The "you cannot prove a negative" argument

[Doreen]

You've made the same mistake Doreen has.

See above.

Oh, honestly Glaucon, I never made a mistake. I believe you finally qualified that statement I kept throwing back at you by putting negative assertions in reaction to positive ones outside the category of claims - partially, since you say yes and no. Or defined a term - claim - in a not necessarily obvious way.
And thus

Untestable claims remain philosophical curiosities, interesting from a logical perspective but outside the bounds of reasonable assertion.

cannot be seen to referring to these kinds of negative statements.

I think if you go back through the thread you will see how important it would have been for either you or Fraggle to actually have referred to the above statement - which I kept re-citing - rather than assuming I needed to hear about the difference between open and closed systems, which I really did not. I think you projected a potential error that was 'up' in the thread onto me, rather than seeing the very specific nature of my response. Thank you Parmalee for getting this focus noticed!

As far as this negative claims are not really claims, yes and no...

I hate to say this but, yes and no.
It does indeed constitute a claim, but the claim is entirely contingent upon a preceding claim [that of the (positive) assertion].

Or, put in other words, one can posit an object, but one cannot posit the denial of an object [without the precedent assertive posit].

Contingency eliminating the quality of claimness. Hm.

It seems to me that both you and the theist are making claims from the perspective of an agnostic.

To put this another way, I can see one viewing the negative as not a 'real' or 'full' claim if there were some reason one had to choose between the positive and the negative, the latter becoming a kind of passive default. But it isn't.

If the positive is a philosophical curiosity for the reasons you've given, the negative, based on the positive is at least as curious, even if inductive methodologies indicate it is the more likely of the two. Curiousness not being a synonym for unliklihood from some experiencer's vantage. The curiousity comes in with what the reader or listener is supposed to do with the claim or 'non-claim'. There is very little the listener or reader can do with the non-claim either. It just floats there at least as uselessly as the positive claim. There is certainly nothing one can do with it - another, but broader, way of saying it is untestable.

The agnostic, however, will further consider it a claim, even if it is one he or she is more sympathetic towards as far as liklihoods.

And apart from remaining silent there is the, it seems to me, wonderfully clear

I do not know what you are referring to.

This seems the perfect response for the materialist positivist pragmatic phenomenalist to the positive assertion.

It 'works'. It is true.

 

[mordea]

I never really understood the line of reasoning behind this argument. Can someone who believes in it and uses it please explain it to me and some examples of how it's used?

Whether you can prove a negative (or a positive, for that matter) depends on the level of proof demanded. Philosophically speaking, no statement, either negative or positive, can be 'proven' with 100% definity. This is due to the subjectivity of human perception.

However, if the level of proof is 'beyond reasonable doubt', then yeah, you can prove a negative. They do it in courts of law all the time. For example, one can prove that they were not at the crime scene with an alibi.

 

[parmalee]

I was merely attempting to indicate that to dismiss Fraggle's comments out of hand was not appropriate. I was paying more attention to the 'spirit' of what he said, as opposed to any particular interpretation. To wit: that people often make use of terms incorrectly.

hmmm. are you sure that you read that particular post? personally i just see it as some of the usual bullshit, and perhaps suggestive of an inability to read. and i'll go ahead and make my little "joke" a bit more overt: so, jungian archetypes--rational claims? testable? or tiresome, hippy bullshit? if that is science, then i am going to have to demand that lacan be awarded a posthumous phd in mathematics (see sokal for relevant criticism here).

Glad to see I've made myself understood [somewhat..].

but the fact is: your statement does not stand on it's own--it needs the qualification to make sense.

I hate to say this but, yes and no.
It does indeed constitute a claim, but the claim is entirely contingent upon a preceding claim [that of the (positive) assertion].

Or, put in other words, one can posit an object, but one cannot posit the denial of an object [without the precedent assertive posit].

that's actually what i thought, or what i *suspected*, rather, that you were getting at. and it kind of makes sense to me, but see below...

... Clearly, I've been reading too much Frege as of late...

funnily, i'm re-reading an essay about frege: diamond's "frege and nonsense" (and two chapters later, "frege against fuzz"--that sounds exciting.) she argues that frege (and wittgenstein) entertain a very different notion of nonsense, at least within analytic philosophy. and, of course, she gets into the matter of carnap on heidegger's nothing (in "what is metaphysics?," also funnily enough--as that is one of the first places in which he sketched out the notion of "thinking" alluded to above.) carnap finds a sentence in which heidegger employs "nothing" in the ordinary sense, and then he finds "the nothing is prior to the not"--what can this possibly mean if nothing is conceived in the "ordinary" sense? IOW equivocation, and nonsense--according to carnap. but it seems that frege does not abide, what he calls, "well-formed" nonsense. yeah, i know it's a lot more complicated than that--my point pertains more simply to just a general lack of agreement.

but the funny thing here is that it seems as though carnap didn't even bother to read the whole essay--not surprising, he had a habit for such: don't like these particular bits in the tractatus, just ignore 'em--or pretend they're "sarcasm." i mean, heidegger pretty much spells out his case for equivocation, within the freakin' essay.

anyhow, i'm still torn about this statement (sans qualifications), as it stands alongside the other statements above:

Untestable claims remain philosophical curiosities, interesting from a logical perspective but outside the bounds of reasonable assertion.

personally, i'm inclined to say that some (carnap, for instance) might describe it as nonsense, whereas frege (and probably wittgenstein) might simply describe it as false.

i mean, if the "assertion of denial" is then a claim, how can that possibly make sense? that is, without qualifications--which you only offered one post above. likewise, considered alongside

getting back on track (considering the qualifications), where does all this leave the borogoves and the lithy toves? let's suppose we ha'nt got the jabberwocky (the text, that is). are you saying that it would not be reasonable/rational for one to assert that there are, in fact, no borogoves or lithy toves? if i were to make this claim:

there are no borogoves.

is that a nonsense claim? or is it simply false? or neither? i mean, so far as we know, noone said that there were any borogoves. (we'll pretend that google yields zero hits.)

or, is the positive assertion somehow implicit in the denial?

i'm not being impossibly vague for no reason at all: the borogoves and the nothing (heidegger's nothing) are related. setting aside whether or not something is implied in the denial (assuming the absence of a precedent assertion): what the hell is a borogoves? does it make sense in the first place to deny it, if we don't even know what it is?

it's unfortunate that it always comes back to the "god" example, given that we are trusting those who don't "believe" in it to define it. it's kind of amusing that creator/master builder/"cosmic watchmaker" is always assumed, and given some of the staggering inconsistencies i've encountered, it kind of puts the matter of "equivocation" into perspective, as well.

like Doreen remarked: from the perspective of agnostic, it does certainly seem that both the atheist and the theist are making claims--the sort of claims that fall "outside the bounds of reasonable assertion." i don't know how much you recall about the essay, "what is metaphysics?," but i would describe it as very much, uh, apophatic in spirit (i'd say more kierkegaard--of even st. john of the cross--than sarte). putting it in "god" talk: the only "claims" being made are that one can't really make any claims.

it's unfortunate that the example ("god," that is) wasn't something entirely different, like, say other minds.

Speaking more generally on the topic at hand, and in particular on this distinction between classes of proof-amenable systems, it should be noted that there is the notion of supervenience to consider.

This is to say, the domain of formal logic [and other closed systems...] will always also be rational [ the notions of "inductive rational assertions", "reasonable", and other of this ilk that have been used here.]. However, the converse is not the case: the domain of rational, does not necessarily have to be logical.
Thus, the distinctions I've mentioned throughout this thread.

Supervenience

i'll look through that article, though i noted some reference to donald davidson in there (bleh). supervenience is a strange notion to me, in part because it differs so much from the ordinary sense in which the term "supervene" is employed.

"the domain of rational, does not necessarily have to be logical." we've gone through some of this before, given the sense in which i am inclined to think "thinking" i would actually take it a bit further though. for me, "what works" often supercedes what is rational, or what is usually conceived as rational.

 

[parmalee]

now supposing one makes an assertion of godlessness, would the denial of such an assertion then be a "rational claim"? or would simply the denial of godlessness (is the precedent claim implied?) be adequate?

ehhh, these "god" examples are frustrating for so many reasons, so maybe it should be dropped for the time.

so then, would you concede that the following is an untestable claim?

there is something beyond that which is experienced.

i would have to argue that that would be a sufficiently untestable claim, though i do not want to say "for obvious reasons." for in saying "for obvious reasons," i would seem to be appealing to some idea of what it is that i had in mind, and which was governing the course of my actions or inquiry; IOW i would be appealing to something beyond that which is experienced.

perhaps that term "something" is awkward, and some sort of name ought to be given to this implied, well, substratum, i guess. but i suppose that might be even more "awkward," as one might then come to think that this term does stand for something, when no such thing (a meaning) has been specified. so, something it is.

would it then be rational to claim, "there is not something beyond that which is experienced"? according to the rules glaucon described, this would indeed be a rational claim; though i honestly do not see how one could consider that a rational claim. isn't this claim every bit as untestable as the preceding one?

interestingly, in supposing that the above claim ("there is not something..."), which is the denial of the preceding untestable claim ("there is something beyond..."), one would again be appealing to that something which lies beyond--specifically, an idea as to what can or cannot be rationally asserted. so that certainly can't be right; right?


edit: i realize there might be some concept/object confusion in the above and i considered using "beyond what is experienced and what is thought." likewise, i realize that there are plenty who would in fact assert that "there is nothing beyond"; it's just that i would not think that a rational claim. my contention is that everyone entertains irrational claims and beliefs, whether or not they chose to acknowledge such is another matter.

so, how about the claim, "there exists a person (or persons) who entertains only rational convictions"--not testable, correct? so about the denial of this claim (which is my contention), "there exists no person who entertains only rational convictions"--is that then a rational claim?

in short, i feel that glaucon's contention--re: the denial of an untestable claim being a rational assertion--is anything but in the spirit of scepticism.

 

[glaucon]

now supposing one makes an assertion of godlessness, would the denial of such an assertion then be a "rational claim"? or would simply the denial of godlessness (is the precedent claim implied?) be adequate?

Again, when we're dealing with situations like these, ultimately it comes down to the content of the proposition. Given that we're dealing strictly in the 'open system' domain of induction, while the formal structure of an argument entails its validity, only the content of the argument determines its sense.
Strictly speaking, you're right: the denial of the assertion is amenable to a rational analysis.

However, as you've noted:

ehhh, these "god" examples are frustrating for so many reasons, so maybe it should be dropped for the time.

the content here is problematic, at best.

What I was really driving at is that it's always important to distinguish between the assertion of a denial and the denial of an assertion...

so then, would you concede that the following is an untestable claim?

i would have to argue that that would be a sufficiently untestable claim, though i do not want to say "for obvious reasons." for in saying "for obvious reasons," i would seem to be appealing to some idea of what it is that i had in mind, and which was governing the course of my actions or inquiry; IOW i would be appealing to something beyond that which is experienced.

I agree with all you say. Though, I'd maintain that it's fair to say that it is such for "obvious reasons". The reason being that it's simply too vague. How could we possibly even formulate an hypothesis concerning "something"?

would it then be rational to claim, "there is not something beyond that which is experienced"? according to the rules glaucon described, this would indeed be a rational claim; though i honestly do not see how one could consider that a rational claim. isn't this claim every bit as untestable as the preceding one?

Aah, now this, I like. Yes, you've definitely understood me. This is, to me, definitely a rational claim.
It is quite amenable to verification, in a roundabout manner of using reductio ad absurdum: identify something that has not been experienced.

so, how about the claim, "there exists a person (or persons) who entertains only rational convictions"--not testable, correct? so about the denial of this claim (which is my contention), "there exists no person who entertains only rational convictions"--is that then a rational claim?

Lovely.
This reminds me of quantificational logic [QL], and interestingly, that is where the answer lies:

You're right about the first case being not testable. IN QL, this would be translated as "there exists at least one person such that A [only rational convictions]". However, you've got the second case wrong: it's correct denial would be [again, in QL]: "for all persons, A". Obviously, this second case is easily testable; all you have to do is find one person that has a single non-rational conviction. [Just visit a church...].

Again though, I'd say what's more significant here is the content of the claim: isn't it obvious that there are no people who hold only rational convictions?
[Although, I have to say, this notion itself is a worthy topic. Are convictions 'innate'? If so, can they be rational? If not, they must be learned. If so, then are they rational?]

in short, i feel that glaucon's contention--re: the denial of an untestable claim being a rational assertion--is anything but in the spirit of scepticism.

Aah, but it is skepticism that is the source of all knowledge...

 

[Pachomius]

The title of the thread is "

The "you cannot prove a negative" argument."


Allow me to propose some observations.

1. People into an issue must concur on what the issue is exactly about.

2. For example, the issue can be about the existence or non-existence of something, understanding something as some anything that has being anywhere, anytime, in any sense, or all in the mind of man or in some other mind we can think of in our mind.

3. Or it can be about whether something is true or not not.

4. Or whether something works or does not work.

5. So, when someone says that you and I and every human cannot prove a negative, we must ask him what exactly are you dealing with, existence, or truth, or workability, etc.

Now, you cannot prove a negative is very routinely resorted to by atheists to dispense themselves from all and any arguments that God does not exist.

And they atheists will insist that since theists are the ones making an affirmative allegation, it is their burden to prove, it is not the burden at all on the atheists to prove -- on the pseudo idea that the burden is on the party making a claim.

Now, that seems to be the only pseudo proof, if at all we can use the word proof here: that atheists cannot prove a negative and that atheists as they do not claim God exists, they have no burden whatsoever to prove anything in regard to God not existing -- besides, no man can prove a negative.

That makes atheists altogether bereft completely and exhaustively without any rational and factual grounds to deny the existence of God!?


But returning to the socalled principle, you cannot prove a negative, as I said, parties into an issue must concur first what exactly is the issue they are into.

If they are into the issue of something existing or not existing, then the party challenged to prove a negative must ask his opponent whether the issue is about the existence of some being like say Bigfoot AND ALSO where and when Bigfoot is existing.

Within that qualification of namely existence where and when which must be supplied by the opponent, then it is possible to prove a negative if indeed the where and when is provided by the opponent to be in the house and at present where and when both parties are into the discourse of the existence or non-existence of Bigfoot.

All the party challenged to prove a negative in the present instance, is simply to search the house completely, in every nook and corner, and even dismantle the house entirely, and establish that no Bigfoot has been found, or he actually catches Bigfoot -- in which case he has proven the existence of Bigfoot -- so now we everyone know that there is a Bigfoot...


Now, let us come to atheists, tell me atheists here, can you prove there is no God in the nose in our face?

 

[AlexG]

Now, let us come to atheists, tell me atheists here, can you prove there is no God in the nose in our face?

Can you prove that there are no invisible unicorns in your nose? You can't prove the negative.

 

[iceaura]

Proof of non-happenstance are different from proofs of impossibility.

Whether or not there are black swans is not the same kind of question as whether or not there are marsupial swans. Whether or not there are lottery tickets extant with winning numbers on them is not the same kind of question as whether or not there is a formula for the roots of a quintic.

 

[Yazata]

You cannot prove a negative.

I never really understood the line of reasoning behind this argument.

It isn't an argument, it's an assertion.

It's often repeated on internet discussion boards, but logically speaking it's false.

You assume the positive and use reductio ad absurdum. This is how you can prove a negative.

Right. In the words of the Oxford Guide to Philosophy p.793,

"The negation of a proposition P is proved by taking P as a premiss and demonstrating that, in conjunction with previously established premisses or axioms, a contradiction follows."

What's more, one can sometimes prove a negative by simple enumeration.

Suppose there are six things in my drawer. I want to prove the proposition 'There are no snakes in my drawer'. So I open my drawer and look at object #1, nope, not a snake. Proceeding through each object in turn, I verify that each one isn't a snake. We do this all the time in real life.

Of course this only works when the universe of discourse is fixed and finite.

It doesn't work so well when the universe of discourse is open and unbounded. If we don't know how many animals exist in the natural world, checking each animal in turn and verifying it isn't a snake doesn't guarantee that the next animal we check won't be. We can only conclude that there are no snakes in the world when we are sure we've looked everywhere and checked every animal.

It's important to recognize that the same problem applies to positive statements too. We can observe that all swans in our experience have been white, and perhaps even rashly conclude that 'all swans are white', before we happen upon our first black swan.

That's the famous problem of induction, the problem of explaining how open-ended universal conclusions might be drawn from finite data-sets of particular instances. The relevance of this problem to things like the laws of physics should be obvious.

 

[Pachomius]

Pachomius said:

Now, let us come to atheists, tell me atheists here, can you prove there is no God in the nose in our face?​

Can you prove that there are no invisible unicorns in your nose? You can't prove the negative.

I seem to see the routine recourse to this kind of a sentence above from atheists, reproduced below:

Can you prove that there are no invisible unicorns in your nose?
​

It is supposed to be parallel to my question to atheists above, reproduced below:

Can you prove there is no God in the nose in our face?
​

But there is a crucial difference, in that in the question from AlexG there is an apparent double negative phrase, namely: no invisible unicorns, while in my question there is a single negative phrase, namely: no God.

So, I like to ask AlexG, what is the purpose you are pursuing in writing a double negative phrase, no invisible unicorns?

Suppose we use the verb "to exist" instead of "to be, is or are," so the two questions will be modified thus:

From me a theist, Pachomius:

Can you prove there does not exist ( instead of "is no" ) God in the nose in our face?
​

From an atheist, AlexG:

Can you prove that there do not exist ( instead of "are no" ) invisible unicorns in your nose?

​

Now, I admit that I cannot prove that God does not exist in our nose, because God is everywhere.

​

What about you, AlexG, can you prove invisible unicorns do not exist in your nose?


I see a very intriguing basis for starting a new thread, here is the title of the thread:

To prove God not existing, atheists conflate God with invisible unicorns.​

I will get it started once I have posted this message.

​

 

[Yazata]

I seem to see the routine recourse to this kind of a sentence above from atheists, reproduced below:

Can you prove that there are no invisible unicorns in your nose?
​

It is supposed to be parallel to my question to atheists above, reproduced below:

Can you prove there is no God in the nose in our face?
​

But there is a crucial difference, in that in the question from AlexG there is an apparent double negative phrase, namely: no invisible unicorns, while in my question there is a single negative phrase, namely: no God.

Let me ask you a question, Pachomius. Is God visible to human sight? Is he the kind of being that one can take photographs of, collect samples of, measure with instruments and study with the methods of physical science?

If your answer is 'yes', then a whole lot of additional questions follow. How do investigators find this God in order to study him? How can researchers be sure that what they've found is God and not something else? (How does one distinguish between a god and a super-powered space-alien?) And wouldn't answering 'yes' make God another part of what theology considers the created order, thus denying God's transcendence and creating problems for the idea that God is the physical universe's creator?

If instead you answer 'no', if you want to say that God isn't a physical being alongside other physical beings, if you want to say that God is transcendent and has an entirely different kind of being than the tables and the chairs, then you would seem to be agreeing with the invisible unicorn analogy, by suggesting that God is also invisible to objective physical sight. The only difference would be that invisibility is implicit in the case of God, part of properly conceiving of the deity.

Now, I admit that I cannot prove that God does not exist in our nose, because God is everywhere.

If God is everywhere, then he wouldn't seem to be visible in any particular place. So you seem to me to be going with the implicit invisibility option and hence implicitly agreeing that the invisible unicorn analogy is a good one.

Both God and the unicorn are invisible as far as our human senses and the methods of physical science are concerned. The difference between them is that the unicorn seems ridiculous and trivial, while God is the object of religious faith and devotion. That suggests to me that the difference between them might be more subjective and psychological than it is objective and ontological.

Somebody's claim to have somehow spiritually and nonphysically perceived God might tell us more about the psychology of the one making the claim than it tells us about the nature of whatever was supposedly perceived.

 

[kx000]

Yes you can.. If we knew everything that is logical we would certainly know what isn't rational if we ever cared to look. I believe the issue is proving a negative is very, say negative. Proving someone isn't satisfactory is society and sending them up the river, or proving the all mighty doesn't exist both changes our essence to a grey of sorrow and changes our mood. We have a better conscious to only prove positives.

 

[C C]

Let me ask you a question, Pachomius. Is God visible to human sight? Is he the kind of being that one can take photographs of, collect samples of, measure with instruments and study with the methods of physical science?

Yah, there is that. In the context of platonic tradition, God would be one of those "necessary conditions", intellectual or transcendent "forms" that made the sensible world possible; and/or an abstract rule-system that regulated nature. Invisible yet effective[*footnote at bottom]. But if sticking strictly to Biblical canon and literal interpretations of it, a personal God has instead directly manifested occasionally as physical phenomena and concretely interfered with the formulaic progress of its clockwork reality. Thus making that something testable (or approaching such) in terms of examination of past evidence.

Fundies seemingly can't have their cake and eat it too; God can't remain aloof from and behind the scenes of the extrospective world without invalidating or heavily making metaphorical the Abrahamic literature. Philip K. Dick once revived some older notions as to how to circumvent such a dilemma, but the result appears ad hoc / over-convenient and opens the door to unmitigated skepticism about everything over the past two thousand years being a deception. Still, it's a potential "way out" for literalists if one of them could craft a detailed framework for such that was internally consistent and didn't conflict with their conceptions of the ancient canons.

- - - - - - - -

* Similar to how evidence of an overarching brain is nowhere to be found in a dream as the provenance of the dream; or how [in sci-fi] the higher-level computer lacks empirical presence as the ultimate source of a virtual reality within that virtual reality. A truly consistent phenomenal world [which the former examples usually don't perfectly qualify as] would internally function via the mechanistic interdependence of its own components, dodging appearances of a metaphenomenal "outside" being the ground for making that possible. The latter actually needing to be quite unlike the former (nonmaterial versus material] in order to avoid an infinite regress of nested physical or natural realities.

There would be a pseudo-causal relationship between the two that made them "one" system, but conclusive evidence would be elusive within the concrete world or the experienced and reason-apprehended product. Mere speculations that resisted becoming a warranted belief. ["Pseudo-causal" in the sense that cause / effect affairs conventionally refer to familiar relationships organized in space / time rather anything a priori to that.]

 

[Spellbound]

Let me ask you a question, Pachomius. Is God visible to human sight? Is he the kind of being that one can take photographs of, collect samples of, measure with instruments and study with the methods of physical science?

Yes, He is that kind of being.

If your answer is 'yes', then a whole lot of additional questions follow. How do investigators find this God in order to study him?

Excursion into reality. Reality is That. Reality is Supreme.

How can researchers be sure that what they've found is God and not something else?

Because reality is unmistakable.