Does logic fail us?

[Prime]

Hi All,

I was having a discussion with someone who believes she cannot rely on logic for the reason that apparently, 1+1 can be disproved to be 2 (or something to that effect).

I was wondering if anybody could elaborate on this?

Prime.

[Dravyga]

1+1 = 11 which equals 3 in binary.

[DaleSpam]

Hi Prime, welcome to SciForums,

There are a variety of algebraic "proofs" that show that 1+1 != 2. All of the ones that I have seen divide by zero at some point. It's not that logic has failed, it's just that you are doing a mathematical operation that is not defined.

Ask your friend for the proof. If you see at some step that they have something like a/(b+c) then look and see if b=c. If so you can point out the error to your friend immediately.

-Dale

[Tom2]

I was having a discussion with someone who believes she cannot rely on logic for the reason that apparently, 1+1 can be disproved to be 2 (or something to that effect).


As others have said, ask her to show her work. It will certainly be the case that she has made a mistake somewhere. If anything it should serve to convince her that she cannot rely on illogic.


Ask your friend for the proof. If you see at some step that they have something like a/(b+c) then look and see if b=c.


That would be a/(b-c), but I'm sure you know that.

[DaleSpam]

That would be a/(b-c), but I'm sure you know that.Oops. :o

Quite right, how embarassing.

-Dale

[Crunchy Cat]

Hi All,

I was having a discussion with someone who believes she cannot rely on logic for the reason that apparently, 1+1 can be disproved to be 2 (or something to that effect).

I was wondering if anybody could elaborate on this?

Prime.

Yeah, it's an interpretation trick. It boils down to:

1x + 1 = 2

and the value of x is > or < 1. For example, if we give x a value of 3 then:

3 + 1 != 2

or more specifically:

4 != 2

Logic is working just fine.

[CANGAS]

She will not tell you ? :eek:

Why are you asking a third ( and fourth and fifth.... ) party?

I think maybe your friend likes to play tricks on you and especially try to get you into trouble with strangers. :D

[Dinosaur]

If mathematics & logic had serious flaws, I would worry about bridges falling down, airplanes crashing, accounting programs making mistakes, et cetrera.

Be serious! Does your friend have even a clue about all the devices that would not work if mathematics & logic were flawed?

[CANGAS]

Including these computers.

[Zephyr]

Windows is a bad example.

And there are limits to logic, as Gödel pointed out.

[Dinosaur]

The limits due to the Goedel proof are a far cry from any claim that logic is flawed or in some sense not usable for practical purposes.

[Prime]

OK! Thanks for all the replies. Just to be clear and to give some context; she is not my friend. I met her that day and I mentioned some things to do with her religion and why I don't / can't agree. She took me to the pub and we had a 2 hour "discussion"; the logic issue is one of the items that I thought about afterwards.

With regards to Godel's Proof (I don't have a mathematical background) but from what I understand of it; in principal no system of logic can ever capture the whole of the truth; I agree with Dinosaur that it's a far cry from saying logic is flawed.

Prime.

[Zephyr]

Of course. Limits don't remove logic's usefulness. Nonetheless I think it's wise to recognise those limits ;)

[Arkantos]

I don't know if I remember, but does Godel have anything to do with something lik this?

"this sentence is false in this logical system"

[Zephyr]

I think so ... either you can prove the sentence true or false - either of which is a contradiction; or you can't do either, so your system is incomplete. Incompleteness is the lesser evil.

[Dinosaur]

I think goedel proved that certain logical systems are either incomplete or inconsistent.

Incomplete meaning that there had to be one valid theorem (or statement) that could not be proven. Such a theorem (or statment) could be added to the system as an axiom, enlarging the scope fo the system & allowing for other valid but unprovable statemenst/theorems.

The alternative to incompleteness was inconsistency, which does not seem like a plausible or desireable alternative.

His proof applied to non trivial systems. I beleve that the actual proof is very difficult to understand, although dumbed down versions provide the basic concept. It is a reducto ad absurdem proof.

Goedel's proof was the final result of a project started by Gauss & Riemann to prove the consistency of the basic axioms of mathematical logic. The byproducts of that project were the geometry of curved spaces, Principia Mathematics (by Russel), and all sorts of other wonderful results.

[funkstar]

The proof isn't actually that difficult, but one has to be very particular with which level of interpretation is used where.

[Dinosaur]

FunkStar: I have read many descriptions of Goedel’s proof which were easy to understand and which provided the general concept of the proof. When I actually read a serious version of the proof, it seemed very difficult.The proof isn't actually that difficult, but one has to be very particular with which level of interpretation is used where.Could you suggest a site with a formal version of the proof that is not too difficult? I did not have the patience to follow the proofs at the following sites.http://www.cs.auckland.ac.nz/CDMTCS/chaitin/georgia.html http://www.ltn.lv/~podnieks/gt5.html#BM5_3The above are typical of the level of formal proofs I have encountered.