This is something me and a few friends have discussed a few times and we come up with different answers. So Escapists what do you think can a negative be proven.
Poll: Can you prove a negative ?
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That would definitely depends upon the negative you're trying to prove, and there's a lot of philosophical implications that can get mixed up in it too.
Suppose I claim that there is no chainsaw attached to my left hand. That's claiming a negative. I present my left hand to be analyzed and confirmed by chainsaw experts that it is not a chainsaw, as well as undergo tests to prove it is not a chainsaw. By that, I have proven a negative. So it depends.zombie goat fetish said:
Um...
"-1"
^
That number is a negative.
The proof is in the negative sign.
... Is, uh... that what you're talking about?
"-1"
^
That number is a negative.
The proof is in the negative sign.
... Is, uh... that what you're talking about?
you can prove a negative. You can't prove an impossibility. We can't defy gravity, that doesn't mean it's impossible, only that we don't know how.
I suppose you could prove a very limited impossibility, like "it is impossible to defy gravity by thought alone, but you can't prove a useful impossibility.
I suppose you could prove a very limited impossibility, like "it is impossible to defy gravity by thought alone, but you can't prove a useful impossibility.
You cannot prove all negatives or all positives, but you can prove many of both. In fact, the most correct ways to describe scientific results are "I proved my hypothesis incorrect" or "I failed to prove my hypothesis incorrect"
Depends on the nature of the statement.
Mathematically speaking, following things are possible:
You can prove X is true,
You can prove X is untrue,
You can prove there's a proof for X,
You can prove that there's no proof for X (even if you assume X to be true).
NB: Absence of proof is not proof for absence, and vice versa.
Thus a proof of a negative can be possible, given certain circumstances. However often a proof is done by showing the opposite is true (-> falsification, falsifiability). As such the statement "there are no black swans" can be disproven by finding one black swan [the original example used "all swans are white" as hypothesis to be disproven]; note quite the same, but i figured it relevant to the discussion
Mathematically speaking, following things are possible:
You can prove X is true,
You can prove X is untrue,
You can prove there's a proof for X,
You can prove that there's no proof for X (even if you assume X to be true).
NB: Absence of proof is not proof for absence, and vice versa.
Thus a proof of a negative can be possible, given certain circumstances. However often a proof is done by showing the opposite is true (-> falsification, falsifiability). As such the statement "there are no black swans" can be disproven by finding one black swan [the original example used "all swans are white" as hypothesis to be disproven]; note quite the same, but i figured it relevant to the discussion
There is nothing in formal logic that prohibits demonstrating a negative. The Modus Tollens argument, for example, is pretty much based around demonstrating a negative.
For those who don't know, Modus Tollens is the name given to an argument that has the following form:
Premise 1: If it is the case that 'P' then it is the case that 'Q'
Premise 2: It is not the case that 'Q'
Conclusion: Therefore it is not the case that 'P'
(In better notation:
P -> Q
¬Q
Therefore, ¬P)
Modus Tollens is important in formal logic because it's a valid form of argument; i.e. if the premises are true then the conclusion must also be true. The only way to resist a Modus Tollens argument is to show that one of the premises is false, but this is also the case with any valid argument, hence why - from a formal logically standpoint - demonstrating a negative claim is not innately harder than demonstrating a positive one.
[pedantry]
Also, again from a logical standpoint, the 'it depends' answer is unnecessary since, given how the question is worded, if it's possible to prove a negative under any circumstance then it is possible to prove a (unspecified) negative. In regards to this question, any 'it depends' answer is therefore equivalent to a 'yes' answer.[/pedantry]
EDIT: To everyone saying talking about the 'philosophical implications' rendering the question difficult/impossible to answer, the only major philosophical matter that would cause that is the question of what constitutes a 'proof', the answer of which has equal bearing on proving a positive claim. Since the question is not 'is proof possible' we can presume it contains the tacit clause 'assuming it's possible to prove a claim' (if it were assuming proof be impossible, there'd be no point asking specifically about negative claims after all). Hence, the question of the nature of proof can safely be left-out of the discussion.
For those who don't know, Modus Tollens is the name given to an argument that has the following form:
Premise 1: If it is the case that 'P' then it is the case that 'Q'
Premise 2: It is not the case that 'Q'
Conclusion: Therefore it is not the case that 'P'
(In better notation:
P -> Q
¬Q
Therefore, ¬P)
Modus Tollens is important in formal logic because it's a valid form of argument; i.e. if the premises are true then the conclusion must also be true. The only way to resist a Modus Tollens argument is to show that one of the premises is false, but this is also the case with any valid argument, hence why - from a formal logically standpoint - demonstrating a negative claim is not innately harder than demonstrating a positive one.
[pedantry]
Also, again from a logical standpoint, the 'it depends' answer is unnecessary since, given how the question is worded, if it's possible to prove a negative under any circumstance then it is possible to prove a (unspecified) negative. In regards to this question, any 'it depends' answer is therefore equivalent to a 'yes' answer.[/pedantry]
EDIT: To everyone saying talking about the 'philosophical implications' rendering the question difficult/impossible to answer, the only major philosophical matter that would cause that is the question of what constitutes a 'proof', the answer of which has equal bearing on proving a positive claim. Since the question is not 'is proof possible' we can presume it contains the tacit clause 'assuming it's possible to prove a claim' (if it were assuming proof be impossible, there'd be no point asking specifically about negative claims after all). Hence, the question of the nature of proof can safely be left-out of the discussion.
Any attempt to prove something doesn't exist would only prove that you haven't found it.Stoike said:
It certainly depends on many factors, though I will say one thing -- or, rather, repeat one thing that another man much smarter than I once said:
"That which can be asserted without proof can be dismissed without proof." - Christopher Hitchens
To me, this is the more important point. When people talk about this subject, it is usually with respect to the question of the existence of a supernatural being/force in the universe (or "God," for many). Ultimately, there is no objective proof for the existence of a supernatural being/force, so why should atheists like myself be required to prove nonexistence? If existence is asserted without proof, it can be dismissed without proof.
"That which can be asserted without proof can be dismissed without proof." - Christopher Hitchens
To me, this is the more important point. When people talk about this subject, it is usually with respect to the question of the existence of a supernatural being/force in the universe (or "God," for many). Ultimately, there is no objective proof for the existence of a supernatural being/force, so why should atheists like myself be required to prove nonexistence? If existence is asserted without proof, it can be dismissed without proof.
This is false, actually. There are many things which can be proven to not exist. It's quite easy to prove that a largest prime number doesn't exist, or that no bijection between the naturals and the reals exists, or that no computer program exists which solves the halting problem and so on and so on. Those aren't simply things we haven't found yet, they provably do not exist.BlackWidower said: