With the advent of computers and the creation and adoption of so many computer programming languages, are logic symbols still valuable or are they a relic of the past?
If logic symbology remains relevant and valuable, can you give an example?
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Logic symbols are extensively used, especially in programming languages. As a random example I have been working with lately, this 2014 paper featuring a new block cipher shows this very well in appendix H:
; Linear Layer and Inverse Linear Layer: L0 movw t0, s0 ; t1:t0 = s1:s0 swap s0 swap s1 eor s0, s1 eor t0, s0 mov s1, t0 eor s0, t1
eor means 'exclusive or', so out of 7 instructions here, 3 use a logical operation. And this is not just something that happens in assembly. My Python implementation of the same cipher uses logic intensively as well.
But also think of bitmasks and other uses of logic in computing science.
Logic teaches you to think, and to reason precisely and correctly. It teaches you to recognise hidden assumptions. All this is incredibly useful in different fields - philosophy, but also science.
If you want to talk about logic versus computer science, how about computational complexity, which was basically founded by logicians?
Determining whether or not a logical formula is a tautology is the most famous problem in coNP, which is to say that it is a problem immediately relevant to the P vs. NP problem, whose resolution would win a million-dollar from the Clay Institute (as well as international fame and a place alongside Turing and Boole in the annals of logic and computer science).
Logical operations are the very starting point of circuit complexity, which is the most promising direction to seek provable big-picture results in computational complexity, and — speaking of modern computing technology — is also one of the easiest gateways to the formalism of quantum computation.
Now, if you'd rather focus on the necessity of the symbology: technically you might not need it — but would you teach algebra without arithmetic symbols? The symbology of logic is nothing more or less than an efficient notation — albeit one without which you can accomplish very little in practise except muse deeply about the square of syllogisms a la scholastic philosophers.