Any real examples of formal logic necessary for solving scientific problems?

Discussion in 'Physics & Math' started by Speakpigeon, May 8, 2018.

1. SpeakpigeonRegistered Senior Member

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You may have noticed I made a crucial distinction, though. One that's relevant to what you say here. Between our intuitive sense of logic and formal logic in general. My personal interest is in our intuitive sense of logic. I'm working on that.

My OP question, however, is not about that. It's about formal logic and it's possibly necessary role in at least some scientific discoveries.

Yes, I understand that.

I did it twice already in my life. I know it can work! Yet, I still have no idea how I did it except that I did spend a lot of time thinking about the original issue... Well, sure, I would have guessed as much.

And I will guess you're not much more advanced in understanding how it works.

I like very much your horse-&-cart metaphor. Me, being French, I call that unmetaphorically changing the conceptual framework. And, yes, either way, you have to go out on a limb and start with seemingly very crazy ideas. And find the missing bit if at all possible. And reassemble whatever you got, into something really beautiful and shiny.

Still, that wasn't te purpose of my OP. My question here is about formal logic and it's possibly necessary role in at least some scientific discoveries.

Sounds a much less conceptual and much more empirical issue, I would say.

Let's not bother that horse yet.

Sure, but let's stick to the OP here.

I'm looking for evidence of the necessary and non-trivial role of formal logic in at least some scientific discoveries. Do you have any?

Me to,
EB

Last edited: May 17, 2018

3. SpeakpigeonRegistered Senior Member

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That's too bad. I'll be fooled then.

Ask me another one. My brain couldn't refrain from fishing out an old and nearly forgotten geometrical proof I saw when I was much younger.

Still, I think you're missing the point here. I'm not looking for somebody to convince me I'm wrong. I'm looking for evidence I'm wrong. If you can't produce the evidence I'm asking for, that's just too bad.

All you've produced so far is a link to an experienced scientist saying explicitly the logic he used for the Bell's Theorem was child play. Either he's an idiot and you're an idiot for posting the link, or he's smart and then I don't see how that fits with what you seem to be saying.

And whatever you could come up with as far as arguments are concerned would be beside the point. I'm asking for evidence of the actual use of formal logic in science. Haven't seen any such for now.

I can wait, though. Whenever you have the time.

That all sounds like circumstantial evidence to me. Not quite irrelevant but this judge just decided it wasn't going to be enough. Can you come up with actual material evidence?
EB

5. arfa branecall me arfValued Senior Member

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It isn't "used exactly". All physics is based on explaining observations.

Ask yourself a question like: how do I explain the observation that a compass needle moves? Or, how do I explain that I can use a voltmeter to measure voltages in some electronic circuit? Or explain why water flows downhill? Anything physical can be explained without having to invoke logic which is entirely formal--approximate logic does the job well enough.

The explanations are generally approximate. Using formal logic to formulate an explanation is quite possibly not really necessary. Despite Bell's theorem, all quantum experiments have only statistical results--in a sense, all the logic pertaining to physics is about statistics, sampling and so on. "Exact" statistics is a non-sequitur.

7. SpeakpigeonRegistered Senior Member

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I thought theoretical physics at least was the development of " mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena", and that "in some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations".

That's what I suspected as to most of physics but I had a doubt concerning the more theoretical things like Relativity and String Theory.

OK but what about theoretical physics and things like String Theory?
EB

8. arfa branecall me arfValued Senior Member

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Theoretical physics isn't useful unless the theories explain observed facts. A theory (anyone can put one together, but to rock and roll, so to say, it has to endure a lot of skepticism), that breaks the "laws" of physics, especially the 2nd law of thermodynamics, it isn't a good theory.

String Theory hasn't so far, been much of a revolution in theoretical physics. Which is not to say it isn't a good theory.

9. iceauraValued Senior Member

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28,768
And as pointed out for you, it's necessary in all scientific areas in which intuitive logic is central, to audit and correct and at times inspire intuitive logical reasoning. That's one of its roles - it has others, as Bell's Theorem demonstrates, but that one alone is sufficient to answer the OP.
- - -
There are others:
The task was to come up with one on your own, not remember one handed you by others.
The intent was to illustrate for you the dubious nature of your dismissal of the kinds of formal logic central to scientific endeavor as somehow too simple or basic to count. You regarded the description of the proof of Bell's Theorem ("fun with numbers") as a dismissal of its central importance, for some reason.
You insist on ignoring or dismissing the evidence provided. The computers, the stats, the ubiquitous presence of formal logical reasoning in designing and evaluating research, are all somehow not "evidence".
Computers run on formal logic. Seriously. Anything done by a scientist using a computer employed formal logic, by necessity at times. Is that not evidence for the OP question?

Last edited: May 18, 2018
10. SpeakpigeonRegistered Senior Member

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To repeat myself, the link you provided doesn't include any formal logic.

You're obviously mixing up different things here.

First, I'm in fact absolutely convinced of the crucial role of logic in the whole of science, including physics. That's for logic. And I didn't ask about that.

I'm not a scientist so I don't know about the precise role of formal logic in science. Formal logic. That's what I'm asking about.

If I understand you, you seem to suggest now that physicists have to use formal logic but that they don't use or produce any formal proofs.

If that's so, then too bad but that's it. I'll have to accept that physicists may use formal logic but that I won't have any material evidence of that.

I haven't dismissed anything, on the contrary. I took the link you provided at face value:
Again, I'm interested in the use of formal logic. There's none and no evidence of it in the link you yourself provided. Logic, yes, formal logic, no.

Possibly, but that's for computer specialists to say. I was asking scientists what scientists themselves do. If you have evidence of the kind of formal proofs used in the computer sciences, I would be very interested but it's for you to produce it.

So, for now, logic, yes, I'm sure it's necessary in everything we do including physics. Formal logic, perhaps, but I'm waiting to see the evidence. I don't say it doesn't exist, only that I haven't seen it yet. And I would in fact very much welcome it. That's what I'm asking in the OP.
EB

Last edited: May 18, 2018
11. Beer w/StrawTranscendental Ignorance!Valued Senior Member

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4,756
I drew a large bath once, hopped in, the water overflowed.

So, got up, ran the street naked yelling "Eureka!"

No wait, maybe was a dream. Or, even someone else? Is that formal logic, anyway?

12. arfa branecall me arfValued Senior Member

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Lots of theoretical and experimental physicist use computers, but most of them wouldn't write operating systems, or even much of their own software, instead using off-the-shelf products.

What though, constitutes a successful "use" of a computer, by a scientist? How do they know if they've given the simulation enough input? Generally the input won't be a faithful description of the system in question, it will be approximate.

13. iceauraValued Senior Member

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28,768
Of course - the request was for an example of scientists using, not inventing, formal logic.
To repeat myself, yes they do. The link to the proof of Bell's Theorem was explicit - even the old-fashioned notation was laid out for you.
Meanwhile: Computers run on formal logic.That was another example.
The others also apply, not as brazenly but just as obviously.
I asked above whether your interest was in notation, rather than formal logic itself (that's partly why I linked you to an alternative notation, which is sometimes used by electrical engineers and programmers dealing with recursion)
Exactly. Although Bell did, and so do all the other proofs of Bell's Theorem, the more common employment is as a tool rather than a research subject itself. They use already proved theorems, usually.
It's an obvious and indisputable fact - computers run on formal logic. Look at them.
Logical proofs, proofs of theorems in formal logic, are no more part of using formal logic than mathematical proofs are part of using mathematics. Do you agree that scientists use mathematics?
Meanwhile, the formal logical operations "And", "Not And", "Or" and the like are built into the very hardware of a modern computer. https://en.wikipedia.org/wiki/NAND_gate .

Last edited: May 19, 2018
14. SpeakpigeonRegistered Senior Member

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904
To me it's an example of scientists using computers, not formal logic. If I followed your logic, I would have to agree that I use Quantum Mechanics when I scratch my nose. I think you're being just a little bit too literal here.

Still, I would certainly assume that theoretical computer scientists have to use formal logic in at least some of their work but I don't actually know if the specific kinds of computers and software concerned are those scientists need for things like String Theory or Quantum Mechanics. Have you a view on that?

Also, I'm sure some formal logic can always be used. The question is however whether that's really necessary. I asked "How much is formal logic necessary", meaning I'm specifically interested in the level of complexity of the formal logic required. And I don't know yet whether that's indeed "seriously complex" or not, although I do have indications that it may become or even already is indeed very complex. Though no evidence as of now.

I will assume you're referring to the bit called "proving Bell's Inequality". So, alright, you win, we can see that as using formal logic, but although it's not exactly obvious or trivial it's not terribly difficult to understand either. I'm would assume any bright scientist could get to see it's true without necessarily resorting to pen and paper. I see formal logic in this case as a convenience, not a necessity. Although, I accept it's a matter of appreciation.

It just happened a few months ago that my brain told me one particular logical formula I was considering was a logical law (tautology). I couldn't on the moment explain why that should be. I had to look at it in details, and use pen and paper, to make sure it was true. This took me several days. I can see now why it is true and that it's not so terribly difficult to understand but it's not trivial. I would say the level of complexity was broadly on a par with Bell's inequality, perhaps more complex but less complicated.

I certainly see complication as making pen and paper necessary, but in a trivial way, just like you have to use pen and paper for a long addition. For complexity, I'm not sure where the break-up point is and whether the break-up point is at all reached in the sciences or in any other activity with a practical purpose.

So, yes, formal logic if you like, but really necessary?

Now you're just contradicting yourself here. If, as you claimed several times, using computers that required formal logic is to use formal logic, then using formal logic that required logical proof is to use logical proof. No?

I think that's why I asked "how much", i.e. to what extent. I wouldn't expect scientists to go into logical proof. The question was as to how much explicit formal proof they really need to use.

Now, I have to accept that my question could have been framed better and more carefully. Sorry for that.

Still, I guess I have the answer now, anyway. So thanks for the links, this should really help.
EB

15. iceauraValued Senior Member

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28,768
No one can use a computer without using formal logic. That is what a computer does.
No, the question was how much or how often or how significantly scientists and science need and use formal logic, and the request was for examples.
Nobody knows whether science can be done without employing formal logic. It never has been.
Complexity is a completely different matter. You appear to be once again underestimating the difficulty of employing formal logic - it's quite difficult to employ even the simple stuff.
You are confusing following an argument with making one. The formal proof was absolutely necessary in making that argument, and in interpreting the results of experiment. That is rare; scientists normally use already proved, standard, tool kit, theorems - many so familiar they are simply assumed.
?
I'm not sure what happened to your train of thought, there, but you asked for examples of scientific employment of formal logic and I provided three to six (depending on how you count) significant ones. Only one required the scientist to prove a theorem in formal logic - the most common, use of a computer, does not even require a basic knowledge of formal logic. A rote task has been mechanized.

16. SpeakpigeonRegistered Senior Member

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904
Iceaura, I think I've said whatever I could possibly say. There would be no point repeating ourselves.
Next time I'll try to be more careful in framing my question, but then again, if the issue had been entirely clear to me I wouldn't have needed the ask the question to begin with.
EB

17. arfa branecall me arfValued Senior Member

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6,234
Suppose the scientific problem depends on some computer program for a solution.
Is there a way to check that a given program will run successfully (i.e. won't halt with an error)?

Yes, there is! It involves the use of formal logic techniques (it's called Hoare Logic, q.v.). The underlying lattice is a Boolean lattice of abstract points, a successful program is a path through these points. Hence "success" is just a point in a lattice of Boolean logic.

But of course, this is only possible if you constrain the inputs to a finite set, for one. You also have to prove that loops iterate correctly, or more generally, given a code-section (which might contain loops), you can define pre- and post-conditions that have to be true before and after the code-section runs.

Although, this kind of logic (proof of correctness) is usually used in critical systems design (say, aviation computers, or medical equipment), those problem domains certainly are scientific, being physical and all.

18. SpeakpigeonRegistered Senior Member

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904
Yes, I worked in the mass transit industry where because of specific technical safety concerns they had at the time they had to use what's called in French "automates à états finis", or finite states automata, which seems to be exactly what you are talking about. I would see that as an engineering methodology but I don't actually know how exactly it came about and how formal and rigorous are the foundations of that.

My real concern is as to how useful it could be to have a logic method in full agreement with our intuitive sense of logic. I guess like most people, it seems to me that the reach of our logical intuitions is limited to situations we can reduce to rather simple mental abstractions. As I see it, our use of formal logic is meant to extend the reach of our intuitions by allowing us the analyse a problem into a chain of basic steps, basic steps that are so small we can solve them intuitively.

We already have and use a large number of very different methodologies, whether or not they include the use of computers. I assume that all these methodologies incorporate the basic assumptions made for First Order logic (except, possibly, for non-classical logic methods, if at all used). My problem is that I still haven't found any proper justification that any of these methods is consistent with our sense of logic. That in fact never seems to even register as an issue!

It may well be that our sense of logic somehow makes up for our methodological shortcomings, but I suspect not.

Whatever the case may be in this respect, I was looking with my question to get a sense of the potential importance of the problem and how useful it could be to have a method that would really be consistent with our sense of logic.

What I take out of all the answers I got here and elsewhere is that our practice is a hodgepodge of formal and intuitive bits no one could possibly justify. The most extended formal practice seems to be the automated logical proofing applied on an experimental basic to what seem to me to be very theoretical mathematical problems, such as the Formal Proof of the Cantor-Bernstein-Schroeder Theorem, whose usefulness escapes me, except as a case study, i.e. fundamental research.

I also take the very difficulty of obtaining any straightforward answer to my question, here and elsewhere, as rather suggestive of both the extent and murkiness of the problem. Although, I'm sure plenty of able practitioners are hard at work trying to come up with the goods! Meanwhile, I'm not really advanced in my search for a straightforward answer. Thanks anyway to those who tried.
EB

19. iceauraValued Senior Member

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28,768
In the more common event, our intuitive sense of rightness or fitness leads us to something we can define or describe carefully, and to check our possibility we break it down into a chain of basic steps so small and simple that we can establish or even verify them by formal logic.

The basic situation being that we differ in intuition, but we have the logic in common.
And also that having so good a handle on a question that we can break it down into small formal logical steps implies a solid intuitive grasp.

20. Confused2Registered Senior Member

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516
There's an old logic logic problem about which person has a cat etc - here called the Notable Neighbours problem.
http://www.oocities.org/heartland/plains/4484/lp9702.htm
Do you regard that as a problem (normally) solved by formal logic?
It can (obviously) be solved by trying possibilities until no contradictions are found - I suspect that might well be what is going on when working out where the horse ought to go (in relation to the cart).

Once a model becomes predictive - eg the Standard Model (Higgs) and Special Relativity (time dilation) - would the predictive stage fit your idea of applied 'formal logic'? If A and B are true then C must also be true. Isn't any test of any theory the result of the application of formal logic?

21. SpeakpigeonRegistered Senior Member

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904
I'm not sure who you expect should answer that.

Also, there's already an OP. Do you have something to say about it?

If not, well, your questions are great, so I guess you might just as well start a thread on that.
EB

22. arfa branecall me arfValued Senior Member

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6,234
Our "sense of logic" isn't necessarily useful, though. I mean, what is it?

Is it the sense that Schrodinger, Bohr, Einstein et al. had when they were trying to formulate Quantum Mechanics? If it was, it turned out to be pretty much useless, indeed "common sense" is useless in QM. You pretty much have to abandon ideas about what "should happen", even the idea of "happen" isn't really that useful, except to our, hmm, sense of logic (!), causality and so on.

23. RandwolfIgnorance killed the catValued Senior Member

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4,172
Perhaps something like this?

Using formal logic in biology
October 10, 2012 Carson Chow Biology, Medicine

The 2012 Nobel Prize in physiology or medicine went to John Gurdon and Shinya Yamanaka for turning mature cells into stem cells. Yamanaka shook the world just six years ago in a Cell paper (it can be obtained here) that showed how to reprogram adult fibroblast cells into pluripotent stem cells (iPS cells) by simply inducing four genes – Oct3/4, Sox2, c-Myc, and Klf4. Although he may not frame it this way, Yamanaka arrived at these four genes by applying a simple theorem of formal logic, which is that a set of AND conditions is equivalent to negations of OR conditions. For example, the statement A AND B is True is the same as Not A OR Not B is False. In formal logic notation you would write

.
The problem then is given that we have about 20,000 genes, what subset of them will turn an adult cell into an embryonic-like stem cell. Yamanaka first chose 24 genes that are known to be expressed in stem cells and inserted them into an adult cell. He found that this made the cell pluripotent. He then wanted to find a smaller subset that would do the same. This is where knowing a little formal logic goes a long way. There are