According to you, I cannot prove my claim if my claim is false. That implies that being able to prove the claim true in the first place requires my claim to be a fact. This is why you have to dance between two contradictory facts:But the question is not what the facts are, but what is the difficulty in proving the facts. — TonesInDeepFreeze
...and the fact that this comparison requires dancing between two contradictory facts is just one of the things that makes this meaningless. There's also the fact that there's no meaningful way to measure "ExBx when ExBx is true" despite our having a metric, because that underspecifies what you're talking about.What is the difficulty in proving ExBx when ExBx is true vs. the difficulty in proving ~ExBx when ~ExBx is true?
Wrong direction. I think burden of proof for claims applies in a wide variety of areas having nothing to do with winning debates. Furthermore, debates of the type you're describing seem to be relatively rare. The OP of this very thread had an example where a person's partner is trying to convince the person that there is a bear in their house... that's a claim with a burden, but there's no debate going on here... just the search for a bear. And that's not a win. The problem here is not that I dislike the word team, or the word win. It is that I think your view that this thread is about "winning debates" is cartoonish.You're serious? It's a characterization of the problem if the context were a debate. If you don't like "team" and "win" then: — TonesInDeepFreeze
But you said:I might be corrected on this, but I don't recall making a claim about "burden of proof" in sense of a rhetorical obligation — TonesInDeepFreeze
"Burden of proof" is literally in the title of this thread.Rather the situation is:
"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
They're invoking P and arriving at either a proof of ExBx or a proof of ~ExBx depending on what the state of affairs are. And by our metric they expend the same exact effort Team A or Team B would in proving it. So your red herring accusation doesn't hold up in terms of the difficulty of proving a negative claim or proving a positive claim.They're discovering the facts, not claiming what the facts are, as opposed to the Positive claimer and Negative claimer who both are claiming what the facts are. — TonesInDeepFreeze
According to you, I cannot prove my claim if my claim is false. That implies that being able to prove the claim true in the first place requires my claim to be a fact. — InPitzotl
What is the difficulty in proving ExBx when ExBx is true vs. the difficulty in proving ~ExBx when ~ExBx is true?
The comparison is meaningless. Convince me otherwise. — InPitzotl
I think burden of proof for claims applies in a wide variety of areas having nothing to do with winning debates. — InPitzotl
Person A sustains his claim when he proves there is a black dog. Person B sustains his claim when he proves there is not a black dog. — TonesInDeepFreeze
I might be corrected on this, but I don't recall making a claim about "burden of proof" in sense of a rhetorical obligation
— TonesInDeepFreeze
But you said:
Rather the situation is:
"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 — InPitzotl
"Burden of proof" is literally in the title of this thread. — InPitzotl
They're discovering the facts, not claiming what the facts are, as opposed to the Positive claimer and Negative claimer who both are claiming what the facts are.
— TonesInDeepFreeze
They're invoking P and arriving at either a proof of ExBx or a proof of ~ExBx depending on what the state of affairs are. And by our metric they expend the same exact effort Team A or Team B would in proving it. — InPitzotl
What is the difficulty in proving ExBx when ExBx is true vs. the difficulty in proving ~ExBx when ~ExBx is true?
The comparison is meaningless. Convince me otherwise. — InPitzotl
Repeating the comparison doesn't get you any closer to convincing me that it's a meaningful comparison. Suppose I have a function f(x). I can say f(0) might be 1. I can say f(0) might be 2. I can say 1<2; that's comparing 1 to 2. But I propose that saying "f(0) if f(0) is 1 is less than f(0) if f(0) is 2" is gibberish.What you're asking requires that I repeat myself. — TonesInDeepFreeze
That's entirely correct. You didn't say anything there about who has "burden of proof". And:So what? I didn't say anything there about who has "burden of proof". — TonesInDeepFreeze
...that is also correct. That the burden of proof is the main subject of the thread doesn't entail that you can't also comment on individual points that have arisen.So what? That burden of proof is the main subject of the thread doesn't entail that I can't also comment on individual points that have arisen. — TonesInDeepFreeze
..but that is incorrect, or at least it's not the whole story. In this post:The point I have lately been commenting on has been the difference in difficulty between proving ExBx and proving ~ExBx. — TonesInDeepFreeze
...you're explicitly telling me what something you call "the situation" first is not, and second rather is. What is meant by declaring "the situation" to be that second thing and not that first thing you don't state, but there's some implication that you really, really want me to care about that second thing and to not care about that first thing.The situation is not:
"Team A, discover whether there is a black dog; and Team B, discover whether there is a black dog."
Rather the situation is:
"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
Sure, but there are symmetric descriptions of each of these things for Team A, Team B, and Team C in all of those scenarios. ~ExBx is identical to saying |{x:Bx}|=0. |{x:Bx}|=1 implies everyone might end early. |{x:Bx}|=2 and everyone will end early.Whether Team C [could end] early depends on whether ExBx is true or ~ExBx is true.
Team A might prove its claim and end early only if ExBx is true.
Team B cannot both prove its claim and end early. — TonesInDeepFreeze
To me, "discovery" versus "proof" is just a case of special labeling by you. The raw core of what is going on in terms of the cost of the thing and the thing being done that has that cost is that some entity undergoes some process J, which will end at some point when a black dog is discovered in a dog house or all dog houses have been searched, the former of which we get to label as the condition ExBx and the latter as the condition ~ExBx.If the discussion here is only about a Team C that is out to discover which is the case but not at the outset to make a claim one way or the other, then that it is a very different discussion from the one that had been presented here, which is that of opposing views being claimed, not just discovery. — TonesInDeepFreeze
I'm not interested in who is making claims, because it doesn't seem to affect how many steps J goes through, or what we are "J'd" in believing by the fact that J ended early or not whatever the case may be. ExBx is a positive claim. ~ExBx is a negative claim. I don't need claimants to give these those labels.If the discussion here is only about a Team C that is out to discover which is the case but not at the outset to make a claim one way or the other, then that it is a very different discussion from the one that had been presented here, which is that of opposing views being claimed, not just discovery. — 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 — InPitzotl
"f(0) if f(0) is 1 is less than f(0) if f(0) is 2" is gibberish. — InPitzotl
That's entirely correct. You didn't say anything there about who has "burden of proof". — InPitzotl
That the burden of proof is the main subject of the thread doesn't entail that you can't also comment on individual points that have arisen. — InPitzotl
What is meant by declaring "the situation" to be that second thing and not that first thing you don't state — InPitzotl
but there's some implication that you really, really want me to care about that second thing and to not care about that first thing. — InPitzotl
If you want me to be interested in Team-A-winning — InPitzotl
Person A sustains his claim when he proves there is a black dog. Person B sustains his claim when he proves there is not a black dog. — TonesInDeepFreeze
Whether Team C [could end] early depends on whether ExBx is true or ~ExBx is true.
Team A might prove its claim and end early only if ExBx is true.
Team B cannot both prove its claim and end early.
— TonesInDeepFreeze
Sure, but there are symmetric descriptions of each of these things for Team A, Team B, and Team C in all of those scenarios. — InPitzotl
Analogous to A3, B is missing the case where you discover a dog earlier.Clearly, proving "no dogs are black" is more difficult, as defined above, than proving some dogs are black. See A1 and B1 vide supra. — TheMadFool
You failed to prove your claim — InPitzotl
Sure, but it's just as easy to disconfirm N as it is to prove E. Not only is it just as easy, but in our toy scenario it's literally the same thing. And it's just as easy to prove N as it is to disconfirm E. There will be some state of affairs, whatever it is... that might be E, or it might be N. If it is E, then P for both E and N are exactly as difficult as each other. If it is N, the P for both E and N are exactly as difficult as each other.What I'm saying is it's easier to prove E than N for the simple reason that N requires a complete search of ALL dogs while E doesn't necessarily require that. — TheMadFool
Sure, but it's just as easy to disconfirm N as it is to prove E. — InPitzotl
But you can only prove N if N, and you can only prove E if E. Since N and E cannot both be true, the comparison between the proof of N and the proof of E is illegitimate.Yes but I'm not talking about disproving N which is equivalent to proving E. I'm interested in knowing whether it's easier to prove N or easier to prove E. — TheMadFool
But you can only prove N if N, and you can only prove E if E. Since N and E cannot both be true as states of affairs, the comparison between the proof of N and the proof of E is illegitimate. — InPitzotl
But given we're talking about empirical claims, I think you get into trouble when you entertain comparing something real to something hypothetical. Would it be easier for me to prove the Goldbach conjecture is true, or to prove the Goldbach conjecture is false? The real answer is that I can only prove at most one of those things, and the other one, given I can't prove it, leaves me nothing to compare that proof to. Would it be easier for me to prove there is intelligent extra-terrestrial life in our galaxy, or to prove there isn't intelligent extra-terrestrial life in our galaxy? Again, the real answer is that I can only prove at most one of those two things (presuming it's well defined enough to be crisp).The whole point of this thread is to compare such pairs of statements (a positive statement and its negation, the corresponding negative statement) in re which is easier to demonstrate as a truth. — TheMadFool
he real answer is that I can only prove at most one of those two things — InPitzotl
Exactly. That's why even though it takes n steps to prove there are no black dogs, if you find one on step 2 you can stop.Indeed but proving one disproves the other (contradictory). — TheMadFool
Exactly. That's why even though it takes n steps to prove there are no black dogs, if you find one on step 2 you can stop. — InPitzotl
Yes. But in proving "some dogs are black", you have proved your initial claim futile! Searching that third dog won't do you any good.But then you haven't proven "there are no black dogs". You've proven "some dogs are black." — TheMadFool
FTFY.Sowe'll[you'll] disregard your comment about it, after I've pointed out it was not apropos. — TonesInDeepFreeze
I'll take that as a position statement, since you didn't bother convincing me of anything. That leaves my position that your comparison is meaningless untouched.And it's not a meaningful comparison to what I said. — TonesInDeepFreeze
That is clearly false, because you keep replying to me and "merely stating" things directly to me.I have no interest in what you care about. — TonesInDeepFreeze
The neutrality of the terms has nothing to do with my lack of interest in what you're telling me.I even made this clear when I said (twice) that we can reduce to more neutral terms — TonesInDeepFreeze
...where 1 and 3 respectively are:(1) compared with (3) gives difficulty more to Team A — TonesInDeepFreeze
Your (1) as phrased is closest to 3 in my table. Your (3) is a great match to 2 in my table.(1) If ExBx is true, then Team A will prove its claim and might do so early. ... (3) If ~ExBx is true, then Team B will prove its claim but it won't do so early. — TonesInDeepFreeze
Consider this. We have Joe who always makes a negative claim, and George who always makes a positive one. It cost one dollar to do one J step. For apples to apples comparisons, George and Joe are going to attempt to prove every theorem that goes their way, and they will always check all of the metaphorical dog houses in the same order. Let's say there are several thousands of such claims. Then by the last claim, George and Joe paid the same amount of money trying to prove their negative and positive claims. Sure, if we ignore all of those times George paid $n to find out he was wrong and Joe paid $k<n to find out he was wrong, George might pay less total money than Joe. But that is not a real argument that positive claims are cheaper than negative ones.And, again, for the question of proving a claim, (2) and (4) are not relevant in the same way that (1) and (3) are. — TonesInDeepFreeze
If (1) can happen to George (4) ipso facto can happen to Joe. If (3) can happen to Joe (2) ipso facto can happen to George. The symmetry here guarantees equal grounding for costs paid.And, again, for the question of proving a claim, (2) and (4) are not relevant in the same way that (1) and (3) are. — TonesInDeepFreeze
Sure, we can do that. But only one possible world is our actual one. But there's nothing stopping us from partitioning the actual world. There exists no black dogs... in Saskatchewan. There exists a black dog... in Uzbekistan. But how would this help, say, getting George to pay less money than Joe?We can consider two possible worlds: World A in which ExBx is true and World B in which ~ExBx is true. — TonesInDeepFreeze
Only if you partition George and Joe's piles by what you want to call "that is a proof" do you have a chance that George pays less than Joe. But that requires you to cherry pick, and I literally mean requires. Without cherry picking there is no cost benefit.You may take the subject of this discussion to be whatever you like, but where the sense is taken to be "how difficult is it to prove?", then it seems to me that it is more difficult for Team A. — TonesInDeepFreeze
There exists no black dogs... in Saskatchewan. There exists a black dog... in Uzbekistan. — InPitzotl
cherry pick — InPitzotl
Sowe'll[you'll] disregard your comment about it, after I've pointed out it was not apropos.
— TonesInDeepFreeze
FTFY. — InPitzotl
I have no interest in what you care about.
— TonesInDeepFreeze
That is clearly false, because you keep replying to me and "merely stating" things directly to me. — InPitzotl
The neutrality of the terms has nothing to do with my lack of interest in what you're telling me. — InPitzotl
I've no problem with that; but to be more precise, we don't know U will prove its claim in 1 step. But we do know U will prove its claim in less than n steps.Team U will prove its claim possibly in only 1 step. Team S will prove its claim only in n steps. — TonesInDeepFreeze
You're mixing metaphors. Cherry picking is a type of selection bias where a person selects data that appears to confirm a conclusion (the metaphorical "cherry picking") while ignoring data that disconfirms it. "Cherries to cherries" sounds more like apples to apples (and its twin idiom "apples to oranges") which refers to comparing comparable things (in the case of apples to apples) or incomparable things (in the case of apples to oranges).I take the context to be comparing cherries to cherries. — TonesInDeepFreeze
I gave you that exact model. I'll back fill it with justification. If we're using a metric that taking 4 steps is half as difficult as taking 8 steps, then the thing we're measuring is how many steps we take. Hence, George and Joe both pay one dollar every time they take one step. So if George pays 5 dollars, it means he took 5 steps. If Joe pays 6 dollars, then George took less steps than Joe did.It is not clear how to compare the blend of (1) and (2) with the blend of (3) and (4). — TonesInDeepFreeze
There's just the single point I'm uninterested in, without you telling me why I should be. If I were generally uninterested in what you have to say, I wouldn't be talking with you.But I appreciate your candor in telling me that you're not interested in what I have to say. — TonesInDeepFreeze
Team U will prove its claim possibly in only 1 step. Team S will prove its claim only in n steps.
— TonesInDeepFreeze
I've no problem with that; but to be more precise, we don't know U will prove its claim in 1 step. — InPitzotl
You're mixing metaphors. — InPitzotl
"Cherries to cherries" sounds more like apples to apples — InPitzotl
George [...] Joe — InPitzotl
There's just the single point I'm uninterested in — InPitzotl
What does it mean to be asked to prove a negative? — TheMadFool
What about burden of proof? The received wisdom is that the person making a positive claim is the one who must produce the proof. This squares with what I've said. It's harder to prove a negative existential claim than a positive one; thus, if only because its easier, the burden of proof falls on those making positive existential claims. — TheMadFool
I ought to call myself an agnostic; but, for all practical purposes, I am an atheist. I do not think the existence of the Christian God any more probable than the existence of the Gods of Olympus or Valhalla. To take another illustration: nobody can prove that there is not between the Earth and Mars a china teapot revolving in an elliptical orbit, but nobody thinks this sufficiently likely to be taken into account in practice. I think the Christian God just as unlikely — Bertrand Russell
Why not first disambiguate between formal and less formal construals of key terms such as ‘negative claim’ and ‘proof’? There are obviously many proofs which substantiate negative claims — Cartesian trigger-puppets
Gx = x is God
1. God exists: (∃x)(Gx)
2. God does not exist: (∀x)(¬Gx)
God exists is an affirmative statement and is translated in logic with the existential quantifier (∃
∃) i.e. we only need one thing that is a god to prove it.
God does not exist, in logic, requires the universal quantifier (∀∀) and to prove this statement we need to show how each and everything in the universe is not God.
It's easier to prove God exists than God does not exist or, negatively expressed, it's next to impossible to prove God does not exist. Hence, we can't prove a negative. — TheMadFool
existential vs. universal quantification. — TheMadFool
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