/sci/ - Science & Math

tl;dr

Is the lack of a position the same as the negative position? If not, how do I denote that in formal logic?

yaknow, you coulda just asked
"how do i backup atheism as the lack of a position with logic?" and saved a few lines and masking it

>>3174222

Actually, it came about from a conversation where I was trying to create a model of agnosticism not as an independent position, but subsections.

Yes I'll admit it has connections to religion, but it also has other applications in modal logic and even science.

I'm genuinely curious how to describe the relationship, because I tried things like ¬(¬A∧A), but that felt too exclusive.

Plus, I was specifically trying to keep this from devolving into a "BLAH BLAH AGNOSTICFAG!" "HURR DURR ATHEISM IS A BELIEF" type thing.

Hey OP.
Look at this:

John might have a unicorn stuffed in his anus.
But Jack isn't sure.
He sees no evidence for it.

So should Jack believe in the anus unicorn and start making temples and killing for his behalf??

John might have a smiley spoon from outerspace
But jack isn't sure.
He sees no evidence for it.

Should Jack believe in the smiley spoon and start making temples and killing for its behalf??

ETC.

No one does that.

You dont worship santa.
You dont worship peterpan.
You dont worship 2headed dragon from 11th dimension.

And god is no exception from them.

In practice there is no such thing as: 100% non existent.
Everything is possible.

But logic dictates that we dont start believing in every crap were hear.

Just give up silly theist/agnostic.

>>3174302

This is exactly what I was trying to avoid...

Sorry if I seem mean, but your post is completely irrelevant to what I was trying to find out.

>>3174189
has someone told you he has an apple? well then you have to believe he has an apple. if nothing has been said or seen of john and his apple then you have to conclude that john does not have an apple. You're not making this statement precisely. But the implications of not-knowing are the same the negative assertion.

OP, just disregard the faggots who say that lacking belief in god = belief that there is no god. Its pretty obvious that this is what you are really asking about.

>>3174316
cut the shit fucking moron.
You're an underage shithead who thinks he can disprove atheists.

We've been there, done that, came back.
Do something productive instead.

>>3174316

Give up OP, this isn't the right board. People here aren't interested in knowledge, or logic, they just use it to insult each other, they make a mockery of science really. In this environment, neutral stances are the most despised of them all: after all, you're refusing to play their game, and to this bunch of insecure faggots, that's the worst insult.

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>>3174363
It's pretty clear at this point (and even at the beginning) that this is an agnostic vs atheist thread. So I'll get the ball rolling.

Agnosticism isn't a neutral position. it doesn't sit between atheism and theism.

My only formal experience with logic was due to a single discrete math course, so take this for what it's worth...

But in general, propositions ONLY have true/false conditions. You might say: A="Johnny has an apple", then ¬A="Johnny does not have an apple"

If you don't know for sure whether he has an apple, you wouldn't make a proposition about it in either way.

>>3174378

See what I mean OP?

>>3174336
Respond to this OP! It's the best I can contribute. I'm trying to help you but I can't put it into philosopher shorthand as I don't understand it.

You're confusing different things.

"Johnny has an apple" and "Johnny doesn't have an apple" are talking about whether Johnny actually has an apple or not, regardless of what you believe.

"I'm believe that Johnny has an apple" and its negation are statements about your beliefs, which as a statement is completely separate from whether or not he has an apple.

The second part of the confusion stems from English itself. You're asking whether the lack of a belief implies belief in the opposite, i.e. if you do not believe that Johnny has an apple, does it mean that you believe that he doesn't have an apple?

The problem there is that you're trying to fit 3-gate logic into 2-gate logic. You can believe that he has an apple or that he doesn't have an apple, or you can simply not believe anything.

If A is "Johnny has an apple", then maybe you could say that not believing either is (A V ~A).

I don't think this simplistic logical system is apt for what you want. Look into lambda calculus maybe.

>>3174387
You know that was right and you can't argue otherwise.

Op,

"I'm not sure if Johnny has an apple" is not "I don't think Johnny has an apple."

Instead, you could hold either the positions that:

1. I believe Johnny has an apple,
AND
2. I am not sure Johnny has an apple,

simulataneously, since these answer different things, one is about knowledge and the other is about belief.

If someone asked you, "do you believe Johnny has an apple," and you said "I'm not sure if johnny has an apple" this would be an arbitrary and unrelated answer to the question being asked you, you might as well be answering "hey look at that duck over there!"

>>3174189
Johnny is an agnostioc apple

>>3174336

Thank you. Yes this is helpful.

Any positive assertion is at a disadvantage because the default is a lack of knowledge, right?

Another problem I'm having is essentially equal events, like for instance schrodinger's cat. Since there is an equivalence of the negative and positive assertion, the prominence of the distinction between the "I don't know" position and the other is quite clear, because the implications don't seem to be the same as the negative assertion.

Does that make sense?

>>3174405
btw or you could hold the position that:

"I don't believe johnny has an apple
+
I'm not sure if johnny has an apple."

If someone asks you if you believe something, that is a different question entirely than if you know something, it's like apples and oranges.

So since they cover completely different things,

"Is saying "I'm not sure he has an apple" the same as "He doesn't have an apple"?"

are UNRELATED concepts other than that they both have apple in the sentence.

>>3174389

Yeah sorry it took so long, but read here >>3174413

>>3174413
The cat is an analogy and too many people stretch it beyond its limits for comparison. when you're talking about knowledge of an actual cat then it would be the same situation as John and his apple, wouldn't it?

However, Schodinger's cat is much more than this as it deals with quantum events. Ask a QMfag. I'm out. :(

>>3174405
>>3174418

Yeah I see what you're saying, but I guess I'm trying to find the distinction between a default lack of belief, and a disbelief, if that makes sense.

A: Johnny has an apple.
~A: Johnny has no apples.

B: I don't know if Johnny has an apple.
B: I do know if Johnny has an apple.

The absence of a position, as you put it, is in fact a new statement. B is not related to A, and B is much less useful than A (in general). Typically, we strive only to make statements about things which can be verified, so it's not useful to talk about how little you know about johnny's apples unless that statement is being used directly to show something else about how little you know; in which case you'd be using B and not A.

>>3174424
>mfw I got a response from OP just because I'm needy and despite being an idiot inexperienced in this field
>mfw other more respectable answers got ignored

>>3174433

Yeah that might have been a bad choice, but I gained a little insight while thinking about it.

For the apple problem, I discovered the reason why a position of I don't know (or the possible equivalent 'I don't think so') is because there are seemingly an infinite number of ways that he cannot have an apple, but a very limited number of ways that he can have the apple. So in this case it is uneven.

So that's what I'm having trouble with now is truly equal events. The prominence of the distinction between the 'idk' position and the belief/disbelief is greater.

I guess I might've already answered my question with that insight...

>>3174440
Another way to think about it: If Johnny has an apple, then he will eat it. If Johnny does not have an apple, he will not.

Not knowing whether johnny has the apple has no bearing on these outcomes whatsoever. Yes, you won't know the outcome either, but he'll eat it if he's got it just the same. There's no need to notate a lack of verification upon the premises.

You have many choices, OP:

P(johnny has an apple) = 0 equiv of ~(johnny has an apple)
P(johnny has an apple) = 0.01
P(johnny has an apple) = 0.5
P(johnny has an apple) = 1
P(johnny has an apple) = indeterminate.

>>3174440

Yeah, I'm trying to figure out, in a situation where something for sure isn't known, there is an innate ignorance.

So, is the default position of ignorance the equivalent of a position of disbelief?

While I realize they are different statements, it seems, as another poster pointed out, that their implications are the same so they could essentially be treated as the same thing.

But what I'm starting to think now, is that this only works for lopsided mutually exclusive events, where as if you have a truly even chance of something happening the implications of the position of ignorance are different than that of disbelief.

So I guess what I'm wondering now is, what causes this discrepancy with truly random events?

The truth is, unfalsifiable statements are meaningless. Before having a stance one should be asking himself if it's even worth the effort of taking it, if it matters at all having or not having one. We forget that logic, words, concepts, are all tools contingent to human life. The absence of a position is the same as saying "does it even matter?". And it doesn't. We wouldn't give a fuck about inexistent entities if other people didn't make a big deal about them.
Life is short, don't waste time on meaningless shit.

> Is the absence of a position the same as the negative of a position?

No.

> Like I consider "Johnny has an apple" A, and "Johnny doesn't have an apple" as ¬A, but I'm having trouble representing the lack of a position.

You represent it by not writing anything. Neither A nor ¬A are known so you write neither.

Beyond that, you might want to look at modal logic and specifically epistemic modal logic.

>>3174530
>The truth is, unfalsifiable statements are meaningless
That's an unfalsifiable statement.

Here is your answer OP:
http://en.wikipedia.org/wiki/Don't-care_term

Yes and No. To your perception, yes. To global knowledge, no. If you can't see it, it means that from your perception it doesn't exist. You perceive the negative. You don't see the apple. However, that doesn't mean it doesn't exist because you don't perceive everything. So thus, in your reference frame it may mean a negative, but from a global view it is either a positive or a negative. So thus, our term 'maybe' really means "It doesn't exist from my point of view, but my view of the world isn't king so it may still exist."

In truth, there are no maybes. There is simply positive or negative position (as you put it). However, we do a very poor job at detecting these positive or negative positions.

http://en.wikipedia.org/wiki/Bayesian_probability

Time to /thread this. Got a little proof via reductio ad absurdum.

Let <span class="math"> E(object) [/spoiler] be the existence of an object.
Let <span class="math"> K(object) [/spoiler] be the knowledge of evidence for the object.
Axiom 1: <span class="math"> E=0 \Rightarrow K=0 [/spoiler]
(If an object doesn't exist there is no knowledge of evidence for its existence.)

Prop. 1: <span class="math"> E=0 \Leftarrow K=0 [/spoiler]
("I'm not sure he has an object" is the same as "There is no object")

Using Prop. 1;
<span class="math"> E=0 \Leftrightarrow K=0 [/spoiler]
therefore
<span class="math"> E(object) = K(object) [/spoiler]
Conclusion: If an object exists I have knowledge that it exists. This cannot be true - proposition 1 is false.

>>3174743
>golfclap
You have proved the obvious.

>>3174761
I'll take that as a complement.

>>3174743
Your axiom is actually wrong anon; even false hypotheses (e.g. existence claims) can have evidence going for them. And the conclusion is blindingly obvious so as to make formal logic superfluous.

>>3174545
I think he's looking for something more along the lines of http://en.wikipedia.org/wiki/Ternary_logic

ITT: Trying to get a reasonable discussion about logic and /sci/ turns it into religious logic