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

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

1. ### SpeakpigeonValued Senior Member

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How exactly is logic used for solving scientific questions?

How much is formal logic necessary for solving scientific problems?

As I see it, most of us have an intuitive sense of logic, and this has to be very useful throughout our lives and just about for every situation we can think of, including scientific activities. Given that, I came to wonder what more does formal logic specifically brings to the table compared to our intuitive sense of logic and beyond the convenience of the formalism that come with it?

Having a formal language to express the more complicated logical relations is obviously very useful, even necessary nowadays with the development of technology and science. But beyond the mere convenience of formal logic as a language, I am interested in the necessity of using formal logic in the sciences.

So, could anybody give real examples where using formal logic was effectively necessary for solving a scientific problem?

I'm really mostly interested in First Order Logic, but Second Order examples should also be of interest to me.

Thanks,

EB

3. ### Beer w/StrawTranscendental Ignorance!Valued Senior Member

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There's math, there's reproducible experiment, and there's data that can make future predictions (climate change).

Not all sciences are so closely affiliated to math as physics uses.

5. ### iceauraValued Senior Member

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It's used for checking one's answers, and focusing one's doubt when the answers are wrong.

And it's all but indispensable in that role, especially in areas (such as probability and statistics) that human intuition handles with difficulty if at all.

A clear and well-understood example currently active would be the derivation, proof, and implications, of Bell's Theorem.

Last edited: May 16, 2018

7. ### SpeakpigeonValued Senior Member

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Thanks!
Can you give a literal example of the reasoning (logical formulae?) involved?
I would need to get a clear sense of the level of complexity of the kind of logic required.
Essentially, I'm not sure that the situation isn't somewhat like having a long addition to tot up. If the result is important to you, you will use pen and paper rather than do it in your head, even though that would be possible to do given that additions are fairly simple in their principle.
So, isn't the logic involved even when working on Bell's Theorem just a long chain of implications?
Something like ∀x/F(x) → G(x) and ∀y/G(y) → H(y) and ∀z/H(z) → K(z) ...
EB

8. ### exchemistValued Senior Member

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I don't think formal logic, apart from that obviously embedded in mathematics, is used much at all in science, because science does not generally involve logical proof. There are some mathematical theorems with physical significance, such as Bell's theorem, the Jahn-Teller theorem, etc, but the validity of these depends on the assumptions of the model on which they are based, and these assumptions are not provable. A lot of scientific advance proceeds by induction rather than deduction, but there are no real rules. All one needs is a testable hypothesis about nature and reproducible observations to test it. Which comes first is unimportant.

Last edited: May 16, 2018
9. ### iceauraValued Senior Member

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It's usually basic stuff. It can get fancy if a complicated chain of reasoning has gone south, but in my reading and experience this is a standard level: https://faraday.physics.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html
Don't underestimate a long chain of implications.
The question of where to concentrate one's doubts when things have - as they normally have - gone wrong somehow, is often one of basic logic: what are the assumptions of your argument.
The questions of whether or not you have tested your hypothesis, whether or not those other observations are reproductions, and so forth, are answered via basic logic.
The current debate surrounding the .05 p-value criterion involves logical formalities, for example.

10. ### SpeakpigeonValued Senior Member

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And here's a quote from the link. It's the one assumption about logic they think they used:
I guess it says it all.
Thanks.

Still, I would assume things like the String Theory to be somewhat more loaded with logical considerations... Any view on that?
EB

11. ### iceauraValued Senior Member

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The one assumption he used about logic is that logic
(of the kind employed, the T/F/Meaningless excluded middle stuff normally referred to by the term "logic", and my assumption of what you are referring to as well)
is a valid way to reason. That is not a trivial assumption, as he demonstrates.

Otherwise, note that in these matters what looks simple in hindsight has often been - historically - a nut too tough for dozens of geniuses over decades or even centuries of effort to crack. This is a general fact and common observation.

Yeah, it looks easy: try it.

12. ### exchemistValued Senior Member

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Of course, but this is nearly all just common sense stuff to find where you have made an error. This is not, I suggest, what he means by "formal" logic.

13. ### iceauraValued Senior Member

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Again: people who can do that well are not easy to find. "Common sense" at that level is not common.
I am not convinced he has a clear conception of what he means by having formal logic be a necessity in the doing of science, or it being employed in science. For example, any scientific effort involving a digital computer using the common software of our time is making extensive and elaborate use of formal logic - that's fairly obvious, no? - but I don't think that's what he's talking about.

14. ### exchemistValued Senior Member

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He is presumably talking about something like the example he gave:

"Something like ∀x/F(x) → G(x) and ∀y/G(y) → H(y) and ∀z/H(z) → K(z) ..."

I have never seen anything like that used anywhere in science.

15. ### iceauraValued Senior Member

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There's a pile of it buried in the software of the computer you're using now. Different notation, all 1s and 0s - is that the critical factor, the notation?

The reasoning involved in planning, designing, and analyzing, interpreting, research is of that kind quite often. Again, is the notation/nomenclature the central matter of interest?

Would this count: https://en.wikipedia.org/wiki/Laws_of_Form ?

Last edited: May 16, 2018
16. ### exchemistValued Senior Member

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Our poster is not asking what makes our computers work. He is asking about the tools used in the process of doing science.

17. ### SpeakpigeonValued Senior Member

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I made a clear distinction in the OP between our sense of logic and the kind of formal logic the mathematicians of logic are working on, for example ZFC. I'm not at all worried about our sense of logic, understood literally as a "sense", but I think that to the extent that formal logic would play an actual role in mathematics and science, scientists should worry about it, and by implication mathematicians too.

Now, what you say and the link you provided suggest to me formal logic doesn't play any role at all in science. Only our sense of logic certainly does.

So, yes, assuming our sense of logic works is no trivial assumption but it just happens I'm not worried about it.

I also read the bit about their consideration of the possibility that logic be "invalid". That would be my worry too if they used formal logic to any substantial extent but that doesn't seem to be the case.

Sorry I'm not going to pretend to be able to clarify the issue of the particle-wave duality although it may help to say that I don't believe it is a logical issue and that I would assume instead it's a conceptual framework issue. Just change the one that's used. I've always thought it's crap.

I'm sure the science of it would be beyond me if I ever tried it. I'm only interested in looking into the possibility of straightening up formal logic if it was of any real, practical application.

It seems not.
EB

18. ### SpeakpigeonValued Senior Member

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I sort of covered the computer angle with the word "technology" in the OP. I assume that the same problem as in science could affect the technology of computers, with respect to both software and hardware.

So, yes, I understand there's logic involved and the same question applies as in science, i.e. how much formal logic v. our sense of logic. And I would assume each kind of activity may have its own idiosyncrasies in this respect.
EB

19. ### iceauraValued Senior Member

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That's one of them. Computers run on formal logic.
Mechanizing the employment of formal logic in science was a great advance - the critical roles played by formal logic have no more striking illustration.
All of the advances in quantum physics involving "entanglement", that you hear about on the news, derive from and rest on that formal logic you found in that link.
Formal logic is among the primary means of auditing research and assessing claims. Science, critically, incorporates accountability.

I'm beginning to suspect that you seek examples not of formal logic itself but of the particular notation involved in the standard pedagogy.

Last edited: May 16, 2018
20. ### SpeakpigeonValued Senior Member

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And the linked paged itself says that "the whole proof is an exercise in logic, at about the level of the "Fun With Numbers" puzzles one sometimes sees in newspapers and magazines".

So, sure, it's still formal logic, but it's minimally complex formal logic. To me, this compares with doing additions. Fun with numbers.

So, the logic really required seems to me to be in this case the sense of logic the scientists no doubt have, obviously expressed using some formal language. The rest seems to be just pen and paper, and being careful doing your additions.

Yes, I explicitly acknowledged in the OP the necessity of using a formal language to express the logic used. Obviously, some minimal amount of logical reasoning will be crucial. As I understand from your link, it seems this is covered by our sense of logic.

No, I couldn't care less as to the specific notation. I'm looking for evidence that doing science might in some cases require doing a bit of non-trivial, sophisticated, possibly complex, logical work. So far, it seems not.

Did I misunderstand something here?
EB

21. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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It seems you misunderstand logic and science. Other than that you are doing a 'bang up job'.

22. ### iceauraValued Senior Member

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Formal logic will often fool you. It often looks simple, trivial, in hindsight, and the pros are often self-deprecating about it.

There are dozens of proofs of the Pythagorean Theorem, say, and most of them are exercises in logical reasoning at about the level of the proofs of Bell's Theorem. Can you come up with one on your own, even after being given the result you seek to prove?

The link in post 12 may be of interest - the entire work deals with the very simple, uncomplicated, foundation of formal logic - and as the author notes, nevertheless it taxes "the whole of one's powers".

And that's why I posted the comment about how deceptively difficult it is to do something like unto what Bell did. As posted: "Try it".

There's a reason that theorem is world famous, and its proof a landmark event, and nobody had come up with it in thirty years of attention by the best and the brightest.

And the contribution of formal logic is front and center, rather than being hidden in those "chains of implications" or the invisible machinations of software; it makes a good example.

Last edited: May 17, 2018
23. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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I sort of share your (?) What ever it is about logic

I think what you might be on about is informally known as "thinking outside of the box" or a "what if it is not such and such. What if ......"

Outside the box and What if...... moments really do need a rethink about what ever is being considered.

Put the cart before the horse THEN work out how to put the horse before the cart to fit in with observations (reality) or look for reality by new methods

In the end though it must have a logical path from start to finish and confirm to physics