Are there unquestionable answers?

[shemp]

Is there anything so absolutely true that it cannot be questioned?

[Upchurch]

No?

[Keneke]

ITTIA

[Mercutio]

Originally posted by shemp
Is there anything so absolutely true that it cannot be questioned? I never question any of the answers I get from the "ask Shemp" thread...

[Upchurch]

Originally posted by shemp
Is there anything so absolutely true that it cannot be questioned? Oh, wait! what about mathematical identity?

1 = 1
0 = 0
True = True
False = False

How do you question that in a meaningful way?

(I realize, of course, that one could always question the language in which the answer was stated. Like, "what does '=' mean? If we were to accept this as a legitamite, then every answer can be questioned through incomplete understanding of what the answer means.)

[LuxFerum]

Originally posted by Upchurch
Oh, wait! what about mathematical identity?

1 = 1
0 = 0
True = True
False = False

How do you know that you didn't make a mistake?

[A_Feeble_Mind]

Originally posted by Upchurch
Oh, wait! what about mathematical identity?

1 = 1
0 = 0
True = True
False = False

How do you question that in a meaningful way?

(I realize, of course, that one could always question the language in which the answer was stated. Like, "what does '=' mean? If we were to accept this as a legitamite, then every answer can be questioned through incomplete understanding of what the answer means.)

What about my favorite mind-blowing mathematical truth:

.9 repeating = 1

Can we question that? It sure makes my head hurt. :)

[frisian]

Originally posted by A_Feeble_Mind


What about my favorite mind-blowing mathematical truth:

.9 repeating = 1

Can we question that? It sure makes my head hurt. :)

I want a better answer to that as well.

I got a poor one once, but since it was poor I don't recall it.

[A_Feeble_Mind]

Originally posted by frisian


I want a better answer to that as well.

I got a poor one once, but since it was poor I don't recall it.

1/3 = .3 repeating
2/3 = .6 repeating

Thus, .3 repeating (1/3) + .6 repeating (2/3) = .9 repeating (3/3 = 1)

Still hurts the head, though.

[LW]

Originally posted by frisian


I want a better answer to that as well.

I got a poor one once, but since it was poor I don't recall it.

See http://www.randi.org/vbulletin/showthread.php?s=&threadid=29713 for everything you have always wanted to know about that subject (and much what you probably don't want to know).

But be warned that the very first post contains a typo which makes the 'proof' invalid. There are numerous different (xouper counted 17) valid proofs for it buried within that thread.

[frisian]

Originally posted by A_Feeble_Mind


1/3 = .3 repeating
2/3 = .6 repeating

Thus, .3 repeating (1/3) + .6 repeating (2/3) = .9 repeating (3/3 = 1)

Still hurts the head, though.

Yeah, exactly. Didn't care for the answer... well it's durn close eh?

[frisian]

Originally posted by LW


See http://www.randi.org/vbulletin/showthread.php?s=&threadid=29713 for everything you have always wanted to know about that subject (and much what you probably don't want to know).

But be warned that the very first post contains a typo which makes the 'proof' invalid. There are numerous different (xouper counted 17) valid proofs for it buried within that thread.

I read through "page" 1, perhaps will look through the whole thing later.

Thanks for the heads up.

[frisian]

Heh.

I asked my brother in law this question...

"does NOT work as a valid defense during a police sobriety test, as a general rule"

[epepke]

42.

[xouper]

frisian: Didn't care for the answer... well it's durn close eh?Don't make me get on my pedant's hat here. :)

It's not "durn close", it's exactly equal.

As for the number 17, well, I just pulled that out of my a... , er, thin air. I didn't really count all the different explanations. :D

[phildonnia]

Originally posted by epepke
42.

I was wondering how long that would take. Thought that would be the first reply.

[frisian]

Originally posted by xouper
Don't make me get on my pedant's hat here. :)

It's not "durn close", it's exactly equal.

As for the number 17, well, I just pulled that out of my a... , er, thin air. I didn't really count all the different explanations. :D

.9 "forever" is exactly equal to 1?

[Dorian Gray]

Yeah, that didn't sit well with me either, frisian.

Square them both infinite times - 1 squared infinitely will always be 1, but .999.... squared infinitely will tend towards zero.

[triadboy]

"Do these pants make my butt look fat?"

Unquestionable answer: "No, dear."

[Walter Wayne]

Originally posted by shemp
Is there anything so absolutely true that it cannot be questioned? There will always be some to question any answer. The truer the answer, the kookier the person questioning will be.

Walt

[Walter Wayne]

Originally posted by Dorian Gray
Yeah, that didn't sit well with me either, frisian.

Square them both infinite times - 1 squared infinitely will always be 1, but .999.... squared infinitely will tend towards zero. Not true. .999... squared is .999... no matter how many times you do it.

Edited to add: but that is for the other thread.

Walt

[xouper]

frisian: .9 "forever" is exactly equal to 1?Yes. Absolutely and unequivocally. They are two different notations for exactly the same number.

Dorian Gray: ... but .999.... squared infinitely will tend towards zero.Not correct. No matter how many times you square 0.999... it will always equal 0.999...

You may benefit from reading the thread cited previously by LW.


Edited to add: I see Walter beat me to it. :)

[ceo_esq]

Originally posted by shemp
Is there anything so absolutely true that it cannot be questioned? How about cogito, ergo sum? Of course, you can question it about me, but you can't really question it about yourself.

[Keneke]

Originally posted by ceo_esq
How about cogito, ergo sum? Of course, you can question it about me, but you can't really question it about yourself.

That's what I meant by ITTIA. "I think therefore I am."

[Dorian Gray]

Virtually the same, but not exactly the same.

[Dorian Gray]

x = .99999.....

10x - x = (9.99999... - 0.99999...) distributes out in the following ways:
x(10 - 1) = 0.99999...(10 - 1),
x = 0.99999......

[Fun2BFree]

1/9 + 8/9 =9/9=1
1/9=0.11111(repeated infinitely)
8/9=0.88888 (repeated infinitely)
.88888(repeated infinitely) + 0.11111(repeated infinitely) will always be 0.99999 (repeated infinitely)

You can do this with 2/3 and 1/3 or 3 x 1/3 or any two fractions that have the 9 in the denominator that will add up to 9/9---no matter how you do it you will always get 1 on one side and 0.999999 repeat on the other --multiple lines of evidence all leading to the same thing is very strong evidence that the result need not be questioned..They are equal--not nearly so or very close to the same--in our numbers system they are the same---(Neutrality and infinity or two concepts that are very hard for many to understand)

[xouper]

Dorian Gray: Virtually the same, but not exactly the same.What do you mean by that? I know the definitions of the words you used, but I'm not getting your point.

Dorian Gray: x = .99999.....Wouldn't this conversation be more appropriate in the other thread instead of hijacking this one? If you don't agree that 0.999... is exactly equal to one, then I'd like to politely insist that you read that other thread before making any further comments.

Fun2BFree: [stuff snipped]All that stuff has already been posted ad nauseum in that other thread. No need to repost it here.

[phildonnia]

Originally posted by Keneke


That's what I meant by ITTIA. "I think therefore I am."

I think Descartes meant "Cogito Cogito Ergo Cogito Sum."
(or "ITITTITIA")

[Dorian Gray]

A discrete fraction isn't exactly equal to a repeating decimal, either. I can give you 1/9 of something, but I can only approximate giving you .11111........ of something.

Which is also why 1 >< .99999.....

[xouper]

Dorian Gray: A discrete fraction isn't exactly equal to a repeating decimal, either. I can give you 1/9 of something, but I can only approximate giving you .11111........ of something. Which is also why 1 >< .99999..... You are absolutely and unequivocally wrong. :hit:

If you wish to continue arguing for your own ignorance, please do it in that other thread instead of hijacking this one.

[Dorian Gray]

Okay, I will show off my unbelievable ignorance in that topic.

Thanks for the advice, X.

But there are no unquestionable answers.

[Underemployed]

Robotman put it this way: "'I think I think, therefore I think I am, I think' - the guy was a lot more insecure than history portrayed him."

Here's an unquestionable answer: Yes, you are going to die.

[epepke]

Originally posted by phildonnia


I was wondering how long that would take. Thought that would be the first reply.

So did I. I'm on the committee of pointing out the bleedin' obvious, so I figured I'd provide some sort of closure.

[evildave]

1=1 ... One what? What units are we using? One orange and one orange? Are any two oranges equal? By weight? By flavor? By texture?

0=0 ... Zero what? Do we really ever have zero of anything? Zero gravity? Zero atmosphere? The closest thing you have here is a convention, setting a requirement for a 1998 Toyota pickup truck in your living room, you might say there are zero. You might yet say there are zero 1998 Toyota pickups if you have a 1999 Toyota pickup in your living room, but for most requirements of pickup truck in living room, any old model year, or even model pickup truck will generally do.

True=True or False=False is simply by convention of definition. Most people over, or under-qualify or otherwise botch the prepositions for true or false in a given situation. Just because you can blubber something half-remembered about equation from your grade school algebra/geometry, doesn't mean that true or false relate to anything you're trying to demonstrate.

As for the decimal fractions, it's only one kind of approximate representation of values. Even most programmers use floating point (not the same as real) without realising what a mess a 32 bit floating point value is. They'll merrily use it for location, not realising that it represents extreme precision near the origin, while absurdly poor resolution far away from it (i.e. 1.3 units is not the same as 1000000.3 units). Using floating point values for position is the same as never really knowing where it is. A representation of 1/3, instead of 0.3333... can be used to do a little math to come up with a function that defers division until later, and that will always yield better results than sticking to floating point values from the beginning (assuming you did the math right and checked the results). Not always important, but occasionally critical.

As for, "Yes, you are going to die!", this doesn't really answer anything. Yes? Really? When? How? What is death for you, personally? A tunnel with angels on the end? Lights out? What? Are you dead when you're still on life support, and the doctor can't get any reaction from you, or might that be a spinal injury?

[scribble]

Originally posted by Upchurch
[B]Oh, wait! what about mathematical identity?

1 = 1
0 = 0
True = True
False = False

How do you question that in a meaningful way?



You could ask UcE if he were around. To bad he's left forever...

[Ratman_tf]

Originally posted by ceo_esq
How about cogito, ergo sum? Of course, you can question it about me, but you can't really question it about yourself.

I don't think so. What if you are a simulacrum programmed to think it's aware?

[espritch]

I don't think so. What if you are a simulacrum programmed to think it's aware?

If you could program a simulacrum to do that, how would you know it wasn't aware?

[xouper]

evildave: As for the decimal fractions, it's only one kind of approximate representation of values.To clarify, sometimes a decimal representation is an approximation (irrational numbers, for example), but sometimes it's an exact value. For example, the decimal notation 0.333... is not an approximation. It is an exact value. Anytime the repetend of a decimal expansion is completely specified, it is an exact value, not an approximation.

[Ratman_tf]

Originally posted by espritch


If you could program a simulacrum to do that, how would you know it wasn't aware?

Technically, you couldn't. But there's also a difference between being unable to determine if something is so, and wether it is actually so or not. I hope that made sense.

[roger]

Originally posted by xouper
For example, the decimal notation 0.333... is not an approximation. It is an exact value. Anytime the repetend of a decimal expansion is completely specified, it is an exact value, not an approximation. Of course. However, dave was speaking in the context of floating point numbers on computers, in which case 1/3 is represented by a decimal expansion of finite length, and thus only approximates 1/3.

[Jimmy]

Are there unquestionable answers?

So far, this seems like an unanswerable question. :) I'm no genius, though.

Wouldn't pi or the square root of 2 be the same quantity universally? It doesn't really matter what base is used, it still would be the same quantity. I suppose that that can be questioned as well. *Shrug*

[c4ts]

You know those answers fundies give you when you ask them to shut up? Those are unquestionable answers.

[Keneke]

Well, then, because of the simulacrum argument, perhaps the unquestionable answer is...I am. Perhaps I am a figment of someone's imagination, a line of code, or an actual human being, but... I am.

[Dorian Gray]

I think all answers are questionable. For any answer, you could ask "What do you mean by that?"

[evildave]

Originally posted by xouper
To clarify, sometimes a decimal representation is an approximation (irrational numbers, for example), but sometimes it's an exact value. For example, the decimal notation 0.333... is not an approximation. It is an exact value. Anytime the repetend of a decimal expansion is completely specified, it is an exact value, not an approximation.

And here's the problem with it: in a machine representation, there are a finite number of bits to store the value. You can't demostrate that the value doesn't stop at or after the mantissa after any arbitrary divide (or multiply by fraction). So the calculator (or FPU) has to do something to *approximate* the vinculum. It looks like it will be all nines, so fudge it. Add the 'epsilon' and call it a whole.

[Yahweh]

Originally posted by shemp
Is there anything so absolutely true that it cannot be questioned?
The fact that "I exist" is one example...

Of course leave it to the Nihilists to question everything... stupid Nihilists...

[xouper]

evildave: And here's the problem with it: in a machine representation, there are a finite number of bits to store the value.I agree with your explanation of the limitations of floating point numbers as used by computers. I just wanted to clarify (for the peanut gallery) that those limitations do not apply to the decimal expression of real numbers in mathematics. We can certainly discuss the problems of machine representations, but that has nothing to do with the previous discussion of 0.999... = 1.

[evildave]

But the proofs for 0.999... = 1 are based on other numeric representations. You can't prove 0.999... is anything but LOTS of nines. Somewhere, somebody "fudges" it. Either by making the value between .999... and 1.0 "infinitely small" (i.e. sub-'epsilon'), or assuming it's zero. Any way you slice it, you get a fudge.

1/3 * 3/1 = 1, but 0.3333... * 3.0 isn't necessarily ever 1.0, except by "fudging" it.

Three times an imprecisely represented value is three times the error. The matter is complicated by math that results in lots of repeated numbers before some other value; enough that nobody bothers to check. 0.3333....345..., or 0.333....321... won't tally, but they can easily be assumed to when the error is remote enough. Just a matter of "close enough" again.

[LW]

Originally posted by evildave
ou can't prove 0.999... is anything but LOTS of nines. Somewhere, somebody "fudges" it.

Please, please, please.

Go to read the above-linked thread before posting any more posts on this subject.

Please.

I really mean it.

Either by making the value between .999... and 1.0 "infinitely small" (i.e. sub-'epsilon'), or assuming it's zero.

In the other thread Suggestologist has been asked for quite a long time to provide a real number that lies between 0.99... and 1 but he has failed to do so. Can you give it? If they are different, then it should be an easy thing to do since there's an uncountable number of real numbers between any two real numbers.Though, I'd once more suggest you to read the other thread before answering to this, and to answer in the other thread.

Three times an imprecisely represented value is three times the error.

0.33... is a precisely represented number.

[xouper]

evildave: But the proofs for 0.999... = 1 are based on other numeric representations. You can't prove 0.999... is anything but LOTS of nines. Somewhere, somebody "fudges" it. ...Dave, you are wrong. Please take LW's advice and read that other thread before you make any more comments on this issue. And please take this conversation to that other thread instead of hijacking this one.

How many times does this need to be said??? :hit:

[DialecticMaterialist]

My answer to this would be two-fold.

First that there are no "unquestionable answers" in the sense that there are no "answers" we literally cannot question again. I can technically do this forever. For example I can ask "What color is three?", "Where is the universe?" and "What do you think of three sided squares?" Whether these questions are meaningful or have any epistemic merit is a different matter entirely though.

Thus my second point, if we mean by the original question however that all questions are meaningful or epistemologically worthwhile; the answer I will give is "no."


To illustrate why real fast I will have to invoke the regress model.

Basically it is that "conclusions" (answers) are based on "premises" (proof and evidence); which are themselves in their own way "conclusions", themselves based on "premises"; which are themselves based on premises. And so on, ad infinitum- or maybe not.


The latter comment refers to the fact that ultimately, we have to stop/begin somewhere, with some final premises or we go on for infinity.

This leads to two approaches- infinitism, and finitism/ foundationalism.

Infinitism is usually rejected as absurd, since we cannot ground knowledge in something infinite and it seems to lead to mere relativism. If we cannot ultimately justify any premise, how do we even justify infinitism over foundationalism?


This makes infitinism inconsistent with itself and thus a worse theory.


Foundationalism however is consistent, but it has to start somewhere. With some final epistemic premises or standards. These final standards are usually called axioms, and are considered the basis for all justification.

Now by final I don't mean the end road for all knowledge, so much as the beggining. They are only "final" in the sense that they are the last thing we can test extrinsically via by other standards.


Now this being the case, and axioms be the bottom line or final premises, questioning them cannot really be too constructive. This is because any "questioning" would already presuppose the truth of these axioms, so all answers would be in some sense circular.

Now I am not saying questioning axioms in general is not good however. This is because since axioms are not extrinsically proven, (proven by other standards) which is what a "question" ultimately demands, false axioms can be extrinsically disproven. Thus asking questions may help us find false axioms, perhaps by showing that they can be disproven in theory, or that they contradict others axioms, or that they are not evident in the sense of being similiar to other axioms and necessary for logic and reasoning.


Axioms for example do have certain traits: they cannot be disproven even in theory, they cannot contradict other axioms, they are not sufficiently upheld by earlier premises and they are evident (provide a basis for evidence.)

An example of this is the statement " I am having sensations right now."

That is almost certainly true, it cannot be disproven in theory, it is not sufficiently proven by other premises, and it is evident in that it is necessary for future reasoning.


Another example is the claim "I exist." I cannot disprove that in theory, as it leads to contradictions.

Some others are the laws of identity and noncontradiction, objectivism, the basics of geometry. etc.



Lastly, since axioms are considered "evident" in that they can prove latter claims, which would not work if they were not "evident" as we cannot support something evident from something not evident-- and since axioms are not proven by any outside standard, i.e. not made evident by external premises- they are considered self-evident. For what makes them evident can only come from the self.

[ceo_esq]

Originally posted by Ratman_tf


I don't think so. What if you are a simulacrum programmed to think it's aware? The question then becomes, if you are a simulacrum programmed to think it's aware, do you exist? I think the answer is still unquestionably yes.

[xouper]

DialecticMaterialist: Axioms for example do have certain traits: they cannot be disproven even in theory, they cannot contradict other axioms, I assume you mean that within any given consistent system axioms cannot contradict other axioms within that same system, since that would render the system inconsistent. There is no requirement, however, that axioms from different systems be non-contradictory. Euclid's Fifth Postulate and its contradictions are an example.