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This is ultimately one of the most important things to know, in any debate, formal or informal. It's basically the concept that tells you whose turn it is to prove, establish, or demonstrate something. Trying to reassign the Burden of Proof when it's on you is a fallacy, and generally a bad tactic.

1. Burden of proof is always on the first person to make a positive assertation. For example, the opening poster.


2. Negatives cannot be proven. For example:



You can't prove a negative because you can't give evidence that something doesn't exist, or doesn't happen. There is no documentation of a non-phenomena, and a photo of nothing when you're trying to prove unicorns don't exist is not evidence. Hence, Inky needs to come up with proof of a unicorn. This can be summed up with the phrase "Absence of evidence is not evidence of absence."

Negative proof is allowed in the American criminal law systems- "The defendant is not guilty because it can't be sufficiently proven that he is guilty."


3. The type, or rigour, of proof needed varies.

The more outrageous the claim, the more empirical proof is needed. The more commonplace the claim, the more likely you can get away with explaining your train of thought and not citing a supporting concept. It depends on the debate and the claim.

You really can't. But you could prove Jesus is real.

Would you mind clarifying this? I have no idea what are saying here.



Actually it is impossible to prove universal negatives.



If you are going to use this as an example of proving a negative, you really ought to prove it. As it happens, there is no proof of this claim.



Indeed it is, and it is impossible to "prove." However, the opposite of it is also impossible to prove, which makes this a true statement. The burden of proof lies on the affirmative statement.



This does not prove a negative. It disproves a positive.

It is not funny in the slightest. You blatantly misuse logic in each of these examples, as each requires the presupposition of a universal negative (now bold).

There is something that prevents people from always making negatives for which I will simply call the Appeal to Probability and Statistics. If you cannot provide evidence that denotes the possibility of event X there is no reason to assume, because event X cannot be disproven or proven, whether positive or negative statement, the validity of the idea.



However let it be noted that the ideals behind this as a rebuttal are quite clear stating that, again, if it is your only rebuttal and there is sufficient evidence stating otherwise whilst not proven it can be disregarded. For instance should I say "Prove I don't Exist" if you should collect enough information regarding my existence, the norm, and various other aspects whilst not proven without a shadow of a doubt you may disregard my existence.

A Negative claim is not Auto-Win.



Using a Lack of Proof as Proof doesn't apply here; there isn't enough information for a conviction and thus without proof it doesn't make the defendant not-guilty; it just means that hte defenant cannot be convicted. The defendant can still be kept under watch if found "Not Guilty", which doesn't mean that they are not actually guilty but rather cannot be convincted, for purposes of Serveying Suspicious Behavior.

If what you said was true then what I said must be false.


Good God I'm tired.

Listen, I've had enough of this kind of ignorance. The negative I relied on is TRUE and is not derived by means of induction. I never assumed that my position is correct. I know my position to be correct! Get out your compass and draw a circle. Now, count how many sides it has. Answer: ZERO! And all circles are like that, the only difference is size. An object that is all one curve has no sides. Therefore, it cannot very well have four sides now, can it?! This is not like swans, where a single black swan is enough to ruin the proposition that "No swans are black," which is an inductive matter and hence susceptible to the problem of induction. This is a deductive matter that anyone can deduce from the very definitions of the terms themselves:



"Contained by a single line." In the singular, not the plural. So even if you consider the circumference of a circle to be a side, then it's still impossible for a circle to have four sides, since 4>1. You lose. Again, I might add!

A bystander might argue that this is all well and good, but since mathematics is constructed, only in pure mathematics one can prove universal negatives. This is untrue. For example, take invisible pink unicorns. Now, it is quite true that you can't prove with airtight certainty that unicorns do not exist (problem of induction again), but the universal non-existence of invisible pink unicorns can be demonstated from the armchair: you can't be pink and invisible at the same time!

That's the real dilemma: your position amounts to a rejection of the validity of logic itself. If you truly believe there is a possibility that four-sided circles might exist then please explain why you even take such a possibility seriously. Or if you don't believe that four-sided circles could exist, please explain to us why in the absence of any kind of proof (since you obviously don't belief that it can be proven even though I managed to do it) you do believe that. I've explained my position. I feel I'm owed an explanation of yours. For example, do you believe in the provability of universal affirmatives, like say, "All living people exist?" If so, are you unaware that the proposition "No living people are non-existent" has the same content, only expressed negatively? Of course if you don't believe in the validity of universal statements, then that leaves you (barring complete epistemological nihilism) with statements like, "Some living people exist, and some living people are non-existent." The absurdity of which is self-evident...

I find it terribly hypocritical that you would charge me with making (non-existent) logical errors when you reject the authority of logic to begin with. Note that while it is true that logical axioms are not in the strict sense provable, their validity is not in question and they are perfectly defendable: if anyone tries to refute them, they'll inevitably fail since in the act of making their arguments they'll have no choice but to steal the concepts. Such attempts make as much sense as arguing that one does not exist, and fail for the same reasons. So I do not "assume" the validity of the axioms I and everyone else use (well, everyone else except for yourself, apparently); there is no real begging of the question involved in these processes, so your objection merely amounts to unschooled whining. And if the validity of the axioms of logic is given, then the provability of universal negatives follows, as I have amply demonstrated already.

Axioms are self-evident and are defendable as reliably valid through retortion - which means if you construct arguments to refute them, you wind up with self-refuting arguments. That means axioms are prior to proof. You don't have to worry about the validity of an axiom, if it is a true axiom. ANY NEGATIVES I RELIED UPON ARE IRREFUTABLY TRUE, AND THEREFORE CAN BE TRUSTED TO GIVE US AN ANSWER THAT IS CORRECT. If you disagree, find a way to refute my arguments without whining that I'm taking an invalid circular approach, which is not the case. You can start by proving that that the proposition "No circle has four sides" does not follow from the proposition, "Circles do not have sides." All I am doing is following the logical consequences of how squares and circles are defined. If you can't understand the argument, which appears to be the case, then just say so!

Yes, I am relying upon a negative, the Law of Non-Contradiction, which incidentally appears to be a provable theorem in Propositional Logic, though I don't understand the argument. Don't tell me I can't rely on the Law of Non-Contradiction, because that as the same as telling me I can't rely of logic. But that is what you are claiming anyway: "Here you admit axioms are not provable, yet you seem to make the claim they can "prove" something." "Not provable" is not the issue. The issue is, is the truth of the axiom in doubt? And the answer to this is no. And since they are trustworthy, they can be used foundationally.

The real issue is not "You can't prove a universal negative," but "There are no universal negatives that are reliably true," because if even a single universal negative was reliably true, it could be used in a syllogism to actually prove a universal negative in the strict definition of the term. There is no question of circularity, only of the reliability of the negative premiss. You objection of circularity is an irrelevant argument. Note that "There are no universal negatives that are reliably true" is self-refuting.

If you really believe my reliance on a negative premise to prove a negative is invalid, then it follows that reliance on a positive premise is also invalid, since every positive can be rewritten as a double negative. For example, "All circles do not have four sides." If you believe that both positive and negatives can't be proven, then you believe nothing whatsoever can be proven, and if that is the case please tell us whether or not that is what you believe in your next post.

As for your response, "your use of ad hominem attacks greatly discredits your position," (a) I at least showed my position. Where's yours? (b) What ad hominem attacks? All I pointed out is that your arguments imply you either don't understand and/or don't trust logic. I confess and make no apologies for doing so in a pityless manner. And even if I did make an ad hominem, all you're doing is going after the weakest point I made. Congratulations!

Now, I am going to reiterate: I did provide you with an example, AND I PROVED IT. The validity of the proposition "No circles have four sides" flows logically from the positive proposition "All circles have no sides," which is a self-evident inference from the very definition of the circle itself (Note that the inference still works if you equivocate and consider the circumference to be a side, so both ways, you're screwed).

All squares have four sides. [From the definition of a square.]
No circles have four sides. [Inference from the properties of the circle.]
Therefore, no circles are squares. [Proven universal negative conclusion]

Logical? Yes or no?

Now, if after all that you still believe I have failed to prove that no circles are squares, please explain why. Or concede.

Not admitted it? If you think I haven't admitted it, then you haven't read my post! I made it very well clear that the issue is not whether I relied upon a universal negative to begin with, but whether or not the negatives can be doubted without formulating a self-refuting argument. The Law of Non-Contradiction, one of the three axioms of classical logic, is a universal negative, and I've said that already, but apparently you weren't paying attention.

You also haven't produced an example of an ad hominem attack. What you cited does not have the identifiable structure of an ad hominem argument. If you can't tell the difference between an expression of exasperation and an ad hominem attack, then what the hell are you doing playing ball with people who DO know the difference? Perhaps this guy can set you straight:



Sounds like you in a nutshell!

You are certainly not dealing with MY arguments. All you are doing is reiterating a specious allegation that I am begging the question or using circular reasoning, and I have already dispensed with that objection.

"Well defined" and "universal" are not mutually exclusive. A circle can be well defined (if it wasn't, how would you know you were dealing with a circle and not something else?) and it can ALSO be universally true that no circle can have four sides. If you disagree with this statement, give me a counter-argument. But if you do believe that "No well-defined statement can be a universal statement," then by your own argument that can never be proven, being a universal statement, so all you are doing is lobbing unproven assertions at me, whereas the proper procedure is to provide counter-proofs to the proofs I have already given.

As for reliance on axioms, since you believe that "It is impossible to prove universal negatives," it follows that you also believe that you can't prove that statement, therefore that proposition can only have axiomatic value for you. So for you to slam me for relying on axioms is effrontery of the highest order.



Does that mean you don't believe that it is a universal truth that 2+2 will always equal 4?

The statement "No circles have four sides" is rather specific, since it pertains only to circles, and it is universal, since it pertains to all circles. All you are doing is revealing that you do not know what universal affirmatives, uinversal negatives, particular affirmatives, and particular negatives are. A universal negative is simply a proposition that has this form:

No X are Y

And it is perfectly possible to prove such statements by using syllogisms that contain a deductively obtained negative universal premiss in them, as I have already done by proving that "No circles are squares." We can be certain of the truth-content of tautologically derived deductive premisses, such as "No bachelors are married," since bachelors by definition are men who are not in a state of marriage. If your position is that we need an exaustive, omniscient knowledge of the universe in order to obtain reliable universal negative premisses, then that is wrong, because the supressed assumption of that is that all knowledge is inductive, which is false.

So let's go over this again:

All squares have four sides. [From the definition of a square.]
No circles have four sides. [Inference from the properties of the circle.]
Therefore, no circles are squares. [Proven universal negative conclusion]

What is your objection to this? It cannot be that the second premiss is a negative, otherwise why would Aristotle have included ANY such syllogistic figures in his list of valid arguments? If the premisses are not in error, then the conclusion, "Therefore, no circles are squares" is not in error either, and thus refutes your claim that it is impossible to prove a universal negative, which is the real issue your complaints are trying to divert us from. So, do you doubt the first premiss "All squares have four sides?" Or do you doubt the second premiss, "No circles have four sides?" Here is the argumentation that proves the second premiss:

- A circle, by its very definition, is a two-dimensional plane figure that is bound by a single unbroken curve such that a line drawn from its centre to any point on its edge is equal to any other line drawn from the centre to any other point on its edge.

- Hence, it logically follows from this definition that the number of sides a circle has is zero, since the single unbroken curve rules out the possibility for a circle to have sides in the first place.

- Since zero does not equal four, it follows from this that a circle does not have four sides. Or, to put the same fact negatively, No circle has four sides

If the proposition that all squares have four sides is true, and the proposition that no circles have four sides is also true, then it follows that no circles can be at the same time squares, and hence refutes the spurious axiomatic statement "It is impossible to prove universal negatives." Do not give me any bellyaching that my syllogism contains a negative unless you are either prepared to (a) demonstrate that the four syllogistic figures that contain universal negative premisses as their elements are invalid figures, and thus that Aristotle, Avicenna, Thomas Aquinas, William of Occam and numerous other persons were just too stupid not to have realised it; or (b) demonstate that my rationale for claiming that no circle has four sides is incorrect. Either way your real beef will be with logic itself, and so long as you attempt to do either of these tasks with logical coherence, you will be committing the fallacy of the stolen concept, and your arguments will be self-refuting, and thus false.

So either concede that your position has been refuted, or concede that you believe that logic has no veridical foundations. Choose your poison.