Before we get to study logic, it's quite necessary to understand what kind of study or academic discpline logic is. You have studied quite a number of disciplines, such as sociology, economics, physics, or organizational behavior. It can be seen that these fields of study all carve up the world to study some parts of it in some way. For example, sociology studies human society, and physics studies the properties and nature of things in general. There may be some overlaps here, as the subject matter for sociology, human society, is actually part of things in general which is studied by physics. But actually there is not, because the way sociologists study their subjects is very much different from what physicists do, and if we assume that physicists study all things so that there would be no room for other disciplines which are apparently narrower in scope, then we would miss a lot. So we can take it for our purposes here that sociology and physics are on a par here. They all have a set of methods used for studying, and they both claim some parts of the world, or the universe, as their subject matter. The same goes for the other disciplines such as economics and organizational behavior.
Different as these disciplines are, however, they all share some thing in common. Economists typically put forward their research studies aiming at convincing us of their truth. And that's what sociologists do too, and what physicists do too. That is, they all aim, in their studies, to convince their readers or audience of the results of their studies. These are not merely empirical claims. Physicists do not just want us to believe whatever they want us to believe. They have evidence and reasons to support their claims. And having these are essential for any academic discipline. It's what distinguishes academic disciplines from mere guesswork or superstitions. So we see that, no matter what the subject matter of a discipline is, the practitioners of the disciplines all share some form of thinking when they publish thier research results hoping to convince others. And it is this common ground that is the subject matter of logic.
Hence logic is in a way fundamentally different from these disciplines. The other disciplines have their own fields of study which they carve up from reality, employing a certain set of methods. Logic, however, does not have its own particular field of study in the sense that it does not have a carved up part of reality for it to study and analyze. The common ground shared by the different fields of study are forms of thinking, and it is just these forms that could be regarded as the subject matter of logic. Thus, logic is the study of forms of thought. In other words, logic does not claim any part of reality to study, but it looks at what happens when people in these disciplines make claims, in order to see the structure of thinking implicit in the claims.
What does it mean to say that logic studies forms or structures of thought? Logic is very different from psychology. The latter discipline looks at what happends empirically when humans think. This is not the concern of logic. Logic looks at the strcture of thought, and the causal origin of the thought is of no concern. The thought could have been produced by an intelligent computer, but if it is meaningful then the thought could be studied by logic.
So we can arrive at a clearer conception as to what logic really is. What it certainly is is that it is an academic discipline. That's an empirical proposition. However, the subject matter of logic is such that it does not pertain to any part of reality, nor with any specific method of studying or analyzing the reality. What logic studies, on the other hand, is forms of thought. And it's only that, as the causal origin or the physical nature of thought is of no concern for logic either. Thus we can arrive at a provisional definition of logic as an academic discipline studying form of thought, in so far as they are forms of thought only, and not the causal origins, nor the empirical nature of the thought.
And when forms of thought are presented in such a way that we can get to know them, they come in forms of arguments. We will deal with arguments in the topic after the next. But for now we can understand arguments provisionally. When we argue, what we do is that we try to convince the one we are arguing with. And we use reasons to convince the other party. Logic thus becomes the study of correct and incorrect uses of arguments. When is an argument wrong, and when is it right? These are the central questions of logic.
In What Way Does Logic Study Forms of Thought?
So we see that logic does not study forms of thought empirically. So in what way does it study them? We can see this point when we reflect on what we are interested in when we closely investigate forms or structures of claims. We are interested in knowing what makes good claims and bad claims. If we are interested in other aspects; for example, if we want to know what factors are responsible for one to make a claim he is making, then the question becomes empirical and thus is not the subject matter of logic. Thus, logic is a normative discipline in that it looks at what is good or bad, and not at what is or is not. It studies forms of though normatively, and the aim of logic is to provide a normative theory to find out the method for detecting and producing any good arguments, and for detecting and avoiding bad arguments.
Well, so why do we want to avoid bad arguments and accept good arguments? For one thing, it is of human nature that humans do not want to be deceived. We want to know the truth, and very often the truth would have been inaccessible if not for the use of reasons by humans, reason being the tools humans can rely on to know things which are beyond the power of the senses alone. If we don't have a clear and effective method by which we can separate good from bad arguments, then we just have no effective way to sort out truths from falsehoods or wrong-headed claims. Thus, logic is necessary as a human tool. It is about the only thing humans can use when they deal with the unseen or things that cannot be perceived directly. It is the backbone of science.
Logic, then, is a normative discipline. It does not aim at saying what reality is like, but it tries to point out when an argument form is correct and when not. 'Correctness' and 'incorrectness' are normative concepts because you cannot find instances of correctness or incorrectness in the same way as you can find instances of whales or horses.
We have just had a look at arguments. Now we are in a position to examine them closely. You have just read that arguments are what you have when you argue with your friends or with other persons. But that's a rather unilluminating definition. We need to separate between logical arguments and arguments people have when they are fighting. In this course we will pay attention to the former. However, there are some correspondences between the two. When people fight verbally, sometimes their aim is to try to convince the other side to agree with them. And often they use logical arguments to do that, but sometimes they don't. That's why a fight is a fight, and not a debate or a discussion. However, the logical argument part is interesting to logic because it deals directly with correct or incorrect forms of thought mentioned earlier. Since forms of thought are expressed in arguments. Logic naturally studies arguments, but before that we need to be clear as to what a logical argument is.
We have seen that in arguments we try to get the other party to be convinced of any proposition we want him or her to be convinced. And we use reasons as support for that. Thus, logical arguments can be divided into two parts. The first part, called premises, work as supplier of information and reasons for the other part, called conclusion. This is the basic structure of arguments. Thus we can have a more formal definition of arguments to be sets of propositions consisting of two parts -- premises and conclusion. The premises provide reason or evidence for the conclusion, which is the whole point of the argument. You can see that if we lack any part of an argument, we don't really have an argument. Suppose you have only the conclusion part, you only have a claim and not an argument. But if you have only the premises, you don't have an argument either because no one knows what point you want to get across. For example, suppose you are arguing that Chula students should not wear uniforms (to use the old example in the argumentative writing course), and suppose your reason is that it's out of style to wear uniforms anywhere, then you are making an argument. Your conclusion is that Chula students should not wear uniforms. Your premise is that it's out of style to wear uniforms. (Actually if you are observant enough you'd find that in order to conclude that Chula students should not wear uniforms from the premise that wearing uniforms is out of style, you need another premise -- one should not do things that are out of style. We will deal with this topic extensively when we have gone deeper in the course.)
An argument actually can have no more than one conclusion because if you have more than one you need to provide separate reasons for each of them. But an argument can easily have more than one premises because in order to show conclusively that the conclusion should be accepted we can employ any number of premises we like, and very often just one premise will not do.
Actually in the section on argumentative writing I have written quite extensively about what an argument is. You are adivsed to turn to that section and read it through.
Deductive and Inductive Arguments
Arguments can be divided into two kinds according to whether the conclusion can be conclusively proven to be true if the premises are true. If it can, then the argument is a deductive. But if not, then the argument is inductive. Deductive arguments are those whose conclusions must be true, or can be false, if all the premises are true. Inductive arguments, on the other hand, are those whose conclusions can at most be probable, but they are never conclusive. The reason is that conclusions in deductive arguments are in fact already stated in the premises, or more precisely the conclusions of a valid deductive arguments can be shown conclusively to follow logically from the premises through some mechanical means (as we shall see in Venn's Diagram). On the other hand, there can be no valid inductive arguments because their conclusions state something more than what is already there in the premises. In other words, the conclusions of inductive arguments cannot be conclusively shown to follow, or not to follow, from the premises. What can be shown is only how probable the conclusions are when they are supposed to follow from the premises.
Here is an example of a deductive argument:
All the oranges in this basket are sweet. Therefore, this orange which I have just picked up from this basket must be sweet.
You can see that this argument is obviously valid. It can be valid because it is a deductive argument. That is, the conclusion can be verified through some mechanical means whether it must be true if all the premises are true. In this case, since the premise says all the oranges in the basket are sweet, there is no possibility of any orange in the basket not being sweet.
On the other hand, consider this argument:
All the oranges I have tasted in this basket are sweet. Therefore, all the oranges in the basket (which certainly include those that I have not tasted) are sweet too.
This is an inductive argument. There is just no mechanical means we can use to determine whether the conclusion must be true or not if the premises are. In fact we can never be fully certain either that the conclusion must be true, or must not be true. The conclusion cannot be conclusively proven to be true or false. What we can do is to apply some rules regarding probability or statistics to help us understand in our own way how likely the conclusion is to be true. But "how likely the conclusion is to be true" is very different from "whether the conclusion is true."
The traditional way of characterizing these two kinds of arguments is that a deductive argument is an argument whose conclusion does not state anything further or larger than the scope of what is already said in the premises, but the conclusion of an inductive argument does state more than what is said in the premises. In a way that is true; however, in some cases, like the modus ponens type of argument (If p, then q, but p; therefore, q), it is hard to see how the conclusion is already contained in the premises. Furthermore, advances in logical theory have shown that there can be no systems of mechanical means that can show every type of valid deductive arguments that they are really valid. But this is a hugely complex matter which should be left alone unless you are studying logical theory or higher mathematics. Thus we'd better abide by the conception that deductive arguments are those whose conclusions can be conclusively proven to follow logically from the premises or not, and that inductive arguments are those whose conclusions cannot be shown this way.
If inductive arguments cannot offer conclusively proven conclusions, then what good are they? Well, they are of much use. The discipline of statistics is based on the whole idea of inductive arguments. As humans, we want to know more than our evidence strictly allows us to. Our capabilities of retaining known evidence are limited, and if we are not allowed to go on from the available evidence then our lives would be very limited indeed. We cannot know, for example, that the sun will rise tomorrow, for all our evidence are of the past risings of the sun, and we do not possess an evidence that the sun will rise tomorrow yet. We may argue from our accepted theory that the sun will rise, but then our theories are based on observations, and since their claims are much wider than observations, then the theories suffer from the same problem too.
Since inductive arguments offer conclusion whose scope is wider than that of the premises, they allow us to know more things, even though there are always some chances that the conclusions might turn out not to be true. However, deductive arguments offer us instead the absolute certainty of the conclusion if the arguments themselves are valid. So there are trade offs here. Deductive arguments give you certainty, but at the price of not being allowed to go beyond what is already there in the premises, or to prove something which lies beyond such logical rules as modus ponens. Inductive arguments give you more substance of knowledge, but then there is always a chance of its being false.
These three concepts are essential in logic. Without a firm grasp of them we won't go far in evaluating arguments and in constructing good ones. The simplest one among the three is truth. We won't attempt to define that concept formally here. This issue has been a long standing controversy in philosophy, so we'd better understand this term as we normally do. That truth is the opposite of falsehood. That is, when a proposition is true, things are as what that proposition say, and false otherwise. That's about all we will want to say now about truth, and to some philosophers that's all one is able to say. We know that it is true that grass is green and rain is wet, and false that the sun rises in the west and that air is lighter than earth. In short we will rely pretty much on our intuition here on what truth is. However, truth is a very important factor in logic, for in evaluating arguments what we want is that the arguments should help us arrive at truths rather than falsehoods.
This brings us to the issue of validity. Formally defined, an argument is valid when its conclusion must be true if all of its premises are. The important point you should take note very well is that the premises themselves do not have to be true. What is required for an argument to be valid is only that if we take all the premises to be true, if we suppose them to be true that is, then the conclusion cannot be anything but true.
Let's look at this example of an argument:
(1) All BBA students either wear trousers or a skirt when they come to campus. (2) Kenneth is a BBA student. (3) Therefore, Kenneth either wear trousers or a skirt when he comes to campus.
You can see that this argument is VALID because if we take all the premises [(1) and (2)] to be true, then the conclusion (3), that Kenneth either wears trousers or a skirt when he comes to campus, is nothing but true. This is so because if it is true that all BBA students either wear trousers or a skirt coming to campus, and if it is also true that Kenneth is a BBA student, then we see that it is necessary that Kenneth either wears trousers or a skirt to campus. I think you can see why this must be so. If Kenneth neither wears trousers or a skirt to campus, suppose he wears nothing (!) when he comes to campus, then we either think that he is not a BBA student or not all BBA students wear trousers or a skirt when they come to campus. We cannot consistently maintain (1), and (2), and that (3) is false all at the same time. In other words, if we maintain (1) and (2), then we have no choice but to maintain (3) also, otherwise we would be contradicting ourselves.
Let's look at another argument:
(1) All mammals have eyes. (2) All dogs are mammals. (3) Therefore, all dogs have eyes.
This is a valid argument also. If we suppose that all mammals have eyes, and if we suppose that all dogs are mammals, then there is no doubt that all dogs must have eyes. So far, so good.
Here is another argument:
(1) All mammals have eyes. (2) Seahorses are mammals. (3) Therefore, seahorses have eyes.
We can see that the form of this argument and the argument above is identical. If we suppose that (1) and (2) here are true, then we have to accept that (3) must be true also. However, there is one glaring difference. Sentence (2) in the latter argument is false. Seahorses are a species of fish, and thus they are not mammals. Thus the actual truth or falsity of the premises is not relevant for the validity of the argument. So long as we can make all the premises true together, then we can see whether the conclusion must be true or not. However, if one or more of the premises are false, then even if we can suppose them all to be true, we feel that we miss something and that this kind or argument should be somewhat different from the other type, such as the one above about mammals and dogs. We are prepared to accept the truth of the argument about dogs with no qualms. For the argument is valid, and the premises are in fact all true. This leaves us with no doubt whatsoever that the conclusion must be true. However, in the latter argument about seahorses. Since one of the premises is false, then we feel we cannot accept its conclusion as strongly as in the case of the other argument. Why is this so? Since seahorses are not mammals, the conclusion that they have eyes do not follow from the two premises. The truth that seahorses indeed have eyes is just a coincidence here.
So we need to a way to separate these two types of arguments. We call the arguments which are valid, and whose conclusion IS in fact true (and can't be otherwise) because all its premises are true, SOUND arguments. Valid but unsound arguments have conclusions which must be true if all the premises are true; however, the conclusions themselves may in fact be false. The conclusions of sound arguments, on the other hand, cannot be anything but true.
Here is an example of a valid but unsound argument:
(1) Some cats have long tails. (2) All animals with long tails are tame. (3) Therefore, some cats are tame.
You can see this argument is valid, but it is not sound because it is not true that all animals with long tails are tame. Tigers have long tails, but they are obviously not tame.
Note: Actually arguments need not consist of three sentences (or more accurately, propositions, as we shall see later in the next chapter). Here is an example of an argument which consists only of only two propositions:
"He's a genius and a crook. So he is a crook."
This argument is valid even though it has only one premise. But the one premise suffces to make the argument valid. So it is really possible for arguments to have only one premise. On the other hand, arguments can well have more than two premises. Suppose I have an argument of this form
Premise 1
Premise 2
Premise 3
Premise 4
...
Premise n
_________
Conclusion
The form shows that it is possible to have arguments whose premises are more than two. So why do we seem to be stuck with arguments with only two premises? Well, they seem to be the most manageable and substantive enough to merit serious attention. Besides, if you have arguments with many premises, chances are that you have reduce them and make them into several separates arguments all of whose essential premises are two or less. Since arguments with two premises appear easiest, we'll start with them first, and in the chapter following that we'll look at other types of deductive arguments.
- Valid argument
- An argument such that if all of its premises are true, its conclusion must be true, or an argument such that all of its premises cannot be true (they are inconsistent) -- in that case the argument is called vacuously valid.
- Invalid argument
- An argument is invalid if and only if all of its premises and the negation of the conclusion can be true at the same time. That is, an argument such that if all of its premises are true, the conclusion can be false.
- Sound argument
- An argument is sound if and only if it is valid and all of its premises are true.
- Deductive argument
- Deductive arguments are those the content of whose conclusion does not exceed that of the premises. Thus it is possible that the conclusion must be true if the premises are true; that is, the conclusion can be conclusive. The qualities of being valid and invalid can be applied to this type of arguments.
- Inductive argument
- Inductive arguments are those the content of whose conclusion exceeds that of the premises. Thus inductive arguments can never be conclusive, because we never know how to guarantee that the exceeded content in the conclusion must be true while the content of all the premises doeso not cover it. However, inductive arguments can be stronger or weaker regarding the acceptability of their conclusions. If strong, then the conclusion is likely to be true, but if weak, then it is likely to be false. Questions of validity do not apply to inductive arguments because there can be no mechanical means to check them.