What advantages does being able to symbolize our arguments provide? Are there disadvantages to using the techniques of symbols associated with modus ponens and modus tollens that make the structure of our arguments more explicit and clear?
The advantage of using symbols to make an argument is that it provides a "container" in which to put all examples mentally, a big picture, rather than a series of particular instances. For example, if I say that if A=B and B=C, then A=C, I need not go through countless examples to demonstrate the truth of that statement to someone. Numbers are infinite, so a symbolic representation is of great advantage. People cannot wrap their minds around all possible examples.
On the other hand, people do need examples to see a "truth," a way of connecting with their own experiences that a symbol does not provide. The only way concepts get into our brains at all is through our five senses and a connection with what is already there. This is the disadvantage of the use of symbols, a lack of concrete examples.