👉 Mathematical "but"s, or logical connectors, are used to introduce a contradiction or counterexample in an argument, signaling that the proposed reasoning is flawed. In formal logic, a "but" typically connects two premises to show that if both are true, the conclusion cannot logically follow, thus invalidating the argument. For instance, if one argues that "All humans are mortal" and "Socrates is human," a "but" could be introduced to argue against the conclusion that "Socrates is immortal" by pointing out the contradiction between being human (and thus mortal) and being immortal. In essence, a "but" in math or logic serves to highlight inconsistencies or exceptions, challenging the validity of an argument by demonstrating that its premises cannot all be true simultaneously under the given conditions.
