How is formal logic applied in scientific research?

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Formal logic is essential in scientific and technological research, guiding reasoning and decision-making processes. The discussion highlights the importance of applying formal logic beyond intuitive understanding, particularly in fields like mathematics and programming where logical principles are foundational. Participants emphasize the need for practical examples of how formal logic theory is utilized in research, rather than just theoretical concepts. The conversation suggests that while intuitive logic suffices for many tasks, a deeper understanding of formal logic can enhance scientific inquiry and application. Overall, the thread seeks to explore the tangible applications of formal logic in research settings.
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I'm working on a research project on logic and would be interested in real examples of the use of the theory of formal logic for any scientific or technological research. I'm well aware that logic, to begin with our intuitive sense of logic, is necessary to just about everything we do in life and especially in the sciences and in the industry. My interest is in actual examples of the specific use of the theory rather than the mere formalism of modern logic.
Thanks.
EB
 
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Speakpigeon said:
I'm working on a research project on logic and would be interested in real examples of the use of the theory of formal logic for any scientific or technological research. I'm well aware that logic, to begin with our intuitive sense of logic, is necessary to just about everything we do in life and especially in the sciences and in the industry. My interest is in actual examples of the specific use of the theory rather than the mere formalism of modern logic.
Thanks.
EB

What about logic in programming? It's not hard for a computer to distinguish between 'or' and 'and'.

Everytime we do mathematics, we have to follow basic logic laws.
 
Math_QED said:
What about logic in programming? It's not hard for a computer to distinguish between 'or' and 'and'.

Everytime we do mathematics, we have to follow basic logic laws.

Yes, for mathematics and computers. And as I said, I'm entirely convinced we use logic all the time, competently or not, in just about everything we do. However, as you suggest here, we can go a very long way merely using our intuitive sense of logic, provided we also learn the basic vocabulary and language of logic, like "conjunction" etc. My question is about the use of the theory. How much of logic theory, beyond the basic intuitive notions and language, do scientists, among others, need for their fundamental or applied research work, in practical terms?
EB
 
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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