Logic
Given that philosophy is conducted through the use of argument and reason, it follows that we need a method for evaluating arguments. This is where the need for logic arises. But, the study of logic itself can be difficult and may seem irrelevant, especially in the way it is taught in college-level logic classes. Thus, I am often confronted with the question: What is the point of studying logic? Before examining the basic elements of logic, let me address this question.
This is a very common and quite understandable question especially given the difficulty of the subject and the abstract nature of much of formal logic. What possible purpose could be served in learning logic? When will you ever use logic? Let's look at some reasons and attempt to make the case for the importance of learning logic.
I think several distinct arguments can be made.
1. The relevance argument
2. The argument from the nature of logic
3. The mental exercise argument
4. The general knowledge argument
A common question concerning logic is how it could be relevant to the major of the student or his career. This is a stunning point if one thinks about it in light of the nature of logic which we'll address below. However, one consideration is offered by the economist Thomas Sowell. Relevance is something you can only assess after you've learned a subject. You can't tell until then whether something is relevant to your life or not. Closely related to this point is the fact that none of us knows for sure what will happen next in our life and so we can never be absolutely sure that a subject, any subject, will not be relevant. Think about it. As a 20-year-old, you might say “I know I'm never going to use this in my career or life.” Assuming (which is a safe assumption) that you'll live for 50-70 more years, how can you say this? How do you know for that length of time what will be relevant to your life and what won't? I took logic as a sophomore majoring in telecommunications and could have easily believed at the time that I might never use logic again. Who knew I'd end up teaching it!?
Logic is concerned with training the mind to think clearly. Given this, let's ask the question again: When will I ever need logic? OK, so you're asking: When will I ever need clear thinking? Now, the importance of learning logic should be crystal clear. There isn't a single area of life where clear thinking wouldn't be beneficial to some degree. The real issue here is not whether logic is useful, but how can logic and what we do in a formal logic class help improve our thinking. The real question is not whether clear thinking is needed but how can learning about categorical syllogism, truth tables, and natural deduction improve our ability to think clearly. I think I have some answers to those questions.
One of the reasons such questions come up in the first place is the apparent strangeness of formal logic. It looks so different than our ordinary use of language because it is a formal symbolic system abstracted from ordinary language. What we are attempting to analyze in logic is the underlying nature of inferential thinking and to do so we must inspect the form of our reasoning by separating it from its content. Doing so makes it look irrelevant for the same reason that looking at a car engine out of context looks irrelevant to the working of the car. Think about it. If you looked at the engine of a car without ever addressing the purpose or context you would never connect that mechanism with driving your car. If you never bothered to look under the hood you might not even know there is such a thing as an engine! For all you know there's nothing under the hood. So, if you look at the engine for the first time it looks strange. So too does the inner workings of thinking and reasoning. It's only after studying formal logic that you begin to see that the principles of logic are connected with ordinary thinking. So by studying the underlying depth of the subject you can get a greater appreciation of the ordinary application and in the process become better at that application.
Let's look at what formal logic (or symbolic logic) is forcing us to do not from the standpoint of using the principles of formal logic directly, but from the standpoint of the underlying skills these principles are drawing on. In categorical logic, you have to read statements carefully to make distinctions between terms that on the surface sound similar. You have to recognize general rules by looking at specific cases. In propositional logic, you have to recognize the general rules underlying the use of certain words and recognize these principles in different situations. Finally, in natural deduction, you have to take a set of rules and apply it in an orderly method to solve a problem. OK, look at the skills being used here: rule recognition, abstraction, planning, problem-solving, making distinctions. It is these skills that logic is training you to improve and it is these skills that represent the real practical benefits of learning logic.
Perhaps an analogy will help. Some people go to the gym to work out. They lift weights, do stair climbing, walk machines, etc. Do they do these things to improve their ability to lift weights, climb stairs, and walk? No, they do them for some other benefit which these exercises indirectly lead to. It's the same with the mind. We need some form of exercise for the mind and that's what logic is. The benefits of logic are indirect. That is, what we do in logic is improve our ability to do something else.
So, why don't we just practice the thing itself instead of practicing the skills indirectly by learning logic? Well, the answer is that we do this as well but logic represents a more rigorous form of exercise. Look at it like this. When you walk to your car or to class you are getting some exercise benefit. But, you may also go to the gym. When you carry groceries from the store to your car you are getting some exercise benefits. But, you may also lift weights. Why? Because the more casual form of the exercise isn't vigorous enough to get the true benefit of doing the exercise. It's the same with logic. When you read a book or magazine you are getting some benefit to your mental exercise. But, you need to train your mind in a more rigorous fashion forcing it to do more involved thinking. Like all exercises, your muscles are sore at first until you get used to the exertion. In time you find you are better able to handle the exercise and your general thinking skills improve as a result.
Learning is a funny thing in how it works. The more you know, the more you can learn and the more you know the easier it is to learn something new. Learning, then, is about making connections. The more general knowledge you have the easier it is to make connections. So, in this vein logic adds one more subject of knowledge to your mind allowing you to make more connections thus making the learning of anything else easier. Not only that, since the subject matter of logic is based on inferential reasoning the very skill of making connections is being learned as you go through your training in logic.
If you know something about psychology, understanding philosophy is easier because they're connected. That's an easy one to see. But there are so many ways that one field of knowledge is connected to another that we don't see immediately. Learning about logic makes it easier to learn about computers. How so? Computer programs are nothing more than logic commands. OK, but what if you're not programming a computer, only using it? Still, there is a benefit to understanding the method of following rules; thinking in an orderly fashion, recognizing that one step follows from another. All these are skills that logic teaches. There are other connections to consider as well but too numerous to list here. However, you might consider that others have thought about these issues long before you got into the classroom. It is not to punish you that they have decided you should take such classes as logic. Their experience in life (sometimes 20, 30, or 40 more years of experience than you have) has shown them that there are benefits to learning about subjects such as logic. You can benefit from their experience. Of course, the alternative is to learn about the benefits the hard way. That is, by forgoing these skills now and discovering that you need them at the worst possible moment.
Given that you don't know what might be useful later in life, and the obvious utility of logic in training the mind, and the connections between different subjects which make learning easier, it only makes sense to obtain as much knowledge as you can while you can get it. There's no better time than right now to add to your knowledge. Even knowledge which has no direct benefits now might be useful to you later on in a direct way and is certainly useful to you now in indirect ways. Some students come to logic class (and perhaps many others) with the attitude of just wanting to get the grade. That's unfortunate. First, you’re paying for something you're not taking delivery on which doesn't make a lot of sense. Like going to the store and purchasing a new big-screen plasma TV and paying for it but not picking it up! Students have told me that once they leave the class they'll forget everything they've learned. That's unfortunate too. Again, you're paying for something and not taking delivery. But also you're missing out on something that WILL benefit you shortly and MAY benefit you later in life as well. Are you willing to discard useful information so quickly? Think twice before doing that. Not only with logic but with every other subject you encounter. Besides, it costs you nothing to hang on to knowledge. The brain is not a sieve leaking out old information to make room for new or a small container, which must be cleared out to make room for new information. The brain is a complex organ capable of making connections between different knowledge sets, and the more connections you make the more knowledgeable you become. Imagine how much better at information processing and using you'd be if you learned the basics of making connections, inferences, arguments, and deductions. Guess what, Logic teaches all of those skills!
In academia, we've known for years that people with limited knowledge are easy targets for scam artists, tricksters, politicians, and demagogues. What you need to know is that the scam artists, tricksters, politicians, and demagogues know this too. Francis Bacon was right; knowledge is power. And protection. You spend money to protect your computer against viruses, your cars against theft, your health against illness. You're also spending money to protect your mind against harm. The product you purchase to do this is NOT a grade. It is NOT a piece of paper called a degree. It's the knowledge behind them that will help you. You paid for it. Take it!
“A great many people think they are thinking when they are merely rearranging their prejudices." William James
After we discuss logic, it might not come as a shock that philosophers are often accused of ignoring emotion or being unconcerned with emotion which is patently untrue. Throughout the history of philosophy, there have been philosophers who have written about emotions to understand, and in some cases, control them. Plato, Aristotle, the Stoics, Epicurus, Descartes, Hume, Sartre are just a few who have inquired into the nature of emotions. In ethics, there is a theory that claims that moral statements are nothing but the expressions of one's emotions.
But, the point of this essay is not to defend the philosophical investigation of emotions. Instead, I would like to encourage a distinction between thinking and emotion in one limited sense. While philosophers investigate many questions, in their formulation of theories they are usually attempting to tell us what they think about a subject not how they feel. There is a good reason for this which I would advocate when you write about philosophy or any other academic subject. As you write an academic paper bear in mind that in most cases the assignment is to formulate your thoughts and defend them. It is not to tell your professor how you feel. It is certainly not to tell your professor how others feel.
This may seem like a purely semantic point. Perhaps when you use the word feel you're meaning to state what you think. But, words do have meanings and it is important to recognize important distinctions, such as the distinction between thinking and feeling. The most important difference between the two words and the sentiments behind them is that one requires justification and the other does not. When I tell someone what I think it is fair for them to ask me why I think this. What evidence am I presenting to back up my opinion? Is the evidence persuasive and complete or is it inadequate to verify the claim I am making? This is not the case with feelings. If I tell someone I feel hot I do not have to justify this feeling. It would seem strange for someone to demand of me any justification for this or any other feeling. My feelings are what they are. And as many psychologists will tell you, they are neither good nor bad and neither true nor false.
The problem with referring to feelings in philosophy in the way I am criticizing is twofold. First, it is likely inaccurate. When you say something like "Plato felt that there was a realm of the forms" you are not accurately depicting Plato's feelings at all. How could you? We don't know what Plato felt about the Forms since he never told us! However, we do know some of what he thought about the Forms, and if I ask you an exam question about Plato's theory that is what I want you to tell me: what Plato thought, not what he felt. Second, to claim that Plato merely felt a certain way about the Forms is to diminish the philosophical exercise the philosopher was engaged in. The attempt to formulate a theory about something is simply an attempt to take the available evidence and provide the best possible explanation for it. In doing so, the philosopher attempts to anticipate possible objections to his explanation and address them. The philosopher is also prepared to defend his theory in the court of public opinion and allow his theory to be subjected to criticism and debate. If it were nothing more than a feeling, there would be no need to scrutinize it at all. There would be no interest in it at all!
When you write a philosophy exam or paper (or any other paper) you will be asked to explain your views or opinions. You will not be asked to describe how you feel. So, as harsh as this sounds, don't tell me how you feel! Don't tell me how the philosophers you are writing about feel either. Tell me what they thought and why they thought it. Tell me what you think and why you think it.
It is fine to express opinions but you must also explain why you hold these opinions and, more than that, explain why you think your opinions are correct. Many seem to confuse what philosophers do by saying that they just express their opinions. Philosophers do more than this by backing up their opinions with reason. This is the crucial distinction between arguments and opinions. Arguments can contain opinions but to argue for something is to do more than simply express an opinion or a feeling about something.
I find it remarkable how some people can be very tentative about their opinions. This occurs most often in the realm of opinions concerning morality. Someone believes abortion is immoral but doesn't think others should believe this as well. Students will say that everyone has their own beliefs. Of course, this is quite true but the question is, "Are these beliefs justified?" This is why we need to examine the reasons behind the opinions. If the opinions are not justified then no one should hold them. On the other hand, if the opinions are justified and backed up by good reasons, shouldn't everyone agree with them?
To this many will respond by asking "But, who am I to tell someone else their beliefs are wrong?" The point is that you are not telling them because you are not examining their beliefs; they are! One of the useful skills you can take from any philosophy course is a method for examining your beliefs and justification for them. The point of the examination is not necessary to change your beliefs although if you discover they cannot be justified perhaps they need to be changed. It could easily be the case that you find a stronger justification for them than you suspected even existed. In any case, it is the examination that is valuable. We are always being encouraged to examine our feelings. While philosophy is not unconcerned with feelings, the main point of philosophy is to allow us to examine our thinking.
Another way of looking at this is that the examination of one's beliefs is done by appealing to objective criteria we can use to determine whether our beliefs are justified. They are important to understand to successfully examine one's beliefs and opinions and are quite easy to understand with a little work. However, the fact that this takes work at all probably explains why many prefer to simply talk about feelings. There's no work involved in justifying feelings because feelings don't need justification!
Logic is defined as the science of evaluating arguments. This may be a little misleading because of the specific use of the word argument. In philosophy, the argument does not simply mean disagreement. If you were to say that Ford produces better cars than Toyota and I was to say that Toyota produces better cars than Ford we would be disagreeing but not necessarily arguing. An argument must contain two elements. First, there must be the main point that is being argued for. This is called the conclusion. Arguments are sometimes confused with opinions because the conclusion of many arguments is an opinion. However, arguments are more than opinions because they contain a second element; the premises. In an argument, facts must be presented to support the conclusion and these facts are the premises. So now it should be clear why the example above is not an argument. While you may state that Ford produces better cars than Toyota for this to be an argument you must present reasons why Ford produces better cars than Toyota.
So we've established that arguments contain two parts. The purpose of the premises is to provide support for the conclusion. This support can be provided in two ways giving rise to two types of arguments. In deductive arguments, the premises support the conclusion as a matter of necessity. Another way of thinking about this is that if the premises in a good deductive argument are true, then the conclusion must also be true. On the other hand, in inductive arguments, the premises support the conclusion as a matter of probability. So, in a good inductive argument, if the premises are true the conclusion will probably be true.
This distinction becomes very important when we begin evaluating arguments. If an argument is, in fact, inductive (as most arguments in philosophy are) then saying that the premises do not necessarily support the conclusion will be an unfair criticism. After all, the intent of inductive arguments is only to provide probable support. This may cause you to ask whether inductive arguments aren't always inferior to deductive arguments. This may be one way of thinking about it. However, there are many kinds of arguments that cannot be deductive. For example, if we want to make predictions or use statistical reasoning in an argument, we are arguing inductively. The very nature of some arguments is inductive. While we may wish it to be otherwise, there's little that can be done about this. We have to evaluate arguments within their proper context. This goes for all arguments and, as we'll see, is an important point to keep in mind when we consider various philosophical arguments.
Another important consideration concerning evaluating arguments is the notion of proof. Throughout this book we will be looking at various philosophical arguments which purport to prove a certain conclusion; for example, the existence of God. People often misunderstand the concept of proof by thinking that proving something demonstrates conclusively that something must be true. While this may be the case for deductive arguments, as we've seen it cannot be that way for inductive arguments. Since most philosophical (and scientific) arguments are inductive, it is impossible to conclusively prove the conclusion of these arguments true. That is, we will not be able to preclude evidence that may arise in the future to count against our conclusion. This being the case proofs in philosophy tended to attempt to find the most probable conclusion that fits the available evidence.
"We cannot pretend to offer proofs. the proof is an idol before whom the pure mathematician tortures himself: In physics, we are generally content to sacrifice before the lesser shrine of plausibility." Arthur Stanley Eddington
The proof is a seriously misunderstood word. This probably accounts for its rare usage in the natural sciences. In one important sense no one can "prove" the theory of evolution, or the big bang theory, or relativity, or string theory, or whatever theory you want to talk about. But, and this and this and this is important, that does not mean that there is not sufficient evidence to warrant thinking these are good theories. To use Eddington's word words, we can say they are plausible. In some cases, very plausible. What makes the word proof tricky is that it is sometimes used in philosophy in the one area you'd think everyone would be wary of using it: to prove the existence of God. Many people believe that God's existence cannot be proven. Let's stipulate to that for the sake of argument and vow only to use the word proof in areas where certainty appears attainable, like mathematics. The parallel postulate can be proven.
So what do we do with areas of empirical research? What do we do about God? Let's look for evidence and evaluate theories based on their plausibility and efficacy in explaining and accounting for that evidence. We need a set of criteria to evaluate theories to determine which best account for the evidence we have. A good suggestion comes from a critical thinking text titled How to Think About Weird Things by Theodore Schick and Lewis Vaughn. In it, they outline five points to use in the evaluation of theories. Let's look at them.
First, a theory should be testable. If you can’t even figure out how to go about determining if your theory explains the evidence you don't have a good theory. As they point out testable means your hypothesis "predicts something more than what is predicted by the background theory alone." In short, we need this criterion because if there's no way to tell whether a theory is true or false it's no good to us.
Second, a theory should be fruitful. What this means is that a good theory should make novel predictions. It should not only account for the evidence at hand but be able to address evidence that comes in later and even predict such new evidence. They point out that Einstein's theory of relativity is a good example of a fruitful theory because it made the novel prediction that light would be visible from a star behind the sun. After all, the light would be bent by the gravitational field around the sun to be visible on earth. And, concerning criterion number one, this was a testable claim. Once tested, it was verified.
Third, a theory should have a wide scope. That is, a good theory explains a wide field of evidence. One of the differences between theories and hypotheses is their scope. Hypotheses address specific questions whereas theories attempt to provide a broad explanatory device. Theories that can explain a wide array of things are preferred, other things being equal, to more narrow theories.
Fourth, a theory should be simple. This term should not be confused with simplistic. Many scientific theories are complex in terms of our ability to understand them but simple in the sense that they postulate fewer underlying entities or assumptions. A good example of this is the difference between Copernicus and Ptolemy. Ptolemy's geocentric theory could explain the orbits of the planets but it was quite complex whereas Copernicus' theory explained the same observable phenomena with less complexity. So, other things being equal, that theory was the better theory. Think of it this way. Suppose I come up with a theory to explain how the lights in my housework but it involves little gremlins running inside the light bulbs. Someone else can explain the same phenomenon but without postulating gremlins. So, their theory is simpler than mine. It should also be pointed out that my gremlin theory may fail on other criteria as well such as being testable.
Finally, a theory should be conservative. Not in the political sense of the word. Rather, it should fit in with other things we know. If we have an explanation for something that we think is fairly certain and accurate then a new theory should fit in with that prior explanation. If it doesn't fit that may indicate our prior knowledge is flawed. We have to be open to that possibility but the burden of proof is on the new theory. An interesting examination of how this process works is offered by Thomas Kuhn's book The Structure of Scientific Revolutions.
Now, for the payoff. While many may hate to hear this, judging by the criteria above, the theory of evolution and the big bang theory do quite well. In fact, as the philosopher, Daniel Dennett puts it "evolution is about as well established as the fact that water is H2O." This doesn't mean that the theory isn't open to revision. But, all available evidence seems to point in favor of it. A similar statement could be made about the big bang theory again, with the proviso, "at this time." So far as we know now. This will always be the case for any theory in science. As Karl Popper pointed out, "the demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever."
So, why do people find this a hard pill to swallow about the theories I mentioned above. I suspect it's because they do not know about them and based on this lack of knowledge they conclude that these theories do damage to some of their cherished beliefs. No book has been more reviled since its publication than Darwin's Origin of Species. But, I suspect no book has been left unread as often! Scientists have no problem with entertaining objections to their theories, but the objections should be based on some knowledge of the theory. I cannot devote myself here to explaining in sufficient detail the theories I'm addressing though I could if put to the test. But that is not the point of this essay.
My point, as a philosopher, is to encourage learning and inquiry. But first comes learning. As you’ll see in this book, philosophers are all too willing to subject other philosophers to criticism. But they do so from the standpoint of understanding their opponent's theory. We owe the same to any theory be it in philosophy, theology, or science. It does no good to criticize or dismiss a theory out of hand without a thorough understanding of what the theory says and what phenomena it is attempting to explain.
Many say they do not believe in the theory of evolution or the big bang. But the word "believe," like the word "proof," is being misused here. A theory is not something to be believed or disbelieved. The question is whether the evidence warrants our tentative acceptance of the theory. Does the theory do what it claims to do? That is, does it provide us with an adequate explanation of the evidence at hand? If so, it's a good theory. You are certainly free to think otherwise but this doesn't change the fact that the theory is supported by the evidence.
Of course, any theory may turn out to be wrong but as David Hume said "the wise man proportions his belief to the evidence." If the evidence warrants it, the theory should be accepted. This does not amount to conceding everything to the world of science because there are many questions science cannot answer. These include questions of value and meaning such as:
Does my life have a purpose?
Does the universe's existence have a purpose?
Is abortion immoral?
Is it ever right to lie?
Here is where the value of philosophy lies because it is a philosophy that attempts to examine these questions and reason to useful answers. Not necessarily definitive answers. There may be no definitive answers to these questions. But, we can examine them in the light of reason and come to some interesting conclusions. But, these conclusions can be furthered by the work scientists do as they attempt to explain the natural world in which we live. After all, asking about the purpose of our lives is a question that can be dealt with much better if we have some understanding of life. To ask whether the universe's existence has a purpose can be answered more clearly if we have some understanding of the universe itself. It is misguided to reject the information that science gives us which may pertain to these and other questions. The scientific method is, after all, the most reliable means we have of gaining information about the natural world. Information, without which, we would not be able to philosophize with any sophistication at all.
Finally, don't accept the conclusion of an argument just because you like it, and don't reject the conclusion just because you dislike it. In each case, you need to consider the reasoning used and determine whether the conclusion is supported by the premises and whether the premises are true. Wanting something to be true does not make it true and wanting something to be false does not make it false. The questions we examine can be difficult but applying the rules of reason can make our job of evaluating philosophical arguments easier and more fruitful.
No good system of reasoning would be complete without a foundation and in logic, this foundation consists of three laws of thought. In essence, these laws represent the fundamental principles from which all our reasoning proceeds. They are considered self-evident which means that merely understanding them should be enough to recognize their truth. Because of their self-evident nature, they can be used to deduce other important philosophical principles. Before considering these principles (and while we're still on the subject of proof) we should recognize that these laws of thought cannot, themselves, be proven. As Aristotle pointed out in his Metaphysics concerning one of these laws: "some indeed demand to have the law proved, but this is because they lack education; for it shows lack of education not to know of what we should require proof and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity so that even so there would be no proof."
The first of these laws of thought is called the law of non-contradiction. What this says is that nothing can both be and not be at the same time and in the same respect. This may not seem very interesting but we can use this law to demonstrate that philosophical arguments are not merely people's differences of opinion. Since we've raised the example of proving the existence of God let's look at this. Some people say that there is no way to prove the existence of God and, after all, it's just a matter of opinion anyway, so what does it matter. However, we can use the law of non-contradiction to demonstrate that there is something more going on. Concerning God, there are two (and only two) possibilities: God exists. God doesn't exist. They cannot both be true. But if it were just a matter of opinion, they could both be true. So clearly, this is not merely an opinion-based question. Not only that from the fact that God cannot both exist and not exist we can deduce something else interesting.
What we can deduce is that either one or the other of these two possibilities must be true. This, as it turns out, is the second law of thought: the law of excluded middle. What this asserts is that something either is or is not. This seems non-controversial however, some people find it confusing. Many mistake-mistakes mistake mistakes this for saying that everything must be either black or white with no in between-between. But aren't there some gray areas in life; never mind in philosophy? However, a closer inspection of what the law of excluded middle is saying should clarify this point. What the law asserts, using the black or white example is that everything is either black or non-black. Put this way, it should be true.
The final law of thought is the law of identity. What this asserts is that something is what it is. Again, this seems non-controversial and uninteresting. However, as we will see, when discussing the philosophy of mind, the law of identity will have interesting philosophical implications. I'll elaborate on this in a later chapter but keep this idea in mind. It will become useful.
Before concluding our remarks on logic, we need to consider some common mistakes in reasoning; what we call fallacies. We should attend to these for two reasons. First, we want to be able to identify these mistakes if they occur in the philosophical arguments we will be analyzing. Identifying fallacies may come in handy when considering non-philosophical arguments as well. Second, we should familiarize ourselves with fallacies to avoid committing them ourselves.
Aristotle originally identified many of these fallacies and later philosophers added them o the list. We will not be addressing every fallacy but I will mention some of the more philosophically relevant ones.
1. Begging the question: this fallacy occurs when the conclusion of an argument is used as one of the premises. So, it seems as if you're proving something when in reality you're restating your premise as the conclusion. For example, if I were to argue as follows: Of course, God exists because only God could create the immensely complex universe.
2. Equivocation: This fallacy occurs when the meaning of a critical word is changed within the argument. In other words, we use one word in two different ways. Example: Any law can be repealed by the legislative authority. So, since the law of gravity is a law, it too can be repealed by the legislative authority.
3. Composition: occurs when an attribute is transferred from a part of a whole to the whole when the attribute cannot transfer. For example ,Atoms are invisible so a piece of chalk that is composed of atoms must be invisible.
4. Division: is the reverse of composition. It occurs when an attribute is transferred from the whole to the parts when the attribute cannot transfer. Example: Salt is non-poisonous and salt is composed of sodium and chlorine. Therefore, sodium and chlorine are non-poisonous.
5. Appeal to authority: this fallacy occurs when an unqualified expert or irrelevant authority is used to support the conclusion of an argument, for instance, if I were to cite an economist's expertise to support my argument in physics.
Appeal to authority is particularly relevant to Aristotle who, in the Middle Ages, was considered an important authority in philosophy and learning in general. So much so, that Aquinas referred to him as The Philosopher. Aristotle's influence extended so far and wide that many subjects he wrote about were not advanced for centuries because of his perceived authority. So, while Aristotle was Plato's best student and most vocal critic, many of Aristotle's students, and many who were influenced by him, were less critical. Indeed, unlike Plato, Aristotle's most prominent student was not a vocal critic of Aristotle's theory. He was not as much interested in metaphysics as he was in the implications of such speculation. Instead of being concerned about the nature of reality, he was interested in changing it; at least the reality of geopolitics in the ancient world. Alexander the Great, the student I'm talking about, was much more interested in empire-building. Naturally, philosophy was affected by this and other empires as well. In fact, within a couple of centuries, the philosopher was to become the emperor of the world's most powerful empire. The empire was Rome and the emperor-philosopher was Marcus Aurelius. It is to the story of philosophy during and after the Roman Empire that we turn now.
This is a very common and quite understandable question especially given the difficulty of the subject and the abstract nature of much of formal logic. What possible purpose could be served in learning logic? When will you ever use logic? Let's look at some reasons and attempt to make the case for the importance of learning logic.
I think several distinct arguments can be made.
1. The relevance argument
2. The argument from the nature of logic
3. The mental exercise argument
4. The general knowledge argument
A common question concerning logic is how it could be relevant to the major of the student or his career. This is a stunning point if one thinks about it in light of the nature of logic which we'll address below. However, one consideration is offered by the economist Thomas Sowell. Relevance is something you can only assess after you've learned a subject. You can't tell until then whether something is relevant to your life or not. Closely related to this point is the fact that none of us knows for sure what will happen next in our life and so we can never be absolutely sure that a subject, any subject, will not be relevant. Think about it. As a 20-year-old, you might say “I know I'm never going to use this in my career or life.” Assuming (which is a safe assumption) that you'll live for 50-70 more years, how can you say this? How do you know for that length of time what will be relevant to your life and what won't? I took logic as a sophomore majoring in telecommunications and could have easily believed at the time that I might never use logic again. Who knew I'd end up teaching it!?
Logic is concerned with training the mind to think clearly. Given this, let's ask the question again: When will I ever need logic? OK, so you're asking: When will I ever need clear thinking? Now, the importance of learning logic should be crystal clear. There isn't a single area of life where clear thinking wouldn't be beneficial to some degree. The real issue here is not whether logic is useful, but how can logic and what we do in a formal logic class help improve our thinking. The real question is not whether clear thinking is needed but how can learning about categorical syllogism, truth tables, and natural deduction improve our ability to think clearly. I think I have some answers to those questions.
One of the reasons such questions come up in the first place is the apparent strangeness of formal logic. It looks so different than our ordinary use of language because it is a formal symbolic system abstracted from ordinary language. What we are attempting to analyze in logic is the underlying nature of inferential thinking and to do so we must inspect the form of our reasoning by separating it from its content. Doing so makes it look irrelevant for the same reason that looking at a car engine out of context looks irrelevant to the working of the car. Think about it. If you looked at the engine of a car without ever addressing the purpose or context you would never connect that mechanism with driving your car. If you never bothered to look under the hood you might not even know there is such a thing as an engine! For all you know there's nothing under the hood. So, if you look at the engine for the first time it looks strange. So too does the inner workings of thinking and reasoning. It's only after studying formal logic that you begin to see that the principles of logic are connected with ordinary thinking. So by studying the underlying depth of the subject you can get a greater appreciation of the ordinary application and in the process become better at that application.
Let's look at what formal logic (or symbolic logic) is forcing us to do not from the standpoint of using the principles of formal logic directly, but from the standpoint of the underlying skills these principles are drawing on. In categorical logic, you have to read statements carefully to make distinctions between terms that on the surface sound similar. You have to recognize general rules by looking at specific cases. In propositional logic, you have to recognize the general rules underlying the use of certain words and recognize these principles in different situations. Finally, in natural deduction, you have to take a set of rules and apply it in an orderly method to solve a problem. OK, look at the skills being used here: rule recognition, abstraction, planning, problem-solving, making distinctions. It is these skills that logic is training you to improve and it is these skills that represent the real practical benefits of learning logic.
Perhaps an analogy will help. Some people go to the gym to work out. They lift weights, do stair climbing, walk machines, etc. Do they do these things to improve their ability to lift weights, climb stairs, and walk? No, they do them for some other benefit which these exercises indirectly lead to. It's the same with the mind. We need some form of exercise for the mind and that's what logic is. The benefits of logic are indirect. That is, what we do in logic is improve our ability to do something else.
So, why don't we just practice the thing itself instead of practicing the skills indirectly by learning logic? Well, the answer is that we do this as well but logic represents a more rigorous form of exercise. Look at it like this. When you walk to your car or to class you are getting some exercise benefit. But, you may also go to the gym. When you carry groceries from the store to your car you are getting some exercise benefits. But, you may also lift weights. Why? Because the more casual form of the exercise isn't vigorous enough to get the true benefit of doing the exercise. It's the same with logic. When you read a book or magazine you are getting some benefit to your mental exercise. But, you need to train your mind in a more rigorous fashion forcing it to do more involved thinking. Like all exercises, your muscles are sore at first until you get used to the exertion. In time you find you are better able to handle the exercise and your general thinking skills improve as a result.
Learning is a funny thing in how it works. The more you know, the more you can learn and the more you know the easier it is to learn something new. Learning, then, is about making connections. The more general knowledge you have the easier it is to make connections. So, in this vein logic adds one more subject of knowledge to your mind allowing you to make more connections thus making the learning of anything else easier. Not only that, since the subject matter of logic is based on inferential reasoning the very skill of making connections is being learned as you go through your training in logic.
If you know something about psychology, understanding philosophy is easier because they're connected. That's an easy one to see. But there are so many ways that one field of knowledge is connected to another that we don't see immediately. Learning about logic makes it easier to learn about computers. How so? Computer programs are nothing more than logic commands. OK, but what if you're not programming a computer, only using it? Still, there is a benefit to understanding the method of following rules; thinking in an orderly fashion, recognizing that one step follows from another. All these are skills that logic teaches. There are other connections to consider as well but too numerous to list here. However, you might consider that others have thought about these issues long before you got into the classroom. It is not to punish you that they have decided you should take such classes as logic. Their experience in life (sometimes 20, 30, or 40 more years of experience than you have) has shown them that there are benefits to learning about subjects such as logic. You can benefit from their experience. Of course, the alternative is to learn about the benefits the hard way. That is, by forgoing these skills now and discovering that you need them at the worst possible moment.
Given that you don't know what might be useful later in life, and the obvious utility of logic in training the mind, and the connections between different subjects which make learning easier, it only makes sense to obtain as much knowledge as you can while you can get it. There's no better time than right now to add to your knowledge. Even knowledge which has no direct benefits now might be useful to you later on in a direct way and is certainly useful to you now in indirect ways. Some students come to logic class (and perhaps many others) with the attitude of just wanting to get the grade. That's unfortunate. First, you’re paying for something you're not taking delivery on which doesn't make a lot of sense. Like going to the store and purchasing a new big-screen plasma TV and paying for it but not picking it up! Students have told me that once they leave the class they'll forget everything they've learned. That's unfortunate too. Again, you're paying for something and not taking delivery. But also you're missing out on something that WILL benefit you shortly and MAY benefit you later in life as well. Are you willing to discard useful information so quickly? Think twice before doing that. Not only with logic but with every other subject you encounter. Besides, it costs you nothing to hang on to knowledge. The brain is not a sieve leaking out old information to make room for new or a small container, which must be cleared out to make room for new information. The brain is a complex organ capable of making connections between different knowledge sets, and the more connections you make the more knowledgeable you become. Imagine how much better at information processing and using you'd be if you learned the basics of making connections, inferences, arguments, and deductions. Guess what, Logic teaches all of those skills!
In academia, we've known for years that people with limited knowledge are easy targets for scam artists, tricksters, politicians, and demagogues. What you need to know is that the scam artists, tricksters, politicians, and demagogues know this too. Francis Bacon was right; knowledge is power. And protection. You spend money to protect your computer against viruses, your cars against theft, your health against illness. You're also spending money to protect your mind against harm. The product you purchase to do this is NOT a grade. It is NOT a piece of paper called a degree. It's the knowledge behind them that will help you. You paid for it. Take it!
“A great many people think they are thinking when they are merely rearranging their prejudices." William James
After we discuss logic, it might not come as a shock that philosophers are often accused of ignoring emotion or being unconcerned with emotion which is patently untrue. Throughout the history of philosophy, there have been philosophers who have written about emotions to understand, and in some cases, control them. Plato, Aristotle, the Stoics, Epicurus, Descartes, Hume, Sartre are just a few who have inquired into the nature of emotions. In ethics, there is a theory that claims that moral statements are nothing but the expressions of one's emotions.
But, the point of this essay is not to defend the philosophical investigation of emotions. Instead, I would like to encourage a distinction between thinking and emotion in one limited sense. While philosophers investigate many questions, in their formulation of theories they are usually attempting to tell us what they think about a subject not how they feel. There is a good reason for this which I would advocate when you write about philosophy or any other academic subject. As you write an academic paper bear in mind that in most cases the assignment is to formulate your thoughts and defend them. It is not to tell your professor how you feel. It is certainly not to tell your professor how others feel.
This may seem like a purely semantic point. Perhaps when you use the word feel you're meaning to state what you think. But, words do have meanings and it is important to recognize important distinctions, such as the distinction between thinking and feeling. The most important difference between the two words and the sentiments behind them is that one requires justification and the other does not. When I tell someone what I think it is fair for them to ask me why I think this. What evidence am I presenting to back up my opinion? Is the evidence persuasive and complete or is it inadequate to verify the claim I am making? This is not the case with feelings. If I tell someone I feel hot I do not have to justify this feeling. It would seem strange for someone to demand of me any justification for this or any other feeling. My feelings are what they are. And as many psychologists will tell you, they are neither good nor bad and neither true nor false.
The problem with referring to feelings in philosophy in the way I am criticizing is twofold. First, it is likely inaccurate. When you say something like "Plato felt that there was a realm of the forms" you are not accurately depicting Plato's feelings at all. How could you? We don't know what Plato felt about the Forms since he never told us! However, we do know some of what he thought about the Forms, and if I ask you an exam question about Plato's theory that is what I want you to tell me: what Plato thought, not what he felt. Second, to claim that Plato merely felt a certain way about the Forms is to diminish the philosophical exercise the philosopher was engaged in. The attempt to formulate a theory about something is simply an attempt to take the available evidence and provide the best possible explanation for it. In doing so, the philosopher attempts to anticipate possible objections to his explanation and address them. The philosopher is also prepared to defend his theory in the court of public opinion and allow his theory to be subjected to criticism and debate. If it were nothing more than a feeling, there would be no need to scrutinize it at all. There would be no interest in it at all!
When you write a philosophy exam or paper (or any other paper) you will be asked to explain your views or opinions. You will not be asked to describe how you feel. So, as harsh as this sounds, don't tell me how you feel! Don't tell me how the philosophers you are writing about feel either. Tell me what they thought and why they thought it. Tell me what you think and why you think it.
It is fine to express opinions but you must also explain why you hold these opinions and, more than that, explain why you think your opinions are correct. Many seem to confuse what philosophers do by saying that they just express their opinions. Philosophers do more than this by backing up their opinions with reason. This is the crucial distinction between arguments and opinions. Arguments can contain opinions but to argue for something is to do more than simply express an opinion or a feeling about something.
I find it remarkable how some people can be very tentative about their opinions. This occurs most often in the realm of opinions concerning morality. Someone believes abortion is immoral but doesn't think others should believe this as well. Students will say that everyone has their own beliefs. Of course, this is quite true but the question is, "Are these beliefs justified?" This is why we need to examine the reasons behind the opinions. If the opinions are not justified then no one should hold them. On the other hand, if the opinions are justified and backed up by good reasons, shouldn't everyone agree with them?
To this many will respond by asking "But, who am I to tell someone else their beliefs are wrong?" The point is that you are not telling them because you are not examining their beliefs; they are! One of the useful skills you can take from any philosophy course is a method for examining your beliefs and justification for them. The point of the examination is not necessary to change your beliefs although if you discover they cannot be justified perhaps they need to be changed. It could easily be the case that you find a stronger justification for them than you suspected even existed. In any case, it is the examination that is valuable. We are always being encouraged to examine our feelings. While philosophy is not unconcerned with feelings, the main point of philosophy is to allow us to examine our thinking.
Another way of looking at this is that the examination of one's beliefs is done by appealing to objective criteria we can use to determine whether our beliefs are justified. They are important to understand to successfully examine one's beliefs and opinions and are quite easy to understand with a little work. However, the fact that this takes work at all probably explains why many prefer to simply talk about feelings. There's no work involved in justifying feelings because feelings don't need justification!
Logic is defined as the science of evaluating arguments. This may be a little misleading because of the specific use of the word argument. In philosophy, the argument does not simply mean disagreement. If you were to say that Ford produces better cars than Toyota and I was to say that Toyota produces better cars than Ford we would be disagreeing but not necessarily arguing. An argument must contain two elements. First, there must be the main point that is being argued for. This is called the conclusion. Arguments are sometimes confused with opinions because the conclusion of many arguments is an opinion. However, arguments are more than opinions because they contain a second element; the premises. In an argument, facts must be presented to support the conclusion and these facts are the premises. So now it should be clear why the example above is not an argument. While you may state that Ford produces better cars than Toyota for this to be an argument you must present reasons why Ford produces better cars than Toyota.
So we've established that arguments contain two parts. The purpose of the premises is to provide support for the conclusion. This support can be provided in two ways giving rise to two types of arguments. In deductive arguments, the premises support the conclusion as a matter of necessity. Another way of thinking about this is that if the premises in a good deductive argument are true, then the conclusion must also be true. On the other hand, in inductive arguments, the premises support the conclusion as a matter of probability. So, in a good inductive argument, if the premises are true the conclusion will probably be true.
This distinction becomes very important when we begin evaluating arguments. If an argument is, in fact, inductive (as most arguments in philosophy are) then saying that the premises do not necessarily support the conclusion will be an unfair criticism. After all, the intent of inductive arguments is only to provide probable support. This may cause you to ask whether inductive arguments aren't always inferior to deductive arguments. This may be one way of thinking about it. However, there are many kinds of arguments that cannot be deductive. For example, if we want to make predictions or use statistical reasoning in an argument, we are arguing inductively. The very nature of some arguments is inductive. While we may wish it to be otherwise, there's little that can be done about this. We have to evaluate arguments within their proper context. This goes for all arguments and, as we'll see, is an important point to keep in mind when we consider various philosophical arguments.
Another important consideration concerning evaluating arguments is the notion of proof. Throughout this book we will be looking at various philosophical arguments which purport to prove a certain conclusion; for example, the existence of God. People often misunderstand the concept of proof by thinking that proving something demonstrates conclusively that something must be true. While this may be the case for deductive arguments, as we've seen it cannot be that way for inductive arguments. Since most philosophical (and scientific) arguments are inductive, it is impossible to conclusively prove the conclusion of these arguments true. That is, we will not be able to preclude evidence that may arise in the future to count against our conclusion. This being the case proofs in philosophy tended to attempt to find the most probable conclusion that fits the available evidence.
"We cannot pretend to offer proofs. the proof is an idol before whom the pure mathematician tortures himself: In physics, we are generally content to sacrifice before the lesser shrine of plausibility." Arthur Stanley Eddington
The proof is a seriously misunderstood word. This probably accounts for its rare usage in the natural sciences. In one important sense no one can "prove" the theory of evolution, or the big bang theory, or relativity, or string theory, or whatever theory you want to talk about. But, and this and this and this is important, that does not mean that there is not sufficient evidence to warrant thinking these are good theories. To use Eddington's word words, we can say they are plausible. In some cases, very plausible. What makes the word proof tricky is that it is sometimes used in philosophy in the one area you'd think everyone would be wary of using it: to prove the existence of God. Many people believe that God's existence cannot be proven. Let's stipulate to that for the sake of argument and vow only to use the word proof in areas where certainty appears attainable, like mathematics. The parallel postulate can be proven.
So what do we do with areas of empirical research? What do we do about God? Let's look for evidence and evaluate theories based on their plausibility and efficacy in explaining and accounting for that evidence. We need a set of criteria to evaluate theories to determine which best account for the evidence we have. A good suggestion comes from a critical thinking text titled How to Think About Weird Things by Theodore Schick and Lewis Vaughn. In it, they outline five points to use in the evaluation of theories. Let's look at them.
First, a theory should be testable. If you can’t even figure out how to go about determining if your theory explains the evidence you don't have a good theory. As they point out testable means your hypothesis "predicts something more than what is predicted by the background theory alone." In short, we need this criterion because if there's no way to tell whether a theory is true or false it's no good to us.
Second, a theory should be fruitful. What this means is that a good theory should make novel predictions. It should not only account for the evidence at hand but be able to address evidence that comes in later and even predict such new evidence. They point out that Einstein's theory of relativity is a good example of a fruitful theory because it made the novel prediction that light would be visible from a star behind the sun. After all, the light would be bent by the gravitational field around the sun to be visible on earth. And, concerning criterion number one, this was a testable claim. Once tested, it was verified.
Third, a theory should have a wide scope. That is, a good theory explains a wide field of evidence. One of the differences between theories and hypotheses is their scope. Hypotheses address specific questions whereas theories attempt to provide a broad explanatory device. Theories that can explain a wide array of things are preferred, other things being equal, to more narrow theories.
Fourth, a theory should be simple. This term should not be confused with simplistic. Many scientific theories are complex in terms of our ability to understand them but simple in the sense that they postulate fewer underlying entities or assumptions. A good example of this is the difference between Copernicus and Ptolemy. Ptolemy's geocentric theory could explain the orbits of the planets but it was quite complex whereas Copernicus' theory explained the same observable phenomena with less complexity. So, other things being equal, that theory was the better theory. Think of it this way. Suppose I come up with a theory to explain how the lights in my housework but it involves little gremlins running inside the light bulbs. Someone else can explain the same phenomenon but without postulating gremlins. So, their theory is simpler than mine. It should also be pointed out that my gremlin theory may fail on other criteria as well such as being testable.
Finally, a theory should be conservative. Not in the political sense of the word. Rather, it should fit in with other things we know. If we have an explanation for something that we think is fairly certain and accurate then a new theory should fit in with that prior explanation. If it doesn't fit that may indicate our prior knowledge is flawed. We have to be open to that possibility but the burden of proof is on the new theory. An interesting examination of how this process works is offered by Thomas Kuhn's book The Structure of Scientific Revolutions.
Now, for the payoff. While many may hate to hear this, judging by the criteria above, the theory of evolution and the big bang theory do quite well. In fact, as the philosopher, Daniel Dennett puts it "evolution is about as well established as the fact that water is H2O." This doesn't mean that the theory isn't open to revision. But, all available evidence seems to point in favor of it. A similar statement could be made about the big bang theory again, with the proviso, "at this time." So far as we know now. This will always be the case for any theory in science. As Karl Popper pointed out, "the demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever."
So, why do people find this a hard pill to swallow about the theories I mentioned above. I suspect it's because they do not know about them and based on this lack of knowledge they conclude that these theories do damage to some of their cherished beliefs. No book has been more reviled since its publication than Darwin's Origin of Species. But, I suspect no book has been left unread as often! Scientists have no problem with entertaining objections to their theories, but the objections should be based on some knowledge of the theory. I cannot devote myself here to explaining in sufficient detail the theories I'm addressing though I could if put to the test. But that is not the point of this essay.
My point, as a philosopher, is to encourage learning and inquiry. But first comes learning. As you’ll see in this book, philosophers are all too willing to subject other philosophers to criticism. But they do so from the standpoint of understanding their opponent's theory. We owe the same to any theory be it in philosophy, theology, or science. It does no good to criticize or dismiss a theory out of hand without a thorough understanding of what the theory says and what phenomena it is attempting to explain.
Many say they do not believe in the theory of evolution or the big bang. But the word "believe," like the word "proof," is being misused here. A theory is not something to be believed or disbelieved. The question is whether the evidence warrants our tentative acceptance of the theory. Does the theory do what it claims to do? That is, does it provide us with an adequate explanation of the evidence at hand? If so, it's a good theory. You are certainly free to think otherwise but this doesn't change the fact that the theory is supported by the evidence.
Of course, any theory may turn out to be wrong but as David Hume said "the wise man proportions his belief to the evidence." If the evidence warrants it, the theory should be accepted. This does not amount to conceding everything to the world of science because there are many questions science cannot answer. These include questions of value and meaning such as:
Does my life have a purpose?
Does the universe's existence have a purpose?
Is abortion immoral?
Is it ever right to lie?
Here is where the value of philosophy lies because it is a philosophy that attempts to examine these questions and reason to useful answers. Not necessarily definitive answers. There may be no definitive answers to these questions. But, we can examine them in the light of reason and come to some interesting conclusions. But, these conclusions can be furthered by the work scientists do as they attempt to explain the natural world in which we live. After all, asking about the purpose of our lives is a question that can be dealt with much better if we have some understanding of life. To ask whether the universe's existence has a purpose can be answered more clearly if we have some understanding of the universe itself. It is misguided to reject the information that science gives us which may pertain to these and other questions. The scientific method is, after all, the most reliable means we have of gaining information about the natural world. Information, without which, we would not be able to philosophize with any sophistication at all.
Finally, don't accept the conclusion of an argument just because you like it, and don't reject the conclusion just because you dislike it. In each case, you need to consider the reasoning used and determine whether the conclusion is supported by the premises and whether the premises are true. Wanting something to be true does not make it true and wanting something to be false does not make it false. The questions we examine can be difficult but applying the rules of reason can make our job of evaluating philosophical arguments easier and more fruitful.
No good system of reasoning would be complete without a foundation and in logic, this foundation consists of three laws of thought. In essence, these laws represent the fundamental principles from which all our reasoning proceeds. They are considered self-evident which means that merely understanding them should be enough to recognize their truth. Because of their self-evident nature, they can be used to deduce other important philosophical principles. Before considering these principles (and while we're still on the subject of proof) we should recognize that these laws of thought cannot, themselves, be proven. As Aristotle pointed out in his Metaphysics concerning one of these laws: "some indeed demand to have the law proved, but this is because they lack education; for it shows lack of education not to know of what we should require proof and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity so that even so there would be no proof."
The first of these laws of thought is called the law of non-contradiction. What this says is that nothing can both be and not be at the same time and in the same respect. This may not seem very interesting but we can use this law to demonstrate that philosophical arguments are not merely people's differences of opinion. Since we've raised the example of proving the existence of God let's look at this. Some people say that there is no way to prove the existence of God and, after all, it's just a matter of opinion anyway, so what does it matter. However, we can use the law of non-contradiction to demonstrate that there is something more going on. Concerning God, there are two (and only two) possibilities: God exists. God doesn't exist. They cannot both be true. But if it were just a matter of opinion, they could both be true. So clearly, this is not merely an opinion-based question. Not only that from the fact that God cannot both exist and not exist we can deduce something else interesting.
What we can deduce is that either one or the other of these two possibilities must be true. This, as it turns out, is the second law of thought: the law of excluded middle. What this asserts is that something either is or is not. This seems non-controversial however, some people find it confusing. Many mistake-mistakes mistake mistakes this for saying that everything must be either black or white with no in between-between. But aren't there some gray areas in life; never mind in philosophy? However, a closer inspection of what the law of excluded middle is saying should clarify this point. What the law asserts, using the black or white example is that everything is either black or non-black. Put this way, it should be true.
The final law of thought is the law of identity. What this asserts is that something is what it is. Again, this seems non-controversial and uninteresting. However, as we will see, when discussing the philosophy of mind, the law of identity will have interesting philosophical implications. I'll elaborate on this in a later chapter but keep this idea in mind. It will become useful.
Before concluding our remarks on logic, we need to consider some common mistakes in reasoning; what we call fallacies. We should attend to these for two reasons. First, we want to be able to identify these mistakes if they occur in the philosophical arguments we will be analyzing. Identifying fallacies may come in handy when considering non-philosophical arguments as well. Second, we should familiarize ourselves with fallacies to avoid committing them ourselves.
Aristotle originally identified many of these fallacies and later philosophers added them o the list. We will not be addressing every fallacy but I will mention some of the more philosophically relevant ones.
1. Begging the question: this fallacy occurs when the conclusion of an argument is used as one of the premises. So, it seems as if you're proving something when in reality you're restating your premise as the conclusion. For example, if I were to argue as follows: Of course, God exists because only God could create the immensely complex universe.
2. Equivocation: This fallacy occurs when the meaning of a critical word is changed within the argument. In other words, we use one word in two different ways. Example: Any law can be repealed by the legislative authority. So, since the law of gravity is a law, it too can be repealed by the legislative authority.
3. Composition: occurs when an attribute is transferred from a part of a whole to the whole when the attribute cannot transfer. For example ,Atoms are invisible so a piece of chalk that is composed of atoms must be invisible.
4. Division: is the reverse of composition. It occurs when an attribute is transferred from the whole to the parts when the attribute cannot transfer. Example: Salt is non-poisonous and salt is composed of sodium and chlorine. Therefore, sodium and chlorine are non-poisonous.
5. Appeal to authority: this fallacy occurs when an unqualified expert or irrelevant authority is used to support the conclusion of an argument, for instance, if I were to cite an economist's expertise to support my argument in physics.
Appeal to authority is particularly relevant to Aristotle who, in the Middle Ages, was considered an important authority in philosophy and learning in general. So much so, that Aquinas referred to him as The Philosopher. Aristotle's influence extended so far and wide that many subjects he wrote about were not advanced for centuries because of his perceived authority. So, while Aristotle was Plato's best student and most vocal critic, many of Aristotle's students, and many who were influenced by him, were less critical. Indeed, unlike Plato, Aristotle's most prominent student was not a vocal critic of Aristotle's theory. He was not as much interested in metaphysics as he was in the implications of such speculation. Instead of being concerned about the nature of reality, he was interested in changing it; at least the reality of geopolitics in the ancient world. Alexander the Great, the student I'm talking about, was much more interested in empire-building. Naturally, philosophy was affected by this and other empires as well. In fact, within a couple of centuries, the philosopher was to become the emperor of the world's most powerful empire. The empire was Rome and the emperor-philosopher was Marcus Aurelius. It is to the story of philosophy during and after the Roman Empire that we turn now.