Renlund ties himself in knots during General Conference

[Dr. Shades]

Just generally curious here. Do you not allow for paradox? Yes, logical inconsistency merits further review, but there are things that are illogical and true.

Will you please give me an example?

[Physics Guy]

Yeah, I'm also curious about JohnW's concept of paradox. I don't think anything true can really be illogical. I admit that humans are not very good at logic, so things often surprise us that ideally shouldn't, but if something is true then I think you can always thresh out its proper logic eventually and then kick yourself for ever having confused it.

This case with Renlund looks a lot more like a simple self-contradiction chasing its tail to try to explain away the problem. The paradoxes I know don't look like that. They're like the vase versus two faces, that look different from two different starting points. This looks more like a kid trying to explain to a parent that the word scribbled on the cover of their math notebook is really the well-known funny term FNCK.

[Rivendale]

Yeah, I'm also curious about JohnW's concept of paradox. I don't think anything true can really be illogical. I admit that humans are not very good at logic, so things often surprise us that ideally shouldn't, but if something is true then I think you can always thresh out its proper logic eventually and then kick yourself for ever having confused it.

This case with Renlund looks a lot more like a simple self-contradiction chasing its tail to try to explain away the problem. The paradoxes I know don't look like that. They're like the vase versus two faces, that look different from two different starting points. This looks more like a kid trying to explain to a parent that the word scribbled on the cover of their math notebook is really the well-known funny term FNCK.

A while back I posted about DCP using the Ramanujan Summation as an example of seemingly illogical things can be true. I can't really think of a true paradox either. A and not A seems to be claimed by some by crawling over or under or around the laws of logic to make that conclusion.”

[Physics Guy]

Ramanujan famously added up of all the positive whole numbers to get -1/12, even though the sum is (a) obviously infinite, (b) obviously positive, and (c) obviously not a fraction. This is not exactly a truth, though. It's an alternative concept of addition to the usual one. What's true is that there is a way of defining addition which makes Ramanujan's answer correct. It's obviously not the same as the usual kind of addition. When you put it that way, it's not so paradoxical.

It is still kind of surprising, because the alternative concept of addition doesn't sound so radically different when you first hear it. It sounds as though it's just spelling something out more precisely than one usually does, but in a perfectly sensible way. The surprising part is that this seemingly sensible way of defining addition more precisely leads to results like Ramanujan's, for infinite sums.

Math is full of situations like that. So is human law, for that matter. Some legislature passes a law, or some court sets a precedent, that sounds fine at first, but turns out to have perverse implications.

As far as I know, though, you always can thresh out just how the perverse implications work. They're not true but illogical. They're just surprising to humans who can't immediately see all the logical consequences of a set of assumptions.

[JohnW]

Just generally curious here. Do you not allow for paradox? Yes, logical inconsistency merits further review, but there are things that are illogical and true.

Will you please give me an example?

I'm not exactly thinking of logic in its strictest sense (I'm certainly no logician). I'm thinking of logic as we personally encounter it. We come across illogical but true things all the time in life. This happens most often when we have missing information or if our premises are incorrect. For example, a few weeks ago I had a leak in my water lines in our yard. It was a frustrating leak and was costing us quite a bit of money. We couldn't find any wet spots and dug holes all over the yard while searching. I finally began a thorough, methodical search of the lines by digging up parts of the line, capping sections and seeing if the leak continued after the cap. I slowly began to rule out chunks of the yard. I would call this a highly logical way to approach the problem. During this process, I cut a natural gas line. Natural gas lines simply weren't in my calculations. I didn't realize PVC was sometimes used for natural gas lines. As an aside, shortly after this event I hired the job out.

I know this isn't a great example, but right before I cut that gas line, I was sure it was a water line. I was so sure that it took me quite a few seconds for the truth to work past my logical construct.

Yes, this is more practical logic and not rigorous logic, but it feels the same for the person going through the struggle. If I were better at logical analysis, I could come up with an example with two premises that logically support one conclusion, but it would conclude something completely different if the third premise is included. A similar thing can be done if one of the premises is false.

Ultimately logic is a system that processes information. It doesn't help you if you have bad information or missing information. The basic assumption of logic is that all your premises are true and that you have absolutely all the pertinent information. This rarely happens in real life. Some people will argue that makes logic useless in real life. I happen to believe that it just means we must use logic carefully.

[JohnW]

Yeah, I'm also curious about JohnW's concept of paradox. I don't think anything true can really be illogical. I admit that humans are not very good at logic, so things often surprise us that ideally shouldn't, but if something is true then I think you can always thresh out its proper logic eventually and then kick yourself for ever having confused it.

This case with Renlund looks a lot more like a simple self-contradiction chasing its tail to try to explain away the problem. The paradoxes I know don't look like that. They're like the vase versus two faces, that look different from two different starting points. This looks more like a kid trying to explain to a parent that the word scribbled on the cover of their math notebook is really the well-known funny term FNCK.

Yeah, I think this is what I'm talking about. It is possible you could argue that if we knew absolutely everything about a situation, there would be no true paradoxes. In real life, we rarely know everything about a situation. I come across situations all the time that feel like paradoxes. I come across situations that are completely illogical, but absolutely true. Sometimes, they turn out to be just a misunderstanding of the situation. Other times, I can't really tell.

If a person is never willing to question their logic, they will often be wrong.

[Doctor CamNC4Me]

JohnW,

I don’t want to speak for Dr. Shades, but since his quoted part pertains to a contextual narrative where you responded to a gospel topic posted by IHAQ, it follows that he wasn’t looking for an example outside the Mormon church or its policies/doctrines.

- Doc

[Physics Guy]

I agree that mistakes in our assumptions are often exposed by contradictions. I can’t think of any cases where the right reaction for me has been to shrug off the contradiction as a failure of logic and just go on as I was nonetheless. Reality bites.

Sometimes the mistake turns out to be easy to correct without any disturbingly large changes in my world view. Sometimes, though, I think you have to face hard facts and admit you were wrong about something important.

[Gadianton]

The usual definition of truth starts with non-contradiction, and so it would be impossible for a paradox (something that when false is true, and true if false) to be "true".

However, continental philosophy went in a different direction, and doesn't want to grant the law of non-contradiction as base rock reality. There are no explicit discussions about this, but I think it's what it amounts to.

phenomenology and existentialism take physical reality as primal. And back around 2000, I ran into a physicist who had no connection to postmodernism, who argued that a contradiction might be possible in some universe even if we can't imagine it. At the time I didn't appreciate how important it was for a physicist to be saying that, and years later I was never able to find the conversation. (I'm not saying he was right, but that he appreciated the end-game of empiricism without having a phil background).

The fundamental tension is between realism and empiricism. realism = some kind of ultra-math model behind everything. empiricism = what do my instruments record (that physicist I mentioned).

Most people who consider themselves commonsense non-nonsense people waffle back and forth between "logic" and "evidence". The problem with empiricism is relativism of the kind JohnW might be suggesting. However, "logic" isn't any better. Making logic bedrock leads to the explorations of modal logic and essentially, theology, that common-sense people hate. All the new atheists are more in the empiricism, bordering on relativism camp than camp logic. That's why you can never find a decent debate between an atheist today and a Christian (with the exception of Sean Carroll, who to PG's horror accepts many worlds), because atheists today have no interest in logic as a formal discipline. That's where Christian debaters want to begin, because it validates theology at least so as an exploratory means, where atheists want the quick kill, and get right to physical evidence and dismiss the case with prejudice.

[Physics Guy]

I didn't know that Carroll has really endorsed the Many Worlds interpretation of quantum mechanics, but if he has then Gadianton is quite right that I'm horrified. The volume of evidence that we have accumulated so far is infinitely far short of what it would take to warrant belief in uncountably many unobservable copies of everything.

Staking so much upon quantum mechanics, in particular, seems to me to indicate a failure to understand what we know about quantum mechanics. Quantum mechanics is such a simple theory that it is easily the kind of thing that could work without actually being quite right. That it's a big part of the truth is incontestable, but that it's the whole truth isn't obvious at all. Its treatment of the important issue of measurement, especially, is crude to the point of kludge.

I've never thought before of a divide between logic and empiricism, but once you suggest it, it's obvious. The appeal of logic, after all, going back to Plato and his good ol' cave, is that you can be sure of something before you go and check it, from pure logic. When that works it makes you glad that you have a rational soul. When it doesn't, you learn.

Not having to come down on this either way is one of the things I like about theoretical physics. I can tell you what we think the answer should be. I still encourage you to check it as well as you can. And this dialog reproduces itself, almost fractally, in every detail of the design of the experiment. At every step the measurement is laden with theory, but it really is a dialog and the outcome really can be that the best understanding we have of the measurements is that they contradict theory.

The fatal words are "quick kill". Nothing worthwhile is quick.