Suppose I start a religion one of whose key tenets is that 2+2 = 4

[Donald Ian Rankin]

Does that then mean that maths can no longer taught in schools?

Clearly, the answer is "no", but how do you square that with the 2nd ammendment (especially if my arch-rival founds a competing religion teaching that 2 + 2 = 5)?

[valerief]

1. Magic underwear! Magic underwear! I vote for classes on ONLY magic underwear!

[TechBear_Seattle]

2. What does the right to bear arms have to with mathematical religion? n/t

[baldguy]

8. If you don't agree with him, he can shoot you.

Not much different from most other religions, in that respect.

[Donald Ian Rankin]

24. Sorry; see below. Good catch...

[SteelPenguin]

3. no matter what math your religion follows I don't think guns should be in schools

Basically no matter what you think 2+2 equals, I don't think students should be allowed guns in schools.

[Kutjara]

4. It's not a religion if it's based on provable fact.

Religion requires faith and faith is, by definition, the belief in something that can't be empirically proven. Therefore, "Twoplustwoequalfouritarianism" isn't a religion. It's missing the key ingredients of wishful thinking and credulity.

[thunder rising]

9. aye, but can you prove it? If not, for you, it is religion.

[Kutjara]

12. By that reasoning, anything a particular individual can't directly prove...

...becomes an item of "religion" for them. So, for example, because I can't fully explain how my car's fuel injection system works, the system is, for me, a matter of religious faith?

I don't think it's necessary that I personally be able to prove something in order for it to be "fact" and not "faith." It is sufficient that SOMEONE has proved them, using a set of falsifiable procedures and tests that are open to scrutiny by people knowledgeable of the field. It is the falsifiability and transparency of the experimental or observational process that makes something "science" and not "religion." If people "tested" religions using the same rigor, membership in the major faiths would dwindle overnight. But the priests, mullahs, and rabbis can rest easy: there's no danger of an outbreak of mass rationality anytime soon.

[Zebedeo]

53. Is there a

"set of falsifiable procedures and tests that are open to scrutiny by people knowledgeable of the field" that proves that humans evolved from single-celled organisms that spontaneously formed from nonliving matter, without the involvement of God? If so, please set forth in detail that "set of falsifiable procedures and tests."

[Boojatta]

15. What do you mean by "empirically proven"?

For example, if a man named Saul/Paul was struck blind by a light in the sky that his companions couldn't see, then what would it have taken for him to "empirically prove" that he was actually (temporarily) blind?

Religion requires faith and faith is, by definition, the belief in something that can't be empirically proven.

[Kutjara]

16. We can accept that Saul/Paul believed himself to be blind.

We can even accept that he, through some neurological phenomenon, was temporarily blinded. Of course, the story may be entirely fictitious, created for a theological purpose or to teach a lesson, but it is certainly possible for someone to have experienced hysterical blindness, since such things are well documented in the medical literature.

What we don't have any evidence for is an external phenomenon that caused the blindness. Indeed, the sensation of a bright light preceding the onset of blindness accords well with the symptoms of hysterical blindness reported by other sufferers. A sort of "optic nerve storm" of conflicting signals first gives the sensation of a bright light, before the whole system overloads and then, as it were, "reboots." (Incidentally, a similar mechanism has been posited for the "tunnel of light" phenomenon associated with "near death" experiences).

As for there being a real light in the sky that only Saul/Paul could see? Well, that has to remain in the "unproven" category. As has been often noted, "extraordinary claims require extraordinary proof."

[Boojatta]

17. How would Saul of Tarsus empirically prove that his sight returned at the touch of Ananias' hand?

11 And the Lord said unto him, Arise, and go into the street which is called Straight, and enquire in the house of Judas for one called Saul, of Tarsus: for, behold, he prayeth,

12 And hath seen in a vision a man named Ananias coming in, and putting his hand on him, that he might receive his sight.

13 Then Ananias answered, Lord, I have heard by many of this man, how much evil he hath done to thy saints at Jerusalem:

14 And here he hath authority from the chief priests to bind all that call on thy name.

(...)

18 And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized.

From:
Acts 9 (King James Version)

[Kutjara]

18. He can't.

Third hand accounts of events that may or may not have occurred in the distant past are hardly a firm basis for any kind of rigorous proof. They either have to be taken on faith, or regarded as allegories or "lessons."

[Boojatta]

19. On the day that Saul's sight returned, what could he have done

to "empirically prove" that it returned at the touch of Ananias' hand?

[Kutjara]

20. He could have walked across the room unaided, or picked up...

...an object from a distant table, thereby demonstrating the return of his sight.

The real issue here, however, is not what Saul believed happened, but what we can know about the event, given the amount of time that has passed and the reliability of the source material. We must first ask, was there even a Saul? Was he a single person or a portmanteau of several individual stories, collected under a single name? Did the events happen as reported, or was the blindness of one person conflated with the "restoration" of the sight of another? Did the events occur in the order described?

There are too many imponderables in the story to ever come to a definitive view on Saul's "miraculous" cure and, frankly, the Bible doesn't have the best track record for truth in reporting anyway. That's not a criticism, by the way. It is only in our era that the literal "truth" of the Bible is of such obsessive importance. Earlier generations were happy to read the stories as allegories.

[Boojatta]

21. In the year 3008, who will be able to empirically prove that YOU ever existed?

[Kutjara]

28. We'll have to wait and see.

If records from the present age survive, then some evidence of my existence may be contained therein. If I happen to be buried in soil with just the right balance of acidity, my body may even survive. Failing that, some trace amounts of my DNA may persist in things I have touched. The DNA of my offspring will also contain the coded proof of my existence.

Otherwise, there would be no way to prove I existed, but so what? I'm not making any claims of having been miraculously cured of anything. My life has, so far, been delimited within the bounds of physical possibility as we currently understand it. It is unlikely I will be sending an assertion of supernatural agency into the far future, requiring proof or refutation. I will be just one of the billions (by that time possibly trillions) of people who have briefly inhabited the planet. My story will be simply one among many, requiring no miracles or Gods to explain it.

[Boojatta]

43. "I'm not making any claims of having been miraculously cured of anything."

Do you claim that you haven't been miraculously cured of anything? If people in the future are to include you in a list of people who deny having been miraculously cured of anything, then they will require assurance that you actually existed.

[Boojatta]

22. Did the Spanish Inquisition have no employment opportunities for obsessive or compulsive people?

It is only in our era that the literal "truth" of the Bible is of such obsessive importance. Earlier generations were happy to read the stories as allegories.

[Kutjara]

27. Arguably, the Inquisition was less about a literalist interpretation of the Bible...

...and more about consolidating the Church's secular power. "Heresy" could be just about anything the Church said it was, and was frequently tailored to fit the particular circumstances of whomever happened to be the enemy-du-jour of Holy Mother Church.

[Donald Ian Rankin]

25. I think that the veneration of the supernatural would be religion even if it were provable.

Even if the ghosts of my ancestors came to visit me every night, if I worshipped them it would still be a religion.

If you don't agree with that, imagine that twoplusianism has some other tenets too, that do fit your definition of a religion.

[Kutjara]

29. I see your point, but I don't think what you describe could be called religion.

It would be lacking the essential element of "faith," since "God" would be an identifiable entity. We'd be worshipping "that guy over there" rather than some numinous entity in the sky, onto which we can project all our hopes and dreams. We don't really have a concept for that kind of "worship," except perhaps for the kind of thing that happens around celebrities. :evilgrin:

[Donald Ian Rankin]

34. I don't think faith is a necessary component of religion;

I think it's just that it's a major element of Christianity, and we tend to think of Christianity when we say religion.

[Kutjara]

37. I guess we have to disagree there. For me,...

...faith is the key element that makes a philosophy into a religion. Aside from certain secular Buddhist traditions, all religions place a core body of doctrine that must be accepted on faith alone at the core of their teachings. If you don't accept the faith, you aren't in the club.

[knitter4democracy]

30. I've always wondered about 2+2=4, though.

I'm just saying, I wonder if it can be impirically disproven as well. I've never done that great in math classes, though, and mostly because apparently I think of numbers differently. I can totally see how 2+2 couldn't equal 4.

[Kutjara]

31. I think 2+2=4 is on pretty solid ground.

The counting numbers and basic arithmetical operations have a pretty large body of proof propping them up (Kurt Godel notwithstanding). The "proofs" you see that show 2+2='something else' inevitably rely on a division by zero somewhere, rendering the result meaningless.

[knitter4democracy]

32. I've never seen those proofs.

I've just always wondered about the space a number inhabits and wondered what you do with adding or subtracting that, too.

[joshcryer]

40. Such a proof is inherently impossible, as Godel proved with Incompletness.

It does make ones mind go a bit haywire when you cannot prove that the foundations that which our mathematics exist cannot be proven itself.

But nature provides the substrate in which we can observe the truth of such calculations, we just cannot write nature down on paper. :)

(This is why I'm a theist, because it's quite nice, and it also has the plus of annoying atheists.)

[Donald Ian Rankin]

41. Not exactly, I think. Godel's theorem is more complicated than most people think it is.

It's like the second law of thermodynamics, or most of quantum physics - it's easy to explain in a way that makes people think they understand it, but very hard to actually understand - it's taken me years of mathematical training (albeit specialising in different areas) to understand that I don't understand it.

[joshcryer]

46. I admit my understanding of Incompleteness stems from the book "Godel, Escher, Bach"

But yeah. :)

[knitter4democracy]

44. I think numbers are more complex/abstract than we admit.

Maybe it's just me.

[Duer 157099]

5. Empirical proof

I remember learning stupid tedious proofs in math, horrendous long steps that I had to learn in order to PROVE something as simple and obvious as 2+2=4.

Just because we take it for granted now, doesn't mean it hasn't been PROVEN already.

I'd like to see the proof (mathematical proof, that is) that 2+2=5.

[thunder rising]

10. Thats easy enough, I just swap the symbol 4 with 5 and we are done. the symbols are conventions,

not laws.

[Duer 157099]

11. Um... I don't think so

Symbols have meaning, if they didn't we wouldn't be having this conversation.

[cyborg_jim]

14. The meaning comes from the convention. not the symbols

[Donald Ian Rankin]

36. It's in Russell's "Principia Mathematica", and takes hundreds of pages.

It's very obscure, and very dull.

Roughly, we define the integers by the operation "successor of", and addition by the rules

s(x) + y = x + s(y)
x + 0 = x

so

s(s(0)) + s(s(0)) = s(s(s(0)))+ s(0)
= s(s(s(s(0)))) + 0
= s(s(s(s(0))))

There's an awful lot more to it that I never learned, though.

[Realityhack]

6. Teaching facts is allwoed

Regardless of how many or how few religions hold them to be true. Similarly you can teach facts about religion (comparative religion).
Some people hold a religious belief that excludes evolution as a possibility, yet we teach it based on it's scientific merits.

[thunder rising]

7. I assume your religion would be borrowing certain semantics from mathematics while dropping others..

good luck.

[Festivito]

13. Too many here believe separation is the rule/right.

Instead free exercise should be the right.

In the case of the 5er, the parents involved should do what is reasonable, be allowed to have their own ways taught. If it were half the students as 5ers to half 4ers, they can be taught at separate times and have recess while the other is taught. Or, they could be taught both and questioned appropriately.

It is reasonable to tell the parents they may have problems in other classes, colleges, and universities, but, let's accept that the scenario given is meant more for humor than for its goodness as a hypothetical. After all, it could be a religion of relative Einsteins, except that he was a Spinozaist.

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=389&topic_id=3876867&mesg_id=3884247

[Donald Ian Rankin]

26. I'm inclined to disagree - rights of the child trump rights of the parent.

The right of a child to have a good education trumps the right of a parent to deny them that; the state has a duty to ensure that all children get a basic start in life.

Also, if you're talking about young children, I agree with Richard Dawkins that talking about a 4ian child or a 5ian child is as misguided as talking about a Marxist or a Keynsian child; there are just children of 4ian or 5ian parents.

[Festivito]

33. You mean the right of the state trumps right of parents.

That is, the state can decide that the parents are wrong and force the child into education the parents deem wrong.

I don't know if you would always want a child's desire to trump that of a parent. For example, if the child wishes to practice Christian Science and not have a life saving operation because one parent is CS while the other is not, I could see a judge determining between the two parents and trumping the child depending on age and perceived maturity.

I must disagree with your disagreement with me.

[Donald Ian Rankin]

35. The power of the state should trump the power of the parents.

The right that is trumping the right of the parents is that of the child, not the state, but the power of the parents to assess the child's interests should be trumped by that of the state.

The child's desires are not terribly important - the child's power to assess its own interests should be trumped by both that of the parents and that of the state; children should have to be educated even if they don't want to.

[Festivito]

38. Back to your original contention.

I think I see it in light of its humor, or, perhaps even more so, its humour.

The current American fervor for separation between church and state has become ridiculous in my way of thinking, but understandable because the issue mixes with worker rights being privately protected and educational rights currently publicly protected. That mix is a uniquely American mess.

I'm trying to get us back on track in my own way.

I also hope you do not mind that I tried to figure out where you were coming from by researching you. My grandfather chose a name representing his desire to fight with God, and the family has been fighting ever since.

Best wishes, and here is the website of my favorite Saturday listening.

http://www.folkslikeus.org

[Donald Ian Rankin]

23. Correction: by "Second", I of course meant "First"...

[joshcryer]

39. Godels Incompleness ties in well here.

With Incompletness it is impossible to prove that 2+2=4 within the confines of the axioms presented (ie, you cannot make a mathematical proof saying 2+2=4, it is merely an observational given; you can take two things, add them with two things, and you will have four things, the substrate for this calculation is nature, mathematical proofs cannot provide such a substrate since it will always require adding another substrate to qualify the proof, ad infinitum).

Cute thought experiment.

[Jim__]

42. You can indeed prove that 2+2=4 - assuming reasonable and consistent notation..

The Peano Axioms with 2 additional axioms of arithmetic (given at the cite) are sufficient to prove it. What Godel's Incompleteness Theorem says about this is that the Peano Axioms cannot prove that they themselves are consistent. However, the Zermelo-Fraenkel (sp) axioms are sufficient to prove that the Peano Axioms are consistent. So, we have a proof, using consistent axioms that prove that 2+2=4.

For reference, here are Godel's Theorems:

Theorem I:
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,<1> but not provable in the theory.


Theorem II:
For any formal recursively enumerable (i.e., effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

I don't believe you can find any conflict between my claim and those theorems. It is not just my claim, of course. It's a well-known mathematical fact.

[joshcryer]

45. Yeah but you have to keep creating new axioms.

The axioms themselves cannot be represented in the proof!

[Jim__]

47. Creating new axioms?

The Zermelo-Fraenkel axioms, as they stand, are sufficient to prove the consistency of the Peano Axioms. The axioms for Peano Arithmetic, as they stand, are sufficient to prove that 2+2=4. What new axioms are you talking about? There is no claim that Peano Arithmetic is complete with respect to Number Theory.

[joshcryer]

51. How are you going to formalize Zermelo-Fraenkel?

You can't formalize it in itself, can you?

[Jim__]

52. Zermelo Fraenkel is a basis for set theory.

As such, Godel is very clear that it can't be used to verify its own consistency. IIRC, Godel speaks of Zermelo Fraenkel in his paper. He notes that it is incomplete (if it's not actually in his paper it is in papers that talk about his paper). He did not question the correctness of proofs based on Zermelo Fraenkel - and, afaik, mathematicians in general accept proofs based on Zermelo Fraenkel.

[cyborg_jim]

49. That's not how it works

Godelean incompleteness means that there will always be some undecidable proposition in a suitably powerful formal system - a proposition which one could, if one wanted to, decide one way or the other as an axiom of another formal system.

But that says nothing about a simple proposition such as "2+2=4".

[joshcryer]

50. Why not? To formalize that equation in its entirety is impossible.

I'm assuming here that we're including the axioms that we want to formalize *within* the formalization.

[cyborg_jim]

54. Formalising that euqation is entirely possible

It's not self-referential.

[Silent3]

48. I always liked the qualified equation "2 + 2 = 5...

...for sufficiently large values of 2."