Got the Memo Yet? You Can Indeed Prove a Negative!

[Bob the Unbeliever]

God is conceivable, but not definable. Because we conceive of God as infinite, and inexplicable. As the ultimate mystery.

Except..... almost nobody does that, do they? No-- they most certainly do not.

No--- they have a very specific idea of what they think this "god" of theirs wants them to do-- and all too often, that includes persecution of specific groups of people, and the god people wish to control their behavior, deny them basic human rights and worse-- lock them up or kill them outright.

If everyone who believed in god, believed their god was as you say-- in-definable? Nobody would need to worry about being persecuted for believing in a slightly (or even radically) different "not defined" god.

And there would never be a protest against gay marriage-- in fact? That issue would not even come up, gays having the right to marry would have been granted from the beginning. In fact, being gay wouldn't even be noteworthy...

No, the problem is people do define their gods very specifically, and always seem to know exactly what this god wants.

Those of us looking on from the outside? Are never surprised that these gods' wants and opinions always-- no exceptions-- coincide with the believers own wants and opinions.

 

[Kangaroo Feathers]

To: To Whomever it May Concern
From: Your Doting Uncle Sunstone
Date: March, 23, 2018
Subject: Have You Gotten "the Memo" Yet On Proving a Negative?


In folk logic, it is impossible to prove a negative. So it is impossible, according to folk logicians, to prove that Santa Claus, the Easter Bunny, unicorns, the Loch Ness Monster, God, Bigfoot, and @Debater Slayer's morals don’t exist.

Even some pretty bright bulbs in such power-house disciplines as physics, chemistry, biology, and erotic dance are on record here and there as saying things like, "One of the laws of logic is that you cannot prove a negative".

*cough* *cough* However, all or almost all professional logicians¹ would laugh at such a notion. "Hah! Hah!", they would laugh! "Hah! Hah!" (<--------- Disclaimer: This is a mere simulation of logicians laughing. Real logicians might or might not laugh in a similar manner. No logicians were hurt during the creation of this simulation.)

Seriously, I never in my university days came across even a single text or paper by a professional in logic or in epistemology that said you could not prove a negative. Not one! And I was studying that kind of stuff back then! And women. I was studying women too!

Moreover, I did come across texts and papers in peer-reviewed journals that argued persuasively (in my opinion) that you can indeed prove a negative -- just as well as you can prove anything else (and prove them inductively, deductively, and abductively).

Just one example here, just one example, to keep things short and to the point:

One of the most basic rules or laws of logic is called the "Law of Non-Contradiction". Here's one formulation of it: "A proposition cannot be both true and not true at the same time." Nothing is both true and false at the same moment.

Please take a moment to notice that the law is a negative statement.

Now, I won't go into the gory details here, but you can actually prove that law is true, prove it according to rigorous, air-tight, reasoning (although it's a little complicated, as I recall). So, right off the bat, with a very basic law of logic, we have a case of proving the negative.

Inductively and abductively speaking, you can also prove negatives! To be precise, you can prove them just as well as you can prove anything else inductively or abductively.

So you have now "gotten the memo" on whether you can or cannot logically prove a negative.

Please enjoy the rest of your day and accept my apologies for yet once again being insufferable.

Comments? Rave Reviews? Observations? Deranged Rants?


cc @Terese


Proving Negatives

You Can Prove A Negative

Evidence of Absence

Burden of Proof

The Mythic Difficulty in Proving a Negative

Argument from Ignorance

________________________
FOOTNOTES:
1) I refer, of course, to the tiny handful of professional logicians that I myself long ago used to know when I was a young and stunningly handsome² philosophy major with a concentration in logic and epistemology. I mean, what on earth did you think I meant by "all or almost all logicians"?
2) I am here citing my esteemed mother's opinion of my natural male beauty. She once or twice said I was "handsome". I've added the "stunning" myself because I am certain she meant that too, but just forgot to say it. And of course, mom would never lie to me. Never!

In the words of Sagan; "there's a dragon in my garage", and before him, Wittgenstein; "you can't prove there isn't a rhinoceros in the room with us right now".

When you can prove either wrong, let me know.

 

[shunyadragon]

To me, that's an interesting statement because conceiving of something, thinking about something in symbolic terms (which is the only possible way to consciously think about something. i.e. in symbolic terms), is to define something. You might or might not be aware of having defined god when you think of god as "infinite" -- but you have indeed defined god, so far as I can see.

So I'm wondering what you mean when you say, "God is conceivable, but not definable"? Do you mean any and all concepts of god are inadequate to fully reference the mystery of god? I'm guessing that's what you mean, but I'm not sure that's what you mean.

This is an attempt to define an attribute of God as infinite, and not God. If the concepts of time and space are limited to the nature of universe(s) and the greater cosmos and God has no such limitations, but could possibly be described with the attribute of being eternal. That would also be an attribute of God and not defining God.

 

[Sunstone]

In the words of Sagan; "there's a dragon in my garage", and before him, Wittgenstein; "you can't prove there isn't a rhinoceros in the room with us right now".

When you can prove either wrong, let me know.

I believe you have misunderstood the OP. Go back and check the bolded parts. Sagan and Wittgenstein are making legitimate points, but they are not addressing the issue of proving a negative using the same considerations as I am using. If after you check the bolded parts, you are still confused, then read the second article linked to in the OP at the bottom. If after that, you still don't understand where the OP is coming from on this issue, then there is very likely little I could say to enlighten you about it, and we'll have to agree to disagree.

 

[shunyadragon]

In the words of Sagan; "there's a dragon in my garage", and before him, Wittgenstein; "you can't prove there isn't a rhinoceros in the room with us right now".

When you can prove either wrong, let me know.

Empirically you can determine the presence of dragons and rhinos in the room and garage. For elephants, they have peanut breath.

 

[Sunstone]

I don't see that as *my* limitation, but as a limitation of a faulty concept.

Come, come, my dear Polymath! Don't you see why it's your limitation? Why, everyone knows Shunyadragon is like some wives: It's always you at fault!

 

[Kangaroo Feathers]

Empirically you can determine the presence of dragons and rhinos in the room and garage. For elephants, they have peanut breath.

That is both Sagan and Wittgenstein's point. You CAN'T empirically PROVE either the presence nor absence of dragons nor rhinos. You can gather evidence for or against, but no matter how much evidence you gather, neither position can ever be proven.

 

[Kangaroo Feathers]

I believe you have misunderstood the OP. Go back and check the bolded parts. Sagan and Wittgenstein are making legitimate points, but they are not addressing the issue of proving a negative using the same considerations as I am using. If after you check the bolded parts, you are still confused, then read the second article linked to in the OP at the bottom. If after that, you still don't understand where the OP is coming from on this issue, then there is very likely little I could say to enlighten you about it, and we'll have to agree to disagree.

I think we may be running afoul the difference between a semantic definition and an empirical reality. Yes, a statement can be either true or false, and the whole framework of formal logic exists to determine which is which, so yes, in that regard there is a subset of abstract concepts that may be proven or disproven. When it comes to matters of reality, what thing are or are not, and the history thereof, you cannot, in fact, prove a negative.

You may, of course, gather a great deal of evidence that the negative case is, in fact, the truth, but it's still noth the same as proving a negative.

 

[shunyadragon]

That is both Sagan and Wittgenstein's point. You CAN'T empirically PROVE either the presence nor absence of dragons nor rhinos. You can gather evidence for or against, but no matter how much evidence you gather, neither position can ever be proven.

It depends on how you are using 'proven,' because in general I reserve the concepts of 'proofs' to logic and math. I believe by inductive and deductive reasoning it can be determined empirically 'beyond a reasonable doubt,' or logically true or false whether dragons, rhinos or elephants are present in the garage or rooms.

I go for more practical and down to earth basis for what is 'proven,' falsified, demonstrated beyond a reasonable doubt,s and what is fallacious. To much effort trying to play the intellectual game of 'gotcha.'

.

 

[Sunstone]

I think we may be running afoul the difference between a semantic definition and an empirical reality. Yes, a statement can be either true or false, and the whole framework of formal logic exists to determine which is which, so yes, in that regard there is a subset of abstract concepts that may be proven or disproven. When it comes to matters of reality, what thing are or are not, and the history thereof, you cannot, in fact, prove a negative.

You may, of course, gather a great deal of evidence that the negative case is, in fact, the truth, but it's still noth the same as proving a negative.

Our differences appear largely semantic. I agree with you in at least one important sense: In non-deductive logics -- i.e. inductive and abductive logics -- the conclusions cannot be "proven". That is, they are never entailed by the premises. I believe that is the ultimate reason people so frequently say, "You cannot prove a negative".

And yes, if one were to speak strictly, one might truthfully say, "You cannot, through either induction or abduction, prove a negative though you can through deduction". However, the claim being made in the OP is slightly but significantly different.

The claim being made in the OP is that you can prove a negative (in induction and abduction) just as well as you can prove a positive. "Prove" being intentionally used here in a loose, but popular, way rather than in any formal sense (I wanted non-experts to understand what I meant, and I assumed experts might be able to figure out what I meant from context).

As it happens, the same epistemic limits that apply to negative propositions also apply to positive propositions, such that inductively demonstrating the positive proposition, "Cats have two eyes, excluding birth defects and losses", is just as "hard" as inductively demonstrating the negative proposition, "No cats have more or less than two eyes, excluding birth defects and losses." Just as hard, but no harder.

If you have not already read it, but are both (1) genuinely interested in this topic, and (2) concerned with possessing a true understanding of it, then I strongly recommend you read Stephen Hales' fun, humorous, and easy article on this subject (Here's the link). It's short and he's made the ideas accessible. As an added bonus, the article is famous -- people reference it all the time.

Thanks for your interest in all this!

 

[Kangaroo Feathers]

It depends on how you are using 'proven,' because in general I reserve the concepts of 'proofs' to logic and math. I believe by inductive and deductive reasoning it can be determined empirically 'beyond a reasonable doubt,' or logically true or false whether dragons, rhinos or elephants are present in the garage or rooms.

I go for more practical and down to earth basis for what is 'proven,' falsified, demonstrated beyond a reasonable doubt,s and what is fallacious. To much effort trying to play the intellectual game of 'gotcha.'

.

That's goal post shifting

 

[shunyadragon]

That's goal post shifting

No, my view has never changed. You need to be more specific.

 

[Polymath257]

I think we may be running afoul the difference between a semantic definition and an empirical reality. Yes, a statement can be either true or false, and the whole framework of formal logic exists to determine which is which, so yes, in that regard there is a subset of abstract concepts that may be proven or disproven. When it comes to matters of reality, what thing are or are not, and the history thereof, you cannot, in fact, prove a negative.

You may, of course, gather a great deal of evidence that the negative case is, in fact, the truth, but it's still noth the same as proving a negative.

OK, can you prove a negative to the same extent as you can prove a positive? Because the same objections seem to apply equally to positive statements. We can't know that there really is a chair in this room. All we can know is that we get an image and other sensory information that suggests strongly the existence of a chair. No proof is evident, it seems.

Well, if that is the tactic, then we can't know anything about the real world. Which, again, seems to be contradicted by the fact that we are communicating via machines built upon such an understanding.

 

[Polymath257]

This is an ideal that you may want to reconsider. As an artist, myself, I would find this presumption horrifically toxic to my own psyche. To "define" our reality is itself kind of artifice. To then presume that artifice is "objective factuality" would be to then remove all meaning from it! (shudder!)

Interesting. I have almost the same emotional reaction to the idea of NOT defining some things so we can understand them better. Precision of language is a good thing. Vagueness isn't helpful for attaining knowledge.

When people define words to be anything they want (like 'God'), that only leads to confusion and a reduction in communication. It may be personally meaningful, but it is personally meaningful that tomatoes taste horrible. That doesn't mean anyone else will agree.

And I strongly disagree that defining things removes all meaning from them! In fact, for me it is exactly the opposite! Ideas gain meaning by being well defined. They lose meaning by being vague and opinion-centered. At least, that's how it works for me.

But then, I'm not an artist.

"God" is already meaningful to them. Whether it's meaningful to you is your own problem/responsibility. If some theist is foolish enough to think what's meaningful to you is somehow his responsibility, then I guess you both deserve each other. And the colossal waste of time that will then ensue.

Yes, emotionally meaningful. That isn't the same as being meaningful in the sense of having a truth value. And, in questions of knowledge, as opposed to opinions, it is truth value that is one of the criteria.

 

[Curious George]

Interesting. I have almost the same emotional reaction to the idea of NOT defining some things so we can understand them better. Precision of language is a good thing. Vagueness isn't helpful for attaining knowledge.

When people define words to be anything they want (like 'God'), that only leads to confusion and a reduction in communication. It may be personally meaningful, but it is personally meaningful that tomatoes taste horrible. That doesn't mean anyone else will agree.

And I strongly disagree that defining things removes all meaning from them! In fact, for me it is exactly the opposite! Ideas gain meaning by being well defined. They lose meaning by being vague and opinion-centered. At least, that's how it works for me.

But then, I'm not an artist.



Yes, emotionally meaningful. That isn't the same as being meaningful in the sense of having a truth value. And, in questions of knowledge, as opposed to opinions, it is truth value that is one of the criteria.

Hdjdie ok jushdjdj jdjdjeb tiriugd bzhsueg dheudhjd uwhsjdhyks.

 

[Sunstone]

This is an ideal that you may want to reconsider. As an artist, myself, I would find this presumption horrifically toxic to my own psyche.

I think when Polymath says a statement is meaningless, he is referring to the semantic content of the statement, while when you say the statement is still meaningful, you are referring to the emotional and spiritual meaning of the statement.

Apples and oranges.

I think Polymath is right that many concepts of deity are semantically meaningless and/or factually refuted, while you are right that many concepts of deity are emotionally and spiritually life-affirming and useful.

By the way, Joseph Campbell's "cosmic dancer" is someone who is at home in both worlds, who is equally adept at dealing with both kinds of meaning.

 

[Willamena]

To: My Doting Uncle Sunstone
From: An Interested Party
Date: March 24, 2018 (note, no comma after the month)
Subject: Have You Gotten "the Memo" Yet On Proving a Negative?

quote]Just one example here, just one example, to keep things short and to the point:

One of the most basic rules or laws of logic is called the "Law of Non-Contradiction". Here's one formulation of it: "A proposition cannot be both true and not true at the same time." Nothing is both true and false at the same moment.

The liar's paradox is both true and not true at the same time, hence why it is the paradox.

There are three versions of the Principle of Non-contradiction, the second version being the most useful. The second version says that it is impossible to hold a thing to be and not to be ("hold," of course, refers to belief; there is either belief, or there isn't). There are arguments against this version, citing 'contradictory beliefs,' but its foundational value is binary truth (the first version of the principle: something is or it isn't), and hence they rely on a version of 'truth.' The third version, the one you quote, is predicated on the first and the second: we formulate ideas about the world, and those ideas will either represent the world factually or fictionally. The value of the liar's paradox lies in exploiting this quality. Most good humour also lies in exploiting this quality.

Inductively and abductively speaking, you can also prove negatives! To be precise, you can prove them just as well as you can prove anything else inductively or abductively.

I suspect that accepting any such arguments would rely on an ontological model that includes the possibility of non-existence as a thing, rather than a non-thing. That's not acceptable (to some of us). Things exist.

 

[Kangaroo Feathers]

OK, can you prove a negative to the same extent as you can prove a positive? Because the same objections seem to apply equally to positive statements. We can't know that there really is a chair in this room. All we can know is that we get an image and other sensory information that suggests strongly the existence of a chair. No proof is evident, it seems.

Well, if that is the tactic, then we can't know anything about the real world. Which, again, seems to be contradicted by the fact that we are communicating via machines built upon such an understanding.

Nope. You can't be sure the chair is in the room, either. You can just think it very, very likely the chair is in the room. It is possible there is no chair. It is possible there is no room.

 

[Sunstone]

The liar's paradox is both true and not true at the same time, hence why it is the paradox.

So far as I know, the paradox's significance is to demonstrate the "incompleteness" of formal systems of logic. But it is not to be understood as referencing an actual or external state of affairs. Hence, it does not negate the principle of non-contradiction. At least, it does not negate it's application to the real world, so to speak.

Of course, I'm probably wrong about that since I'm wrong about everything.

 

[Polymath257]

Nope. You can't be sure the chair is in the room, either. You can just think it very, very likely the chair is in the room. It is possible there is no chair. It is possible there is no room.

Fair enough. Solipsism is always a fallback position. Or the Matrix or brains in a vat.

But that didn't answer the question of whether we can establish a negative to at least the same degree we can establish a positive. In your case, vary, vary, very likely to be true.