The Power of Logic
So far on this blog, I have covered rationality, empiricism, addressing the question of what science can prove, and the importance of good rules of reasoning in the Long Term Survival Model. Indeed, that is a lot of information to consider. But today, we’re going to talk about quite possibly one of the most important ‘good rules of reasoning’ that we have to work with: logic. Specifically, we will talk about the power of logic as it is applied to a variety of different fields of study and, most importantly, how logic pertains to your continued survival and even thriving well being. Logic is often misunderstood in popular culture much the same way that the phrase “empirical evidence” often is. Most of the time, someone will remark rather informally that they “do not follow” someone’s “logic.”
I want to talk about logic in the formal sense, particularly: propositional logic. So let’s get into it.
There are two aspects to logic itself that we can talk about at a basic level immediately. One is validity and two is soundness. Logic looks at the relationships between statements, or sentences, and the relationships between those sentences in the form of arguments. Here is an example of a simple logically valid argument.
If the sky is grey, then it is likely to rain.
The sky is grey.
Therefore, it is likely to rain.
This is logically valid for reasons which I may go into later but the important part in the scope of how logic is applied to concepts within research and discovering truth with the motivations behind long term survival would be whether or not the argument is sound. This above argument is a very simple, “modus ponens” style argument and can be determined by logic to have a good structure. Within the system of logic, arguments are concerned only with good structure, not so much whether they are actually true or false, or even good arguments in the traditional sense of the word at all.
Imagine for a moment that we want to symbolize the above argument into a workable form that we can then manipulate within the system of propositional logic. We might symbolize “the sky is grey” as G and “it is likely to rain” as R. In that particular case, the argument itself would then be symbolized this way:
If G, then R.
G
Therefore R.
Forgetting what the sentences actually mean here for a moment, we might consider what would happen if we switched around a few symbols and their relationships. What if it was arranged as:
If G, then R.
R
Therefore G.
If you’re an avid practitioner of propositional logic (as I’m sure all of the thousands of readers that come to this website certainly are) then you would know immediately, without having to revert the symbols back to sentences, that this argument was invalid in the formal sense. Sometimes, our intuitions also work in the case of these particular types of arguments and we recognize that the reasoning and structure of the argument itself has gone awry. Other times, it is not so obvious. For example, the argument above can be reverted back to sentences in this way:
If the sky is grey, then it is likely to rain.
It is likely to rain.
Therefore, the sky is grey.
Again, thinking about this in terms of structure, we must admit to ourselves that something strange may have just happened with our mode of reasoning. In terms of structure, the argument has suddenly become “invalid” as the rules of formal logic allow. The only thing that logical structure actually refers to is really that the order in which we create premises, assign them truth values (of true or false), and then come to conclusions must be done according to certain rules. If those rules are violated, then the arguments we have created, no matter how true they may be in the real world, are actually arguments that follow bad rules of reasoning within the system of logic.
Logic does not always work perfectly when applied to real world concepts but it remains one of the number one tools used throughout the field of philosophy. Philosophy is at the foundation of a variety of fields, including sociology, psychology, law, and many aspects of political science. Indeed, other fields have also been influenced by and continue to influence philosophy, such as quantum physics and astronomy. Logic is the system through which the majority of all philosophies are understood, refuted or accepted, created or destroyed.
I will not be able to teach you the entire system of propositional logic (or other forms of formal logic) here in a single blog post. However, it is important to understand that propositional logic is priceless within the course of introducing yourself to more advanced subject areas that you may have even had problems with in the past. For instance, simple mathematical operations are often no different than what the basic system of logic has previously allowed.
Consider the math problem: (5*4)(3+2)
In order to solve the above mathematical operation you would have to follow an order of operations. Logic, too, has an order of operations. Perhaps a distinct difference in how logic is typically taught in classrooms versus mathematics style of teaching would be that with logic rules are typically written out along the side of a problem. In mathematics, the number of rules that we are required to follow, as well as the theoretical space we are often working in, is vastly more large and complex. Logic has but two values to work within: true and false. Mathematics, on the other hand, can work within a variety of theoretical spaces, all of which address all matter of numbers and even non-numbers, stretching into infinity in every direction.
In understanding that learning the entire system of propositional logic can be highly beneficial, what more then can we derive about what there is to say on the matter? How does logic pertain to our daily lives and our state of well being?
My class instructor, Curtis Haaga, at the University of Houston, actually remarked when we began some of our first few days of class as saying that there was not much of a use for being able to do logic and work within its system in the real world. He claimed that the activity of filling out a bunch of papers with symbols and their relationships according to a set of rules was something we would only do in that class. In particular, working with those symbols and the question of ever doing that again – probably true, we will probably never do such a thing in a real world application.
As for the rest of it, I must respectfully disagree. On the contrary: logic is the underlying system of reasoning which will allow everything else that I talk about here on this site relating to the scientific method, discovering the truth, working from life’s context, and many other ideologies as working eloquently, beautifully, and at the end of the day: fairly simply. A little less reliably, the field of logic aids us in understanding how we reason in general.
Logic ties into Long Term Survival in a few different ways. For one, the formulation of the argument itself for the Long Term Survival Model is comprised of logical relationships. It is done this way for multiple reasons. For one, we can start this way to retrieve some falsifiable hypotheses from which to work from. For example, in defining survival as our own physical state of living in combination with whether or not we have children – we can then ask a few important questions. Am I alive? Do I have children? The answer to these questions and determining whether those answers are true or false can then lead us to a conclusion for that part of the Long Term Survival argument, which can then serve as the base premise for further parts of the argument.
This is how we can determine whether or not we are actually carrying out the proper set of daily actions in our lives. Perhaps one day soon, I will actually post the entire logical argument for Long Term Survival Theory and you can see a little bit of how it works. Essentially, if you care about survival, then you will care about doing the things associated with it. And, when we redefine the word ‘survival’ from its traditional form to the one associated with Long Term Survival Theory, it becomes that much more meaningful.
In this way, we can discover the power of logic. It reveals itself to us in the form of falsifiable or testable philosophies, arguments from the sciences, or forming the basis for reasoning – be it real or artificially constructed. Without logic, our other good rules of reasoning become only moot. So go forth, and be logical. 
