclusion.
If the test comes back stamped !INVALID! , it is not the real world (if it exists) that is invalid, it is the conclusion that is falsified.
Your argument comes down to stating that certain axioms must be taken as true, not subject to testing or debate, and this is known as the logical fallacy of special pleading.
Ok I did not ASSERT that an axiom is true ,(sic) factual and demonstratable, (sic) in and of itself. The definition of an axiom and the dictionary did it for me. If an axiom is not what it says it is then what is it?.(sic) Again I have demonstrated and proved the validity of these propositions numerous times.
One definition did, many definitions said they were assumptions. The one that said it did said they were "self evident truths" -- and a "self evident truth" is defined as an assumption used for the basis of an argument ... the other definition for an axiom.
Further I only quoted the dictionary because the dictionary gives the most accurate discription (sic) of what an axiom is and what it does. If you have a problem with it talk to the people that wrote it. It should be clear that I also said the axiom defines and describes itself, without any verbage (sic) from the dictionary, it is self evident. Lets try it this way for yopu(sic) . Is an axiomm (sic) that an axiom, is an axiom. Get the point. In other words an axiom doesnt (sic) even need the dictionary to describe it for it to be true.
But when you only use one definition, cherry picked to match your preference, and ignore the more numerous definitions that contradict it, then you are engaged in special pleading, a logical fallacy. Ignoring the others does not demonstrate your position is valid.
Would you say that dictionary definitions are self-evident truths?
Re: No, no! Backward! One Step Forward, Two Steps Backward! Promenade Right!
You seem to be doing pretty good up to this point and I can agree with MOST, but not all of what you said up to this point about the use of Logic.
Then you are learning. Good.
You accuse me continually of EQUIVOCATION, but you are doing this on the premise that your METHOD is the only method of a ACTUAL fact gathering. Im (sic) saying that your INTERPRETATIONS of the definitions are limited by the very nature of the case.
Actually I show that you are equivocating by demonstrating the two different meanings -- such as formal science and natural science. You are still confusing the two, hence you are still equivocating.
Hence you make this type of statement,
The other thing to note is that by this definition of logic as a science, it is the study of how logic works, the abstraction of valid methodology regardless of the content of the argument, and not the application of it. I am not sure Dawn understands this distinction. Whenever you make a logical argument about the real world or about the imaginary world of Kirk and Spock and "they" et al (poor al), then you are no longer talking about the (formal) science of logic, rather about the application of the basic methods derived, the theorems and assumptions and the structures that produce valid arguments. Of course the application means we are no longer talking about logic as a formal science.
Wrong. Only an assertion would mean that it can have no application. It must of necessity be demonstrated why a this is not true. The truth of an axiom can, apply and relate specifically to the real world and have application to draw conclusions that are indeed FACTUAL. Limited interpretations and assertions dont (sic) acommplish (sic) this task.
No, an axiom is assumed to be true for the purpose of making an argument. Application of logical methods to the real world and testing against facts is not part of the science of logic, as it "uses a different methodology" and it is the study of the structure of logic independent of the content of the argument.
There are no conclusions that are "FACTUAL" all on their own, no matter how many times you assert this assumption.
However, your simple task, without all of this rehtoric, (sic) would be to show why an axiom BY DEFINITION, is not valid (not abstract)as (sic) it stands and does not and cannot correspond to the REAL WORLD. I cant (sic) believe this simple truth is that difficult to see. Again why is mty (sic) statement abouve (sic) about an axiom False. Listen . (sic) Axiom, "Self-evident TRUTH (this of course has to have application in the real world. that (sic) needs no PROOF. Yhis (sic) of course would mean it was measurable and testable. Wow that is so simple.
Because it can be false. It is assumed to be true for the sake of constructing the argument.
A self-evident truth (or an axiom) can be a common phrase that we assume is true from usage: "the sun rises in the east and sets in the west" would be such a "truth" ... even though it (1) involves the definition of east and west in a tautology and (2) is false - the sun stays (relatively) stationary, and the earth spins on it's axis. We say "sunup" and "sundown" not because these are true statements but because they are self-evident truths (that are in fact wrong).
Tell me how either of those can be interpreted as (1) not involving assumption or (2) not applying to logic.
Ignoring the definitions that say axioms and self-evident truths are assumptions does not demonstrate that your argument is valid.
Do you think dictionary definitions are self-evident truths? Then what do you do with ones that contradict others?
Your job, should you choose to accept it Mr. Phelps, is to provide a self-evident truth that is absolutely and positively true without testing or assumption.
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