Proof by contradiction/indirect proof — TheMadFool
since positive claims precede their negation (~p can be only after p) and since to assert a proposition one needs proof, it follows that positive claims need to be proven first. — TheMadFool
the difficulty of a proof is proportional to the number of cases you have to test by that method. The weakness of this approach is simply that it only applies when you're using "proof by testing each case". — InPitzotl
The irrationality of [the square root of] two can be demonstrated using proof by contradiction — InPitzotl
If I'm trying to show there aren't any black dogs, but it turns out there are, I still stop early once I find the black dog. — InPitzotl
3. The house = the universe
4. The bear = god — TheMadFool
I think you're focused too much on proof by contradiction.
— InPitzotl
[it's] the only method which makes proving a negative easier than proving the positive. — TheMadFool
In regard to difficulty in re existential claims that pertain to the physical, it goes without saying they're much easier to prove than their negations but, as your example shows, positive existential claims that are amenable deduction are sometimes harder to demonstrate than their negations. — TheMadFool
proving the positive, particular affirmative (Some A are B) is definitely easier than proving the negative, universal negation (No A are B). Experts agree on that and I defer to their expertise. — TheMadFool
Insofar as categorical statements are the issue, proving the positive, particular affirmative (Some A are B) is definitely easier than proving the negative, universal negation (No A are B). Experts agree on that — TheMadFool
https://en.wikipedia.org/wiki/Proof_by_contradiction#Irrationality_of_the_square_root_of_2The ordinary proof that the square root of 2 is irrational is not a proof by contradiction. — TonesInDeepFreeze
You want to prove S. So you're going to "set about trying to prove it" by commencing a task P. Essentially, P is a search algorithm; you're searching for a black dog.Suppose I wanted to prove S = some dogs are black. I begin looking for black dogs and either I find one or I don't. — TheMadFool
In the table above, the min and max columns are metrics of difficulty. What drives both min and max to be n on rows 1 and 2 is the fact that # black is 0, not the fact that you're claiming S (row 1) or ~S (row 2). In fact, each pair of rows {1, 2}, {3, 4}, {5, 6}, and {7, 8} show the same min and max metric.In regard to difficulty in re existential claims that pertain to the physical, it goes without saying they're much easier to prove than their negations but, as your example shows, positive existential claims that are amenable deduction are sometimes harder to demonstrate than their negations. — TheMadFool
But the claim has nothing to do with the difficulty (e.g., row 1 is exactly as difficult as row 2). The difficulty (how many things you need to search) depends on the state of affairs (in this view, how many black dogs there are). You don't know that state of affairs until you finish the task P, and once you do that, you no longer need burden of proof... it's already been met.In other words, it's harder to prove S than ~S. — TheMadFool
It is to move from agnosticism.
— Down The Rabbit Hole
Why? To me, you need a reason to believe something. If there is no reason, then disbelief is warranted. That is to say that the truth of the belief in question can be rejected, or denied. — Pinprick
you need a reason to believe something. If there is no reason, then disbelief is warranted. That is to say that the truth of the belief in question can be rejected, or denied.
— Pinprick
To actively claim something does not exist, you have a burden of proof — Down The Rabbit Hole
"There exists a fish with blue fins and a green body."
I don't assume that is true and I don't assume that it is false.
"There exists a striped kangaroo."
I assume that is false. — TonesInDeepFreeze
This would be using evidence to reach a conclusion. — Down The Rabbit Hole
I wouldn't be surprised at all if there were some striped kangaroos. — Down The Rabbit Hole
I just don't think we should lower our burden of proof based upon the difficulty of obtaining evidence. — Down The Rabbit Hole
I wouldn't be surprised at all if there were some striped kangaroos.
— Down The Rabbit Hole
I think you mean you would be surprised. — TonesInDeepFreeze
On the other hand, if an outlandish or "out of thin air" existence claim is asserted, it doesn't seem reasonable that the denier would have as great a burden to prove false as the assertor has to prove true. — TonesInDeepFreeze
What the chart indicates is what the chart was intended to indicate. It sounds like you're spinning tales about what it indicates. I'm not sure those tales are meaningful.That chart seems to capture discovery not proof. — TonesInDeepFreeze
I'm not sure what that entire scenario is about.Suppose someone says to you: — TonesInDeepFreeze
You're thinking about this wrong. Let's just as a device call every place that a dog could be a "dog house". So if we want to find out if there's a black dog, we need to search all of the dog houses. Here, a dog house is analogous to a photo. Likewise, all of the dog houses is our analog to a stack of photos. In other words, there is only one stack of photos."I have two stacks of photographs. — TonesInDeepFreeze
Your hypothetical reward system is all messed up. Guessing when you don't know should be worthless. Finding out should be valued. You have that exactly backwards... your reward system rewards only guessing and lucking up.You can choose to prove ...and I pay you $500 ... — TonesInDeepFreeze
You've yet to actually argue against the critique... given it's the same search being done on the same dog houses, it's the same amount of effort regardless of what you pick. Imagining rigged rewards for guessing when you don't know and lucking up doesn't change the fact that it's just those dog houses with those dogs in it that we search in, and that doesn't change no matter what we wish up to be true before we do the search.But, clearly, one should choose the best chance at having the shortest labor time - by choosing to prove there is a picture of a black dog. — TonesInDeepFreeze
No, that's not the question. The question is whether it's easier to prove a negative claim or a positive claim.The question was "Which is easier to prove: ExBx or ~ExBx ?" — TonesInDeepFreeze
Joe claims there's a God. George claims there's no God. The former is a positive claim. The latter is a negative claim. Which of those two things is easier to prove?Suppose a theist claims that god exists, and you being an atheist claims the contrary, god doesn't exist. If now you're asked to prove god doesn't exist, that would be proving a negative. — TheMadFool
1. It is easier to prove that the Four Color Theorem is false than it is to prove that the Four Color Theorem is true.The only way that question makes sense is to compare ExBx when it is true vs. ~ExBx when it is true, because if ExBx is false then there's no proof of it and if ~ExBx is false then there is no proof of it. — TonesInDeepFreeze
The question was "Which is easier to prove: ExBx or ~ExBx ?"
— TonesInDeepFreeze
No, that's not the question. The question is whether it's easier to prove a negative claim or a positive claim. — InPitzotl
Goldbach conjecture — InPitzotl
You're trying to tell me that you can compare the proof of a true thing being false to the proof of it being true — InPitzotl
or maybe that simply not knowing whether you're comparing the proof of a true thing being false to the proof of it being true or you're comparing the proof of a false thing being true to the proof of it being false makes sense out of it somehow. — InPitzotl
Sure. But generally speaking we agree that one of them is true, and one of them is false. And with the metric/method under consideration, we don't know which is which until either we find the black dog, or we searched all of the dog houses among the single set of dog houses.An existential vs its negation. — TonesInDeepFreeze
How nice of you, but "black dog" only came into the discussion as an example because the discussion started to be about black dog as an example.I used 'black dog' only because it came into the discussion as an example. — TonesInDeepFreeze
Okay, so let's talk about dogs then. What exactly is your problem with my table, as it applies to the metric we were discussing in regards to empirical determination in a finite domain?The point in the discussion I have recently been addressing is not questions of deductive determination, but rather empirical determination in a finite domain. — TonesInDeepFreeze
one of them is true, and one of them is false. And with the metric/method under consideration, we don't know which is which until either we find the black dog, or we searched all of the dog houses among the single set of dog houses. — InPitzotl
How nice of you — InPitzotl
but "black dog" only came into the discussion as an example because the discussion started to be about black dog as an example. — InPitzotl
What exactly is your problem with my table — InPitzotl
The basis is that you volunteered that you only talked about it because it was mentioned.I don't see a basis for your sarcasm. — TonesInDeepFreeze
Whereas that's true, it was TMF that started both the thread and the black dog discussion.The thread didn't start with "black dog" and went for a while without it. — TonesInDeepFreeze
I'm saying something much more specific. The question in this thread is about the burden of proof as it applies to negative claims versus positive claims. The notion being suggested is that positive claims have a burden of proof because such claims are easier to prove. That is TMF's idea, and I think it's too generic to be correct. My suggestion as to where the burden lies is more: "it depends". In other words, a claim merely being negative or positive does not tell you which of the two claimants has a burden or what it is. In terms of TMF's easy theory, it doesn't even change the task, or how difficult it is to go about it (see below).You said that the question was not as I couched it, so I merely replied that the question indeed used the example of "black dog". — TonesInDeepFreeze
You replied to it. You said this:I don't claim to understand what you intend to say with your chart. — TonesInDeepFreeze
But let's take that as an example. Your task is to prove there is not a black dog. That is rows 2, 4, 6, 8.That chart seems to capture discovery not proof. For example, the min in row 4 is 1 only because we discover that there is a black dog and give up trying to prove that there is not one. But that is not the task. The task is to prove there is not a black dog. — TonesInDeepFreeze
That condition holds in rows 3, 5, 7.If there exists a black dog, then proving there exists a black dog might end early. — TonesInDeepFreeze
That's row 2.If there does not exist a black dog, then proving there does not exist a black dog will not end early. — TonesInDeepFreeze
That's row 1.If there does not exist a black dog, then there is no proof that there exists a black dog, and trying to prove that there exists a black dog will not end early. — TonesInDeepFreeze
That condition holds in rows 4, 6, 8.If there does exist a black dog, then there is no proof that there does not exist a black dog, but trying to prove that there does not exist a black dog might end early. — TonesInDeepFreeze
I don't see a basis for your sarcasm.
— TonesInDeepFreeze
The basis is that you volunteered that you only talked about it because it was mentioned. — InPitzotl
a claim merely being negative or positive does not tell you which of the two claimants has a burden or what it is. — InPitzotl
I don't claim to understand what you intend to say with your chart.
— TonesInDeepFreeze
You replied to it. You said this:
That chart seems to capture discovery not proof. For example, the min in row 4 is 1 only because we discover that there is a black dog and give up trying to prove that there is not one. But that is not the task. The task is to prove there is not a black dog. — InPitzotl
So that wasn't so difficult. — InPitzotl
Here's the discussion leading up the black dogs:Only that you said that the question was not "Which is easier to prove: ExBx or ~ExBx ?", so I replied that the existential was the question and I only referred to black dogs in particular because that was being discussed — TonesInDeepFreeze
I'm approaching the issue with an open mind without any preconceptions or prejudices. My aim was to discover for myself why the burden of proof has to be borne by those making a positive claim and not the one making a negative claim. — TheMadFool
My answer would be, "it depends". — InPitzotl
...and so on.On what exactly?
PA= Particular affirmative (positive existential claim): Some As are Bs e.g. Some dogs are black — TheMadFool
But the reason they don't capture a difference in challenge is because the state of affairs is the same. You have the same number of total dogs and the same number of black dogs.For odd n, row n+1 - min max - is the same as row n. They are the same because, as far as I can tell, they don't capture the difference in the challenge of proof. — TonesInDeepFreeze
Okay, you've made a claim that this is the situation. Back it up.Team A, you win if you prove there is a black dog; and Team B, you win if you prove there is not a black dog. — TonesInDeepFreeze
Here's the discussion leading up the black dogs — InPitzotl
the state of affairs is the same — InPitzotl
Team A, you win if you prove there is a black dog; and Team B, you win if you prove there is not a black dog.
— TonesInDeepFreeze
Okay, you've made a claim that this is the situation. Back it up. — InPitzotl
Tell me what "Team A wins" has to do with negative versus positive claims in relation to burden of proof. — InPitzotl
what about Team C, who just wants to figure things out without making claims? — InPitzotl
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