Language, Mind, and Brain

T. W. Simon, R. J. Scholes, T. W. Simon, R. J. Scholes

• Publisher: Psychology Press
• Year: 2019
• ISBN:
  9781317738046
• Edition: 1
• Topic: Languages & Linguistics
• Subtopic: Linguistics
• Index: Languages & Linguistics

The chapters in this volume are extended versions of material first presented at the National Interdisciplinary Symposium on Language, Mind, and Brain held April 6-9, 1978, in Gainesville, Florida. First published in 1982. Routledge is an imprint of Taylor & Francis, an informa company.

1	Logic, Reasoning, and Logical Form

Gilbert Harman

Princeton University

I want to discuss two related issues. (1) Does logic play any role in the actual reasoning people do? (2) Do sentences of a natural language like English have logical forms?

In order to address these questions, we must, to begin with, distinguish inference or reasoning, on the one hand, from proof or argument, on the other. Inference or reasoning is a process of trying to improve one’s overall view by adding some things and subtracting others. A proof or argument consists in one or more premises and a sequence of steps, each of which is supposed to follow from premises or previous steps in accordance with certain rules of logic, the last step being the conclusion. Reasoning and argument may well be closely related enterprises, although as I will explain in a moment this is not obvious. In any event, it is very important not to confuse reasoning and argument so that, for example, one wrongly comes to think of reasoning as involving premises, intermediate steps and a final conclusion reached by applying so-called “rules of inference” or one wrongly comes to think there is such a thing as “deductive reasoning” or “inductive argument” or “practical syllogisms.” These are just confusions.

Reasoning is a process of trying to improve one’s overall view. If it made sense to speak of premises and conclusions of reasoning, the premises would be everything one accepts at the start and the conclusion would be everything one accepts at the end. But it is misleading to speak of premises and conclusion since some of one’s “premises” might be abandoned in the course of reasoning and since one’s “conclusion” will contain primarily what one has believed all along.

Reasoning is a holistic process in the following sense. One seeks to make minimal changes that will improve one’s overall view, for example one attempts to make one’s view more explanatorily coherent by adding explanations of things previously unexplained and by rejecting things that do not fit in well with other things one accepts (also discussed in Harman, 1973, chaps. 7, 8, 9, 10; 1975-76, pp. 431-63).

Rules of argument or proof are local rules of logical implication, applying to particular propositions, saying that this sort of proposition follows from those. “Whenever propositions of those sorts are true, then a corresponding proposition of this sort is always true.” For example, whenever a disjunctive proposition P or Q is true and so is the negation of one of the disjuncts not P, then the other disjunct Q is always true. Such a principle is sometimes called a “rule of inference,” but that is misleading. Rules of inference tell one to improve one’s overall view in various ways, but inferring a logical consequence of one’s beliefs is not always an improvement. There is the problem of unnecessary clutter. And there is the problem of inconsistency. Inconsistent propositions logically imply everything; but, when one discovers an inconsistency in one’s beliefs, one should not infer everything. Indeed, in that case it may not be clear what to do, especially if the inconsistency results from a paradox of some sort. Perhaps one should just ignore it and try to stay away from it, in the way that some mathematicians try to stay away from the set theoretical paradoxes. This shows that the rule that P or Q and not P always imply Q does not mean that, if one believes both P and Q and not P, one may infer Q. Perhaps one should not bother to clutter up one’s mind with that information. Perhaps one already believes not Q and should stop believing P or Q or not P or should sit tight and hope this inconsistency in one’s beliefs will not lead to trouble.

Now, it is not immediately obvious that logic is more relevant to reasoning than is arithmetic or geometry or physics or chemistry. Perhaps logic is simply the study of certain features of the world, differing from other subjects only in being more general and abstract.¹ For, if logic is specially relevant to reasoning, it is not immediately obvious in what way it could be specially relevant.

It might be said that arithmetic, geometry, physics, chemistry, and so on merely provide premises, whereas logic provides rules of inference that allow us to derive specific conclusions from those premises (cf. Carroll, 1895). There may be something to this idea, but it cannot be completely correct, since principles of logic are rules or laws of implication and not, strictly speaking, rules of inference. It might be said that logic is needed in order to get from our finite statements of theory to their infinite consequences, from our finite number of explicitly represented beliefs to the infinitely many things we believe implicitly (cf. Quine, 1966, pp. 77-106). This is suggestive but probably cricular if “getting” one thing from another is the same as inferring one thing from another, for then to say we need to use logic in order to “get” to the consequences of our explicit beliefs would seem to amount to saying that logic plays a special role in reasoning.

Let us suppose that logic does play a special role in reasoning. What could that role be? Recall that reasoning is a process of trying to make minimal changes that will improve one’s overall view, including changes that will increase the explanatory coherence of one’s view. This suggests that, if logic plays a special role in reasoning, that might be because logic has something special to do with explanatory coherence. And that does seem plausible. Logical inconsistency in one’s beliefs would seem to be a kind of incoherence. And certain explanations seem to take the form of deductive arguments or argument sketches, a point stressed by proponents of the deductive nomological or covering law model of explanation (see Hempel, 1965, pt. 4, pp. 229-496).

An argument consists in premises and a sequence of steps each of which is derived from premises and earlier steps in accordance with certain rules of logical implication. If the argument is to be usefully explanatory, each step will itself have to be immediately intelligible, needing no further explanation. This suggests that, if logic plays a special role in reasoning, it may do so in part because certain rules of logical implication express immediately intelligible connections that can be understood without further explanation. Some psychological investigation of the psychology of reasoning might be interpreted as attempting to discover which rules of logical implication expresses such immediately intelligible connections (e.g., Wason & Johnson-Laird, 1972).

In working this out in detail, we would have to distinguish explaining why something happened from explaining why it is true that it happened. For suppose one knows that, either John’s car is in his garage, or he is out driving; one looks in the garage and sees the car is not there; and one concludes that John is out driving. Then one’s reasoning involves an argument that does not explain why John is out driving; at best it explains why it is true that John is out driving but does not give a reason why John is out driving.

The suggestion, then, is that logic is specially relevant to reasoning because logic is specially relevant to explanatory coherence and because reasoning involves (among other things) trying to improve the explanatory coherence of one’s view. Deductive arguments are specially relevant to reasoning because explanations can take the form of deductive arguments—in reasoning one comes to accept not just the conclusion of the argument but the whole argument; one accepts it as expressing an explanatory connection between its premises and its conclusion.

The last part of this suggestion, about deductive arguments, can be broken down into two parts. First, there is the idea that arguments of some sort play a special role in reasoning by serving as explanations. Second, there is the further suggestion that the rules people follow in constructing such arguments are rules of logic. (Of course we must allow that people sometimes make mistakes and argue fallaciously). To see the force of this second idea, notice that any general proposition could conceivably be used as a rule of implication that could connect steps of argument. For example, the proposition that all metals conduct electricity could be treated as the rule that X is a metal implies X conducts electricity. Such a rule would authorize the following simple argument:

Copper is a metal.

So, copper conducts electricity.

What is being suggested is that people do not construct arguments like this that appeal to nonlogical rules but always treat the nonlogical principles as premises in arguments that proceed in accordance with rules of logic, as in this argument:

Copper is a metal.

All metals conduct electricity.

So, copper conducts electricity.

This is obviously a highly speculative suggestion.

In order to evaluate this suggestion, we must at least ask why it should be true. What is it about principles of logic as compared with other principles that could give them this special function? What distinguishes principles of logic from nonlogical principles?

It is often said that logical principles are formal in a way that nonlogical principles are not. The principle that P or Q and not P always imply Q refers only to the forms of the propositions involved. The principle that X is a metal implies X conducts electricity refers not only to the forms of the propositions involved but also their content. This idea might be useful to us if there should be a nonarbitrary way to distinguish elements of nonlogical content, like metal and electricity. If, on the other hand, the distinction between elements of logical form and elements of content should turn out to be an arbitrary one, then the distinction between logical and nonlogical principles would be arbitrary and it would not make sense to suppose that logical rules play a special psychological role in the construction of arguments. And, of course, even if there is a nonarbitrary distinction between logical and nonlogical elements, not every such distinction would give logical rules a special function in argument construction.

Presumably, any useful nonarbitrary distinction will have something to do with grammar. Elements of logical form must be grammatically distinctive in some significant way. Now, reflection on a number of examples suggests this: Elements of logical form are members of small closed classes and elements of nonlogical content are members of large open classes, where the relevant classes are classes of atomic elements of the same logical category. Logical categories include predicates, sentential connectives, quantifiers, etc. For example, or is an atomic sentential connective. The class of atomic sentential connectives is small and closed in that new atomic sentential connectives are not easily added to the language. So, or is an element of logical form by this criterion. On the other hand, metal is an atomic predicate. Atomic predicates form a large open class to which new members are added all the time. So metal is an element of nonlogical content by this criterion (see Harman, 1979).

There is, then, some reason to think that the distinction between logical principles and others has a syntactic or grammatical basis, if it is based on a distinction between elements of logical form and elements of nonlogical content that has such a basis. Another possible indication of the role of syntax is the surprising fact that general logical principles cannot be stated in ordinary language as ordinary generalizations but must be stated one level up as generalizations about the truth of propositions. We can generalize from “Copper conducts electricity,” “Silver conducts electricity,” and so on, to “All metals conduct electricity”; but we cannot in ordinary English generalize from “Copper does not both conduct electricity and not conduct electricity,” “Snow is not both white and not white,” “It is not the case that both all men are moral and not all men are mortal,” and so on without making use of what Quine calls semantic ascent (see Quine, 1972, pp. 11-12). We have to say, “Every proposition of the form not both P and not P is true. It would not be good English to try to express this directly as, for example, “Nothing is both it and not it.” We can perhaps say, “Nothing is both so and not so” (?), if “nothing” means “no proposition” and “so” means “true” or “the case,” but this clearly does involve semantic ascent.

These grammatical considerations indicate that logic has a different function from other aspects of one’s view of the world. Logic is built into one’s language and is relatively fixed. One’s view of the world is not built into the same extent and changes constantly over time. One’s view of the world is finitely represented. Logical principles are not normally represented as part of one’s view, except as a relatively late and sophisticated development using semantic ascent. Logical principles must therefore be manifested as rules of argument. These rules enable a finite representation of one’s view to express infinitely many implications. Rules of logic are therefore part of a relatively fixed system of representation in which one’s changing view of the world is expressed.

Now, linguists and philosophers of language do put forward hypotheses about the connection between grammatical structure and logical form in sentences of a natural language like English. Such hypotheses presuppose that there is a nonarbitrary psychologically real distinction between aspects of logical form and aspects of nonlogical content. This presupposition would seem to make sense only within a framework like the extremely speculative one that I have been sketching.

This may explain why those who put forward hypotheses about logical form feel compelled to provide a finite truth conditional “semantics” for sentences analyzed in the way they propose to analyze them. It is generally agreed that any such proposal should permit a statement of truth conditions for the sentences being analyzed. Sometimes all that is required is an account of truth conditions in relation to one or another model or interpretation. Sometimes the stronger requirement is imposed that the account of truth conditions imply all appropriate instances of the schema “x is true if and only if p,” where what replaces “x” names or designates a sentence under analysis and what replaces “p” is that very sentence or a translation of it. The stronger requirement makes sense given that logic requires semantic ascent....