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Author Topic:   The "Axioms" Of Nature
Straggler
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Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 196 of 297 (487024)
10-27-2008 6:41 AM
Reply to: Message 193 by ICANT
10-26-2008 10:57 PM


Re: Re:Axiom
ICANT if something is self evident but also turns out to be untrue is it an "axiom of reality"? I would say not. And I think you would agree.
So they exist you just can't ever know they exist, is this your position?
Truths exist. But we can never know when or if we have found one. Yes that is my position.
They don't need to be true. They must be true and are, else they are not "axioms of reality".
Absolutely. Have we ever had so much agreement ICANT?
Straggler writes:
An "axiom of reality" specifically would actually need to be true as compared to reality. And known to be absolutely true. Not just assumed or "taken for granted" or an arbitrary decision or subjectively decided to be "self evident". It would need to be true as compared to reality.
Wouldn't that make it a scientific fact? Which I am told does not exist.
Exactly. More agreement!!!
"Axioms of reality" cannot exist for exactly the same practical reasons that indisputable scientific facts cannot exist. Namely that we cannot ever know what is indisputably true.
ICANT writes:
1. a self-evident truth that requires no proof.
The one he quoted is a scientific definition giving an example.
What is self evident to you may not actually be true as compared to reality. Which kind of contradicts your previous argument, that axioms of reality actually need to be true as compared to reality.
You cannot have it both ways.
The universe exists today.
That makes it necessary that:
The universe has always existed.
OR
The universe began to exist.
It is a proposition that is self-evident.
This has been proven by the lack of any attempt to disprove the axiom, and we are at 192 Posts.
If you disagree then give an alternative that will disprove the axiom.
You haven't even tried yet, all you have done is make assertion after assertion.
Is that an axiom? Anyway.........
I have explained to you why you can never know something to be axiomatic regarding reality. You have just not listened. I will try again.
120 years ago things were waves or particles.
That would have been self evident and axiomatic at the time. But it was wrong. Reality disagreed. No one could have predicted that QM would be discovered. But it was.
I have absolutely no idea what alternatives there could possibly be to your question. But neither of us can be 100% sure that no other possibility will ever be discovered or could possibly exist. The fact that we cannot think of one now may tell us more about our ignorance and lack of imagination than it does anything about the truths of reality.
That is the point. That is why "axioms of reality" can never be known.
Whatever you consider to be an "axiom" now is only ever one discovery away from being overturned.
Tentative conclusions of the tested hypothesised scientific sort are the best we can ever hope for.
Do you understand now?
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.
Edited by Straggler, : Spelling and quote box formatting.
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 193 by ICANT, posted 10-26-2008 10:57 PM ICANT has replied

Replies to this message:
 Message 198 by Agobot, posted 10-27-2008 7:29 AM Straggler has replied
 Message 201 by ICANT, posted 10-27-2008 8:28 AM Straggler has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 197 of 297 (487025)
10-27-2008 6:54 AM
Reply to: Message 129 by Coyote
10-24-2008 1:36 PM


Re: So what?
In this, creation "science" is methodologically the exact opposite of real science.
As I think is all too obvious in Bertot's stated methodology. He seems to need to know what conclusion he is aiming for in order to determine which one of his infinite number of "axioms" he needs to invoke.
It would be hilarious if it were not so tragic.
Edited by Straggler, : No reason given.

This message is a reply to:
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Agobot
Member (Idle past 5552 days)
Posts: 786
Joined: 12-16-2007


Message 198 of 297 (487027)
10-27-2008 7:29 AM
Reply to: Message 196 by Straggler
10-27-2008 6:41 AM


Re: Re:Axiom
Straggler writes:
Whatever you consider to be an "axiom" now is only ever one discovery away from being overturned.
Tentative conclusions of the tested hypothesised scientific sort are the best we can ever hope for.
Most generalisations are wrong IMO and so is your understanding that all axioms may one day be overturned.
I find your above statement to be too bold and would like to know what you think of:
2+2=4
Is this "tentative conclusion", which happens to be an axiom, ever going to change? If so, How?
Sorry if i have misunderstood your statement, i have big troubles understaning your debate. This thread is by far the biggest confusion i've seen here on EvC, but true axioms do exist, otherwise the universe wouldn't be here(although from certain perspective i seem to contradict my long-held understanding of reality with that statement).
Edited by Agobot, : No reason given.

"Science without religion is lame. Religion without science is blind" - A.Einstein
"I am a deeply religious nonbeliever - This is a somewhat new kind of religion" - Albert Einstein
"Matter is nothing but the harmonies created by this vibrating string..The laws of physics can be compared to the laws of harmony allowed on the string. The universe itself, composed of countless vibrating strings, would then be comparable to a symphony." - Michio Kaku

This message is a reply to:
 Message 196 by Straggler, posted 10-27-2008 6:41 AM Straggler has replied

Replies to this message:
 Message 199 by Straggler, posted 10-27-2008 7:55 AM Agobot has not replied
 Message 226 by Rrhain, posted 10-28-2008 4:55 AM Agobot has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 199 of 297 (487029)
10-27-2008 7:55 AM
Reply to: Message 198 by Agobot
10-27-2008 7:29 AM


Re: Re:Axiom
2+2=4 is not an axiom as I understand it. It is mathematically provable based on prior axioms for a start........
I am no mathematician but I understand that these are the axioms upon which such a conclusion would be derived:
Wiki on Natural Numbers writes:
Peano axioms
* There is a natural number 0.
* Every natural number a has a natural number successor, denoted by S(a).
* There is no natural number whose successor is 0.
* Distinct natural numbers have distinct successors: if a ≠ b, then S(a) ≠ S(b).
* If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all natural numbers. (This postulate ensures that the proof technique of mathematical induction is valid.)
It should be noted that the "0" in the above definition need not correspond to what we normally consider to be the number zero. "0" simply means some object that when combined with an appropriate successor function, satisfies the Peano axioms. All systems that satisfy these axioms are isomorphic, the name "0" is used here for the first element, which is the only element that is not a successor. For example, the natural numbers starting with one also satisfy the axioms.
Full details here Peano axioms - Wikipedia but Rrhain may be able to shed more light on the axioms that underlie arithmetic if none of this makes any sense.
I remember being shown the proof that 0+1=1 once upon a time and it made me very glad I was not studying pure maths.
However we are discussing the "axioms of reality". In this case whatever "axioms" are stated need to be indisputably true with reference to reality.
Axioms in mathematics do not have to be true in relation to anything external. They are simply consistent starting points for the application of logic and can form the basis of descriptions of things that are not at all "real".
The fact that we can use mathematics to model reality is a fascinating topic possibly worthy of it's own thread at some point.
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 198 by Agobot, posted 10-27-2008 7:29 AM Agobot has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 200 of 297 (487030)
10-27-2008 8:23 AM
Reply to: Message 194 by Rrhain
10-27-2008 12:18 AM


Mathematical Axioms and the Relation With Reality
Bertot's nonsense apart I would be interested on your thoughts regarding the possible link between mathematical axioms and reality.
When we say that 0+1=1 we can mean that in a purely abstract mathematical number theory sort of sense. But can we also apply that to reality?
In many ways we can assume in an axiomatic sense that this is objectively 'true' regarding reality. 0 objects + 1 object will result in 1 object.
Can we prove that this will always be true? Not by any means other than mathematically as derived from the axioms that underlie number theory as far as I am aware.
From a mathematicians viewpoint what is the relation between number and reality and could the axioms of number theory be considered as underpinning reality in some way?

This message is a reply to:
 Message 194 by Rrhain, posted 10-27-2008 12:18 AM Rrhain has replied

Replies to this message:
 Message 227 by Rrhain, posted 10-28-2008 5:21 AM Straggler has not replied

  
ICANT
Member
Posts: 6769
From: SSC
Joined: 03-12-2007
Member Rating: 1.6


Message 201 of 297 (487031)
10-27-2008 8:28 AM
Reply to: Message 196 by Straggler
10-27-2008 6:41 AM


Reo you understand now?
Hi Straggler,
Straggler writes:
Do you understand now?
"NO"
Answer this question.
Does the universe exist?
God Bless,

"John 5:39 (KJS) Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me."

This message is a reply to:
 Message 196 by Straggler, posted 10-27-2008 6:41 AM Straggler has replied

Replies to this message:
 Message 202 by Straggler, posted 10-27-2008 8:35 AM ICANT has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 202 of 297 (487032)
10-27-2008 8:35 AM
Reply to: Message 201 by ICANT
10-27-2008 8:28 AM


Re: Reo you understand now?
Does the universe exist?
I would tentatively say 'yes'.
But I could be a brain in a jar existing in a completely different universe and a completely different reality. I could be imagining all of this including you.
I am so sure that this is not the case as to make it irrelevant to all practical intents and purposes but I cannot ever actually prove it not to be so.
Thus I am 99.9999999999999999999999999999999999999999999999.....9999999........999999999999 etc.% certain that the answer to your question is 'yes'.
But in the absence of 'proof' I can never be 100% sure. Thus my answer is tentative to some tiny degree.
Do you understand now?
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.
Edited by Admin, : Too many 9's.

This message is a reply to:
 Message 201 by ICANT, posted 10-27-2008 8:28 AM ICANT has replied

Replies to this message:
 Message 203 by ICANT, posted 10-27-2008 8:48 AM Straggler has replied

  
ICANT
Member
Posts: 6769
From: SSC
Joined: 03-12-2007
Member Rating: 1.6


Message 203 of 297 (487033)
10-27-2008 8:48 AM
Reply to: Message 202 by Straggler
10-27-2008 8:35 AM


Reo you understand now?
Hi Straggler,
Straggler writes:
Do you understand now?
What does science fiction have to do with your reality?
God Bless,

"John 5:39 (KJS) Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me."

This message is a reply to:
 Message 202 by Straggler, posted 10-27-2008 8:35 AM Straggler has replied

Replies to this message:
 Message 205 by Admin, posted 10-27-2008 8:52 AM ICANT has not replied
 Message 206 by Straggler, posted 10-27-2008 8:58 AM ICANT has not replied

  
Percy
Member
Posts: 22480
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.8


Message 204 of 297 (487034)
10-27-2008 8:49 AM
Reply to: Message 190 by 1.61803
10-26-2008 10:29 AM


Re: the mysterious Bang
Okay, but I guess I should mention that Rrhain was also making the additional point that you were not only ascribing to atheists views they do not hold as a group, but the views as you described them seemed to be composed to fit your argument rather than to be accurate characterizations.
But the main point is that the controversy isn't between atheists on one side and theists on the other. It's between the very religiously diverse body of scientists and Christian fundamentalists. If Christian fundamentalists are right about the science then it will be because of the quality of their science, not because of who's atheistic or not.
--Percy

This message is a reply to:
 Message 190 by 1.61803, posted 10-26-2008 10:29 AM 1.61803 has not replied

  
Admin
Director
Posts: 13023
From: EvC Forum
Joined: 06-14-2002
Member Rating: 1.9


Message 205 of 297 (487035)
10-27-2008 8:52 AM
Reply to: Message 203 by ICANT
10-27-2008 8:48 AM


Re: Reo you understand now?
Hi ICANT,
Please stop posting to this thread. Thanks.

--Percy
EvC Forum Director

This message is a reply to:
 Message 203 by ICANT, posted 10-27-2008 8:48 AM ICANT has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 206 of 297 (487041)
10-27-2008 8:58 AM
Reply to: Message 203 by ICANT
10-27-2008 8:48 AM


Re: Reo you understand now?
What does science fiction have to do with your reality?
Hey Bertot started with the Star Trek nonsense
I was simply giving a demonstration of the limits imposed on our knowledge.
You say an "axiom of reality" must be true.
But there are no proofs of reality. Only evidence.
When we are talking about reality and evidence based knowledge -
We can say: The evidence strongly suggests X.
But we can never say: X is indisputably true.
Thus our conclusions are tentative and "axioms" derived from evidence are impossible.
Again consider that 120 years ago the idea that something could be both a wave and a particle would have been considered ridiculous and "axiom" defying. Now we know better. How can you know with 100% certainty that those things you consider to be axiomatic will fare any better?
Edited by Straggler, : No reason given.

This message is a reply to:
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Dawn Bertot
Member (Idle past 105 days)
Posts: 3571
Joined: 11-23-2007


Message 207 of 297 (487044)
10-27-2008 9:02 AM
Reply to: Message 194 by Rrhain
10-27-2008 12:18 AM


Rrhain writes:
Incorrect. A tautology, by definition, is the collection of all possible outcomes of a truth statement such that all are true. The classic example is "A v ~A," but you can have tautologies with multiple propositions and which involve more than mere assertion but also include implication.
tautology
>
-noun, plural -gies.
1. needless repetition of an idea, esp. in words other than those of the immediate context, without imparting additional force or clearness, as in “widow woman.”
2. an instance of such repetition.
3. Logic.
a. a compound propositional form all of whose instances are true, as “A or not A.”
b. an instance of such a form, as “This candidate will win or will not win.”
axiom
-noun
1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.
3. Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
In these definitons it should be very clear that one must start with the root meaning of the word initially to form a foundation for its use in other areas. The example given in the above instance is widow women, a repetition of an actual physical property. The tautology IS NOT the reality ITSELF, which is the widow that is the actual axiom and axiomatic truth. The tautology applies to only the repetition of a physical reality, thus it only has application to the axiom described above. In these instances and definitions it should be clear that what I am describing is not a tautololgy, even though the axiom might involve its principles indirectly.
In the instance of logic it is used in the same fashion to demonstrate a repetition of the real property itself, but that application is only an expression of repetition twords the truth itself, it is NOT the actual reality of the specific axiom, which is established by physical properties, which is naturally limited by certain possibilites in certain instances.
Isnt it interesting when the dictionary explains in a simple sentence (Its use in logic A or not A)what Rrhain is doing so with rehtoric and much eloqunce, it looks like this "The candidate will win or not win"
Even from its use in logic it still only becomes a repetition of the actual physical reality which is characterised by the axiom and axiomatic truth or reality. Again repetition of the axiomatic truth or axiom itself is not the actual property Secondly, and most importantly it does not remove the force of the argument that there are only limited choices that reality will allow in connection with its reality based premises.
In other words, even if we described an axiom as a tautology it would not remove the force of its conclusion that there are only two logical possibilites in connection with reality that it will not allow you to postulate further. An eternal creator is one of those only two choices. Perhaps you could provide us with another solution, eh.
Heres an exercise for you. In a simple sentence give me an example of a tautology, no symbols, no rehtoric and no eloquence, like the dictionary definiton. In other words not the below statement:
The reason I claim that a tautology is a consequence of logic is because it is a term that is defined via logic: The collection of all possible outcomes of a truth statement such that all are true. The simplest version is "A v ~A," but any combination of propositions that are combined such that the final result of the statement is true regardless of the truth value of the propositions is, by definition, a tautology. If you want a more "eloquent" definition, a statement whose truth table contains only "true" is a tautology.
Just a a simple sentence or example not the above explanation, please. Lets see what it looks like, ok?
An axiom is not a "self-evident" truth. An axiom is a declared truth. It cannot be derived from first principles because it is the first principle.
Not according to the dictionary or any observable truth or reality. You just dont get this do you? Something declared is a human expression about reality, like the expression "self-evident". However, your play on words do not change the main force of the definiton of the axiom itself and that is that it is set against reality and physical properties, the conclusion of which are irrefutable and free of contradiction. It is a FIRST PRINCIPLE because it is reality and reason based.
Of the three axioms I gave, "parallel lines always converge," "parallel lines always diverge," and "parallel lines neither converge nor diverge," which one is "self-evident"?
These are examples of postulates in the strictest sense of the word, because they are not reality based. In other words there is no physical property to pit them against, they are hypothetical, therorized contemplations. An axiom that is reality based has to have a physical property to illustrate its conclusions. In your examples there is no way to test any of the results of the conclusions other than imagination. Thats not the case with physical properties and reality based axioms.
In rhetoric, yes, but we are not discussing rhetoric. We are discussing logic and that is not the definition of a tautology in logic. The definition of a "tautology" is a sentence whose truth table only contains "true."
No we are discussing axioms. While logic is useful it can be very tenative and subjective in its conclusions, axioms are not. The sentence whose truth table contains true, is true for a reason and the reason is the axiom itself. A Tautology simply reinforces the truth of it, whether it is used in a rehtorical or logical sense.
A tautology cannot both "include" the axiom and yet be "independent" of it. A ^ ~A is false
.
False. Axioms are characterised as being truths against physical properties. In other words they have to have application to the real world. Hence the experssion, I exist. Existence is demonstrated by the reality of physical things. A tautology is a repetition of this reality, so in this respect it applies to the axiom but is independent of the physical reality of its physical properties. We will wait for your simple sentence or example of a tutology to illustrate this point.
D Bertot

This message is a reply to:
 Message 194 by Rrhain, posted 10-27-2008 12:18 AM Rrhain has replied

Replies to this message:
 Message 208 by Straggler, posted 10-27-2008 9:11 AM Dawn Bertot has replied
 Message 240 by Rrhain, posted 10-29-2008 3:29 AM Dawn Bertot has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 208 of 297 (487045)
10-27-2008 9:11 AM
Reply to: Message 207 by Dawn Bertot
10-27-2008 9:02 AM


Still No Axioms?
Over 200 posts and still not a single axiom cited Bertot.
Your position is ever more ridiculous.
Just to help you along here is an example of a actual set of axioms. Note the structure. A series of short statements. If you ever get around to stating any of these mysterious and unspoken "axioms of reality" might a suggest a similar format. Given you inability so far however I won't be holding my breath........
Example Peano's axioms from Wiki writes:
The Peano axioms define the properties of natural numbers, usually represented as a set N or \mathbb{N}. The first four axioms describe the equality relation.[6]
1. For every natural number x, x = x. That is, equality is reflexive.
2. For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
3. For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
4. For all a and b, if a is a natural number and a = b, then b is also a natural number. That is, the natural numbers are closed under equality.
The remaining axioms define the properties of the natural numbers. The constant 0 is assumed to be a natural number, and the naturals are assumed to be closed under a "successor" function S.
5. 0 is a natural number.
6. For every natural number n, S(n) is a natural number.
Peano's original formulation of the axioms used 1 instead of 0 as the "first" natural number. This choice is arbitrary, as axiom 5 does not endow the constant 0 with any additional properties. However, because 0 is the additive identity in arithmetic, most modern formulations of the Peano axioms start from 0. Axioms 5 and 6 define a unary representation of the natural numbers: the number 1 is S(0), 2 is S(S(0)) (= S(1)), and, in general, any natural number n is Sn(0). The next two axioms define the properties of this representation.
7. For every natural number n, S(n) ≠ 0. That is, there is no natural number whose successor is 0.
8. For all natural numbers m and n, if S(m) = S(n), then m = n. That is, S is an injection.
These two axioms together imply that the set of natural numbers is infinite, because it contains at least the infinite subset { 0, S(0), S(S(0)), . }, each element of which differs from the rest. The final axiom, sometimes called the axiom of induction, is a method of reasoning about all natural numbers; it is the only second order axiom.
9. If K is a set such that:
* 0 is in K, and
* for every natural number n, if n is in K, then S(n) is in K, then K contains every natural number.
We await your "axioms of reality" with keen anticipation

This message is a reply to:
 Message 207 by Dawn Bertot, posted 10-27-2008 9:02 AM Dawn Bertot has replied

Replies to this message:
 Message 209 by Dawn Bertot, posted 10-27-2008 9:40 AM Straggler has replied

  
Dawn Bertot
Member (Idle past 105 days)
Posts: 3571
Joined: 11-23-2007


Message 209 of 297 (487047)
10-27-2008 9:40 AM
Reply to: Message 208 by Straggler
10-27-2008 9:11 AM


Re: Still No Axioms?
Straggler writes:
Just to help you along here is an example of a actual set of axioms. Note the structure. A series of short statements. If you ever get around to stating any of these mysterious and unspoken "axioms of reality" might a suggest a similar format. Given you inability so far however I won't be holding my breath........
Straggler thank you for these set of postulates of the imagination, contemplation and theroretical speculation, which have nothing to do with physical properties, which have nothing to do with even the title of your thread "Axioms in nature" Now perhaps you colud provide some illustrations that have to do with ACTUAL physical properties instead of theorecticl speculation.
Your examples of axioms should atleast correspond to some physical property in reality and not just the imagination. Ill be holding my breath with anticipation.
D Bertot

This message is a reply to:
 Message 208 by Straggler, posted 10-27-2008 9:11 AM Straggler has replied

Replies to this message:
 Message 210 by NosyNed, posted 10-27-2008 9:57 AM Dawn Bertot has not replied
 Message 211 by Straggler, posted 10-27-2008 10:25 AM Dawn Bertot has replied
 Message 219 by Percy, posted 10-27-2008 4:24 PM Dawn Bertot has not replied

  
NosyNed
Member
Posts: 9003
From: Canada
Joined: 04-04-2003


Message 210 of 297 (487048)
10-27-2008 9:57 AM
Reply to: Message 209 by Dawn Bertot
10-27-2008 9:40 AM


Re: Still No Axioms?
Your examples of axioms should atleast correspond to some physical property in reality and not just the imagination. Ill be holding my breath with anticipation.
Bertot, they are given as examples so you know what an axiom is like. They are not intended to be the axioms of nature that is the topic of this thread.
It is your job to supply these axioms of reality that you have been on about for days and days. It appears that you don't have any.
All you have to do now is supply them.

This message is a reply to:
 Message 209 by Dawn Bertot, posted 10-27-2008 9:40 AM Dawn Bertot has not replied

  
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