A Guide to Logic and Reasoning Pt. 1

A Guide to Logic and Reasoning

By: Erasmuth

          In our everyday lives we often hear the terms "logical" and "reasonable" tossed round, and to be honest, I'm starting to think they are losing their original meaning. Of course the definition for being "logical" or "reasonable" simply being in a state of using logic or reason, I'm sure we all understand that. It's the level under that though, the actual process of being logical or reasonable I think some of us are starting to forget. Of course, all it takes is one glance on the internet to see the portion of the population that completely disregards such things. So I thought I'd make up this little guide to get people's brains turning again, and brush off my own skills with a little bit of research.

What IS Logic???

          The first thing we need to cover here is the question, "What exactly IS logic, anyway?" For some reason, a small section of the population seems to think logic is somehow its own kind of religion. Whether this is due to the majority of people being in a religion themselves and project that lifestyle onto the principles of logic is an interesting question, but in the end it's another piece for another time. Logic, in and of itself, is simply a tool we use to make sense of things. Ever catch someone at a lie because of an inconsistency in their story? You used logic to deduce your conclusion. How about any time you've been in an argument where you've rendered someone's point nonsensical because of a faulty assumption, again, you used logic to pick out the bad premise. I could go on and on with a list of examples, but I think you'll understand what I mean when I say, "Logic is a tool we use to make sense of things."

The not so Almighty Logical Absolutes

          If logic was a religion, the logical absolutes are it's doctrine. Logic, however, is not a religion. Therefore there's not really any reason to be impressed when someone starts referring to them, nor are they some kind of divine truth incomprehensible to the average layman. Imagine, if you will, a circle. The inside of that circle, we will label "A" and the outside of the circle we will label "-A." You now have a working model of the logical absolutes and I haven't even told you what they are yet, It all boils down to the most basic Venn Diagram imaginable. The first logical absolute is as follows. "A=A" simple right? just three characters. All that's being said here is for any object, category, or thing "A" if something falls under that same object, category or thing, it is also "A." In the case of our Venn Diagram, if both things are on the inside of the circle. the next logical absolute is equally as simple, "A/=-A" (Read as A does not equal not A, or negative A if you prefer). In our circle analogy, this basically means whatever is on the inside of the circle, cannot be on the outside of the circle. Essentially, something cannot be what it is and what it is not at the same time. The final absolute isn't really about what is and is not in the circle, but rather, about the edge of the circle. This absolute is generally referred to as "The Law of the Excluded Middle" and while it may sound scary to some, all it merely states is something along the lines of, "Everything can be valued as true or false with no middle ground." In the case of our Venn diagram, the edge of the circle looks the same size no matter how close or far away you see it from. There is no neutral ground, only a single, infinitely thin border.

The Caveat

          There is one small problem with the absolutes, however, like any tool they must be used properly and with care. As an example, pretend I hand you two yo-yos that are perfectly identical, literally no way to tell them apart. Then, after I show them to you and let you mess with them for a while, I tell you, "These yo-yos are the same object." Well, they are perfectly identical, so of course they are the same item... or are they? After all, no object we know of can occupy more than one set of coordinates in space so therefore they must be two different objects that just look identical. As you can see, this statement can be evaluated as true or false depending on the context of the statement. Are they the same toy made by the same manufacturer, or are they literally one object expressing itself in more than one place at the same time? When it comes to fuzzy lines like this, it's always a good idea to ask the person putting forth the statement to define what they mean a bit clearer. In this case, to ask me whether I mean literal identicality, or merely siblings from the same factory.

Objective Reality and You

          There's something wrong with you. No, it's not that hairdo, it's not an infection or disease, it's the very fact you're human. Now, personally, I don't consider this a bad thing, but it DOES place an annoying series of limitations on our existence, the one under discussion today being our senses. We are brains in bodies, nothing more. As a matter of fact, simply talking about the brain means that organ has given itself a name and has begun to study itself, a transcendence of self-awareness. While this is interesting and exciting, it also means there's a lag time on our sensory information, and more bizarrely, it means we can't even tell for sure where this information comes from. We could be brains in jars simply being fed this information from an advanced super computer for the purposes of experimentation, or we could really be plugged into the matrix, or any other possible scenario in the seemingly infinite realm of probability. This has been known for quite some time and thus has some terms associated with it to describe the concept. The true nature of reality, that brain in a jar thing that we can't rule out, nor can we even test, is called Objective Reality, or, the way reality actually is. The sensory information we receive and observe is generally called Subjective Reality, or, the way reality seems to be to you. Remember the yo-yos? yeah, that's another example of the limits of human sensory input. They might be the same object expressing itself in two places at once, or they could be two completely independent yo-yos. There's no real way to tell by just looking at them. Sure, the first premise sounds ludicrous as no object has ever been observed to exhibit such behavior, but that doesn't really rule out the possibility I'm afraid. Just like the brain in a jar, these two yo-yos are assumed to be two independent objects, because that's how they behave. Inflicting damage on one doesn't harm the other, any movement of one cannot be detected by just looking at the other, and even if you destroy one, the other will remain. Therefore, it is assumed they are two separate objects. Sure, not being able to rule everything out may seem like a problem at first, but let me ask you this. If they were the same object, and yet acts as two objects, how would you be able to tell otherwise? The answer of course, is you cannot. As far as you can tell, both scenarios would exhibit identical outcomes. Therefore, working with the assumption of them being two separate objects (Or that the reality you experience is real and you are not a brain in the jar) works just as well, if not better than the opposition because one scenario gives you a better ability to explain your surrounding environment.

Occam's Razor

Have you ever been to Paris? I haven't, nor do I plan to in the near future. But there's something about Paris I think you should know. It seems to always be there, but it actually disappears when no one is looking, all the people levitate above a crater in their sleep, and as soon as even one person wakes up, the entire metropolis reappears before anyone is the wiser. This is preposterous, of course, cities don't vanish when no one is looking! At this point I would ask you, "How do you know? Can you prove I am wrong?" Now, the existence of Paris doesn't have much use to anyone unless they're actually going to Paris, so it really doesn't matter, but still, is there any way I could be proven wrong? If I was right, the entirety of the laws of nature would break down and need to be rewritten. While you're thinking about Paris, consider the following ancient question. After you close the door to your bedroom, is it still the way you left it? Without actually observing the room in some way with your senses, there's no way of telling the bed hasn't actually opened the window and flown around the world by some means and landed right where you last saw it right before you open the door to check. For all I know, Paris could instantaneously appear before me as soon as I approach the crater that is usually there. It seems impossible, however, we've already shown there are some scenarios we simply cannot rule out due to our very senses. Enter Occam's Razor. "When two scenarios are presented to you that both could potentially be true, go with the one that takes the least assumptions. That scenario is most likely to be true." Now, back to Paris. For Paris to disappear and reappear would require the relocation of every teeny bit of matter and energy found in the city, and all of it needs to be there once more when I lay my eyes upon it. It's simply easier to believe the city to always exist because it takes less exceptions to the known rules of nature in order for it to be so. Is it still possible for the known laws of nature to be wrong and 'the real laws' allow cities to appear and disappear in an instant? Of course it is seeing as anything is conceivably possible, but remember, the important question is how much explanatory power does this scenario give us? Well, seeing as it is defined to elude scientific testing and evade our senses, we could never hope to uncover the method behind which this city could vanish and reappear, all we could ever hope for is speculation at best. Speculation, however, is not worth trashing the laws of nature and the explanatory power they provide.

Pragmatism

          Pragmatism. A lot can be written about this one subject, and really needs a full piece devoted to it, but I'll delve a bit deeper into pragmatism later. For now, an overview will suffice. Pragmatism is what we call an 'epistemology,' or, a method by which we assign things as true, or false, and goes a little like this. Why do you have beliefs? I'm not just talking about spiritual beliefs either. Why have any beliefs about gravity, germ theory, the existence of Paris, and so on? Well, I hold beliefs because I use them to predetermine outcomes to actions I may take. I believe in germ theory because I can use it to protect myself from disease, and thus far it has worked. The same for gravity, it prevents me from jumping off tall buildings and incurring injury. Essentially, because we hold beliefs to predict the outcome of actions, we can regard any outcome as true so long as it gives us a model that has predicting power. Also, when two or more models have the same amount of explanatory power, we go with the one that takes the least amount of exceptions to our known rules because of Occam's Razor. That's the first half of Pragmatism. The second half allows us to actually peer a little bit into the territory of Objective Reality. This is the process that served as the basis for The Scientific Method, or at least part of it. Since we hold beliefs to predetermine outcomes to our choices, we can use this to predict an outcome that will occur through a specified action, and if it happens, the belief is held to be true... tentatively. So, one could surmise the epistemology of Pragmatism as follows:

1. Erasmuth wants to achieve outcome X.
2. Erasmuth believes doing action A will achieve outcome X.
3. If Erasmuth performs action A and outcome X occurs, then the Belief Z is held to be true until shown otherwise.
4. Else, Erasmuth's belief is false.

Now, let's say I have super powers and believe I can fly around like superman. You could tell me such things are impossible, but as far as epistemology is concerned, you can't go around pushing your epistemology on others, only try to persuade them. So, if you're a good pragmatist and determine my claim to be false. Let's say, however, that I don't use Pragmatism and instead rely on superman comic books to define all that is true. I would determine my claim to be true. This would normally leave us at a stand still and be forced to agree to disagree. But remember, we hold beliefs to achieve outcomes and predict the future as best we can. If I had the power to fly like super man, the first thing I'd do is jump off the highest building and fly away. At this point, whatever reality we are in takes over. We could frame it like this.

1. Erasmuth wants to fly like Superman.
2. Erasmuth believes stretching his arms up and leaping off the tallest building will let him fly like Superman.
3. If Erasmuth Stretches his arms up and leaps off the tallest building and flies away like Superman, Erasmuth's belief is held to be true until shown otherwise.
4. If anything else besides what is expected occurs, Erasmuth's belief is wrong.

It really is that easy. Now, like I said, I have no right to make you follow this epistemology called Pragmatism. Maybe you want to add a third category called "Indeterminable" to describe the concepts and beliefs that cannot be tested, or maybe you want to operate on a gradient of truthiness rather than this black and white Pragmatism, you can do that to. (Google Fuzzy Logic for details.)

In Part 2 (Now Available), we'll be looking at logical arguments and how they are structured, what is a valid argument versus a sound argument, as well as Socratic logic structures. Thank you for your time! ^^