I want to know if the structures of logical arguments changes by logicians over time (like scientific theories might change in light of new evidence)? I also wanted to know if there might also occur changes in existing logical fallacies (other than adding more fallacies to the list) and will it ever happen that the things that are now listed among logical fallacies might become a valid way to reason (I don't think so)?

Logicians have developed many different theories of how logical arguments work, and the theories have plainly changed over time. Nevertheless, many standard examples of argumentation that logicians have long regarded as valid have been remarkably stable throughout history. As a result, what has changed is not so much the underlying reasoning that logicians have sought to capture as the ways in which they have tried to capture it. Specifically, when logicians think about deduction, they seek to capture the form of arguments, but logical form can be represented in different ways. For example, Aristotle sought to capture the reasoning behind classification--meaning arguments in which one predicate includes or excludes another predicate (or the ways in which one class includes or excludes another class). This became his theory of the syllogism. About a century later, by contrast, other logicians sought to capture the ways in which the truth or falsity of whole propositions could entail the truth or...

Are the laws of logic invented or are they independent of human reason? If they are independent, how can they exist immaterially? What does it mean for such laws to exist in a nonphysical way?

The human brain is a physical object, and many people think that logical relationships are the way they are only because our brains happen to work in a particular manner. But there’s a problem with this theory: Our brains work properly in the first place only because they recognize logical relationships—if they didn’t, we would reason incorrectly and would harvest at the wrong times, or drive in the wrong direction, or fail in our efforts to operate a computer. In that case, however, our brains’ mechanisms can’t define what counts as logic. Instead, logic helps to define what counts as a functioning brain. Since we survive only by making logically correct inferences, a correct sense of logical relationships is already part of what constitutes a viable brain, and thus it is the demands of logic, over the course of human evolution, that have shaped the physical structure of the brain, not the other way around. Another common theory is that logical relations are the way they are only in virtue of the rules...

What is the difference between "either A is true or A is false" and "either A is true or ~A is true?" I have an intuitive sense that they are two very different statements but I am having a hard time putting why they are different into words. Thank you.

Perhaps I could add something here too—and perhaps it will be useful: You are right that there is a difference between the two statements that you offer, and the difference has become more significant with the rise of many-valued logics in the 20th and 21st centuries. If one says, “A is either true or false,” then there are only two possible values that A can have—true or false. But if one says, “either A or not-A is true,” then there might be all sorts of values that A could have: true, false, indeterminate, probably true, slightly true, kind of true, true in Euclidean but not Riemannian geometry, and so on. The first formulation allows only one alternative to “true” (namely, “false”), but the second formulation allows many alternatives. The second formulation does indeed require that at least A or not-A be true, but it puts no further restrictions on what other values might substitute for “true.” (For example, perhaps A is true, and yet not-A is merely indeterminate.) The advantage of sticking to...

For the philosophically unsophisticated, why is it significant that logic cannot be reduced to mathematics? What difference would it have made if that project had succeeded; what is import that it failed?

Your ability to balance your checkbook, or to draw logical inferences in everyday life, won’t be affected in the least by difficulties in figuring out just how logic and higher mathematics are connected. Nevertheless, the relationship between logic and mathematics has been an intriguing conundrum for the better part of two centuries. There have been many attempts to understand various aspects of logic mathematically, and perhaps the most famous is George Boole’s Mathematical Analysis of Logic (1847), which laid the foundation for Boolean algebra. Far from being a failure, Boole’s effort seems to have been a smashing success, especially when we consider the extent to which Boolean algebra underlies modern digital computing. Nevertheless, the relationship between logic and mathematics can go in two directions, not just one, and so, just as one might try to understand various parts of logic mathematically, one can also try to understand various parts of mathematics logically. It is this further...