Greetings, dear readers. From this blog, I will try to give definitions to various terms. It is sound, then, I think, to begin by defining what a definition is. Now, we encounter one of the hardest problems with this procedure: circularity. Since in order to define a term, which is a symbol, we will have to use other symbols, don't we have to define these as well? Likewise, shouldn't we then define the symbols we used to define the symbols we used to define the original term? This goes on ad infinitum.
So, we are forced to either stop defining or to end up doing circles, without an end in sight. Things aren't exactly like that, however. Now, I am imprinting my thoughts on a language, which is a symbolic means of communication. I am imprinting them and then publishing the results, fully expecting that when someone reads up to this point, he will have at least a partial understanding of my original thoughts. Is it senseless to expect that much? The answer to this question seems to be an obvious "no" but why exactly is that?
Humans have the ability to identify symbols in a non-symbolic way: with patterns. Our brains, which are neural networks, can learn to identify a stimulus if it is repeated enough times. Consequently, when a person is reading these words here, his mind understands and composes them, up to a point, producing an imprint of the original idea that existed in my mind. A neural network can execute this learning procedure to identify something -a symbol in this case- but because of the way it works, it is not capable of doing so with absolute accuracy. Now, the way we will get around circularity as well as what is the point in defining things start to become apparent.
A definition is a symbolic description of a term. A good definition needs to be absolute and formalistic. Why? Because that's what is missing from the way the human brain interprets symbols. If the learning procedure of the human brain was capable of identifying and processing symbols with absolute accuracy, then the need for symbolic definitions would cease to exist.
All in all, definitions are part of the symbolic representation of the world humans have in their minds. The role of these symbols is to enhance the human mental power by covering for the built-in weaknesses of the inner workings of their brains. To be more specific, definitions are that system that connects all those symbols. For this reason, I believe that studying and extensively using definitions is beneficial to humans.
So, we are forced to either stop defining or to end up doing circles, without an end in sight. Things aren't exactly like that, however. Now, I am imprinting my thoughts on a language, which is a symbolic means of communication. I am imprinting them and then publishing the results, fully expecting that when someone reads up to this point, he will have at least a partial understanding of my original thoughts. Is it senseless to expect that much? The answer to this question seems to be an obvious "no" but why exactly is that?
Humans have the ability to identify symbols in a non-symbolic way: with patterns. Our brains, which are neural networks, can learn to identify a stimulus if it is repeated enough times. Consequently, when a person is reading these words here, his mind understands and composes them, up to a point, producing an imprint of the original idea that existed in my mind. A neural network can execute this learning procedure to identify something -a symbol in this case- but because of the way it works, it is not capable of doing so with absolute accuracy. Now, the way we will get around circularity as well as what is the point in defining things start to become apparent.
A definition is a symbolic description of a term. A good definition needs to be absolute and formalistic. Why? Because that's what is missing from the way the human brain interprets symbols. If the learning procedure of the human brain was capable of identifying and processing symbols with absolute accuracy, then the need for symbolic definitions would cease to exist.
All in all, definitions are part of the symbolic representation of the world humans have in their minds. The role of these symbols is to enhance the human mental power by covering for the built-in weaknesses of the inner workings of their brains. To be more specific, definitions are that system that connects all those symbols. For this reason, I believe that studying and extensively using definitions is beneficial to humans.
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Interesting topic, it might help to know where you're going from here. For instance, I'd say most of the basis of human languages isn't fundamentally based on abstractions, but on the real world. If I wanted to define "rock", I'd just go and point to a rock. It doesn't require abstraction or anything circular. The same goes for most nouns and verbs and even adjectives. (Perhaps this is what you mean by 'symbol'?) Most of the rest is just filler, connectors to make all those concrete concepts flow together cohesively. Clearly dictionary definitions are inherently circular, but that's largely because a dictionary can't point to a rock and say "there, that's a rock", but that's what most people do when they think rock, they think of the object, not a definition. In this case a definition is simply an approximation in words, but the concept doesn't require one. A better example might be an emotion, say happiness. Very concrete, yet impossible to define sufficiently in words.
ReplyDeleteOf course the realm of abstraction is quite concrete in its own way, much of which falls under some form of mathematics. It sounds to me like you're taking a very mathematical/logical approach to communication? If you've read about Gödel's incompleteness thm, and also Whitehead/Russell's Principia Mathematica you realize how hard it can be to codify even basic mathematics. Putting all of communication onto a firm footing seems to be a formidable task as well, does it not? (not to mention one of the advantages of non-analytical/rigorous thought is precisely that we're not susceptible to logical paradoxes and thus the incompleteness theorem shouldn't worry us.)
Hi, thanks for replying.
ReplyDeleteThe intuitive human approach to definitions, what you call "here's a rock" or "the image of a rock in my mind" is what I described as patterns, in the third paragraph. I guess it's so close to our way of thinking that it's easy to overlook but indeed there is a mechanism used by humans to identify and recognise things.
What I mean by "symbol" is objects, a kind of more formal, more properties-based approach to identifying things. Mathematics and logic in general work like this, with entities that have certain properties, isn't it so? So, what I'm really saying is that a symbol can be described with a set of properties, a symbolic definition, if you will. Alternatively it can be defined with patterns or instinctively or however you wish to call that.
I understand the limitations of symbolic systems. I know of the Incompleteness theorem although unfortunately I have not studied it in depth neither have I an understanding of its proof. With that in mind, the whole purpose of what I wrote was to outline that there is a need for such hard definitions. That need arises from the fact that the way humans identify things by default (the "there, that's a rock" thing) has its own limitations, i.e. inaccuracy for the most part.
My perspective comes from computer science. We use both approaches. There's logic programming which is the equivalent of mathematics and hard, symbolic definitions. Then, there are more computational approaches, like artificial neural networks. Both approaches have their advantages and disadvantages so both have some use. So, that inspired me to generalise this concept of symbolic and non-symbolic information management .