The "Axioms" Of Nature

Agobot writes:

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I find your above statement to be too bold and would like to know what you think of:

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2+2=4

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Is this "tentative conclusion", which happens to be an axiom, ever going to change?

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Actually, that is neither an axiom nor tentative. It is a derived conclusion from the axioms of set theory.If you think you're up to it, read Russell and Whitehead's Principia Mathematica where he starts from sand and takes the 60,000+ steps required to prove that 1 + 1 = 2. [From page 362 of Principia Mathematica, Volume 1, 2nd ed. The final steps are in Volume 2: Principia Mathematica]

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true axioms do exist, otherwise the universe wouldn't be here

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I'm pretty sure most everybody here agrees with that statement.But what are they? Given the observational nature of science and given the fact that observation is never perfect, how can we ever know what they are?Edited by Admin, : Reduce image width.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

Straggler responds to me:

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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?

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That's a philosophical question because the nature of science and the nature of mathematics are not quite the same. In math, you can declare things by fiat to be true, you know them to be true. You can do this because you're starting from the beginning and working forward, from causes to effects.Science, on the other hand, has to work backwards from effects to causes. As we know, this observational process can never be known to be perfect and while we can come up with what we think are axioms, they are only held tentatively because all it takes is a new observation to make us change our minds.This is where the philosophy comes in: Can we come up with a mathematics of reality? Most mathematicians (about 80%+) consider themselves "Platonists": The objects described by mathematics are real. "Number" is just as much a property of the universe as mass and energy. The fact that we use mathematics to describe the things we discover in science is, to such a philosophical attitude, testimony to the legitimacy of the claim: The world works mathematically.Not everybody agrees with this idea. My best friend, an astrophysicist, has a hard time with infinity. Oh, it's an extremely useful concept that makes the math go, but that's all it is: A concept. It isn't real. There is no such thing as "infinity" because it cannot be directly shown (to her satisfaction, at least).One possible example of evidence toward this philosophical attitude is that you can come up with multiple foundations to get to the same thing. The Peano Postulates allow you to prove 1 + 1 = 2 fairly easily. But, nobody uses the Peano Postulates for "real world" math. Instead, they use the ZFC (Zermelo-Fraenkel + Choice) axioms. Starting with them, 1 + 1 = 2 is a much more difficult proposition (Russell and Whitehead required more than 60,000 steps and over 300 pages to do it.)Note: There are only 9 axioms in ZFC. All of modern mathematics follows from those nine statements (and infinity is one of them).So to answer your questions: Platonists would most likely say that yes, the nature of reality is mathematical. Non-Platonists would not.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

Agobot writesThis statement is both accurtate and unfortunate. Now we see the objectivity that so many have been saying was missing by both sides. Without even thinking about it and not being deluded by a bunch of nonsense about we cant know his or that or why worry about it anyway. Here we have a somewhat nuteral person in Agobot pointing out the obvious, that one can indeed KNOW simple truths and that All information is not required to achive this goal. Look at his obvious surprise at the way you fellas avoid realityIts unfortunate that it is viewed as a sillly discussion however, due to the fact that the correlation between the simple truth Agobot points out about life ending in death (an obvious axiomatic truth) and the possibilites for the only solutions to the existence of things is perhaps missed. It is. These fellas have deluded themselves and are trying the same with everybody else to convince or make people believe that nothing is KNOWABLE or that NOTHING is for certain. Now watch this point Agobot, reality, truth and the obvious nature of things (axioms) are apparent to you without even trying to reason it out, it "requires no proof" due to it self evident proporties, which is proof in and of itself. Its not until these fellas come along and super inflate the idea of empericism (which is wonderful in and of itself) to the point of nonsense telling people that what you actually see is not what you actually see and things are not what you tink they. Self-evident doesnt really mean self-evident, etc, etc, etc. They then try and twist this lie with rehetoric and silliness to the point that people start asking questions about realites like yours above. You right just stick to your guns and battle thier nonsense like I have been doing for nearly 40 years now.
Heres a good debate to help you TheBible.net The Warren-Flew debate on the existence of God.. Scroll all the way down the page and its at the bottom and you can listen or watch it. Dr. Warren a logician, Philosoher, theologian and experienced apologist puts on a clinic on how one can know the truth verses subjective nonsense.Percy writes:Thanks for the example but I suppose you missed the post where I pointed out that explanations, understanding and things involving physical properties have nothing to do with the existence of things outright. It does not matter (no pun intended) what thier nature or make-up are or are not. That they exist at all is the point. Nothing about them, if they are different or not, etc, etc, will change the truth (axiom) that they themselves will have only one of two choices in the axiom of how they are in existence in the first place. Ofcourse I am still waiting for an alternate explanation besides the only two possible conclusions the axiom will allow. I suppose I am just uninformed and unrealistic about reality correct, give me abreak.Your example while valid really offers nothing to the situation or the elimination of the axiom as an axiom that I presented in this context.Bluejay writes:Willful subborness (stupidity) if you will does not replace reality and obvious truths. Theories dont characterize knowable, demonstratable truth. There is no need to fix (problem solving) things that are not broken, in this instance axiomatic truths in reality and nature. Talk about your double talk.
Ya think. But this is not what Agobot said. "Life" is not the same as "Life Ends". The point is not whether you can state the obvious, it is whether the obvious is real, actual, demonstratable and irrefutable and free of contradiction. You have simply side stepped the axiom in this instance by pointing out that the obvious exists and reaaranging the axioms truths. What in the world does that have to do with the reality and irrefutable truth of its reality. This excally why axioms involve tautologies but have nothing to do with the what makes them real in the first place. Herein lies the problem. So may lines have been drawn in the sand in these places that it is not even understandable that these sciences are sciences or that they cpmpliment eachother and are apart of eachother. In this way the they can remove the possibility of knowing things to the realm of philosophy and say that from a scientific standpoint you cant really know anything. When in reality and based on scientific principles other than just thie methods you actually can.
Axioms are Obvious truths that involve but do not need extrapolation of thought but is there should one require it. These fellas are so caught up in the scienific model that they think everything requires a test of some sort, some things dont. However, if one wishes this it is simply accomplished with axioms as well.
Axioms are the realm of reality and truth even if they are used in maths and logic. Besides this Science involves all methods of reasoning and understanding.
Noseyned writes: Only an over application of the word will allow such conclusions as I have now demonstrated in several posts. Its root meaning is what it is regardless of the science you chosse to involve it in. In these instances I have pointed out the clear distinctions between tautologies and axioms. The "scientific method" does not have a monopoly on the words, reality and primary definitons have this monoploy.Bailey writes:Ofcourse it can be demonstrated in a testable fashion, by reality and nature itself. What other test do you need to demonstrate its reliability? But notice this, if you could and will be proven wrong about an axioms nature, you immediatley follow up with a safegard to your position that says, will it matter anyway. Where is the rational and objectivity in either of these instances. Since both parties ended up winners and not losers, they most certainly do fall squarely within the two. Since this example clearly fails from all angles, you go right ahead and present the "many other possibiltes that could be Posited". This should be fun to watch. Now remember you made the claim that you could? Hop to it* Your just repeating yourself Bailey, get the task that does not include the two or a combination of them.
.D Bertot

Except that it isn't axiomatic that all life ends in death. For example, consider bacteria. When a bacteria divides, are the two resulting bacteria new bacteria, or is one of them the old bacteria and one the new? If you consider them both new bacteria, then what happened to the old one? Its end certainly wasn't death.And if you consider one the old bacteria and one the new, then obviously many bacteria from billions of years ago are still alive. Our understanding of the physical universe, such as about the evolution of stars and solar systems, and about the laws of thermodynamics that tell us that the universe will quite possibly end in heat death and therefore the death of all life, means that we can be pretty sure that all life will end in death, but this is hard-earned scientific knowledge, not a self-evident truth. Then in that case you're in the odd situation of claiming self-evident status for truths that are self-evident only to you.--PercyEdited by Percy, : Grammar.

Bertot, I'd like to put your intuition for self-evident truths to the test: what numerical answer do you get when you multiply no numbers at all?

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"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.

Does all possible life absolutely and necessarily end in death?Can we say with absolute certainty that all forms of life that do currently exist, or might conceivably (or even inconceivably) exist at some point in the future, will end in death?Without having all of the evidence for all life at all times anywhere in the universe that does or will exist this is an extrapolation of incomplete evidence. It could potentially be proven to be wrong. As has happened to so many other things that have at one point or another been considered to be axiomatic. And thus it is not an "axiom of reality" in the sense that it is undeniably 100% true in all possible cases. Self evident to who?If something is "self evident" but turns out to actually be untrue as measured against reality would you still consider it to be an "axiom"?Are your "axioms" effectively necesary assumptions in the form of "self evident truths", but assumptions borne of incomplete evidence all the same?Or must your "axioms" be objectively true as compared to reality in all possible cases?You seem to be conflating the two possibilities but the two are far from certain to be the same.Both ultimately suffer from the problem of incomplete evidence.But which of the two do you actually mean when you say "axiom of reality"? Subjectively "self evident" assumption or objectively true in all cases?Which is it?Edited by Straggler, : No reason given.Edited by Straggler, : No reason given.Edited by Straggler, : No reason given.

Rrhain writes: Thats point I was making earlier Rrhain and that Agobot is making now. Every example he uses in reality you take and equate it to math or logic. Reality is not a THEORY it is real an actual, certain demonstratable conclusions follow from it that are not tenative or subjective like equations in math or logic. Reality, nature and demonstratable truths are what make the axiom what it is or is not. Existence is however a PERFECT example of reality, even if we dont understand all its parts or functions. The axiom is the reality of existence, this is what he is trying to communicate. That existence is what the axiom is composed of. The only way anyone could ignore the force of the conclusions that flow from this reality is to imagine that things dont really exist at all or say the are the imagination of another thing or a dream of something else, which only removes it form one place to another. To do this however one would need to avoid or discard all the evidence of existence in the first place.Para writes:Ah, a puzzle to stump the Bertot. My friend your question is not a bad question it is simply an irrelevent one. There is no answer to your question because numbers are not a real thing. Numbers or any conbination of numbers are only concepts of reality to assist in dealing with reality. Two things are just things, if you wish to ascribe the designation 2 to them then fine, but that does not make them what they are, reality makes the individual things what they are, get the point. So multiplying or not multiplying numbers at all is irrelevent because reality is not comprised of contrived ideas or concepts from which numbers themselve are derived and thier conclusions. Yours is one of an imaginary process and not reality. If one and one is two, its still does not define the reality of the items themself. Next.It would be like imagining numbers to infinity, you may be able to do this, actually write it out or whatever but its still only imagination, they are not real. Its also like the ole question can God make a rock bigger than he can lift. Its not a bad question just irrelevent. The terms "bigger"and "than he can" have no meaning in ETERNALITY, therfore the question is irrelevent, therefore usless for all intents and purposes.See ya this evening got to go to work.D BertotEdited by Bertot, : No reason given.

You have repeatedly ignored the whole issue of incomplete evidence as first explained to you in Message 295The truths of reality exist but how can you know when you have found a 'truth' of reality that is always true as opposed to being true as far as we can currently tell? How do you know it is an "axiom" rather than a conclusion that could be proven to be wrong at a later date?Because it is "self evident"? How many "self evident" seemingly axiomatic conclusions have eventually been proven to be wrong?Conclusions derived from empirical evidence can never be 100% immune from being overturned by new evidence. For this reason there can be no "axioms" of the sort you espouse. Conclusions will always be tentative to some degree. The problem of incomplete evidence will always exist with regard to evidence based investigation.Thus your stated position (axioms of reality)+(deductive logic)=(reliable conclusions) necessarily becomes:(incomplete empirical evidence)+(deductive logic)=(unreliable conclusions)Exactly as discussed at the beginning of this conversation. The truths of nature exist. But how do you know when your evidence leads to a truth rather than something that is almost always true?This is impossible and thus your whole concept of "axioms of reality" is irretrievably refuted.Unless you can provide a solution to the problem of incomplete evidence a hypothesis based approach is the only way forwards. Simply piling more deductive logic on top of incomplete evidence can do nothing but result in unreliable conclusions.Your methods are deeply flawed and your resulting conclusions are wholly unreliable.
As was originally demonstrated way back when we started this discussion.You lose. Again.

Thank you for the reply Bertrot. Thank you for conceding to this point.
This is not to infer that a great many people do not live their lives basing their reality, emotions and decisions by utilizing their own semi-interdependent, yet independent, axiomatic balances or truths ...The fact that the logic founding your proposed axiom may be increased and/or decreased by reasonably constructing the original statements within the absolute knowledge of the framework, seems conclusive enough to deem it variable, not to mention impossible. As we do not have an absolute encompassing universal framework assembled for nature or the universe at this time that we may establish the purposed "axioms of nature" in, they sufficiently meet the criteria that allows them to be established as an unreliable method of deducing reality.Your "axioms of nature" however cannot logically be deemed a wholly refutable hypothesis with the potential to declare reality.If it is not falsifiable, logically, it cannot be wholly refuted. The assertion that your "axioms of nature" are false only because they have yet to be proven true fits squarely within the argumentum ad ignorantiam.The notion that the logic founding your proposed axiom may also be increased and/or decreased by illogically constructing the original statements outside of the absolute knowledge of their framework is likely irrelevant. Demonstrable tests that lead to invariable conclusions. As can be evidenced above, the former question was asked to initiate an intended response, thus ending the debate at hand for me.
The latter question, rhetorical in nature, need not be answered. Bertrot has stated the remains of the participants of the inevitable decimation outcome and the tie/draw participants are all winners !!Let's hypothetically congratulate them and give them their trophies .... oh, wait, one team doesn't exist anymore, and the other is pissed they didn't gain a solid victory.The latter team went as far as to state they don't want a trophy, they want a hypothetical rematch.My reality looks like cheesecloth, and yours has holes too Bertrot ... everybody’s does.This does seem in line with your equating participants who tie for first, second, or third place as "winners". Does it strike anyone as odd that professional boxing, as well as most sporting affiliations, do not record a tie and a draw as a win. Shouldn't it somehow interfere with reality if we are to constitute your logic in this instance? If a tie and a draw are equivalent to wins, why are they not recorded as such in reality?It's simple ...Man has ordained it, and reality sustains it.A win is a win, a loss is a loss, and a draw/tie is a draw/tie.A tie/draw and inevitable destruction are not an invariably realistic equivalent to winning.I thought for sure you would not consider the participants that have been reduced to ashes following a hypothetical incineration, or another variable that concludes in utter decimation, as the winners in any realistic sense of the word.Yet you did.You adhere that a reality that concludes with the assertion ...* "They won or they lost"... as an axiomatic reality, squarely contains the following realistic outcome possibilities ...* a tie/draw
* an inevitable decimation where all participants are reduced to ashI have proposed why the assertion "They won or they lost" is not axiomatic, nor can it logically exist within a reality that contains a tie/draw outcome possibility for the participants or an inevitable decimation outcome possibility where the participants are reduced to ash.You declare all participants winners ...Please support your position or digress. Being that I've provided an "axiomatic truth", and you concede that it fails, I feel we're in agreement.
I think I'll wait until you actually propose an "axiom of nature" that is invariably conclusive before I delve any further.
It's clearly more entertaining to watch somebody else trip over their own thoughts than attempting to prove a false/positive oneself.
In all fairness I do it as well at times, and am entertained in retrospect just the same ... Though I've again provided the statement to prove a point, the assertions above are not all interchangeable. They are not repetitive of one another. They are three separate statements, which show without careful wording, randomness, or forming a question within an absolute knowledge of its framework, a statement cannot be deemed invariable. For this reason, not all simple assertions can be deemed axiomatic.I am not as close minded regarding this potentially valid truth as you might think - please provide your "axiom of nature".ps. The sky is blue, or it is not black.

What happens when a self evident "truth" is found to be untrue?Is it still an axiom?

The question is not irrelevant, it is designed to test your judgment of self-evident truths. I can tell you that there is an answer to my question, and that the answer is indeed numerical. So my question stands, and I dare you to answer it. What numerical answer do you get when you multiply no numbers at all?

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"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.

Three seconds of my life:Huh? Oh Nice Edited by cavediver, : No reason given.

Hi Para, Don't you know by now that he's never wrong? Great question by the way...*Bertot, when your done with that question try adding no numbers. This too has a numerical value.

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"All great truths begin as blasphemies""I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth."--Bill Hicks"I never knew there was another option other than to question everything"--Noam Chomsky

And a "self-evident truth" is something that is assumed to be true because it appears to be.

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self-evident truth - noun
an assumption that is basic to an argument [syn: basic assumption]

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You end up back at axiom, something assumed to be true for the sake of the argument.Bertot's been around this issue before (first thread of his) and refused to accept it then. All he has done here is rehash all his old arguments with no new understanding.see http://EvC Forum: Is Logic a Valid Science in the establishment of ID as Scientific.? -->EvC Forum: Is Logic a Valid Science in the establishment of ID as Scientific.?
and http://EvC Forum: The use of logic in establishing truths -->EvC Forum: The use of logic in establishing truthsEnjoy.

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we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.

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Bertot responds to me:

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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.

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Indeed, but the problem is that you are engaging in the logical error of equivocation.That is, if you have a word that has more than one meaning, it is a logical error to pretend that all meanings are equivalent and can be substituted for each other. You are attempting to do the same thing with "tautology" that creationists try to do with "theory." The word "theory" does mean "educated guess," but it also means "analysis of a set of facts." To pretend that when a scientist talks about a "theory," then he's talking about an "educated guess" is to equivocate. It isn't that the word doesn't mean that. It's that the definition of "educated guess" is inappropriate given the context.That's what's going on here. The topic of the thread is "axioms." That presumes a framework of logic for the discussion, not rhetoric. Therefore, it is inappropriate to use a rhetorical definition of "tautology." It isn't that the word doesn't mean that. It's that the context is one of logic and thus we must use the logical definition.And especially since I was the one who introduced the term into the discussion, then I get to be the one who determines what I meant when I said it. Message 75: It is clear that I am referring to the logical definition of "tautology," not the rhetorical one. I used the phrasings of logic: "A or ~A."Is there a particular reason why you think you are capable of overriding me regarding the meaning of my own words?

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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

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Once again, you engage in equivocation. You are confusing "rhetoric" meaning "oratory" and/or "florid speech" with "rhetoric" meaning "the study of the use of language." The "rhetorical" definition of "tautology" refers to the second meaning. Thus "tautology" is akin to such terms as "anaphora," "antimetabole," "epistrophe," and "pleonasm."

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it looks like this "The candidate will win or not win"

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That is a logical tautology: A v ~A. It is not an axiom.

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In other words, even if we described an axiom as a tautology

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Why on earth would we want to do that? A tautology is not an axiom. A tautology is a derived truth. It is necessarily true, but it is only true because of other factors. An axiom is true, however, independent of all other factors. It cannot be derived from anything. If it could be, it wouldn't be an axiom.That's why we're having such a problem in this thread. You have been asked to provide an axiom of the universe. And since you seem to be forgetting: I agree that there are axioms of the universe. There is a way that the universe works that is consistent and is so "just because," without being derived from anything else.The question put to you is to please give us one of them. So far, all you have given us are tautologies, which you agreed in previous posts were not axioms.So since tautologies are not axioms (and remember that this is MY argument to you), then you have yet to actually answer the question put to you:What is an axiom of the universe?

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In a simple sentence give me an example of a tautology, no symbols, no rehtoric and no eloquence, like the dictionary definiton.

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(*blink!*)You did not just say that, did you? You quoted the definition in your own post! [emphasis added]What part of "A or not A" are you having trouble with? And since the dictionary uses it, why do you discard it as insufficient? What, specifically, is the problem with using symbols? The point is to show that the specifics of the tautology are irrelevant to the nature of tautology. Whether or not we say "win or lose" as opposed to "straight or bent" (to hearken back to another thread that involved a poster who refused to answer a simple question) is immaterial. What makes it a tautology is that it is a statement is always logically true regardless of the circumstances.It is the height of irony that you are harping upon the specific words as if they are important while at the same time inveighing against me for "eloquence." You whine about me writing well and then when I completely abandon all words and deal with the pure abstraction of logical symbology, you whine still.It would appear that what you want is not a well-written discussion nor a precise and thorough discussion but rather one where we follow the advice of Humpty Dumpty where words mean what we choose them to mean and we get to make them mean so many different things. I certainly hope you pay them extra given all the equivocation you are engaging in.Hint: That was a "rhetorical device" called a "literary reference." Let's see if you can figure out what the origin is.

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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.

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Not according to the dictionary or any observable truth or reality.

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Argumentum ad dictionary? Once again, you engage in equivocation, confusing the field of discussion with the field of logic. We're talking about "axioms of the universe" which implies a logical construction. We are asking you for what the fundamental truths of the universe are, something like "conservation of momentum." But instead, you keep coming up with tautologies: "Unwilling or unable," "win or lose," "real or not," etc. All of these are tautologies: A v ~A. None of these are axioms.

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Something declared is a human expression about reality, like the expression "self-evident".

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Incorrect. Remember, I'm the one who brought this term into the discussion. I'm the one who gets to tell you what I mean when I say it. The declaration of axioms are not "human expressions." They are simply truths for which there is no derivation. A tautology is a derived truth. That's why we don't call it an axiom. Axioms cannot be derived. If they could, they wouldn't be axioms.

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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.

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Nice try. That's my argument to you. An axiom is an inherent truth. We all agree to this. Since we all agree, why are you harping on it as if that were the point of contention?No, the question is that we want you to tell us what one is. Give us an example of an axiom of the universe. "Win or lose" is not an axiom. It is a tautology. "Unwilling or unable" is not an axiom. It is a tautology. Tautologies are not axioms.What is an axiom of the universe? And how can you tell?

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These are examples of postulates in the strictest sense of the word, because they are not reality based.

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Huh? You just contradicted yourself. You claim that an axiom is "set against reality" and yet a postulate is an axiom. So which is it?

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In other words there is no physical property to pit them against, they are hypothetical, therorized contemplations.

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Are you saying that there are no parallel lines? If so, then we're going to be differing on a truly fundamental, philosophical level. I say that the objects of mathematics are real. There are parallel lines.

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In your examples there is no way to test any of the results of the conclusions other than imagination.

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Huh? "Test"? There is no "test" of an axiom. If there were, it wouldn't be an axiom. That's the entire point. That's why the mathematicians of the 19th Century were trying so hard to show that the Fifth Postulate was actually derivable from the others. They couldn't do so because it really is an axiom. It cannot be derived from the other axioms. That's why we were able to discover non-Euclidean geometry: We replaced the axiom with a different one.

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Thats not the case with physical properties and reality based axioms.

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Fine. Could you please give us an example of one and then describe how you can tell that it is an actual axiom and not just a hope of being an axiom based upon imperfect observations?"Win or lose" is not an axiom. It is a tautology."Unwilling or unable" is not an axiom. It is a tautology.Tautologies are not axioms.

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No we are discussing axioms.

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Indeed. But so far, the only thing you have given us are tautologies.Tautologies are not axioms.What is an axiom of the universe? Is the conservation of momentum an axiom of the universe? If so, how can you tell? What allows us to declare it to be true rather than conclude that it seems to be true given all observations?

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While logic is useful it can be very tenative and subjective in its conclusions, axioms are not.

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(*blink!*)You did not just say that, did you? Logic is not tentative. "Tentative" means that something is conceivably false. We may not know the reason for it being false, but there is a possibility that it might be such as having imperfect observations.Logical conclusions are not tentative. They cannot be contradicted because they are logical. That's the entire point. However, they are not axioms because they are derived. A tautology is a logical sentence whose truth table has only "true" for its entries. But to construct a truth table, you have to derive the outcome. That's why it isn't an axiom.In an axiom, you only have A and it is always true. There is no way for A to be false. That's the point behind an axiom.A tautology, on the other hand, has the option of the statements in the sentence being either true or false, but the structure of the sentence takes that into account and in the end has all outcomes being true. A v ~A. In this case, A can be true, in which case A v ~A is true. Or, A can be false, in which case A v ~A is true. Again, there is no way for the tautology to be false, but that is because it is derived from the status of A.Tautologies are not axioms. Do you agree with that statement or not?

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The sentence whose truth table contains true, is true for a reason and the reason is the axiom itself.

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Incorrect. The reason is the logic. A tautology is a derived conclusion. That means it is not an axiom. Axioms are not derivable. That's the entire point. You can prove a tautology by writing out the truth table. It is impossible to prove an axiom because that would defeat the entire purpose of an axiom: If you could prove an axiom, it wouldn't be an axiom.

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A Tautology simply reinforces the truth of it, whether it is used in a rehtorical or logical sense.

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Incorrect. A tautology has nothing to do with axioms but instead has to do with logic.

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Axioms are characterised as being truths against physical properties.

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Huh? You just contradicted yourself again.

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Hence the experssion, I exist.

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"I exist" is an axiom? Since an axiom is true by declaration, then there could be no question about it. But there is a question to whether or not you exist. In fact, the question of existence is one of the fundamental questions of philosophy.We might finally be getting somewhere. If we were to pull back to "Something exists," then we might have an axiom.

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A tautology is a repetition of this reality

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Incorrect. Again, you are equivocating. You are pretending that the rhetorical definition of "tautology" (repetition of a point) is interchangeable with the logical definition (a sentence whose truth table only has "true" for its entries).A tautology has nothing to do with axioms. It has to do with logic.

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We will wait for your simple sentence or example of a tutology to illustrate this point.

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A v ~A.That's the version that was in your own definition. Is there a reason why you won't accept the example you provided? Why is your own example not good enough for you?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.