Good afternoon, gentlemen and ladies. Welcome to Phil 201: Formal Logic. I am your instructor, Dr -------. I am afraid I am somewhat unqualified to be a philosopher as I actually did my grad work in theoretical computing, so I hope you will forgive me if I trip over my tongue once or twice.
When you use the word "logic" you may be thinking of a some kind of pattern of thought. For example, you might say "deductive logic" to describe the actions of a detective like Sherlocke Holmes, or "inductive logic" to describe the experimentation of a scientist like Charles Darwin. Formal logic isn't either of those things. Formal logic is an application of a certain kind of
language.
Now, as I use it (and I use it like a computer scientist does, sadly) the word "language" means "set of strings over some alphabet", and an "alphabet" is a "set of distinct characters whose size is finite but at least two". The language we will use in this course is called "the predicate calculus", and it really only came into its own in the late nineteenth and early-to-middle twentieth centuries. Before that time, the languages people used for logic were not as fully developed, as we shall see when we get to the idea of Goedel numbers.
What really distinguishes the predicate calculus from other languages used for logic (and yes, that includes natural languages like English or Greek) is that it is both unambiguous in its semantics and capable of being used to describe how to use itself. Now, many of you are English majors, and you are in this course because you have to take a Phil option; you should know well that English grammars and dictionaries are usually written in English. English, thus, is a tool sufficient for describing how to use the English language. Unfortunately, as those grammars and dictionaries go to show, English is a very flexible and ambiguous tool.
By contrast, consider the language L, which is the set of all strings all of whose characters are drawn from the characters "A", "E", "I", "O", "U", and the space character. This particular language is thoroughly described, but as the rules for constructing strings over that language are too easy to satisfy, the language L cannot be used to describe itself.
... and she drones on, accompanied by the gentle snoring of her students, until one particularly intelligent student stands up and asks ...
IcyMonkey wrote:
I'd actually like someone else to explain to me more thoroughly the logistics of a system describing itself, since I'm having an ongoing argument with MiB about this via AIM and he still maintains that any attempt to delimit the boundaries of logic via logic is inconsistent since "you can't disprove logic with logic".
Well, I did mention Goedel-numbering of statements in the calculus. I don't want to talk too much about that so early, but what it is in essence is translating statements in a logical language, like the propositional calculus, into a mathematical language in order to prove mathematical statements about the original logical statements and about logical statements in general.
The whole concept of "disproving logic", however, is not within the scope of the course. We will show that logic, or rather the propositional calculus, is
consistent -- but that doesn't mean it is "provable" or "disprovable". By requiring the use of the propositional calculus to express logical statements, we will show that we can come to certain valid conclusions mechanically. That is
all.Another student stands up and asks an interesting question:Talauna wrote:
Time distours logic! So how do we know if the current set of logic is even correct to what we see a few days or even years from now?
Time has no effect at all on logic, as we are using it here. Formal logic is a
game with symbols -- not a method for describing what we see in the world. However, if you are interested, there are extensions to the predicate calculus that deal with dynamic states; to learn about those, you should take Phil 301, Dynamic Formal Logic. You're lucky -- I don't teach that course. Professor ------- is its instructor, and he's really smart.