First of all, what is referred to as ‘logic’ in college is not really logic. So-called ‘logic’ classes are concerned with fragments of specific systems of logic, not a single one of which, with the exception of Boolean algebra, has proven to be of either practical or theoretical significance. A system of logic is a set of rules that, when given two statements belonging to some class of statements, says whether or not one of those statements is a consequence of the other.
Any given system of logic is defined only for some specific class of statements. Consequently, such a system is devoid of any significance unless two conditions are satisfied:
(i) When given two members of that class, that system must make it easier than it would otherwise be to determine whether one of them follows from the other.
(ii) There must be important information about the world that is difficult or impossible to know unless it is known, for any two statements belonging to that class, whether one of them follows from the other.
If a given system of logic doesn’t satisfy condition (i), then using it will actually slow down the process of acquiring the information that it can generate; and if it doesn’t satisfy condition (ii), then it is irrelevant how much it expedites the process the process of acquiring that information.
With the exception of Boolean algebra, every existing system of formal logic has utterly failed to satisfy both (i) and (ii). This is easily verified. Pick any two statements; let S1 and S2 be those statements. Then pick any existing system of logic (apart from Boolean algebra); let L be that system of logic. Question: If you want to know whether S1 follows from S2, or vice versa, does L make it easier or harder for you to figure that out? If you find that it is harder to figure out how to use L to answer this question than it is to answer it ad hoc, then L is totally useless, at least in that context. Further, if you find that L is useful at answering that question only when it isn’t worth knowing whether one of those statements follows from the other, then L is, once again, totally useless, in that context and every other.
The rules making up the logical systems that you learn about in college can seldom be applied to a given pair of statements unless those statements are first wrenched into some completely artificial form, and it usually isn’t possible to wrench into the right form unless their logical interrelations are already known.
Dust off your copy of ‘The Power of Logic’ or ‘Tarski’s World’, or whatever textbook you use, and you’ll find that, given two statements, that system is unlikely to be defined for them and that, in the unlikely even that it is defined for them, it is difficult to know how to use that system to determine whether one of them follows from the other unless you already have that information.
In a word, these systems cannot be used unless you already know what you are suppose to learn from them, and these systems are therefore the purest conceivable embodiments of scientific failure.
The authors of these books try to cloak this fact by wittering on about how you’re ‘learning to think rigorously and carefully.’ But this is pure spin. Their system isn’t delivering the goods, and their moonshine about it being about the journey, as opposed to the (non-existent) destination, is just that.
So why do you have to study it? Because otherwise these bureaucrats would be out of job.