Click here for Table of Contents
Click here for home, brianrude.com
Some Thoughts On Reasoning
Next I will try to apply this concept of skill - the brain's ability to sent out a complex and precise pattern of a large number of impulses - to conceptual thinking and learning. My hypothesis is that reasoning is a matter of skill, conceptual skill. To illustrate this idea consider this syllogism:
All cats have fur. This animal is a cat. Therefore this animal has fur.
What goes on in a person's head when contemplating this syllogism? Is it all a matter of association? Is it about the same thing as associating the concepts of "Columbus", "discovery", and "America"? My view is that it is not. It is something more than simple association. It is quite possible for one to not understand this syllogism, but to learn it by rote. This would be a matter of association. However one might just as easily learn the following syllogism by association:
All cats have fur. This animal is a cat. Therefore this animal has feathers.
The difference between this syllogism and the first one is that the first one uses valid logic. The second one is nonsense. The second one can be learned by association, and so can the first one. But that is not enough for the first one. We want something more going on in the learner's mind than just association. What is this something more?
In Chapter Five I discussed the difference between "brain packing" and "structure building". These two syllogisms again bring up this difference. Either syllogism can be learned by simple brain packing, but only the valid syllogism can be learned by structure building. No structure, other than a simple nonsense structure of accretion, can be built up for the second syllogism. Something more than simple association must be involved.
Now consider another example, this time from an episode of "Star Trek" that I happened to notice on television one day. I was not watching the program, but I could hear it from where I was sitting in the dining room. In the story Captain Kirk and his crew were in jail on some alien planet. They heard a faint tapping through one of the walls, which they recognized as Morse Code. They got the letter S, then a T, then an A, an N, and a D, then end of word, then another word, B, A, C, K. There was a moment of intense concentration as all the characters tried to make sense out of the message. Then the meaning dawned on them. The wall of the jail exploded and they made their escape. This may be a trivial example, but I think it is a good one for my purpose here. It appears the brain does something with the raw information. One letter at a time came to them, and one letter is meaningless by itself. The individual letters had to be assembled into a form which had meaning. The characters displayed a second or so of intense, conscious, directed mental effort in order to extract this meaning. It is not enough to receive information. Somehow the brain must act on it, juggle it around in different ways until a satisfactory configuration of the parts of that information is found. The raw information was a series of letters. When properly configured these letters formed a message - "Stand back!" But it took effort to get that proper configuration. The juggling was not automatic. It was a result of conscious voluntary action.
If the brain does something in a situation such as this, does it do it by sending out a large number of impulses in a precise pattern? Captain Kirk's intense mental effort to decode the coded message is certainly consistent with this idea. When one says "I'm struggling to understand", is one talking about such an action by the brain? Is such a struggle of the brain similar to the struggle when one tries to get the motions together to shift gears in a car, or to play a difficult series of notes on a piano? When a teacher admonishes a class, "Now, think about it! Follow the reasoning! It's not so hard!" is she asking brains to do something?
In the last chapter I used three lines of reasoning to argue that perception is a skill. I will attempt to fit those three lines of reasoning to the idea that reasoning is a skill.
The first argument was about attention, and this seems to apply also to reasoning. One can apply reason to what one has in mind, or one can choose not to. One can read a problem in an algebra book, "Train A leaves Pittsburgh going west at 10 miles per hour . . ." and then solve the problem; or one can close the book. I argued that attention is something the brain can do, or not do. In this case it is attention to concepts and relations that we are talking about, rather than attention to perception. But the argument is the same. If attention is required, then the brain must do something. Doing something is at least a first step in satisfying the "large number of impulses in a precise pattern" definition of skill.
The second line of reasoning I used to argue that perception is a skill is the idea that our sense organs receive massive input at all times, most of which must be ignored. This is the "data-sieve" argument. This has some relation to conception. Any given concept has connections to many other concepts. Most of these connections, or associations, are ignored as we pursue a particular line of thought. For example, when I see the word "Pittsburgh" there are many possible associations. When I am looking at a road atlas and planning a trip some of these associations are important and many others are not. When I am studying a list of spelling words the relevant associations with "Pittsburgh" are totally different. When I am studying history, or reading a historical book, yet other associations are relevant. Many other contexts would have widely differing associations with "Pittsburgh" that are relevant or irrelevant. If all associations are elicited every time I see the word "Pittsburgh" then my thoughts would be chaotic and undirected. Part of reasoning, perhaps, consists of allowing only those associations that are relevant to be elicited, and suppressing all others. This can be interpreted as a matter of closing gates. So just as perception requires closing a lot of gates to suppress unwanted information, so reasoning may require closing a lot of gates to suppress unwanted information. Closing gates, I presume, is a matter of the brain sending out signals of some sort. If these signals must be numerous, and in a precise order, then the definition of skill I have used would apply.
A third line of reasoning I used to argue that perception is a skill is that perception must be learned, that it takes practice. Can this general argument be applied to reasoning? Does reasoning take practice? Does one "learn to think"? And if one does learn to think, then does it follow that we should try to teach people to think? And if so, how should we go about it?
On the surface, at least, it may seem that reasoning is not learned. It seems to be more like an ability that one has to a greater or lesser extent, and is not much subject to change. If one is good in math, then that's just the way it is. It doesn't seem generally true that one can learn to be good in math. Those who are not good in math endure what they must and quit when they can.
If reasoning doesn't take practice then perhaps it is not something that can be learned. If it cannot be learned then perhaps it is not a skill. If it is not a skill then I have spent considerable time pursuing a fruitless argument.
We generally think of a skill as being learned. Something we think of as unlearned we generally call a reflex. However learning seldom takes place on a completely blank slate. The propensity to learn can vary greatly. Consider walking. We say walking is learned because we witness all the effort that a baby puts into that learning. And we certainly say walking is a skill. But consider walking and running in animals. A newborn antelope on the plains of Africa must be up and walking within minutes or, at most, hours, or it would surely fall victim to a predator. Is walking learned in this situation? Is walking a skill in this situation, or just a reflex?
I think walking is still a matter of learning, and is properly called a skill, whether in a human or an antelope, but the propensity to acquire this learning is vastly different in the two cases. Humans spend months at the task, or even a year or two, instead of the hour or so that a newborn antelope spends. The propensity to learn must be very high in the antelope compared to the human. But that does not mean the propensity to learn is entirely absent in humans. Part of the difference is in the stage of maturation at birth. Humans are called "altricial", meaning they are born very undeveloped. Antelope, and many other animals are called "precocial" meaning they are born at a rather advanced stage of maturation. Perhaps humans learn to walk as the propensity to learn develops. Perhaps most of the stumbling attempts a baby makes in the early stages of waking are irrelevant to the learning that takes place when the propensity finally is fully developed. One might also conjecture that the propensity to learn to walk in humans is closer to that of antelopes than might at first seem apparent. Perhaps if there were no propensity to learn to walk in humans then eight year olds would still be crawling and most fifteen-year-olds would be getting pretty good at their bipedalism. Compare this to piano playing. This is a line of inquiry that needs to be followed, but not at this point. The point is that any skill depends on learning only to a certain extent, and the propensity to learn different things varies greatly.
In the last chapter I said that the idea that perception must be learned is evidence that it is a skill. Now I am saying that skills don't have to be totally learned. Some skills are automatic, and are more properly called reflexes. If some skills don't have to be learned then the idea that something is learned perhaps is not an argument that it is a matter of skill. However I do not think this is a problem. I started with the basic definition of a skill as the brain's ability to send out a large number of impulses in a precise pattern. This applies whether this results from learning or from instinct. To satisfy the definition it is only necessary to show that the brain output meets the two criteria of number and precision. Whether this brain output is a result of learning or instinct doesn't matter. Learning supports this criteria of number and precision, because if the brain output were not numerous and precise it wouldn't need to be learned. If something is instinctual these criteria do not automatically follow. An action could be instinctual and still be very simple and imprecise. Some simple reflexes probably meet this description. However a behavior such as walking is not simple. Whether a result of a long period of learning , as in humans, or a sudden maturation of instinct, as an the newborn antelope, walking still is complex. Walking is complex whether it is instinctual or learned, so walking is a skill whether it is instinctual or learned. Complexity itself can be taken as evidence of skill.
If reasoning in humans is like walking in antelope, it may be a skill, but perhaps not a skill that we can do much about. We probably can't do much to teach a newborn antelope to walk. All we can do is stand back and hope the instinct for walking kicks in before a predator comes by. Is this the way it is for reasoning in humans?
Educators like to talk about teaching their students to think. I think this is a very important topic, but I have never heard or read anything on it that I thought had any merit. Later in this book I will give my thoughts on it. But first there is a considerable amount of groundwork to lay down. For the rest of this chapter I will try to describe some mechanisms of reasoning. In the next chapter I will discuss mental habits, which I think are very important in reasoning. In other chapters I will develop other ideas that I think have much to bear in the idea of learning to think and reason.
I will spend the rest of this chapter presenting a mechanism by which I think reasoning occurs. This mechanism supports the idea that reasoning is indeed a skill, that reasoning is learned, and that to at least some small extent it can be improved by learning.
Of course I don't know just how the brain works, but some common sense and introspection applied to everyday phenomenon will yield some progress. I will start with the idea of language decoding. Consider this example: A person says to you, "Those roses are pink this year, but I'd swear they were bright red last year". This statement directs your attention to a rose bush. It directs your attention to the color of the roses. And it elicits a consideration of events that transpired a year previously. How does all this happen?
A coherent sentence consists of a string of words that operate on each other. The word "pink" operates on the word "roses". The word "they" also operates on "roses". The word "ago" operates on the word "year", and the two words together make up a phrase that operates on the phrase "were bright red". When I say that a word operates on another word, such as "bright" operates on the word "red", I am only pointing out that "red" becomes something different than if it were preceded by another word such as "dark".
For words to operate on each other they must exist concurrently in the mind. For instance if the word "roses" had dropped out of mind before the word "they" is perceived, then "they" would make no sense. This is just a restatement of the rule of grammar that pronouns should have clear antecedents. Words at the beginning of a sentence, therefore, must be held in some form of short term memory while more words are perceived. When all the words necessary for a thought are simultaneously present in this short term memory, then some form of reasoning must take place. The words are digested into a thought. The thought is retained while the actual words are released from the mind. I picture this process as the workings of some sort of machine in the mind. A string of words is received by this machine and juggled around until they fit together like the pieces of a puzzle. Then the picture on the puzzle is retained, but the string of words is ejected so that a new string of words can come in. The "juggling machine", as I like to call it, then continues to repeat the whole process just as long as more words are forthcoming. Now with this perspective let's go back to the invalid syllogism about cats and feathers, and analyze it in terms of language decoding. In this syllogism the words cannot operate on each other in a totally satisfactory manner. They cannot fit together like pieces of a puzzle. The word "feathers" stands independent of all other words. No matter how much the juggling machine keeps working on the words, "feathers" is just not going to fit in place. Therefore the machine spits all the words out undigested. In the original syllogism, the valid one, the juggling machine has no trouble, no indigestion occurs. The word "fur" in the conclusion fits perfectly with the words of the premises. The words "all" and "fur" operate on the word "cat" in the first premise. The word "this " operates on the word "animal" in the second premise, and the word "cat" in the second premise operates on the phrase "this animal". The second premise then operates on the first premise to produce the word "fur" in the conclusion that operates on the word "animal" of the conclusion. The brain may do further juggling on the syllogism, bringing many concepts and associations from other parts of the brain, from other structures of knowledge, and conclude that this is the only meaning consistent with all the elements.
I presented the "juggling machine" as something linguistic. It works with words. I think in general such "juggling machines" are reasoning machines. Decoding a simple three word phrase such as "the old barn" may not seem like reasoning, but consider the same juggling machine working on the phrase "an empty glass of water". Is this purely linguistic? There is a line in a song, "My uncle used to love me but she died." Is decoding this purely a matter of lingu mutually exclusive associations, and trying to fit the associations into preexisting "templates". If the associations that are elicited fit the associations the mind expects, then the thought is accepted. If the associations are unexpected, failing to fit any template, or somehow conflicting, then the thought is rejected. In the phrase "the glass of water" each word elicits associations in the mind. "Water" is easily associated with "glass". The word "of" elicits the expectation of relatedness. The article adjective "the" is simply expected as idiomatic, it is associated with any noun. Now consider the phrase "the empty glass of water". Here the associations of "empty glass" and "glass of water" are conflicting. Therefore the thought is indigestible. One may consciously consider what might be meant by this phrase. Perhaps the speaker means "that glass which had water in it, but which is now empty". With this interpretation all the associations elicited by all the elements in this phrase are now consistent with previous knowledge. The thought causes no indigestion.
The brain forms hypotheses and tests them by looking for conflicting associations, and by looking for fit into templates. This, I think, is basically what reasoning is, whether applied to language or to thought in general. When a "juggling machine" works on the phrase, "I saw an apple fall to the ground from that tree.", it is operating purely linguistically. When it operates on the sentence, "I see, said the carpenter, as he picked up his hammer and saw", it is doing a little more than simply decoding a string of words. When it operates on the syllogism of cats and feathers, it is primarily reasoning, not language. Yet in any case, it searches for an interpretation which works, in which the elicited associations are not in conflict, and which fit expected patterns or templates. The humor and interest in the second example derives from the brain's inability to definitely latch on to one interpretation and reject the other.
There are two central mechanisms to be explained in this idea of "juggling machines". We must explain how things are held in mind, and we must explain how ideas fit into patterns. I believe the brain holds things in mind by what I will call "poking the spot", and I believe the brain fits ideas into templates by testing associations.
First the brain must hold things in mind. I think this is done by a sort of repetition in the mind. A word, for example, when perceived by sight or sound, elicits associations. This may be simply impulses sent out by certain neurons that cross synapses and elicit other impulses from other neurons. But that is not the end of it. The brain has the ability to repeat the word, except without the actual sight or sound perception, again and again trying to elicit other associations that may be successfully fit into a pattern or template.
I call this "poking the spot", as if a perceived word or idea occupies a particular spot in the brain, and the brain, by poking that spot again and again, elicits associations again and again. When associations are elicited that fit a pattern then the thought is complete. The "juggling machine" has juggled the parts in a satisfactory configuration. Not only must the "spot" of the perceived word or concept be poked, but also various "template spots" must be poked to produce the associations that may or may not fit with the associations resulting from poking the word of concept spot.
This fits the pattern of the brain "doing something". Captain Kirk could have received the letters by Morse code and dismissed them as irrelevant. But he kept them in mind, expecting them to make sense. This is not a passive thing. He consciously and willfully kept the letters in mind by "poking the spot" over and over. Words are templates into which letters can fit. Poking the spot brought forth words which were tested for meaning, that is tested for associations. Of course his success came very quickly. It was a simple matter of language decoding.
The speed with which this may be done, at least linguistically, can be seen with a little introspection. For example, on the news I heard a statement something like, "It was confirmed today by a White House source that . . . . . . " I first interpreted the word "white" as referring to race, the person doing the confirming was Caucasian. Of course the word "house" immediately scotched that interpretation. Consider the speed at which the false interpretation was formed and rejected. My faulty interpretation was formed and rejected between two consecutive words, "white" and "house". If the speaker was talking at 200 words a minute, which is not particularly fast for talking, and if the false interpretation is formed and rejected during the space between the words "white" and "house", then it takes 1/200 of a minute, or about 1/3 of a second, to entertain the race interpretation and then to reject it. Another example occurred with my wife and daughter were telling me about the meal in a Chinese restaurant. My daughter said, "I had sweet and sour shrimp". I distinctly remember a positive response in my mind to the phrase "sweet and sour", because I like sweet and sour pork or sweet and sour meatballs. However my positive response was immediately destroyed by the word "shrimp", as I do not like seafood of any sort. Again consider how fast this processing went. Between the word "sour" and the word "shrimp" would be a fraction of a second, but that was quite enough time for my verbal juggling machine to form a hypothesis, test it, and reject it.
Captain Kirk has a series of letters. His brain keeps them in mind, I think, by continuing to rethink them. Connections are made. These are what associations are. To "poke the spot" again and again is to send out signals that produce associations. When one spot is poked it sends out signals that poke other spots. By doing this repeatedly some associations may finally be made that will "click". That is the associations fit into a preexisting template.
The "templates", I believe, are a set of associations that form a recognizable pattern. Templates are recognized the way faces are recognized, as a set of associations. The syllogism is a basic pattern. Cause and effect is a basic pattern. The conjunctions "and" and "or" are patterns. Hierarchy is a pattern, or patterns. These patterns are built up in early childhood. I think they are primarily built up as a matter of vocabulary. These patterns form the templates that our brain uses to extract meaning from words, from symbols, from situations, and from the environment in general.
"Poking the spot" also fits a slightly different type of reasoning. Consider this next example, which is primarily visual and totally non-verbal: One day when I was working as a band instrument repairman in a music store the boss brought me a microphone stand, consisting of a round heavy metal base, into which screws a threaded metal tube. The threads at the bottom of the tube were damaged. Through extensive use, apparently, the metal at the bottom of the tube got more an more deformed until finally the tube was so deformed on the threaded end so that the threads would no longer take hold. The boss figured I could somehow expand the threaded end of the tube, thereby making it useful again. I could, and I did, but the solution was not obvious at first. I had to figure out a way to do it, and my thought processes are of relevance here. I figured out the solution primarily with visual images, not words. Perhaps some words went through my mind as I thought, but they were of little consequence. I thought by images. I would imagine the end of the tube, imagine some tool pushing against the inside of it. After a few minutes of imagining first one tool and then another, I realized just which tool, a tapered steel mandrel, would do the job. I got out the tool, and it worked.
This is indeed the brain "doing something". I imagined. I produced mental images. I poked spots in my brain that elicited conceptual-perceptual and perceptual-perceptual associations. This imagining was a conscious willful act. I was aware of the willfulness of this imagining because I considered the job a bit of a bother. I like to figure out things, but at the moment I had enough of figuring out things. I was more in the mood to just take on routine jobs, jobs that I knew how to do and could just go ahead and do. Unfortunately there was a second stage to this job. After I expanded the end of the tube so that the threads would grab, I decided that at that point the repair would not last very long. I wanted to reinforce the end of the tube in some way so that it wouldn't deteriorate with use and be right back in the same state in a month or so. Figuring out a way to reinforce it was accomplished in the same was as figuring out the original fix. I used visual images. I would imagine some metal object inserted in the end to stiffen the tube. But what metal object would work? I kept imagining. I kept "poking the spot" again and again, over a period of several days. Eventually, of course, I came up with a good reinforcement.
The willfulness of this imagining, this "poking the spot" was quite apparent to me, because by this time I was thoroughly fed up with the project. Yet I didn't want to leave it only half fixed. I would forget about it for a while, and then realize I had better work on the problem some more. So, again and again, I would consciously "poke the spot" until little by little I came up with increasingly better ideas, culminating eventually in a satisfactory solution.
Imagining often seems effortless, but when one is pressed to come up with a product of imagining, then it doesn't seem so effortless. We may be impressed with the ease in which young children can make up stories in free play, but the same child in the third grade facing a blank sheet of paper and assigned to "write a story" does not feel that imagining is effortless. In the same way talking may seem effortless in many situations, but when one is hard pressed to find just the right words it doesn't at all seem effortless. It can be hard work. Reading can seem effortless at times and not at all effortless other times. Even simple perceiving, such as seeing or hearing, can be not at all effortless at times Attention can be hard work. This does not prove that all these things are done by the brain putting out a large number of impulses in a precise pattern, but it certainly is consistent with that hypothesis.
By this perspective all types of reasoning are essentially the same. All types of reasoning are the result of mental activity in which groups of associations are tested against each other until they fit together in some meaningful way. A "meaningful way" of fitting together, or "template", of course, is a group of associations in itself. This general model of reasoning works for language, including both vocabulary and grammar. It works for syllogisms and logic in general. It works for imagination and spatial relations. Reasoning, by this perspective, is indeed a skill, but that statement is more academic than practical. It does not seem be a skill that can be improved with practice. I believe in general it can be compared to walking. Walking is indeed a skill, but it is learned early, and there is little benefit in practicing walking in adulthood in order to increase the skill. One may walk to increase strength and endurance, but not to increase skill.
It is tempting to think that if all types of reasoning are essentially the same then the brain must be a completely generalized thinking machine. I think this is not the case. It does seem that intelligence is generally global. A smart person tends to be smart in all ways. However there are innumerable exceptions to this rule. I think ultimately the brain will be shown to be a collection of specialized thinking machines. However I will not pursue this line of inquiry at this point as I have very little to go on.
Much of what I have discussed in this chapter applies to very logical or intellectual learning, but we must also deal a great deal of learning that is on a lower level. Habits must next be discussed.