Part 1 – Why The Magic Of Logic Can Save Your Ass In The Eternal Battle With Evil
Humans are dumb. Not only do we spend inordinate amounts of time arguing about nothing. But in most of our arguments we are talking right past each other.
- You are saying one thing
- I think you are saying another
… and vice versa, on and on and on…
This inevitably leads to us getting all emotional and shit for no reason, whatsoever. We know this and yet we keep doing it! No wonder Americans get married for the wrong reasons, divorced inevitably, go to war incessantly, and hate each other more than anyone else on earth.
Things are not getting better: Our kids are rude morons and our adults are whatever rude morons grow up to be.
How do we end an endless cycle of habble-babble? Answer: We need to learn how to talk again. Only this time we aren’t going to use English (nor any other natural language). We are going to construct a fancy-pansy language that is clear as crystal.(1)
Enter the Propositional Calculus: Da’Prop.(2)
Today’s post is the first of 4 on this subject. We’ll learn the basic symbols and some other terminology. IN the next 3, we’ll learn the 9 laws (3 laws per) that will make up our brand of Da’Prop.(3)
Our system is built upon the simplest of foundations: Just four “words”:
- “If … then ____”
With these, we can do some real damage, baby!
What The Hell Is The Propositional Calculus?
A Propositional Calculus(4) is a systematic way of studying the logical implications of combinations of complex propositions (sentences). In other words, arguing! But without the lack of clarity that natural languages force us into.
It will be the foundation of all of the mathematics we will use from now on. I didn’t use that picture of Lon (one of our lifters at Asheville strength ) for nothing. The Propositional Calculus is the like the Roman Centurion of Math! It sets the bar for the rigorous training to follow. It’s also damned cool, and looks good in a bronze skirt.(5)
A Reminder About Natural Languages
For all of their beauty, the natural languages are mighty ambiguous (thus, the beauty!). So if we ever hope to get along, we are going to need to strip our special arguing language bare to the bone. So bare, in fact, that the symbols we are going to use are going to be utterly meaningless, in-themselves. This total lack of inherent meaning is where the power will come from.
While this idea must certainly sound odd to you – deriving power from a stripping away of meaning – remember that this is precisely how one finds power through meditation or in learning the Olympic lifts.
First, you must unlearn everything you have learned. Beginners mind. Today was the first day of your life. You know nothing. You are nothing. Only then can you begin to truly learn and find your true power.
The Symbols Of The Propositional Calculus
Below are primary Symbols we will be using in our new formal language.
- = “and”(6)
- = “or”
- = “not” (basic negation)
- = “implies”, that is “If… then ____”
What goes in front and after each of these we’ll call an Atom, which is simply a letter (like ) or a symbol (like ) – that is, the “content” of your sentences(7). For instance we can now write the string (sentence):
Which means, “If P and Q are true, then Z is true”.
I don’t have the faintest idea what that means beyond what it says. In other words, it’s like poetry. Pretty sounding, but utterly devoid of meaning!
Along with the above, we’ll need some groupers, ways to organize things.
- … = do the logic inside these before moving on to the outside. You remember these from Algebra, no doubt!
- … = the Wardrobe Brackets. I’ll explain why they are mysteriously called that in part 3 – feel the excitement! (It really does have to do with magic and the book you are thinking of.)
In the next episode of this series we will discover The Relationship Laws of Da’Prop:
- The Law of Marriage
- The Law of Divorce
- The Law of Nothingness
Now go lift something heavy,
- well… close enough. We’ll see what Godel had to say about that in time, don’t you worry. The math-life is never more than a step away from chaos! [↩]
- to be clear, there is more than just one, so calling it THE Propositional Calculus is more than a little misleading. [↩]
- we will be standing on the shoulders of the giant Douglas R. Hoftstadter. I have altered some of his terminology in order to make it more relevant for us, but I’ll make references to his terminology wherever possible. Given his stance (that I agree with) that the human brain is an analogy-machine, and given that mathematics is nothing but a giant analogy/metaphor system, and given that he has always taught via massive analogy, I suspect he’d be tickled by that mode of reasoning/teaching being brought into the world of we weightlifters. [↩]
- sometimes called a Sentential Calculus or Propositional Logic. [↩]
- That last bit may be up for debate. [↩]
- In most books on logic, they will use the symbol for (and). That is fine, if you goal is to be logician, mathematician, or get deep into this stuff. But it is also frequently confusing from a visual point of view. I grew up a bit dislexic, and my eyeballs are still out to get me. I find that a and a are mighty similar looking, and yet they are meant to be near opposites! CONFUSING, to say the least. So I am going to use the ever-familar symbol, which also has the added benefit of making us feel smarter and more fancy. [↩]
- we might call them variables, but I want to be careful with that terminology for now. [↩]