realize you are talking to Crashfrog but here is a nice example of Euclid's 5th axiom
The axiom states that if angles a and b total less than 180 degrees then the two lines, line1 and line2, if extrapolated upward far enough, will eventually meet.
In the diagram they are parallel
Your still way above me on this. Put it in simple english. I have to go to work now. Try to do this simple task for me. D Bertot
Re: No, no! Backward! One Step Forward, Two Steps Backward! Now do-si-do!
Dawn Bertot writes:
The above statement is without a doubt, the most LUDICROUS, IDIOTIC AND PERFECT EXAMPLE OF WILLFUL STUPIDITY, THAT I HAVE EVER SEEN OR HEARD.
Then you must not be reading your own posts.
Unbelievable, incomprehensable and completely stupid, is the only way to describe this kind of, lack of objectivity and honesty.
This site does have a set of Forum Guidelines. You might want to check them out.
Your approach seems to be to present your position, repeat it several times, then call those who don't agree with you stupid. If we were to all follow your approach it wouldn't be much of a discussion, and one goal of the Forum Guidelines is to prevent discussion from deteriorating into name-calling contests.
To pick up on one of Ringo's examples, gravity, it is not self-evident that gravity is true. Until Newton it wasn't realized that gravity is what keeps the planets and moons in their orbits, and that gravity was a universal force associated with mass. Something that takes a Newton to figure out could never be considered self-evident.
But beyond that, we're talking about science (natural science, methodological naturalism), and in science there are very few axioms. In fact, it's very difficult coming up with any. I suppose one axiom could be that the physical laws of nature are the same throughout all space and time. This could be considered an axiom not because it is self-evident, but because it has a great deal of circumstantial evidence (i.e., wherever we look throughout the universe we see matter and energy obeying the same physical laws as here on earth) and because it is natural to make the assumption that we live in a rational and comprehensible universe.
I think even that simple assumption is only arguably a scientific axiom, and you'd probably have a hard time coming up with many more. Certainly what you've claimed to be axioms have no place in science, as they are neither self-evident nor true nor science.
Re: No, no! Backward! One Step Forward, Two Steps Backward! Now do-si-do!
The axioms of science would probably be things like the idea that there is an external, objective reality (although even that is not absolutely necessary), that our senses give us largely reliable information about it and that the nature of reality won''t suddenly change for no apparent reason.
It may seem obvious that "dead men tell no tales" is true - but it isn't so evident that spiritualists and numerous religious believers will try to tell us that there is an afterlife and a possibility of communicating with the dead.
Re: No, no! Backward! One Step Forward, Two Steps Backward! Now do-si-do!
Dawn Bertot writes:
Dead men tell no tales, and no particle of EVIDENCE you could provide would refute this axiom.
And that's why it's an axiom: because nobody has refuted it, because everybody agrees that no further empirical evidence is required. If a significant number of people did disagree, it wouldn't be an axiom. It would be a bone of contention.
(And note that some people do believe that the dead can and do talk to them. The only reason "dead men tell no tales" is axiomatic in spite of the dissenting beliefs is because the dissenting beliefs have no tested, empirical evidence to support them.)
“Faith moves mountains, but only knowledge moves them to the right place” -- Joseph Goebbels
Lets say both lines bisect the horizontal lines at exactly 90 degrees. That gives you the base of a square right? A square being a shape with four internal angles of 90 degrees, sides of equal length and opposite sides parallel with each other.
It should be obvious to anyone that if you extend the sides of a square an infinite distance in any direction, they will never meet. This is an Axiom.
Euclid's 5th axiom states that if the angles at which the two lines bisect the third line, added together, total less than 180 then the two lines will eventually converge. they are no longer parallel since the total is NOT 180 but is in fact 179 or 160 or something
Take an equilateral triangle and stand it on one side. The other two sides are both at an angle of 60 degrees to its base. i.e. they converge because their total is 120 degrees. Shift the point of convergence further and further upwards and you get an isosceles triangle with internal angles approaching but never quite reaching 180 degrees total.
As long as the internal angles total less than 180 then the lines WILL converge. That's the Axiom in a nutshell
Coming up on the 300 post mark ladies and gents. Please lets move into summations and closing statements. Any proposed spin off threads should go to [forum=-25].
Summary - What the Science of Logic Can and Cannot Do
In Message 1 Dawn Bertot asserts a role for logic in making ID scientific:
The inclusion of Logic as a science, would greatly enhance the understanding of ID as a science, if it is understood in its prpoer context and usage.
The comments that followed mostly dealt with the definitions of logic and whether it was or was not a science. In Message 58 I proposed a compromise position:
Let's see if we can work on a compromise to establish a common ground for further discussion.
quote:In science, the term natural science refers to a rational approach to the study of the universe, which is understood as obeying rules or laws of natural origin. The term natural science is also used to distinguish those fields that use the scientific method to study nature from the social sciences, which use the scientific method to study human behavior and society; and from the formal sciences, such as mathematics and logic, which use a different methodology.
If I agree that logic is a science (specifically a "formal science" like math), then will you agree that it is not a "natural science" ... yes?
Note further that thus far this is just agreeing to the terminology to use for further discussion.
A simple yes or no will suffice, although reasons for a "no" may be provided.
Dawn agreed to this in Message 63, however it did not appear that what the wiki article said the science of logic is and is not, so this was clarified in Message 73 and Message 76. These are the basic definitions in the dictionary and in wikipedia:
The first definition applies to what is normally used in science to define science, while the second is more general, common language usage. There is no "science of suitcase packing" and this is similar to the scientific usage of theory with a specific meaning and the general usage with a more general meaning.
This also matches wiki's division of "science" (general) into two basic categories, one category for the "empirical sciences" that use the scientific method (which is divided again into "natural science" and "social science") and the other category called "formal science" (which includes logic and math):
quote:Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice.[1] In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research.[2][3] This article focuses on the more restricted use of the word.
Fields of science are commonly classified along two major lines:
Natural sciences, which study natural phenomena (including biological life), and
Social sciences, which study human behavior and societies.
These groupings are empirical sciences, which means the knowledge must be based on observable phenomena and capable of being experimented for its validity by other researchers working under the same conditions.[4]
Mathematics, which is sometimes classified within a third group of science called formal science, has both similarities and differences with the natural and social sciences.[3] It is similar to empirical sciences in that it involves an objective, careful and systematic study of an area of knowledge; it is different because of its method of verifying its knowledge, using a priori rather than empirical methods.[5] Formal science, which also includes statistics and logic, is vital to the empirical sciences.
quote:A formal science is an academic study that is predominantly concerned with abstract formal systems, for instance, logic, mathematics, and the theoretical branches of computer science, information theory, and statistics.
quote:In science, the term natural science refers to a rational approach to the study of the universe, which is understood as obeying rules or laws of natural origin. The term natural science is also used to distinguish those fields that use the scientific method to study nature from the social sciences, which use the scientific method to study human behavior and society; and from the formal sciences, such as mathematics and logic, which use a different methodology.
The "formal sciences" use "a different methodology" as they use "a priori rather than empirical methods" that are used by the other sciences which "use the scientific method" -- a pretty clear distinction based simply on methodology.
The science of logic does not use empirical methods, but the results of the abstract methodology of logic can be used in empirical sciences, just as the abstract methodology of math can be used in empirical sciences. The only concerns for logic and math for their use in empirical sciences is that the methodology is properly applied, and they are assumed to provide sound and valid results as long as they are properly applied.
Thus any application of logic involving empirical methods is not the "science of logic" but the application of logic within "empirical science."
The second assertion by Dawn Bertot that I want to address is found in several messages:
Message 30: The simple fact is, that you can use the science of logic to establish, TRUTH IN FACT.
Message 40: I also stated that there are some conclusions that are valid and true, the conclusion of which are valid, which NEED NO FURTHER EMPERICAL DATA, TESTING, MEASUREMENTS OR PREDICTIONS. THEY ARE AXIOMS. THEY ARE SELF EVIDENT TRUTHS.
Message 168: I said, there are some Facts or Axioms that NEED no further testing, or measurement, indeed in some cases there is no rational or practicle way do this even if you wanted to. They are self evident truths, not just because they are observations, but because they establish themselves without the fear or possibility of contradictions.
The science of logic is concerned with the abstract essence of logic. Again from wikipedia:
quote:As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language.
Among the valuable properties that formal systems can have are:
Consistency, which means that none of the theorems of the system contradict one another.
Soundness, which means that the system's rules of proof will never allow a false inference from a true premise. If a system is sound and its axioms are true then its theorems are also guaranteed to be true.
Completeness, which means that there are no true sentences in the system that cannot, at least in principle, be proved in the system.
Not all systems achieve all three virtues. The work of Kurt Gdel has shown that no useful system of arithmetic can be both consistent and complete: see Gdel's incompleteness theorems.[5]
It is not concerned with the contents of the argument, but how they are put together. Chiroptera also points out the subtle terminology of the science of logic in Message 166:
An argument is valid if the conclusion follows from the premises regardless of whether the premises are true.
An argument is sound if it is valid and all of the premises are true.
In other words, IF the structure of the argument is proper and it does not include any logical fallacies, THEN it is a valid structure, and IF the structure is valid and the premises are true, THEN it is a sound argument. But it is not considered a necessarily TRUE statement.
The essence of this part of the argument is whether you can start with any true statements - statements known to be 100% absolutely and positively true - or whether you have to assume the truth of some statements for the sake of the argument. This comes down to the definitions of "axiom" and "self-evident truth"
quote:An axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation. Therefore, it is taken for granted as true, and serves as a starting point for deducing and inferencing other (theory dependent) truths.
In Message 45 and Message 185 (and others) Dawn Bertot was challenged to provide an axiom or a self-evident truth that was 100% absolutely and positively true, and was not able to do so.
He proposed one that required assumption:
'Message 221 DEAD MEN TELL NO TALES".
Message 241"Dead Men tell no tales" Now, dont just say. Oh yes Dawn but they do leave clues, etc.
You will notice the added assumption in the second version ... but it is not 100% absolutely and positively true for a number of reasons.
Message 227: 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.
Message 257: I thought you were a christian, and I thought christians believed in an "after-life" ... and then there is the whole issue of ghosts and seances ... plus any number of religious beliefs involving communications with ancestors. Personally I don't believe any of them are true, but this is just an assumption on my part: I can't say I am 100% absolutely positively sure that no such communication is possible.
Certainly it cannot be taken as 100% absolutely and positively true by those people that do believe in ghosts and communicating with dead ancestors or relations by seances or other methods.
Again this is not the same as saying you cannot arrive at a fact from the process, that is simply ludicrous. The exact method of the logic of science is not a tool for you to use to establidh (sic) and unwarrented (sic) conclusion.
You can arrive at a conclusion, but not at an (objective) fact. Whether that conclusion is valid depends on the structure of the argument and the absence of logical fallacies, and then, once the structure is valid, whether that conclusion can be sound depends on the truth of the premises (see Chiroptera Message 166). In no case can the conclusion be assumed to be 100% absolutely and positively truesolely on the basis of the logical argument.
Thus you cannot conclude a logical "fact" that applies to the objective world of reality -- the objective reality that is studied by science. You cannot make up reality, and all logical arguments are just intellectual exercises in imagination. You cannot make up a fact.
The basic problem with applying logic to the evidence of reality is that reality does not care about your logic, and that when there is a conflict, a contradiction, then no matter how good your argument was, it is invalidated. That is one reason science is always tentative about all conclusions.
Finally, Dawn Bertot asserted that this would support ID (Message 1):
(Logic) in and of iteself can establish the validity of a designer or the possibility of a designer.
Maybe we can actually get to that topic on round 2 (if this gets that far) ... provided we start it on the basis of what the science of logic can and cannot do.
It CAN make valid arguments that are sound based on axioms that are assumed to be true for the sake of the argument.
It CANNOT make up reality or create an objective fact that is 100% absolutely and positively true in the world of objective reality.
Your still way above me on this. Put it in simple english.
DB you're looking at an axiom that they cover in 8th-grade math. It's not hard to understand. Euclid's fifth axiom is sometimes called the "parallel postulate" because it's a statement about lines and whether or not they're parallel based on the angles at which they intersect a third line.
It's your contention that an axiom is a self-evident truth. If you can't even understand this axiom, doesn't it prove that it's not particularly self-evident? And doesn't that prove that you're wrong about what an axiom is?
I will admit up front I have no idea what is being said here. Ill make a deal with you crashfrog. If you put this in simple understandable language, I will give you a honest answer as to if it is or is not an axiom. Deal.
Here's another clue: the angles of a triangle (in Euclidean space) always add up to 180°. Always ... unless the space is curved (and that would be non-euclidean space ...) ... even if one angle is only 0.834 arcseconds, thats 0°-0'-0.834" or 0.00023167°.
Here's another deal -- you don't get to call anyone stupid who DOES understand this. I'll bet this includes every single person that has disagreed with you about logic, axioms, and self-evident truths.
You also do not get to tell anyone to be objective when all they do is lay out the facts for all to look at ... when they don't call you names ... and especially when only you disagree with them.
Now if you want to come down off your high-horse and discuss your argument for ID, we can do that -- on a new thread, one that starts off with the premises that the science of logic tells us that logic:
CAN make valid arguments that are sound based on axioms that are assumed to be true for the sake of the argument.
CANNOT make up reality or create an objective fact that is 100% absolutely and positively true in the world of objective reality.
So that we don't waste time with falsehoods.
You can even provide a list of axioms to discuss whether they can be assumed to be true for the sake of the argument.
Well, Dawn hasn't ever gotten round to his point about ID, and we haven't managed to educate him as to the meaning of the words he's using. So it's been pretty much a scoreless draw.
Well, Dawn hasn't ever gotten round to his point about ID, and we haven't managed to educate him as to the meaning of the words he's using. So it's been pretty much a scoreless draw.
In the Bertot vs Everyone on this web-thread deabate: the Atheist, Agnostic, Evolutionist and Humanist, have UTTERLY failed to do the following.
They have failed to:
1. Demonstrate that any specific science is exclusive in the fact gathering process. And to demonstrate that the so-called 'scientific method', is the only process to understand the real world or to gather facts from its process
2. To demonstrate that an axiom, with the applied science of deductive reasoing is invalid as a fact gathering process.
3. To demonstrate that axioms by definition and application are not truth an fact in reality.
4. Failed to show why "self-evident" does not mean requires no Proof.
5. They failed to show why the axioms I presented were not in fact true axioms, other than chainging scenarios and words to fit in an answer.
6. Failed to show why true axioms are only assumed to be true and not axioms in Fact by definition and correspondence to the real world.
7. Failed to provide another alternative to the example of the axiom for the source of all things in existence.. Some didnt try, some tried and failed, some admitted they couldnt, others gave up.
8. Failed to show why the axiom of the three possibilites was not exacally applicable to the Proposition.
9. Failure to refute its its truthfulness and application, on their part to the real world and this proposition, demonstrates its validity.
10. They failed to show why the axiom I presented is not a method of eshtablishing ID independent of religious thought or ideas.
11. Thus they have failed to show why Creationism or ID should not be included as a sceintific method in the curriculum in classrooms.
DB you're looking at an axiom that they cover in 8th-grade math. It's not hard to understand. Euclid's fifth axiom is sometimes called the "parallel postulate" because it's a statement about lines and whether or not they're parallel based on the angles at which they intersect a third line.
It's your contention that an axiom is a self-evident truth. If you can't even understand this axiom, doesn't it prove that it's not particularly self-evident? And doesn't that prove that you're wrong about what an axiom is?
No. Absolutley not. I took this to work with me and I studied it and I kept saying to myself, why is Euclid's Postulate not a valid axiom. Granted I dont understand from a mathmatics standpoint all its terms. It fell on me like a ton of bricks. Because its only a postualation and contemplation, that it is not a Axiom because it does not correspond to any specific thing that is real, or that it does not have application in the real world to physical things. For this reason it is simply a contemplation or hypothesis not a true AXIOM.
One can do the samething by imagining a ZERO, with zeros behind it and in front of it streching to infinity, but that doesnt mean it is a real thing, because it does not have application to any physical thing, like a true axiom does.
For example the axiom I provided of the 3 three and only three possibilites correspondes to to physical things that truely do exist and of course their existence requires an explanation in the form of an axiom. thus by a simple application of deductive reasoning one is able to establish a true axiom that correspondes to physical things.
Now if you want to come down off your high-horse and discuss your argument for ID, we can do that -- on a new thread, one that starts off with the premises that the science of logic tells us that logic:
Now I know I have done this beyond any shadow of a doube. But if you want to do it somewhere else that is fine with me.
Re: Summary - What the Science of Logic Can and Cannot Do
Thus you cannot conclude a logical "fact" that applies to the objective world of reality -- the objective reality that is studied by science. You cannot make up reality, and all logical arguments are just intellectual exercises in imagination. You cannot make up a fact.
The basic problem with applying logic to the evidence of reality is that reality does not care about your logic, and that when there is a conflict, a contradiction, then no matter how good your argument was, it is invalidated. That is one reason science is always tentative about all conclusions.
The above statement is simply Ludicrous. It starts with a false premise that nothing is really real, therefore it begs the question as to wheather a FACT IS a REAL THING. Again, you dont need anyones approval for a fact to be real. And you can establish its validity in truth by the simple use of an axiom and deuctive reasoning.
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