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Three Steps Towards a Theory of Informal Logic

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Three Steps Towards a Theory of Informal Logic VII.2&3, Spring&Fall1985 Informal Logic Three Steps Towards a Theory of Informal logic SEALE DOSS Ripon College Formal logic being the kind of enter­ what an alternative theory of logic prise it is, there are many ways one can might involve. Those are the questions be led to doubt the legitimacy of such I propose to deal with here. logic. The effort to reduce even a very Let me begin by supposing three simple case of ordinary reasoning to a things about formal logic itself. First, pattern of symbols can lead one to that what we call formal logic is the out­ realize, for instance, how dogmatic growth of a fundamental thesis about formal logic really is-just as the the nature of correct reasoning; second, attempt to contrive examples of ordi­ that it is this thesis which generates nary reasoning which will illustrate the rubric of formal logic; third, that it such patterns may lead one to sense is also this thesis which generates how misleading it is. the techniques of formal logic. Beyond the barriers of symboliza­ The thesis, of course, is that correct tion lie other sources of doubt; for reasoning is, indeed, a function of example, the truth-table for condi­ formal patterns, patterns which exist tionals is enough by itself to lead one independent not only of whatever it is to suspect that formal logic is wrong, that one is reasoning about, but also just basically wrong in its effort to cap­ independent of anyone actually enga­ ture and clarify the nature of correct ging in such reasoning. Call it Plato­ reasoning. nism if you like, but this assumption It is not surprising that one may be survives even the transition from syllo­ led to wonder, then, about some differ­ gostic logic to modern logic.[1] 'ent way of doing logic, about some dif­ The rubric which it generates in­ ferent way of characterizing correct cludes such things as the definition of reasoning. The trouble, of course, is formal validity, the distinction between not merely that there is no alternative validity and soundness, the distinc­ system available; it is not even clear tion between premises and conclusions, what an alternative system would look the distinction between deduction and like. In fact, it is not even clear that the induction, and even the notion that rea­ alternative to formal logic must be an­ soning is, in fact, a matter of "argu­ other system of logic at all. ment construction" -in short, the very Even so, the mere politics of the mat­ vocabulary in terms of which we are ter suggest the need for at least an now all but forced to talk about logic. alternative theory of logic. For without Finally, the techniques of formal such a theory, without a theory wh ich logic which flow from this basic as­ portrays correct reasoning in non­ sumption (and which reinforce the ru­ formal terms, without a theory which bric of formal logic) include such things will account for correct reasoning in as the transformation of ordinary terms other than abstract patterns, it is sentences into propositions, the use of most unlikely that the enterprise of symbols to represent such propositions, formal logic can be swayed, much less the reliance on inference rules and dismantled. Mere doubt is hardly proof procedures in the construction enough, in logic no less than in other of arguments, and the testing of argu­ matters of dogma and tradition. ments by examination of their symbolic One might ask, then, what an alter­ structure-in short, a devout determi­ native theory of logic would look like, nation to replace all concern for subject 128 Seale Doss matter with the concern for form. ments. What would one be left to That determination, one might add, teach? Faced with such a peril, one reflects the sense in which the thesis, might naturally wish to alter the ques­ the rubric and the techniques of formal tion at hand still one more time, asking logic are quite deeply rooted in Pla­ not how different an alternative theory tonism. But the point of such a sketch might be, but rather: How much of the is not to trace the origins of formal tradition of formal logic can be pre­ logic. It is, rather, to provide some served if the theory behind it is re­ scope to the question of what an placed? alternative to formal logic might in­ Let me illustrate this concern by volve. citing, more or less at random, some of One might now rephrase the question the considerations it provokes. In the at hand, given such a sketch and given search for some alternative to the the doubts and difficulties which formal theory of formal logic, one may wonder logic is quite clearly prey to. How dif­ just how much of the system it has ferent would an alternative theory have generated can be left intact by asking, to be? That is, how different from the for example, whether or not such rules theory of formal logic must a theory of as modus ponens and modus tollens informal logic be if there is, in fact, to can be saved. They do, after all, seem be an alternative theory of logic? quite legitimate. But what shall be their Rephrased that way, the question justification, as rules, if one abandons reflects still another supposition about the theory they are drawn from? If formal logic: that behind its funda­ the theory of formal logic is abandoned, mental thesis, its rubric, and its tech­ how shall one be able to talk, even, niques-ali of which add up to an on­ about such things as antecedents and going system of logic-there is also consequents? About the properties an implicit theory at work. I take it that of conditionals? About the reasons why the theory of formal logic is simply a conclusion can't be drawn from a con­ that correct reasoning is reasoning in ditional and the denial of its antece­ accordance with a demonstrably valid dent? About the reasons why a conclu­ inference pattern - for exam pie, a sion can be drawn from a conditional pattern such as ((P & (P - Q)) - Q). and the denial of its consequent? For I also take it that the system as a whole that matter, how shall one be able to has emerged, over the past twenty­ talk about disjunctions and the law four centuries, as both a reinforcement of excluded middle? About conjunc­ of this theory and a vindication of it, tions and the law of contradiction? as well. One may indeed suspect that If one cannot employ symbols, because the theory of formal logic is wrong, the theory which justifies their use has for the kinds of reasons already sug­ been discarded, how can one make gested, but there is, after all, a deeply sense of the reasons why a statement entrenched tradition at stake here. The and the denial of that statement can't quest for an alternative theory-that be joined together logically? As for is, a theory which would account for statements themselves, without appeal correct reasoning in terms other than to form - and without appeal to propo­ formal patterns-is therefore not likely sitions which will demonstrate such to appeal to the timid. And that, I think, form-how can one make sense of the has a great deal of bearing on the ques­ way in which a statement such as tion of how different an alternative "Mary is shopping since she's down­ theory of logic is really likely to be.[2] town" is logically equivalent to the A truly radical alternative to the statement "If Mary is downtown, then theory of formal logic might, after all, she is shopping"? And so forth. require the sacrifice of the entire sys­ Such considerations are quite natu­ tem it has generated, to include not ral; they reflect the hold which formal only its vocabulary and its techniques logic has upon us. Given that hold, it but also, alas, its professional endear- is also quite natural to wonder how we Towards a Theory 129 could possibly do without the rest of the we have come to call "counterfactual system. What would happen to the no­ conditionals," and so it involves a tion of what an argument is? How could matter with regard to which formal we ever prove that an argument is valid logic is particularly vulnerable. if we abandon formal logic? How could Suppose, now, two historians deal­ we tell the difference between deduc­ ing with the American Civil War and its tion and induction? How could we deal aftermath are led to disagree about with universal quantification, with the what might have happened had the nature of relations, with such things as North not won the war. In speculating logical identity? Must we really dis­ about such matters one historian is card all the things which formal logic led to claim (as a great many have) that has somehow produced, all its cate­ " If the South had won the war, then gories, distinctions, and innovations? slavery would have survived in America Must we scrap an entire legacy? Or for another century." That is, of can it somehow be preserved? course, a counterfactual claim. Suppose These questions can be seductive, the other historian replies by saying to be sure. In light of such considera­ "No, that isn't so. Even if the South tions one may well retreat from the had won the war, slavery would have search for some alternative to formal disappeared in another generation." logic.
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