3 The Great Divide

So far as I can tell, it is still common both in textbooks and in research papers, to draw the distinction between deductive and inductive arguments. Considering the centrality of the topic and the fact that no account proposed seems to solve the problems raised in this chapter, this situation appears to be rather anomalous. The inductive/deductive distinction is problematic but sets a great divide that has prevailed as a framework for study and research. One might argue that standard practice on this matter is all right because the distinction is intuitively understandable, traditional, and so practical as to be necessary. One might wish to make that case despite the problems explained here, arising for accounts based on form; necessitation or its lack; what is intended or ‘claimed’ by an arguer; or the proper application of standards. But I would urge that the underlying theory is not adequate. I submit that the problems raised here remain real and important. They were keenly explored in early editions of the Informal Logic Newsletter (now Informal Logic) but have not been central in more recent discussions of informal logic and argumentation theory.

In this essay, I cite a number of examples to illustrate problems of application with various versions of this distinction. These examples indicate that one can easily find arguments, both in colloquial and academic discourse, that are hard to classify as inductive or deductive. Readers can readily test that claim for themselves, to explore the claims and considerations made here. I was especially concerned with the dichotomous nature of logical tradition on induction and deduction. The standard presumption has a positivist heritage. It was assumed (and, I suspect, still is) that the inductive/deductive distinction is both exclusive and exhaustive. That is to say, no argument is both inductive and deductive, and every argument is either inductive or deductive. At a time when many binaries are being rejected, this particular one appears to enjoy undeserved security. I argue here that its status poses dangers, especially as to the matter of exhaustiveness: the supposition that all good reasoning is either empirical or purely logical serves to distort and buttress false dilemmas of method and justification. Logical positivism is widely discredited, but its implications for the theory of argument continue to be sturdy survivors of their ancestor. Presuming exhaustiveness, one too easily ignores interesting argument types such as a priori analogy (appeals to consistency) and conductive or ‘balance of consideration’ arguments. Both are common within philosophy itself. In past years, these arguments have received more attention from theorists. The question as to whether a priori analogies are deductive has been of some interest, and there have been many accounts, and many doubts expressed, concerning conductive arguments. These types of arguments, one putatively deductive, the other putatively inductive, are discussed in Chapter Four.

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It is traditional to divide arguments into two basic types: deductive and inductive. The division is regarded as important, because it is thought that deductive arguments meet standards that inductive arguments do not meet, and that inductive arguments serve epistemic purposes that deductive ones cannot serve. The theory that there are two and only two kinds of argument, deductive and inductive, may be termed the positivist theory of argument. Where deductivism is monolithic, the positivist theory is dualistic. Theorists long impressed with the force of deductive arguments of course noted the importance of empirical cumulation of data, particularly in scientific work. Recognizing that an entirely deductive account of everyday and scientific knowledge was not plausible, they departed from deductivist rationalism to allow for a second type of argument based on empirical reasoning. The tradition that arguments are either deductive or inductive goes back to Aristotle and was a prominent feature of logical positivism. It fits naturally into a positivist theory of knowledge within which knowledge must come either from logic and mathematics (sources of deductive arguments) or from the empirical sciences (sources of inductive arguments).

1. Versions of the Great Divide

Perhaps because of this venerable tradition, there are several versions of the distinction between deductive arguments and inductive ones. For Aristotle, it was a matter of form. Deductive arguments were syllogistic in nature; inductive ones went from particular premises to universal conclusions. Aristotle’s way of putting the distinction is no longer influential today because it is regarded as too narrow. A look through contemporary texts and monographs will produce a number of different versions of the ‘inductive/deductive’ distinction. These versions differ in two ways. First, they vary in how they explain the content of the distinction. Second, they vary in strategy for applying it – some to arguments directly, some to what is ‘claimed’ for the connection in an argument, some to arguers’ intentions, and some to the standards of appraisal for arguments, rather than to arguments themselves. Here we primarily consider matters of content. In some versions, the two blend together, as will be apparent.

On some accounts, deductive arguments are those in which the premises entail the conclusion, thereby necessitating the truth of the conclusion in any case in which the premises are themselves true. Inductive arguments are those in which the premises, if true, would make it probable that the conclusion is true. Such an account is given in Wesley Salmon’s Logic. On this view, in a deductive argument:

1. if all the premises are true, the conclusion must also be true, and

2. all the information in the conclusion is already contained – at least implicitly – in the premises.

whereas in an inductive argument,

1. if all the premises are true the conclusion is probably true, but not necessarily true.

and

 

2. the conclusion contains information not implicitly in the premises.¹

 

On this version of the distinction, we have a dichotomy of good arguments. Bad arguments would fail to be either deductive or inductive, based on these definitions. If an argument has premises that are irrelevant to the conclusion, or contains an error in deductive reasoning, it will fall in neither category.

A similar account is offered in Robert Neidorf’s text, Deductive Forms, where the inductive/deductive distinction is stated as follows:

In an inductive argument, the conclusion probably follows from the premises. In a deductive argument, it certainly follows. An argument which fails as deductive may nevertheless constitute a good inductive argument.²

Henry Kyburg’s distinction in Probability and Inductive Logic is essentially similar: the distinction is given in terms of success and bad arguments fall into neither category.³ The account appears to be exhaustive, not for all arguments but for all good arguments. Bad arguments are in limbo.

Another way of drawing the inductive-deductive distinction puts all the bad arguments in the inductive category. On this view, deductive arguments are those in which the premises entail the conclusion. Inductive arguments are all the rest. This version may be adopted for the express purpose of guaranteeing exhaustiveness. Often this intent is made obvious by the replacement of ‘inductive’ by ‘nondeductive’, ‘nondemonstrative’, or ‘nonconclusive’. This is the version which Nicholas Rescher must have had in mind when he said: ‘an inductive argument is simply an argument whose conclusion outruns the information provided by its premises.’⁴ The scheme was also adopted by Baruch Brody in his text on theoretical and applied logic. Brody defined validity, and discussed deductive arguments and deductive validity. Then, potentially in a departure from the positivist theory, he allowed that arguments which fail to be deductively valid are nevertheless sometimes ‘perfectly acceptable’ in some other way. ⁵

With this approach the category of inductive arguments will be large indeed. It will include all poor arguments, as well as a motley variety of good arguments. All deductive arguments will be valid by definition. (That is to say, there will be no such thing as an invalid deductive argument.) Inductive arguments will include those in which the premises, if true, would make the conclusion probable; those in which the premises are completely irrelevant to the conclusion; all formal and informal fallacies; analogies; inferences to the best explanation; so-called ‘good reasons’ arguments; and potentially many others. Thus the ‘inductive’ category will explicitly serve as a leftover category. This way of drawing the distinction will guarantee, by definition, an exhaustive and exclusive dichotomy. The result that there are no invalid deductive arguments will be unsettling to many traditionalists, however, and the inductive category will exhibit little coherence.

On a third view, deductive arguments are those in which it is claimed that the premises entail or necessitate the conclusion. Inductive arguments are those in which it is claimed that the premises make the conclusion likely or probable. This kind of account is suggested in Max Black’s Encyclopedia of Philosophy article on induction. Black says:

The name ‘induction’, derived from the Latin translation of Aristotle’s epagoge, will be used here to cover all cases of nondemonstrative argument in which the truth of the premises, while not entailing the truth of the conclusion purports to be a good reason for belief in it.⁶

The most important sources for this version of the inductive/deductive distinction are Irving Copi’s classic texts. In the fourth edition of Introduction to Logic, Copi put it this way:

Accordingly, we characterize a deductive argument as one whose conclusion is claimed to follow from its premises with absolute necessity, this necessity not being a matter of degree and not depending in any way upon whatever else may be the case. And in sharp contrast we characterize an inductive argument as one whose conclusion is claimed to follow from its premises only with probability, this probability being a matter of degree and dependent upon what else may be the case.⁷

This version of the inductive-deductive distinction may be the most standard one. It allows for the commonsensical result that there are both valid and invalid deductive arguments and both strong and weak inductive arguments.

The problems with this account begin with the expression ‘is claimed to‘. When people present arguments, it is often unclear whether logical entailment or merely some less tight support is ‘claimed‘. Their words often do not suggest one or the other. Furthermore, the expression “is claimed” is ambiguous. One may mean by it that the arguer intends one or the other connection or one may mean that the wording, context, and nature of the argument themselves suggest either a deductive or an inductive goal. Since Copi and others who follow him have not made their distinction explicitly intentional, it seems best to follow the direction of the second interpretation of ‘is claimed’ here.⁸ To see what connection is claimed in an argument, we have to study the nature of that argument itself: the stated premises and conclusion, the context, the indicator words, qualifying or hedging words such as ‘probably’ or ‘in all likelihood’, and the logical relationships that exist between the premises and the conclusion. These are in the argument, not in the intentions and beliefs of the arguer. Given the inscrutability of arguers’ intentions, especially when they are distant or dead, this seems a more promising direction. However, it is not without its difficulties.

To see how problems can arise when we try to apply Copi’s version of the inductive-deductive distinction, we can consider several examples from his own exercises. Here is an argument which Copi takes from Etienne Gilson’s The Unity of Philosophical Experience. Since man is essentially rational, the constant recurrence of metaphysics in the history of human knowledge must have its explanation in the very structure of reason itself.⁹

The argument here is:

1. Man is essentially rational.

   Therefore,

2. The constant recurrence of metaphysics in the history of humans has its explanation in the very structure of reason itself.

One could say that the word ‘must’ provides reason to take the argument as deductive. It seems to be functioning as an inference indicator rather than as a modal term within the conclusion claim. However, the word ‘must’ has empirical inference uses too, as in ‘you must be tired after all that hiking yesterday’. One might, alternatively, think that since Gilson is dealing with an explanation for the recurrence of metaphysics, he is hypothesizing, and that his argument should be taken as inductive, a kind of ‘best explanation’ appeal. It will hardly do to say that since Gilson is a philosopher and writing as a philosopher, the argument must be deductive. The case is not easily classified using Copi’s distinction.

Another perplexing case is the following, which Copi quotes from Adam Smith.

A gardener who cultivates his own garden with his own hands unites in his own person the three different characters of landlord, farmer, and laborer. His produce, therefore, should pay him the rent of the first, the profit of the second, and the wages of the third.¹⁰

Copi classifies this argument as deductive on the grounds that it does not appeal to experience to establish what is probably the case, but appeals to principles of equity to prove what should be the case. (This appeal must be a tacit one.) Principles of equity are presumed here not to come from experience, which has been classically associated with induction. Now, there was no reference to experience in Copi’s definition of induction and it is that notion which has been omitted from modern accounts, presumably in the interests of obtaining an exhaustive dichotomy between deduction and induction. What should be at issue, strictly, within Copi’s account, is whether conclusiveness is ‘claimed’ in the argument. The matter of principles of equity has no bearing on this issue: we might appeal to them hesitantly or assuredly; one might cite them to deduce a conclusion about a particular case, or to hypothesis. We can of course make Adam Smith’s argument deductively valid by adding three premises:

1. If a person serves the role of a farmer, he should receive the profit of a farmer.

2. If a person serves the role of a landlord, he should receive the rent of a landlord.

3. If a person serves the role of a laborer, he should receive the wages of a laborer.

But the fact that the argument can be supplemented so as to be deductively valid does not show what is ‘claimed’ when it is unsupplemented. As we have seen, any argument can be supplemented so as to become deductively valid. If that were sufficient to make it ‘claim’ deductive validity, Copi’s view would amount to deductivism. Clearly, that is not his intent, since he seeks to explain a distinction between deductive and inductive arguments.

These difficulties do not arise just because Copi has selected unfortunate examples. The problem is that the inductive/deductive distinction as Copi draws it is difficult to apply to real arguments. Everything depends on what is claimed in the argument about the tightness of the connection between premises and conclusion. This interpretation must somehow be inferred from the wording and the context. But indicators may go in different directions or fail to be present at all. Neither contexts, nor indicator words, nor the logical ordering of claims, nor the nature of the subject provide firm guidance as to what an argument ‘claims’ about the connection between its premises and its conclusion.

Some years back, readers of the Informal Logic Newsletter were treated to a series of critical articles on the viability of the inductive- deductive distinction. Perturbed by the difficulty in applying the distinction to naturally occurring arguments, several writers defended versions of the positivist theory that would transfer the inductive-deductive dichotomy into another domain. Difficulties in applying various versions of the distinction to arguments directly generated suggestions that the distinction must apply elsewhere. One suggestion, put forward by Samuel Fohr, was that the inductive-deductive distinction did not apply to arguments themselves but rather to arguers’ intentions and thereby (derivatively) to arguments as put forward by particular arguers. Another suggestion was that it applied to the standards by which arguments could be assessed.

Fohr maintained that arguments were not merely sets of statements to be found in textbooks, but rather claims made by persons seeking to justify further claims. On this notion of argument, Smith and Jones might make the same claims, using the same words, but offer different arguments, if their intentions were relevantly different. An explicitly intentional account had been offered earlier by Robert Olson in his text, Meaning and Argument. Olson said:

The term ‘imply’ has a stronger and weaker meaning. In its stronger meaning, the premises of an argument ‘imply’ a conclusion if and only if they give conclusive evidence for it. In its weaker meaning the premises of an argument ‘imply’ a conclusion if and only if they give reasonably good but less than conclusive evidence in its favor. If the arguer believes that the premises of an argument necessarily imply the conclusion, the argument is deductive (or necessary). If the arguer believes that the premises of an argument probably imply the conclusion the argument is nondeductive (or probable).¹¹

Fohr endorsed Olson’s account, and put his own distinction this way:

If a person intends that his premises necessitate his conclusion, he is giving a deductive argument. If he intends only that his premises render his conclusion probable, he is giving an inductive argument.¹²

We see a shift here from beliefs to intentions. As Fohr was forced to admit, this version of the distinction makes it non-exhaustive. There are many cases in which those who compose arguments intend only that their premises provide support for their conclusion and fail to have any intention regarding necessitation or making probable. The concept of logical necessitation is a philosopher’s concept that is difficult to teach to students, and that we cannot expect the bulk of ordinary people to contemplate regularly in their day-to-day lives, even whenever they are offering reasons. Many arguments will fall into limbo so far as this statement of the positivist theory is concerned. As one critic pointed out, the man who tells his wife that she should help him paint the kitchen because she promised to do so is likely to have little idea as to whether he intends to prove his conclusion or merely make it probable. He wants her to help with the painting, and he’s telling her why she should do it. In response, Fohr urged that such arguments be assessed according to both kinds of standards (those appropriate for induction and those appropriate for deduction) and maintained that ordinary arguers should have the required intentions regarding their premises and conclusions.

Fohr’s approach would make the philosophical distinction between necessitating and making probable a norm for argumentative intentions. If arguers do not grasp this norm, we have to consider their arguments from both perspectives. However, these arguers should brush up on epistemology and order their intentions to fit our theory of argument.

Another proposal regarding application was stated by Brian Skyrms in Choice and Chance and defended in the Newsletter interchange by David Hitchcock. It moves the dichotomy from arguments to standards of appraisal.

Skyrms criticizes the intentionalist account in a footnote, saying:

.. this will not do, for arguments do not intend anything. People who advance arguments intend many things. Sometimes they intend for the argument to be deductively valid; sometimes they intend it to be inductively strong; sometimes they intend it to be a clever sophistry; and sometimes they don’t know the difference.¹³

The positivist theory of argument, on this version, would say that there are many diverse arguments – some hard to classify – but that there are, broadly speaking, only two types of standards for appraising arguments. These are deductive standards and inductive standards. On this account, the distinction between inductive and deductive is not a distinction between types of argument. Nor is it a distinction between types of intention arguers might have. Rather, it is a distinction between types of standard that may be used for appraising arguments. There are two broad types of standard: deductive standards and inductive standards. Deductive standards are used when we wish to determine whether the premises of an argument entail its conclusion. Inductive standards are used when we wish to determine whether the premises of an argument make its conclusion probable. Skyrms put it this way:

We defined logic as the study of the strength of the evidential link between the premises and conclusions of arguments. We have seen that there are two different standards against which to evaluate the strength of this link: deductive validity and inductive strength. Corresponding to these two standards are two branches of logic: deductive logic and inductive logic. Deductive logic is concerned with tests for deductive validity – that is, rules for deciding whether or not a given argument is deductively valid – and rules for constructing deductively valid arguments. Inductive logic is concerned with tests for measuring the inductive probability, and hence the inductive strength, of arguments and with rules for constructing inductively strong arguments.

David Hitchcock defended Skyrms’ view, saying that the inductive/deductive distinction provides an exhaustive dichotomy of standards of appraisal, rather than an exhaustive dichotomy of types of argument. Hitchcock said that in deductive logic, we are offered a theory of the circumstances in which premises do or do not make it logically impossible for a conclusion to be false given the premises. In inductive logic, we have a theory of the circumstances in which an argument is inductively strong or inductively weak – that is, in which it is more or less probable that its conclusion is true, given that its premise(s) are true. Within each theory there are various types of logic. In deductive logic we have the logic of truth-functional sentence connectives, first-order quantifiers, the logic of identity and so on. Within inductive logic we have the logic of the confirmation and disconfirmation of hypotheses, the logic of analogical arguments, the logic of inferences from sample characteristics to population characteristics, the logic of controlled experiments to prove causal claims, and so on. Then there is the logic of conductive or balance of considerations or good reasons arguments. Possibly there are other standards.¹⁴

Both Skyrms and Hitchcock argue that it is not always easy to decide which sort of standard to apply to a particular argument. For this reason, they believe that it makes more sense to think of a dichotomy of standards rather than a dichotomy of arguments. There are two puzzling aspects of this view, however. First, we may question why we have a dichotomy of standards, rather than a plurality. This question will certainly strike forcefully if we look at Hitchcock’s list for the inductive standards. It is hard to see what analogy, balance-of-considerations reasoning, and the use of controlled experiments to justify causal conclusions will have in common. One suspects that they have been lumped together, seen as involving a common inductive standard (whatever that might be) precisely in the interests of getting an exhaustive dichotomy. The account is slightly anomalous, as Hitchcock acknowledged in reply to critics, because one would presume a connection between the articulation of standards for appraising the inferences within arguments and the existence of arguments to which those standards are appropriately applied. The former should presuppose the latter. The view can be amended to incorporate this point if one says that standards exist and there are arguments to which it is clearly appropriate to apply those standards. But at that point the issue will be whether standards fall broadly into just two types: deductive and inductive.¹⁵ Again, the great divide can be questioned. It is reasonable to suppose that we develop standards of one kind or another because there is a substantial group of arguments to which they are appropriately applied.

Among philosophers, the positivist theory of argument seems to be the most popular theory. It is Copi’s version which is the most commonly accepted, perhaps due to the influence of his texts over several decades. It is also because this view and it alone allows one to apply the inductive-deductive distinction to all arguments and to have good and poor arguments within each category. Salmon, Neidorf, and Kyburg give a version of the distinction applicable only to good arguments. Black and Rescher state one which allows inductive arguments to be either good or poor, but leaves all deductive ones as valid. Fohr transfer the distinction to intentions, with the result that it cannot be exhaustive after all.

Most who rely on a positivist theory of argument have not articulated a particular version, for it has been ‘common wisdom’ amongst logicians and philosophers. They would hold that the theory is exhaustive, that it applies to arguments (as distinct from intentions or standards) and that it allows for good and poor arguments (inferentially speaking) within each category. These presumptions make Copi’s account the most attractive one.

As we have seen, significant problems arise in applying Copi’s distinction, due mostly to the phrase ‘is claimed to’ in the definition. This phrase does not make explicit reference to the intentions of arguers. A person might use words that, as normally understood, make a claim she did not actually intend to make. The Copi version of the inductive/deductive distinction does not commit us to the tight relationship between the intentions of the arguer and the direction and force of the argument. Rather, it requires that we look at the wording of the argument and try to determine whether the argument as stated is claiming a necessary or probabilistic connection between the premises and the conclusion. The difficulty at this point is that indicators may give conflicting signals, or be absent altogether. Hence we are frequently left not knowing whether to classify an argument as deductive or as inductive. We saw problems even with examples that Copi himself selected for exercises. Here is another:

The peculiar evil of silencing the expression of an opinion is that it is robbing the human race: posterity as well as the existing generation; those who dissent from the opinion still more than those who hold it. If the opinion is right, they are deprived of the opportunity of exchanging error for truth; if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error.¹⁶

In this argument of J. S. Mill’s we may ask whether ‘it is claimed’ that the conclusion follows with absolute necessity from the premises. The conclusion is that suppressing the expression of an opinion always robs the human race especially ‘posterity’ and dissenters. It is quite clear what this conclusion is, and it is also fairly clear as to what premises are stated in defence of it. (Interpreters may dispute as to whether the argument contains unstated premises. But for now it is only the classification of the argument as inductive or deductive on the basis of what ‘is claimed’ that is at issue.) There seems to be no conclusive evidence as to how tightly the conclusion ‘is claimed’ to be related to those premises. One might regard the argument as deductive or as inductive.

Nor is this example unrepresentative. As Skyrms, teachers of informal logic, and a number of writers on the inductive-deductive distinction have noted to their consternation, examples like this are all too easy to find. Consider again:

It is the singular feature of such ethnic explanation (of poverty) that it is all but exclusively confined to conversation. The reputable scholar unhesitantly adverts to it in casual interchange but rarely if ever puts it in his books or even his lectures. What is wholly plausible in conversation is wholly impermissible in print. There is obviously something odd about an explanation of poverty and well-being that must be so discreetly handled.

Here John Kenneth Galbraith, in a discussion of mass poverty, argues from the absence of ethnic explanations of poverty in print and in lectures to the ‘oddity’ of these explanations of poverty.¹⁷ It is clear what his conclusion and premises are, but unclear what ‘is claimed’ about the relation between them. The word ‘obviously’ indicates that Galbraith confidently believes his conclusion to be true, but does not indicate whether he believes it to be necessitated, or rather made probable, by his premises.

It is no accident that such examples are easy to find. People who argue do (at least implicitly) distinguish conclusions from premises and ‘claim’ that the latter provide reasons for the former. But they often do not, even implicitly, make claims about what sort of connection is supposed to hold between these premises and their conclusion. A major reason for this is that most arguers have not reflected on the difference between deductive entailment and making probable, and hence would not raise the question about strength of connection as philosophers would like them to raise it. They do not, explicitly or implicitly, ‘make claims’ about an issue that for them does not arise at all. A further problem is that even if ordinary arguers did wish to indicate whether a necessary or probable connection existed, our language provides very few words which would conveniently serve the purpose. (At least, that is true of English.) Indicators such as ‘therefore’ and ‘must’ are sometimes urged by textbook authors to indicate deductive arguments, but are also to be found in arguments that tradition would label as non deductive. Given that the notion of deductive entailment and the related notion of ‘following with absolute necessity’, which Copi uses in his definition, are philosophical constructs, it is not surprising that ordinary language lacks terms that reliably indicate a claim to either sort of connection.

Those who continue to believe that ordinary arguers would do well to master this distinction and learn to observe it should recall that the closely related distinctions of analytic versus synthetic statements, and of necessary versus contingent statements, are contested. It is a commonplace of modern philosophy that these distinctions are difficult to draw with precision. Since Quine’s ‘Two Dogmas of Empiricism’ and Waismann’s ‘Analytic-Synthetic’ series, few philosophers have used these distinctions with confidence. Current analyses of scientific reasoning emphasize the difficulty of classifying terms as either conceptual or observational and the related difficulty in classifying statements as either logical or empirical. Given such acknowledged difficulties, it is a tribute to the sheer force of unanalyzed tradition that the inductive-deductive distinction has remained so prominent as the basis for a theory of argument.

Depending on which version of the positivist theory we are dealing with, we need to find out whether all the information ‘in’ the conclusion is already ‘in’ the premises; whether the truth of the premises would make the falsity of the conclusion ‘logically impossible’; whether the argument or the arguer ‘claims’ or ‘intends’ either of these; and so on. If there are many borderline cases when we try to determine whether statements are analytic or synthetic (or necessary or contingent, or a priori or empirical), there will obviously be borderline cases for arguments as well. The question for arguments can be collapsed into the other: we ask whether the associated conditional is empirical or necessary instead of asking whether the argument is deductive or inductive. If the argument is deductively valid, its associated conditional is necessarily true. If it ‘claims’ deductive validity, it ‘claims’ that the associated conditional is necessarily true. If its author intends it to be deductively valid, he intends that its associated conditional is necessarily true, and so on.

To illustrate this point, consider the following argument from Thomas Kuhn’s early book, The Copernican Revolution. Early in his career, Kuhn felt an obligation to defend what was then an unusual practice – combining the history of science with the philosophy of science. He said:

.. the combination of science and intellectual history is an unusual one. Initially it may therefore seem incongruous. But there can be no intrinsic incongruity. Scientific concepts are ideas and as such they are the subject of intellectual  history.¹⁸

There is a subargument structure here:

1. Scientific concepts are ideas.

   So,

2. Scientific concepts are the subject of intellectual history.

   Therefore,

3. There is nothing intrinsically incongruous about combining science and intellectual history.

Asking whether this argument is deductively valid is, in effect, asking whether its two associated conditionals are logically necessary. These are ‘If scientific concepts are ideas, then scientific concepts are the subject of intellectual history’ and ‘If scientific concepts are the subject of intellectual history, then there is nothing incongruous about combining science and intellectual history’. Are these statements logically, or necessarily true? It is not clear in either case. The first might be said to assume that all ideas are the subject of intellectual history, and thus not to be necessarily true as stated, on the grounds that it assumes something false. On the other hand, it might be said to assume only that scientific ideas are serious ideas and all serious ideas are the subject of intellectual history, and the claim might be made that these assumed statements are true, perhaps even necessarily true. The matter is arguable. Nor are standards of incongruousness precise. It is by no means easy to work out an answer to the question of whether the second conditional is necessarily true. Probably the most cautious answer is to say that neither conditional is necessarily true. We can see from this example just how directly difficulties with the necessary/ contingent and analytic/synthetic distinctions transfer to the inductive/deductive distinction. If we ask whether Kuhn intended either or both conditionals to be interpreted so as to come out as necessarily true, or claimed implicitly that either or both were necessarily true, the problem would not be more easily resolved.

To add to these difficulties, there are further problems that appear when we consider the possibility that arguments have unstated premises. As the topic of missing premises is a large and thorny one for any theory of argument, we cannot pose it as a special problem for the positivist theory. However, it augments difficulties of classification because, as we have seen, any argument can be reconstructed as a deductively valid argument by suitable addition of premises.¹⁹ Perry Weddle, among others, once urged that such possibilities for reconstruction leave too much indeterminacy in classification. He urged a shift to a monolithic theory as a result. One might urge that if an argument can be reconstructed so as to be deductively valid, this in itself may be seen as a reason to think that the arguer must, in effect, have ‘claimed’ that his premises (stated and understood or unstated) would lead with absolute necessity to his conclusion. Some who believe that such reconstructions more accurately depict the direction and force of the original argument will see the emerging ‘fact’ that the reconstructed argument is deductively valid to be a reason for thinking the arguer ‘claimed’ an absolutely necessary connection. But it is not a good reason.

It is not easy to sort actual arguments into the two positivist categories on the basis of the Copi sort of account which constitutes standard logical wisdom on the part of many philosophers today. That many difficulties arise in applying the distinction cannot be denied. What is debatable is not the existence, but the significance, of these difficulties. The distinction between A’s and B’s may be important even though there are many items that are borderline cases and might be classified either as A’s or as B’s. Yet one must acknowledge that application problems do not by themselves show that a distinction is untenable. It is likely that the classifying problems that plague the positivist theory of argument have their counterparts in other pluralistic theories of argument. We might have to choose between a theory with classifying problems and a monolithic theory. That theory would presumably be deductivism, given that no one doubts that there exist at least some arguments that are deductively valid.

There are almost always several ways of interpreting what people say and write. This point applies to arguments as it does to all other discourse. Any theory of argument allowing for several categories of argument will have to make some allowance for this flexibility in interpretation. Those who adopt the theory will have to develop a policy for borderline cases. The fact that there are many cases that are not easily classified according to the positivist theory does not count conclusively against that theory. If one is convinced that the basic dualism of the theory is built around something fundamental and important, one may attribute the many borderline cases to variations in context, the flexibility of written and spoken language, and the problem of missing premises, and decide to maintain some version of the theory.

The key issue is the nature of this basic dualism. The term ‘positivist’ is appropriate for the theory of the great divide because that divide owes much of its domination of our thought to the belief, common some decades back, that mathematics-logic and the empirical sciences are the only two sources of human knowledge. The different versions of positivism are all dualistic, though the dualism appears in different places in the various versions. The key common idea is that there is a basic kind of connection between premises and conclusion that is deductive, and there is one other kind of connection. Only one. The deductive side of the dichotomy seems relatively unproblematic. To be satisfied with the positivist theory, however, we have to be satisfied with both sides. Moreover, and most significantly, one has to convince oneself that this dichotomy is exhaustive. The key issue for any version of the positivist theory, is whether there is just one kind of nondeductive connection.

The usual way of describing an inductive connection between premises and conclusion is to say that the premises, if true, make the truth of the conclusion likely or probable. This may be a way of saying only that the premises have some bearing on the conclusion but fail to entail it. If so, no independent understanding of inductive connection is gained. One has simply, in effect, reiterated one’s belief that deductive connection is an important thing to understand and negatively defined a second derivative category. To have a good understanding of the dichotomy around which the positivist theory of argument is built, one should have an independent and clear understanding of inductive connection. If the theory is to dichotomize arguments, this understanding should yield a distinction that will be relatively easy to apply and that will exclusively and exhaustively divide arguments into the two types.

The term ‘probable’, which is often used in defining inductive arguments, is most naturally applied to contexts where we are expressing roughly quantifiable degrees of confidence in empirical statement and where we are willing, in at least a rough sense, to make quantitative judgments. Probability theories deal with the quantitative assessment of confidence or likelihood of some empirical statements, given a prior quantitative assessment of others, based in the final analysis on relative frequencies. If one is to use ‘probable’ or a related term in order to specify a sense of ‘inductive’ which will provide a firm basis for a clear and exhaustive ‘inductive/deductive’ distinction, one need to define the term more broadly. There are many arguments that have conclusions that are non-empirical and in which, nevertheless, the supporting reasoning is, on the face of it, not deductive. (They appear to be a priori and yet not deductive.) In such contexts, a standard conception of probability is a poor fit.

Consider arguments of the following types:

• consistency arguments by analogy. In such arguments it is urged that case (a) is relevantly similar to case (b); that case (b) has been treated as such-and-such; and that therefore case (a) should be similarly treated. The conclusion is normative; the reasoning is based on parallel cases.
• arguments of the type that Carl Wellman has called ‘conductive’ and which others have referred to as ‘balance-of-consideration’ or ‘good reasons’ arguments (Baier) or as ‘convergent arguments’ (Thomas). In such arguments, several reasons are cited; these appear to bear independently on the conclusion. All premises may be relevant; none taken alone is likely to be sufficient. Frequently the conclusion is normative; it may also be about an issue of classification or interpretation.
• non-conclusive philosophical arguments. These may be of one of the above types. They are noted separately here in the hope that philosophers will be particularly familiar with the idea that in their own discipline there are often arguments that seem to have some force, yet not to be deductively valid. (For example, the failure of many physicalistic terms to apply naturally to such phenomena as belief and thought counts against the mind-brain identity thesis, but how seriously? It does give a reason to think there may be something wrong, or overly-simple, about the thesis. But it does not entail its falsehood. Nor would it be natural to say that this linguistic fact makes it ‘improbable’ that the identity thesis is true. The notion of probability does not fit the case well. And obviously, the truth or falsity of the thesis is not straightforwardly empirical.)

p class=”import-Normal indent” style=”margin-left: 0.7pt; margin-right: 0.5pt; text-indent: 10.05pt;”>There are two themes underlying the idea that an inductive connection is probabilistic rather than necessary. The first is a negative idea: the premises do not necessitate the conclusion. The second is a positive idea: the premises offer some support to the conclusion. This second idea requires clarification; ‘some support’ should not be understood merely as ‘nondeductive support.’ How helpful is it to say that the premises will (if true) make the conclusion more probable? I submit that it is not very helpful.

Appeals in this context to the term ‘probable’ are not useful outside contexts where the conclusion is empirical. The reasons we offer for and against normative and conceptual conclusions are not naturally understood as making these more or less probable. For example, an argument in which abortion is assimilated to infanticide is not one in which the premises, if true, make it probable, or more probable, that abortion is wrong. They provide some reason to think that abortion is wrong. It makes little sense to attach probabilities to normative conclusions of this type.²⁰

If a probabilistic connection is any connection other than a deductive one, then of course consistency arguments, conductive arguments, and many philosophical arguments are based on such a connection. If that connection is allowed to define what an inductive connection is, the inference in question may be said to be inductive. But little understanding is thereby gained.

One may understand probabilistic connection in this broad way. But no information is thereby provided as to what the various inductive arguments have in common. It will not elucidate the category ‘inductive’ so as to yield a balanced dualism in the positivist theory of argument. On this understanding, one has deductive arguments (in which an entailment of conclusion by premises is exemplified, intended, or ‘claimed’) and one has other arguments (in which no entailment is exemplified, intended, or ‘claimed’). The inductive is the ‘other’, about which one has said nothing informative. The broad understanding of probabilistic connection is misleading insofar as concepts of probability are most commonly associated with, and most straightforwardly applicable to, the confirmation of empirical statements by empirical evidence. This association, together with the more fundamental association between induction and scientific reasoning, has led many to ignore the fact that reasoning that is probabilistic in the broad sense is often not probabilistic in the narrower sense. Non-empirical conclusions may be defended by reasoning that is non deductive in the sense that it does not exemplify (or is not intended or claimed to exemplify) the connection of logical entailment of conclusion by premises. The shifting between a broad and a narrower sense of ‘probable’ and related terms makes it too easy to ignore the existence of nondeductive arguments that are primarily non-empirical in character.

In light of these considerations, the basic dualism underlying the positivist theory of argument is not sufficiently clear and compelling to outweigh classificatory problems. Though this is probably the theory of argument most popular among philosophers, and it has a venerable history going back through Hume even to Aristotle, I contend that it is not a satisfactory theory.

The strong philosophical attachment to the positivist theory of argument may be due to two beliefs, both prominent in tradition and both having a firm hold on many. There is first the tradition going back to Aristotle, which maintains that there are two and only two broad types of argument: deductive arguments, which are conclusive, and inductive arguments, which are not. There is secondly the tradition – with the same venerable history – that inductive arguments are the arguments of science: fundamentally induction deals with the empirical confirmation of scientific hypotheses. The problem is not with either of these traditional beliefs but with their conjunction. If one is loyal to both at once, one is led to ignore many arguments common in morality, history, literary interpretation, law, and philosophy.

There are many issues that are neither amenable to techniques of empirical confirmation (not straightforwardly, in any case) nor settled deductively. Inductive logics have dealt primarily with arguments that are classically inductive (enumerative inductive). They may venture occasionally into inferences from correlational data to causal hypotheses, or to the inference-to-the-best-explanation. But generally they fail to include many patterns and style of argument which a naturalistic analysis of discourse would reveal: appeals to authority, arguments from separate reasons, interpretive arguments, ad hominem arguments, consistency arguments by analogy, and various other types of philosophical and legal argumentation. In fact, such arguments are rarely systematically studied under any name.

This is the real danger of the great divide in the positivist theory of argument. One sets up the inductive-deductive dichotomy, making it true by definition that all arguments are either deductive or inductive. Then one looks at the work which has in fact been done by logicians. There are systems articulating various aspects of deductive logic and there are systems called ‘inductive logic’. The latter deal with sampling, generating empirical hypotheses, causal inference, and so on. One readily comes to believe that the types of arguments covered in these standard systems are all the types there are. But many arguments that are inductive in the broadest sense have not been covered.

This theme has been emphasized by Chaim Perelman and L. Olbrechts-Tyteca.²¹ In their substantial book, The New Rhetoric, they offer illustration after illustration of such arguments, castigating logicians and philosophers for having been so mesmerized by the traditional ‘inductive/deductive’ distinction as to have denied their very existence.

The great divide between deductive and inductive arguments is spurious and theoretically dangerous, because it makes it too easy to ignore the many non deductive arguments which are not classically inductive. Confidence in this spurious dichotomy leads one to false simplicity in classificatory categories and falsely founded problems of justification in philosophy and elsewhere. Acknowledging the existence and epistemic legitimacy of other types of argument would alter approaches to such problems as the justification of normative and interpretive statements while at the same time enhancing our understanding of natural argumentation.

Notes

1.Wesley Salmon, Logic. (Englewood Cliffs, N.J.: Prentice Hall, 1973. Second Edition.)

2. Neidorf, Deductive Forms. (New York: Harper and Row, 1967).

3. Henry Kyburg, ‘Ordinary Language and Inductive Argument’, in Probability and Inductive Logic, (New York: Macmillan, 1970), pp. 97-98.

4. Nicholas Rescher, Plausible Reasoning, (Assen: Van Gorcum, 1976), pp. 100-101.

5. Baruch Brody, Logic: Theoretical and Applied (Englewood Cliffs, N.J.: Prentice Hall, 1973), p.74.

6. Encyclopedia of Philosophy, 1967 Edition. Black also notes various narrower senses of ‘induction’.

7. Irving Copi, Introduction to Logic. (New York: Macmillan, 1972. Fourth Edition.), p. 26.

8. A discussion of the intentional interpretation follows; it should not be attributed to Copi.

9. Cited by Copi, p. 27. No indication is given as to what his own classification of this argument would be.

10. Cited by Copi, p. 27. The answer he suggests is on p. 491.

11. Robert G. Olson, Meaning and Argument (New York: Harcourt, Brace, and World, 1975), p. 175. Olson distinguishes simple enumerative induction from induction in the broad sense in which every nondemonstrative argument is deemed to be inductive.

12. Samuel D. Fohr, ‘The Inductive-Deductive Distinction’, Informal Logic Newsletter, vol. ii, 2. See also my ‘More on Inductive and Deductive Arguments’, in Informal Logical Newsletter, vol. ii, 3 and David Hitchcock’s ‘Deductive and Inductive’: Types of Validity, not Types of Argument’, Informal Logic Newsletter, vol. ii, 3.

13. Brian Skyrms, Choice and Chance (Encino, Calif.: Dickenson, 1975. Second Edition.), pp. 11-13.

14. David Hitchcock, ‘Deductive and Inductive: Types of Validity, not Types of Argument’.

15. See Hitchcock ‘Deduction, Induction, and Conduction’, in Informal Logic Newsletter iii, 2, pp. 7-15 and my ‘Assessing Arguments: What Range of Standards?’, Informal Logic Newsletter iii, 1, pp. 2-4. I have profited from a subsequent informal discussion with Hitchcock about this point.

16. Mill, ‘On Liberty’, in The Utilitarians (New York: Doubleday 1960), p. 4.

17. John Kenneth Galbraith, The Nature of Mass Poverty (Cambridge, Mass.: Harvard University Press, 1979), pp. 14-15.

18. Thomas Kuhn, The Copernican Revolution (Cambridge, Mass.: Harvard University Press, 1957), p. vii.

19. See Perry Weddle, ‘Inductive, Deductive’, Informal Logic Newsletter ii, 1, pp. 1-5, and ‘Good Grief: More on Induction, Deduction’, Informal Logic Newsletter iii, 1, pp. 10-13.

20. Compare my comments in ‘Assessing Arguments: What Range of Standards?’ and remarks by David Hitchcock in ‘Deduction, Induction, and Conduction’.

21. Ch. Perelman and L. Olbrechts-Tyteca, The New Rhetoric: A Treatise on Argumentation, (Notre Dame: University of Notre Dame Press, 1969. Translated from French by John Wilkinson and Peircell Weaver.)