Embracing contradictions — A Fog Island Tavern conversation.Posted: March 3, 2018
– Vodçek, tell me, do you have a feeling Abbé Boulah has lost it?
– Bog-Hubert, my friend: you do look worried — did you overdo the testing of your new batch of Eau d’Hole? What in the world makes you ask such questions?
– Well, I just overheard him talk on the phone with his buddy up in town. Out on the deck while I was coming up the ramp; he didn’t seem to mind at all. And he was going on about how we ought to embrace contradictions, of all things. Speaking Latin and quoting Libbett, whoever that was.
– Libbett? Never heard of him. Ah, wait. Libbet’s not a person — at least not one our friend was talking about. Could he have been invoking the old logic rule of “ex contradictione sequitur quodlibet”?
– Was that what he kept shouting? What does it mean?
– It means “From a contradiction you can infer, conclude whatever”. Right, professor?
– Yes indeed. It’s also known as the rule ‘Ex falso quodlibet” It’s a warning about the fallacy of allowing contradictory claims in a system because any statement can be proven from them: anything follows, looking like ‘proof’, even though it’s nonsense.
– I don’t understand.
– Okay. Consider a statement (1) “Wine is good for you, or Abbé Boulah is a Lower Lugubrian spy”. Now we know that wine is good for you — even my doctor tells me that, so that statement is true, which means that whole claim is true. But a statement (2) to the effect of ‘Wine is not good for you’ can also be seen as true, since there are wines that are so vile they make you sick. Not in my tavern, of course. But then the fact that if (2) means the first part of statement (1) is not true would mean that its second part must be true, since otherwise the whole sentence would not be true. This ‘proves’ that Abbé Boulah must be a Lower Lugubrian spy. Or whatever you’d put in that second part.
– They teach that at la Sorbonne?
– Sure do. At least they did when William of Soissons came up with this rule in the 12th century.
– But is there even a place called Lower Lugubria?
– Right, Renfroe, I mean no. Not yet, at least. But the logic proves it, so it must be true, eh?
– Well, I’ll be dipped in Cajun hot sauce. So how come Abbé Boulah can call for anybody to ’embrace’ such nonsense? The government is going to deport him, and where will they send him if there ain’t no such place?
– Bears some looking into. Could it be that he means something else by the ‘quodlibet’ thingy?
– Interesting idea. Yes, I think he could have meant several things. You know he’s been working with his buddy on the planning discourse support platform idea for a while, where one of the problems has to do with whether there should be an ‘expert system’ or Artificial Intelligence component that could look at both the discussion entries and other data bases, and come up with useful comments to the discourse. And their concern has been, quite reasonably, that the planning discourse contains all kinds of contradictory information. Almost by definition — all the ‘pros and cons’, remember? So how can it draw any meaningful conclusions from all that?
– I get it. It’ll all be Lower Lugubrian… So?
– So they have been saying that unless the AI folks can come up with a meaningful way of dealing with the contradictions in the discourse — and in the other data bases, too, I’d guess, — there will be big questions about AI support for the planning discourse.
– Why is that?
– Well, normally, you’d trust whatever such a system comes up with because you think they are trustworthy and reliable — which depends on two things: One, that all the data from which they draw conclusions are true, or at least come with trustworthy probability estimates. And two: that the reasoning rule they use to draw conclusions are ‘valid — meaning that they will actually result in true conclusions if all their premises are true. So if you now admit contradictions in the data gumbo, how can you trust the conclusions?
– Well, isn’t the point of such systems to calculate, based on valid reasoning rules and checked-out facts, which of two contradictory claims is true and which one is wrong?
– That would be nice, wouldn’t it, Sophie. But it isn’t that easy to tell what’s what. Take the big controversy about climate change, and whether it’s all caused by human activity. There are many studies that show how warming trends seem to follow the amounts of CO2 that human activities emit. Using good, reliable data (meaning the data have been confirmed by other independent studies) and reliable scientific and statistical methods, ‘reasoning’ patterns, if you like. So those studies seem to ‘prove’ that human emissions have contributed to global warming. But there are also studies that use data you can’t dismiss as ‘false’, and equally valid statistical methods — that come up with conclusions that say there is no such connection.
– What do you mean, Professor?
– Well, Sophie: it turns out that much depends on what kind of data you are using — for example, whether you are measuring temperature changes on the earth’s surface (on land) or over the ocean, or in the ocean, or in the air, and how high up you are measuring it. And it also depends on what time period you are looking at. So each of the studies may actually be quite ‘valid’ in themselves — reliable data and respectable methods — just looking at different data, and coming up with different results. So it takes some close scrutiny to evaluate those studies — the ‘system’ may report all of them as ‘reliable’ because it doesn’t realize that the kinds of data and the time period may make all the difference. So you still need to take a critical look at the studies.
– Okay. Let’s not get caught up in that climate issue right now. You mentioned that there were several possible reasons for Abbé Boulah’s strange call?
– Yes, thanks for reminding me. At least two, besides simply saying that we need to acknowledge all the contradictions in the discourse, and actively encourage people to express them for discussion and evaluation. Not sweeping them under the rug by pushing for ‘consensus’ or relying on ‘expert’ reports.
– Yes. We’ve discussed that — but people seem to be stuck on unified visions and leadership and consensus; well, I guess it takes time to sink in. But you weren’t done yet, were you, sorry?
– Right. We should also improve our tools for dealing with all those contradictions. Because there are actually some claims — the ‘deontic’ ones, that have to do with what people feel ‘ought to be’ — goals, objectives, concerns about things they don’t like in the current problem situation, or visions about what life might be that’s different — don’t we all wish that we could ‘make a difference’ in our lives? And those premises of planning arguments are not ‘true’ or ‘false’, not even properly assessed as ‘probable’; so logic has some serious trouble with them. Its valid syllogisms don’t apply. And we accept that people have the right to happiness in pursuing different goals. Look at even the common views of ‘costs’ and ‘benefits’ of proposed solutions: they aren’t the same for all affected parties: some of the ‘costs’ that some want to reduce are actually ‘benefits’ (income, profits,) for others, who want more…
– Hmm. You’re making things difficult here. So the government making decisions based of the famous ‘Benefit/Cost Ratio is actually … how should we say…
– Sweeping those issues under the rug? Yes. We need different decision tools.
– But there still could be more behind Abbé Boulah’s attitude?
– Well, maybe he is simply referring to the ‘Systematic Doubt’ method for analyzing a problem and generating solution ideas.
– What in ninety nonsequiturs’ names are you talking about, Professor?
– You never heard about this technique? It’s actually based on a nifty piece of logic — DeMorgan’s second theorem — which says that a the negation of a statement consisting of two or several claims joined by ‘and’, is equivalent to a statement of each of the negated parts joined by ‘or’:
~(a ^ b) = (~a v ~b)
Here, ~ means negation, ^ means ‘and’ ; v means ‘or’).
– So where does the contradiction come in?
– Impatient wench, Sophie. Say you have a problem and try to find a way, a plan, to fix it — eliminate it. Now make a statement consisting of several necessary conditions for that problem to exist: “a ^ b ^ c …” (De Morgan’s theorem works for any number of conditions.) You want the problem you want to go away? This can be expressed as ‘~(a^b^c…). The equivalence of that statement to that of ‘ ~a v ~b v ~c…’ means that if only one of those necessary conditions could go away — negated, c o n t r a d i c t e d, get it? — the whole problem would not exist.
– Ah Renfroe — this gives rise to a beautiful approach to finding many possible solution ideas, don’t you see? The steps are:
* First, you look at the problem and find its all its necessary conditions
* You state those conditions in plain assertive sentences. This way of talking about problems takes a bit of getting used to; we usually just complain about it in negative sentences: such as ‘there isn’t any money in my bank account’ or ‘there’s no place to park’
* Then, you take each of the conditions and negate it: contradict it. Write them out one by one.
* Now you look for ways to make these negated statements come true. There may be no way to do that for some statements, but often two or more. They may not all make sense — some can be plain nonsense or hilariously unfeasible, the process can be a lot of fun — but there may just be one or more good ideas for solving the problem, so you can pickup and elaborate on those.
You have been nudged to look at the problem from any different viewpoints; improving the chances of finding a good, feasible solution. All by contradicting the necessary conditions for the problem to exist.
– So Vodçek, you think this is what Abbé Boulah was talking about? It does make some sense now.
– Who knows, Sophie; we may just have to wait until next time he shows up here to ask him about that. But I can think of one more possibility of what he meant.
– Oh? As interesting as this Systematic Doubt one?
– Well, I’ll let you be the judge of that. It has to do with the meaning of ‘quodlibet’ in that old logic rule. Perhaps the professor can explain it better?
– Ah, I think I see what you are getting at, Vodçek. Yes, it would be quite in style with Abbé Boulah’s sometimes, hmm, unusual, way of thinking. Let’s see. ‘Quodlibet’ comes from ‘quod’ , meaning ‘what’, and ‘libet’ means ‘like’ or ‘please’. So maybe wasn’t referring to the meaningless ‘whatever’, random nonsense. He could have been trying to say that by ’embracing the contradictions’ in a planning situation, and using them with some imagination, we could end up with more creative, imaginative, but also pleasing solutions?
– As compared to just dwelling on the negative aspects about the problem, the complaints?
– Right. You agree, Bog-Hubert? You were the one who heard him talk to his friend — did that sound like it had something to do with Vodçek’s theory?
– Well it sure would explain the last comment I heard him say, that I didn’t understand at all at the time.
– What was that, again?
– I think he mentioned something about misquoting, or changing one of Winston Churchill’s lesser known sayings — but what I heard was: “The price of ‘quodlibet’ is responsibility.”
– Is that what they are saying in Lower Lugubria?