Logic is the study of persuasive reasoning. As such, it concerns arguments that successfully convey credibility from a set of premises to a conclusion. Given this broad definition, there are many possible avenues of discourse and logicians have studied everything from formal inference patterns, to the logic of causation, possibility and necessity, obligation, and inference to the best explanation. Nonetheless, formal deductive and inductive logic are the most historically significant branches of logic, even for the social sciences.
The discipline of logic evolved as a prominent branch of philosophy from the time of Aristotle and marks the first time in history that anyone began to systematize the forms of good reasoning. This systematization was of great benefit to philosophers as they attempted to know the universe of knowledge—covering both nature and human relations—on the basis of intuitive thought, rather than empirical analysis. As the sciences eventually pulled away from philosophy (first "natural philosophy" as it evolved into physics in about the seventeenth century, and then the social sciences arguably following in the eighteenth century, as they too learned that knowledge could be formulated on an empirical basis), it is only natural that they would develop their own methods of inquiry, separate from those of philosophers. Nonetheless, the special relationship of logic to the earliest forms of scientific analysis has survived to the twenty-first century, and has had great influence over the modes of inquiry in economics, history, sociology, anthropology, political science, and psychology, that make up the social sciences.
Logic is logic, whether it is applied to the social sciences, or any other field of inquiry. There is no special type of logic that is particularly suitable to the social sciences, just as there is not one for the natural sciences. The principles of valid reasoning are the same no matter what the subject, and are expressible in symbolic notation that is concerned only with the form, rather than the content, of what is uttered. To say "if I have a dollar then I have some money" is no different, logically, than to say, "If one is president of the United States then one is an American citizen." The form of this type of "if, then" statement (P ^ Q) is known as a "conditional," and, along with "not," "or," "and," and "if and only if" (-, V, &, it forms the backbone of logical syntax. The idea that it is then possible to devise more complex statements using these connectives, to formulate premises and then to draw a conclusion, is to present the form of a "valid" argument in deductive logic, which is one where the conclusion follows necessarily from the premises. As long as the relationship between the premises and conclusion is a deductive one— which is to say that if the premises are true then the conclusion cannot help but be true—then the conclusion follows inevitably from the premises, and does not require any sort of empirical data to support it.
If it is raining then the streets will be wet.
It is raining.
Therefore, the streets will be wet.
This is, however, a long way from saying that such an argument is "sound" (that is, both valid and true) and it is here that the first limit of logic is reached in the social sciences, for as practitioners of an empirical discipline, social scientists are concerned to know whether an argument is sound (for instance whether its premises are true), and not just whether its form is valid. Therefore, we need to gather data in the world to assess this. No matter how powerful the principles of logic, in modern social scientific inquiry logic cannot provide the sole means for testing a theory, since logic is concerned not with truth, but with validity, yet the truth of a theory depends crucially on its conformity with actual experience. Pure logic can be done in an armchair, but science needs to go out into the world (if not for experiment, at least for observation).
In his or her search for causes, it is therefore incumbent upon social scientists to dig deeper into the subject, and find some way to assess whether a statement like "if one uses the death penalty then crime will drop" is true, and this is a tricky business, which deductive logic, at least, cannot adjudicate. However, there is another branch of logic that deals with "inductive" inferences that is much more conducive to empirical inquiry, and which some have felt represents the very type of reasoning that is used in science. In contrast to deduction—which deals with moving from general statements to the particular conclusions that follow from them—with induction one moves from particular statements to a general conclusion, somewhat as if one is gathering data points to see if they form a pattern. This resembles, at least ideally, the form of reasoning that a social scientist uses when he or she is searching for a general regularity. For example, if one were to argue that:
Kennedy’s tax cut in 1961 stimulated the economy
Reagan’s tax cut in 1981 stimulated the economy
Bush’s tax cut in 2003 stimulated the economy
Therefore, tax cuts always (usually, generally) stimulate the economy one is engaging in a form of reasoning that is familiar to social scientists, who seek to make causal explanations and to formulate general theories based on historical evidence. The problem, however, is that this form of reasoning is not valid, as has famously been shown by the Scottish philosopher David Hume. Specifically, the above argument has a hidden assumption (common to all inductive arguments), which is to think that there is a relevant similarity between the future and the past. But this assumption does not always hold. Moreover, even if this assumption is borne out in some cases, it is important to recognize that there is a distinction to be made between "causation" and "correlation" in the social sciences, such that, no matter how solid one’s evidence may be, it is always possible that even the strongest correlation may represent only an accidental connection. Try as one might to obtain the sort of certainty that the "necessary connection" of deductive logic has provided, the social sciences have found this an elusive goal. This represents no particular flaw in the social sciences, for the natural sciences— or indeed any fact-based discipline—would also seem to suffer from this same difficulty.
Nonetheless, the social sciences have embraced the power of logic and have used it in various ways throughout their history to bolster their conclusions and to capitalize on the strengths of clear reasoning. The development of modern probability theory, and especially the invention of regression analysis in statistics, has been a very useful tool for social scientists to identify patterns in their data and to make sure that their hypotheses do not outrun them. The models of rationality that have been used throughout economics and political science—in particular those of rational choice and game theory—reflect another important way that the power of logic has had an impact on research design and model building in modern social science. In psychology, too, where experiments are designed to assess rational cognitive function by using thinly disguised logic games, one sees the influence of logic in social inquiry. Such reliance on logical modes of behavioral analysis, however, has come at a cost, for the new trend of "behavioral economics," and the more general movement toward more realistic and experimental models in the social sciences, have revealed limitations in some of the classic theories in social science. Assumptions about "rational economic man," for instance, may work ideally in our theoretical models, but break down when faced with the irrationality and fractured logic of everyday human experience that constitutes the subject matter of the social sciences.
In another avenue, however, the principles of logic have been unquestionably useful in the social sciences, and that is in research design, the formulation of hypotheses, and the analysis and synthesis of data and theory in social inquiry. Taking a page from the "scientific method" that is allegedly used in the natural sciences, some methodologists have argued that, as empirical disciplines, the social sciences should follow the "five-step method" of observation, hypothesis formulation, prediction, experiment (or learning from experience), and assessment. Despite the storied literature in the philosophy of science, provided by philosophers of science Karl Popper and Thomas Kuhn, that has rightly caused philosophers and others to rethink this simplistic model of scientific method, there is a nugget of truth in it for any discipline that cares to be empirical, which is to be ruthless about the comparison of one’s theory to the data. If a theory tells an individual to expect something, and one does not find it, then there is an inescapable problem for the theory. In a statement attributed to American physicist Richard Feynman, "It doesn’t matter how beautiful your theory is. If it doesn’t agree with experiment, it’s wrong." This form of reasoning is directly related to the "conditional" in our earlier consideration of valid arguments, for it is trivially true that every conditional statement (if P, then Q) implies (indeed, is equivalent to) its "contrapositive" (if not Q, then not P). Thus, if one’s social scientific theory states, "If one is a thirteen-year-old boy then one has had an Oedipus Complex" and one finds a thirteen-year-old boy who has not had an Oedipus Complex, then the original theory is wrong. If a theory has even one exception, then it is not universally true and must either be discarded, or modified in some way to deal with this anomaly. As Popper demonstrated, here the power of logical certainty may be appreciated, since the contrapositive relationship is one of deductive, not inductive, reasoning and therefore may be relied upon as rock solid in its epistemological status.
The role of logic in the social sciences is a mixed one. As in the natural sciences one realizes that, if it is to explain the world, any empirical theory must go beyond the homilies of deductive reasoning and venture forth into the world of experience, with the chance of being wrong as the price of expressing a truth that is not trivial. Still, as we have seen, the power and benefits of logic have not been without value to the social sciences.
