C. L. Hamblin, Fallacies (Methuen & Co. Ltd., 1970).

CHAPTER 8

Formal Dialectic

Let us explore the second half of the definition of fallacy a little a little further and be clearer what it is for an argument to seem valid. The term 'seem' looks like a psychological one, and has often been passed over by logicians, confirmed in the belief that the study of fallacies does not concern them. The arguments that tell against a psychological interpretation of logical terms, however, tell also against this supposition. That B seems to me to follow from A, when in fact it does not do so, implies that I am guilty of error, but it is not in itself grounds for calling the argument from A to B a fallacy. John Smith may believe that it follows from the state of the mining market that the moon is made of green cheese, and, if he so argues, his argument is very likely invalid; but if we discover that his belief is an isolated one without a rationale we shall be inclined to withhold the description 'fallacy' and say no more than that it has no logical foundation. Some similar reaction would be appropriate even if we were to find that a large number of other people shared his belief. We might, it is true, get round to speaking of the belief as a 'popular fallacy', in the sense in which we regard it as a onetime popular fallacy that the earth was flat, but we have put this sense of the word 'fallacy' behind us. An unsystematic belief is not a candidate for the title 'logical fallacy' even when it is in the form of an implication and widely held.

To justify the application of the tag 'fallacy', the seeming-valid must have a quasi-logical analysis. But what is the quasi-Logic within which this analysis is performed?

One kind of case in which we do not hesitate to speak of fallacy is that in which we are confronted with a false logical doctrine. If the invalidity of Smith's argument were due to his thinking that universal affirmative propositions are convertible, or that it is permissible to permute mixed quantifiers, we should identify his fallacy in just these terms. We do not demand, of course, that the fallacy-monger be capable of a clear and explicit formulation of his false principle: it is sufficient that we ourselves discern the operation of such a principle in his reasoning. To weaken the requirement a little further: it is common enough that what we discern is neglect of a true principle rather than conformity to a false. The important thing is that the invalidity must be systematic, and its source re-identifiable in different instances. Once this is said, it is clear that it need not, and ultimately must not, be described psychologically. A formal fallacy is an invalid argument generated by just such a false logical doctrine, and so there is nothing psychological about the seeming-valid except the fact that, for practical utilitarian reasons, we tend to confine consideration to cases in which the false doctrine is one that is liable to be actually held or followed by real people.

There are two ways in which fallacies may fail to be 'formal': they may either, like Begging the Question, be such that they do not rest on formal invalidity; or they may consist of arguments that are, indeed, formally invalid but are such that there is no possible (spurious) formal principle which generates them and gives them their seeming-validity. How are we to analyse these?

The answer, in both cases, is that we need to extend the bounds of Formal Logic; to include features of dialectical contexts within which arguments are put forward. To begin with, there are criteria of validity of argument that are additional to formal ones: for example, those that serve to proscribe question-begging. To go on with, there are prevalent but false conceptions of the rules of dialogue, which are capable of making certain argumentative moves seem satisfactory and unobjectionable when, in fact, they conceal and facilitate dialectical malpractice. Most of Aristotle's Fallacies Outside Language, and many of the stragglers that have been imported into other lists of Fallacies, are analysable within Dialectic in a way they would not be in Formal Logic. The Fallacies Dependent on Language are in a slightly different category and we shall set them aside for separate consideration in the next chapter.

Formal Dialectic, it should be added, does not have as its sole justification the analysis of fallacies; least of all, of those of the accepted list. It is the discipline to which the discussions of fallacies in the textbooks obliquely introduce us, and which represents the unstated raison d'etre of those discussions; and it will probably superannuate them as Formal Logic has superannuated Topics. Its relation to the study of fallacies is, admittedly, not quite straightforward, and we find elements relevant to it, from time to time, in positive theories of reasoning also; but, if the scattered survival of discussions of fallacies requires a justification other than in terms of entertainment value, this is what it must be. We need to see our reasoning in the kind of context within which, alone, these faults are possible.

Let us start, then, with the concept of a dialectical system. This is no more nor less than a regulated dialogue or family of dialogues. We suppose that we have a number of participants -- in the simplest case, just two -- to a debate, discussion or conversation and that they speak in turn in accordance with a set of rules or conventions. The rules may specify the form or content of what they say, relative to the context and to what has occurred previously in the dialogue. They govern the speaker's language and his logic, as well as a number of features of his discourse which are not normally studied under either of these headings.

In our present discussion we shall not be concerned to consider any contact of the dialogue with the empirical world outside the discussion-situation. It is true that the possibility of such contact is often germane to the formulation of dialectical rules and that there are some dialectical phenomena -- ostensive definition, the language of perception, commands, and others -- which cannot be profitably treated in its absence; but our present range of problems does not call for this generality. Here we merely note the omission; which otherwise might leave us open to the kind of criticism levelled against medieval Dialectic by the Renaissance. An interest in Dialectic has frequently been associated, in philosophical history, with a claim to discover knowledge by the use of purely dialectical methods, but this is no part of our present plan.

The study of dialectical systems can be pursued descriptively, or formally. In the first case, we should look at the rules and conventions that operate in actual discussions: parliamentary debates, juridical examination and cross-examination, stylized communication systems and other kinds of identifiable special context, besides the world of linguistic interchange at large. A formal approach, on the other hand, consists in the setting up of simple systems of precise but not necessarily realistic rules, and the plotting of the properties of the dialogues that might be played out in accordance with them. Neither approach is of any importance on its own; for descriptions of actual cases must aim to bring out formalizable features, and formal systems must aim to throw light on actual, describable phenomena. As a matter of emphasis, however, I shall lean towards a formal approach in what follows, since the practical material we aim to illuminate -- fallacious argumentation -- has already been sufficiently described.

Dialectic, whether descriptive or formal, is a more general study than Logic; in the sense that Logic can be conceived as a set of dialectical conventions. It is an ideal of certain kinds of discussion that the rules of Logic should be observed by all participants, and that certain logical goals should be part of the general goal.

The concept of a dialectical system is, at first, quite general and there are many systems that are of no interest whatever to the logician. For example, we can imagine a dialogue consisting of interchange of statements about the weather. Even remark-trading of this kind, however, is not entirely without interest if certain additional requirements are imposed: that a speaker's remarks should be consistent one with another, and that they should be without repetition or, perhaps, mutual implicative relationship; and that there might be some specification of an interaction between the speakers. We might imagine that, in certain circumstances, a speaker is obliged to indicate agreement or disagreement with a preceding remark of the other speaker, as if it were also a question. In fact a question-and-answer system, in which A asks questions and B must provide syntactically correct answers to them, is really simpler than this, since a questioner is not directly involved in the matter of consistency; but, even so, provides a generic dialectical setting for the decision-problems of all the formal logical calculi. A speaker who is obliged to maintain consistency needs to keep a store of statements representing his previous commitments, and require of each new statement he makes that it may be added without inconsistency to this store. The store represents a kind of persona of beliefs: it need not correspond with his real beliefs, but it will operate, in general, approximately as if it did. We shall find that we need to make frequent reference to the existence, or possibility, of stores of this kind. We shall call them commitment-stores: they keep a running tally of a person's commitments.

Rules may prescribe, prohibit, or permit; may be directed to particular people, who play roles in a dialogue; and may be conditional on any feature of the previous history of the dialogue. We shall normally avoid 'permissive' rules, adopting the liberalistic convention that anything is permitted that is not specifically prohibited. (It would, of course, be dualistically possible to frame all rules as permissive ones and prohibit everything they did not license.) The things prescribed or prohibited are linguistic acts of the person concerned, perhaps including the null-act; and a linguistic act is defined as the speaking of a locution in a given language. Since we are concerned mainly with two-person dialogues we can dispense with the phenomenon of discriminatory direction of locutions to one person rather than another, and assume that all locutions are directed to the other participant. The locutions we are concerned with generally represent statements or questions drawn from some prescribed range, but there will be certain others of a procedural nature; and, in any case, it should be borne in mind that it is ultimately their role in the dialectical system that gives sentences this kind of character, rather than the other way about.

We shall assume that speakers take turns politely, but this does not rule out the possibility that a given contribution by a given speaker may be analysable into two or several individual sentences. If it were necessary to be precise on this point we could build into each system a set of rules designed to determine who speaks when: for example, we could stipulate that each contribution of each speaker, except the final contribution of the dialogue, should end with the special locution 'Over!', and that each contribution except the first should immediately follow the saying of 'Over!' by the previous speaker. This would not give protection against filibusters but other means could be devised. We shall not need to involve ourselves in any of these matters in this book.

Rules, then, are of the general form 'If C is the case, sentences of the set S are prohibited for person P'; where prescribing A is the same thing as prohibiting everything else but A. Here C is a specification of a feature of the previous history of the dialogue. More adequately we might define incomplete dialogue as, say, any dialogue not terminating in some standard way, such as with the word 'Finish'; and then let C represent the prior occurrence of some one of a specified set of incomplete dialogues with P as a participant. In practice we are generally interested in rather easily specified sets, as in 'If the contribution of the other party was a question of the form S?, P must now say S or Not-S or I don't know'. Very frequently, too, the past history of the dialogue is sufficiently summed up by the traces it has left in the contents of commitment-stores.

In general, we need to specify two languages: the object-language, which is the one used by the speakers in the dialogue, and the rule-language, which is the language used in stating the rules and contains means for describing features of dialogues in conditionalizing these rules. Again, for present purposes, we shall not need to be very strict about either of these language-specifications; but both will, in some circumstances, be of relevance to the properties of systems.

A system is rule-consistent if its rules are such that it can never arise that one and the same act is both prohibited and prescribed; or, equivalently, there is no circumstance in which all possible acts (including the null-act) would be prohibited. Rule-inconsistency does not always matter in a practical system since sometimes the person who stands to be inconvenienced can see the contingency coming and take steps to avoid it. However, it is very easily avoided in such cases by minor reformulation.

Rule-consistency is a concept applicable to all systems. Questions of consistency may also enter at the level of the object-language, provided that, as is usually the case, we envisage this as containing statements, in some reasonably normal sense of that word. We shall say that a system is semantically consistent if it is never unconditionally possible for a speaker, in a single locution, or in several separate locutions taken together, to be forced to utter a contradiction; and semantically unforced if there is no non-tautological statement that a speaker can be unconditionally forced to utter, or any set of statements of which he can be forced to utter one, other than a set whose disjunction is a tautology. It is semantically unforced with respect to a given (complete or partial) evaluation -- namely, with respect to some allocation of truth-values to contingent statements of the object-language -- if no speaker can be unconditionally forced to utter a falsehood. The concept of a set of rules relative to an evaluation could be an important one in some connections, where the evaluation may be taken as representing shared sensory information and beliefs. A system is semantically open if there is no statement at all, even a tautological one, which a speaker can unconditionally be forced to utter, nor any set of statements of which he can be unconditionally forced to utter one. A semantically open system is semantically unforced. A semantically unforced system is one that is unforced relatively to every evaluation. Semantically unforced systems are semantically consistent. It should be re-emphasized that these characterizations are restricted to systems in which statements occur, and that this stipulation, in a sense, puts the cart before the horse. In the long run, whether a given locution is or is not a statement, question or the like depends upon its place in a dialectical system, and not vice versa. A statement is, ultimately, a locution which has permissibility-rules relating it to an effective commitment-store and governs the permissibility, in similar ways, of subsequent locutions; a question is a locution with respect to which there is a rule requiring one of a specified set of statements as subsequent locution of the other speaker, and so on.

It frequently happens that there are rules at different levels: at one level there are rules which specify, syntactically, what does or does not represent a dialogue of the system in question, whereas, at another level, there are rules which distinguish some dialogues among them as being more rational, or 'better', or a 'win' for this speaker or that, or as otherwise belonging to some more restricted class than dialogues as a whole. Moreover, it is not always clear how we should apply these distinctions. Take the matter of consistency: we have a choice whether to regard an inconsistent statement as unsyntactical, and hence as impossible within a given system properly defined, or to regard it as a perfectly possible locution which is simply of a kind towards which we take a particular attitude. It is perhaps less obvious that we have, in the long run, the same option with regard to various ranges of clearly unsyntactical, ill-formed and meaningless utterances. In ordinary speech, if a participant at some moment gives vent to an unidentifiable noise, we may ignore it and treat it as being no part of our conversation; but we may, depending on details difficult to regulate, choose to regard it as a locution to which we make some response such as 'What do you mean by that?' or 'That is not an answer to my question'. It is a weakness of formal work in these fields that it seeks to draw a hard line where none exists; but again, having noticed this, let us pass on.

We are ready to consider an example; and the one that recommends itself is the Obligation game. This is less fruitful than some other possibles such as the Lincoln's Inn or Buddhist varieties in throwing light on Fallacies, but it is the simplest of the various systems that might interest us. I shall aim to give a version which captures what I take to be the essence of the game in its simplest form, without claim to historical accuracy in detail.

The Obligation game is played by two people, called the Opponent and the Respondent. The language used is a finite propositional language based, say, on elementary propositions a1, a2, . . . ak and truth-functional operators, supplemented with several special locutions. (In place of propositional calculus we could substitute any other finite language of sufficiently normal type; for example, lower predicate calculus on a universe with finitely many individuals and limited variety.) We shall not formalize the rule-language. The Opponent speaks first and his first locution has three parts:

(a) The words 'Actual fact:', followed by an evaluation on the language, consisting, say, of a state-description b1.b2 . . . bk where each bj is aj or -aj. We shall call this statement 'B'.

(b) The word 'Positum' followed by a contingent statement inconsistent with B. We shall refer to this statement as 'C'.

(c)The words 'Propositum 1' followed by a statement, to be referred to as 'P1'.

The Respondent's first locution R1 consists of either P1 or its negation -P1; and, in general, each of the Respondent's contributions Rn (1 i< n < m-1) consists of repeating the preceding locution of the Opponent, or stating its negation. The Respondent's locutions may be reckoned 'correct' or 'incorrect' in accordance with a subsidiary rule to be detailed in a moment. The Opponent's contributions On (2 < n < m-1) are of the form: the words 'Propositum n' (for whatever n) followed by a contingent statement Pn. The Opponent's final locution Om is the words 'Win and Finish' if Rm-1 was incorrect, 'Resign and Finish' if R1 is correct and m=11, i.e. if the Respondent has survived ten proposita.

The answer-rule is as follows. Associated with the game is a commitment-store for the Respondent, consisting of the conjunction of the positum and all the Respondent's answers to date: that is, after the Respondent's nth locution the store contains Cn, where Cj+1 = Cj.Rj for each j = 0, 1, . . . m+1. The Respondent's locution Rn is correct if it is either (i) implied by Cn-1, or (ii) consistent with Cn-1 and implied by B; otherwise it is incorrect.

It can easily be checked that the system is rule-consistent: the only point of any doubt concerns the Opponent's final move. In assessing semantic properties we would do well to regard the Opponent's proposita as yes-no questions rather than as statements, on the grounds that they raise no question of commitment or consistency: only the Respondent's 'answers' do this. The system is then semantically consistent, open and unforced.

A slightly different system, which results from writing into the rules the stipulation that the Respondent must always give the 'correct' answer, can also be proved rule-consistent, as a simple consequence of the semantic consistency of the system just outlined. (The option 'Win and Finish' on the part of the Opponent will, consequently, never occur.) This system is semantically consistent but it is neither open nor, in general, unforced. It is, however, unforced, after O1 has occurred, with respect to a certain valuation constructible in terms of B and C0 as follows: to each statement S of the language is allotted the value 'true' if it is implied by C0, and 'false' if it is counterimplied by C0: otherwise it has the value 'true' if it is implied by B, and 'false' if it is counterimplied by B. We might hence regard the system as semantically unforced with respect to an evaluation if we are prepared to regard the 'actual fact' and 'positum' as characteristic of the game and hence not part of a forcing move on the part of the Opponent. That the modified system is semantically consistent was known to William of Sherwood (?), who regards the Obligation game as illustrating the principle 'From the possible nothing impossible follows'.

Now let us make another modification to the system, of a kind implicit in one of William's (?) examples. Let the Opponent's proposita P1,. . ., Pn consist not of single statements but of nonempty sets of statements, and let each 'answer' of the Respondent consist either of the conjunction of all the statements in the proferred set, or of the conjunction of their negations. For example, let Pj be the set of statements {p1, p2,. . . pi} and hence let Rj be either p1.p2 ..... pi or -p1.-p2 ..... -pi. Let us consider in turn what happens if we do not write in the requirement of 'correctness' of the Respondent's locutions, and what happens if we do so. In the first case the system is still clearly rule-consistent, but it is not semantically consistent since the propositum {p, -p}, for any p, is such that neither the conjunction of the statements nor the conjunction of their negations is consistent; and even the stipulation that, say, the statements p1, p2,. . . pi of any set Pj must be mutually indifferent would still leave the system a semantically forced one. In the second case -- if, that is, the 'correctness' requirement is written in -- the system is not rule-consistent: for it is impossible to achieve a 'correct' Rj in answer to a Pj of the form {p, -p}; and even if statements of a set are mutually indifferent it is impossible to achieve a 'correct' response to both of {p, q} and {p, -q}.

The vagaries of this system are a result of the demand that the Respondent give the same evaluation to each of a set of not-necessarily-equivalued statements. They therefore illustrate the operation of the Fallacy of Many Questions.

A similar result would be achieved by the presentation of proposita as 'biased questions' in the following form: each Pj is a set of two or more (contingent) statements and each Rj is a selection of one of the statements from the set. Such a system is, in any case, a systematically forced one, since any statement p may be foisted on the Respondent by giving him, first, the choice {p.q, p.-q}; and, if 'correctness' is written in, it is rule-inconsistent since a subsequent 'choice' may be {-p.r, -p.-r). A propositum of the form {p.-q, -p.-q) in this system is equivalent in operation to one of the form {p, q) in the previous one.

It follows that a 'biased question' is equivalent to a 'multiple question'.

Now, preparatory to considering some other systems, let us describe in more detail the organization and operation of commitment-stores. We have said that these stores contain statements, but it is not quite clear what this means, and it is better to be quite explicit and say that they contain statement-tokens, in the language of the dialogue or an equivalent one. We can conceive a commitment-store physically as a sheet of paper with writing on it, or as a section of the store of a computer. As a dialogue proceeds items are periodically added and, in some circumstances, deleted. A statement S is added, that is, whenever the speaker 'makes' it, or otherwise incurs it as a commitment such as by having it made to him and taking no steps to deny it; and it is deleted, perhaps with consequential alterations, if he 'retracts' it.

The sum total of the statements in the store at any time is the speaker's indicative commitment. (I say 'indicative' because, in other contexts which will not concern us here, it would be necessary to consider also other kinds of commitment such as imperative and emotive.) For some purposes we can consider the various statement-tokens as effectively conjoined into a single large one, but for other purposes it is necessary to think of them as distinct.

At first sight we would suppose it to be a requirement of the statements in a commitment-store that they be consistent; but, on reflection, we may come to think that, although there does exist an ideal concept of a 'rational man' which implies perpetual consistency, the supposition is by no means necessary to the operation of a satisfactory dialectical system. In fact, even where our ideals of rationality are concerned, we frequently settle for much less than this: a man is 'rational', in a satisfactory sense if he is capable of appreciating and remedying inconsistencies when they are pointed out. We should reflect, too, that consistency presupposes the ability to detect even very remote consequences of what is stored, and that this would itself make nonsense of certain kinds of possible dialectical application. Could we model a discussion, between mathematicians, of the validity of a certain theorem, if we had to model the mathematicians themselves as all-seeing? In a discussion of a proof a participant may be committed to one step, but not yet committed to the next, which may be still under discussion. This, at least, is so in the sense of 'commitment' relevant to dialectical systems: others may use what sense they may.

At the same time, it is clear that certain very immediate consequences of S may be regarded as commitments if S is a commitment, and that flat and immediate contradiction between, say, S and -S is not necessarily to be tolerated. There is a line to be drawn, and this will be a matter for regulation in a given system. A similar, logically rather difficult, question concerns retraction. When a participant 'changes his mind' about a statement S and either simply retracts it or replaces it by its negation it is simple enough to specify that S itself be deleted from his commitment-store; but in practical cases there will often need to be compensating adjustments elsewhere. What is to happen to a commitment S which implies T, when T is replaced by -T? If S is p.q and T is p, it would seem that we should be left with -p.q; but p.q is equivalent to p.(p ≡ q) and the same reasoning would lead us here to -p.(p ≡ q), which is equivalent to -p.-q. The answer is that the concept of 'retraction' is not as simple as it appears on the surface and, again, that rules need to be laid down in particular systems.

It may make these points a little easier to digest if we emphasize that a commitment is not necessarily a 'belief of the participant who has it. We do not believe everything we say; but our saying it commits us whether we believe it or not. The purpose of postulating a commitment-store is not psychological. Although, presumably, the brain of an actual speaker must contain some remote analogy of a commitment-store, it contains much else besides; and the primary theoretical job that commitment-stores do for us is to provide us with a dialectical definition of statements.

In order to illustrate that the problems of the organization of commitment are not insoluble, let us set up a simple dialectical system in which one possible solution is provided. It will, incidentally, be a system in which the concept of Argument is realized, and within which we can model a number of Fallacies.

White and Black are two participants and the language is primarily that of the statement calculus, or some other suitable logical system with a finite set of atomic statements. The axioms of the language are contained in both participants' commitment-stores from the beginning, and are marked in some way to indicate that they occupy a privileged position. White moves first but the system is otherwise symmetrical between them. Locutions may consist of the following forms (I use capital letters S, T, U, . . . as variable statement-names and other symbols and words autonomously):

(i) 'Statement S' or, in certain special cases, 'Statements S, T'.

(ii) 'No commitment S, T, . . . X', for any number of statements S, T,. . . X (one or more).

(iii) 'Question S, T, . . ., X?', for any number of statements (one or more).

(iv) 'Why S?', for any statement S other than a substitution-instance of an axiom.

(v) 'Resolve S'.

This is a 'Why-Because system with questions'. A simple 'Why-Because' system (the simplest feasible) would omit locutions of type (iii). A simple 'question and answer' system could be built omitting locutions of type (iv).

Rules of the system fall into different categories. I shall first lay down a set of rules which do not depend on commitment-store operation and may be regarded as 'syntactical'; then describe the operation of the commitment-store; and later, in the subsequent discussion, suggest additional rules that are framed in terms of the speaker's and hearer's commitments.

Syntactical rules

S1.
Each speaker contributes one locution at a time, except that a 'No commitment' locution may accompany a 'Why' one.
S2.
'Question S, T,. . ., X?' must be followed by
  1. 'Statement -(SvTv . . . vX)' or
  2. 'No commitment SvTv. . . vX' or
  3. 'Statement S' or 'Statement T or
    --------- or
    'Statement X' or
  4. 'No commitment S, T,. . ., X'
S3.
'Why S?' must be followed by
  1. 'Statement -S' or
  2. 'No commitment S' or
  3. 'Statement T' where T is equivalent to S by primitive definition, or
  4. 'Statements T, T ⊃ S' for any T.
S4.
'Statements S, T' may not be used except as in 3(d).
S5.
'Resolve S' must be followed by
  1. 'No commitment S' or
  2. 'No commitment -S'.

Commitment-store operation

C1.
'Statement S' places S in the speaker's commitment store except when it is already there, and in the hearer's commitment store unless his next locution states -S or indicates 'No commitment' to S (with or without other statements); or, if the hearer's next locution is 'Why S?', insertion of S in the hearer's store is suspended but will take place as soon as the hearer explicitly or tacitly accepts the proferred reasons (see below).
C2.
'Statements S, T' places both S and T in the speaker's and hearer's commitment stores under the same conditions as in C1.
C3.
'No commitment S, T, . . ., X' deletes from the speaker's commitment store any of S, T, . . ., X that are in it and are not axioms.
C4.
'Question S, T, . . ., X?' places the statement SvTv . . . vX in the speaker's store unless it is already there, and in the hearer's store unless he replies with 'Statement -(SvTv. . . vX)' or 'No commitment SvTv . . . vX'.
C5.
'Why S?' places S in the hearer's store unless it is there already or he replies 'Statement -S' or 'No commitment S'.

The following is a specimen of a dialogue (with A, B, C as atomic statements and the two speakers distinguished by roman and italic type):

First SpeakerSecond Speaker
Question A, -A? Statement A.
Question B, -B? Statement -B.
Statement B(1). Statement -B(2).
Why -B? Statements A, A ⊃ -B.
No commitment A ⊃ -B; why A ⊃ -B?(3) No commitment A ⊃ -B(4).
Statement B(5). Why B?
Statements A, A ⊃ B. Why A ⊃ B?
Statements -A, -A ⊃ (A ⊃ B). No commitment -A ⊃ (A ⊃ B)(6).
Resolve A. No commitment -A.(7)
Statement -A(8). Resolve A.
No commitment A(9). Why -A ⊃(A ⊃B)?
Statement -A⊃(-AvB)(10). Why -A⊃(-AvB)?
Statements -A⊃(Bv-A), (-A⊃(Bv-A))⊃(-A⊃(-AvB))(11). Question A.C, -A.C?
No commitment A.C v -A.C(12). Statement C.
No commitment C. Statement C. . . (13).
No commitment C. Why B?
Statements B, B ⊃ B. No commitment B; why B?
Statements B, B ⊃ B. . .(14). Statement B(15).
Resolve B(16). No commitment -B.

Comments:

  1. White (roman type) has accepted A but is not going to accept -B.
  2. But Black (italics) must not accept B from White: he can reiterate -B or could equivalently say 'No commitment B'.
  3. White has already accepted A and tacitly accepts it here again. But he both rejects and requires proof of A ⊃ -B.
  4. Black retracts under pressure.
  5. White doesn't need to reiterate B, but it does no harm.
  6. Black has refused to accept -A ⊃ (A ⊃ B) in spite of the fact that it is a tautology, but has tacitly accepted White's self-contradiction -A.
  7. White charges him with it and he retracts.
  8. It is again unnecessary for White to reiterate, but he is aggressive in these matters.
  9. Black says 'Tu quoque' on the contradiction and White chooses the other leg. They are now both internally consistent but are at odds, though neither subsequently notices.
  10. By definition of '⊃'.
  11. The first of these is a substitution-instance of an axiom and cannot be further challenged. The second could be challenged but could be supported eventually by a valid proof.
  12. The presupposition of the question is disallowed.
  13. This can go on for ever.
  14. So can this.
  15. 'All right, have it your own way!'
  16. 'But earlier you said. . .'.

So far the system is clearly rule-consistent. It is also semantically open since it is possible for either speaker to say 'No commitment S', for some S or other, at any time, and hence to avoid all commitment. The inerasable axioms influence the dialogue in no way except in prohibiting 'WhyS?' when S is a substitution-instance of an axiom. The commitment-store rules are, of course, quite irrelevant to the conduct of the dialogue until we have laid down further rules framed in terms of commitment. At the same time the concept of commitment has a clear intuitive meaning and it is instructive to follow the state of the participants' respective commitments through the above sample dialogue. The solution of the problem of retraction, it will be noted, is to separate off the question of consistency, so that retracting S does not necessarily involve retracting anything related to S; that is, not even equivalents such as --S and S.S. It would be possible to relax this stipulation to some extent but particular suggestions for so doing need to be looked at on their merits. Certain extensions of the commitment-mechanism in other directions will be touched on in a moment.

The syntactical rules for questions provide an escape for the addressee of a biased question: 'Question S, T, . . ., X?' can be answered 'No commitment SvTv . . . vX', or 'Statement -(Sv Tv . . . vX)'. The commitment-rules provide that it must be so answered if the addressee is to escape commitment to SvTv ... vX: thus 'No commitment S, T, . . . X' leaves him committed to the disjunction and merely escapes commitment to any particular one of the disjuncts. Is this reasonable, and is this all that needs to be done to model the phenomenon of the biased question? There is at least one further possibility. It might be felt that questions should not be used to make statements, and should not, therefore, themselves commit speaker or hearer in the way that is characteristic of statements. To achieve this, the system could be strengthened by the addition of a rule as follows:

'Question S, T, . . ., X?' may occur only when SvTv . . . vX is already a commitment of both speaker and hearer.

Such a rule could seriously impede the asking of questions since even 'Question A, -A?' would require the prior establishment of Av -A; but it is possible to envisage that, with other adjustments, the admittedly restrictive system that resulted might be seen as representing some kind of ideal of rationality in the use of biased questions. Weaker rules might be considered, such as that the disjunction of answers be a commitment of at least the addressee, or of at least the speaker. At all events rules of this kind are what are required to banish from the system various versions of the Fallacy of Many Questions.

These rules differ from the earlier ones in a way we might describe by saying that they have a discretionary character. What we called 'syntactical' rules define the scope of the system: those now being discussed seem aimed rather at improving the minimum quality of the resulting dialogues or degree of rapport between the participants. It is possible to use biased questions and not lead or be led astray by them; but these rules are what are required to provide a guarantee of unexceptionable use.

Similar rules framed in terms of commitments could be added to give a particular character to statement-making or question-asking. If we regard the sole function of statements to be the giving of information, we shall restrict their use with the rule:

'Statement S' may not occur when S is a commitment of the hearer.
Similarly, of course, for 'Statements S, T'. This is appropriate to a particular kind of statements which we might call 'notifications', and needs to be matched by a view of questions as 'inquiries', with the rule
'Question S, T, . . ., X?' may not occur when any of S,T, . . . ,X is a commitment of the speaker.
On the other hand, statements have another function in language, namely, as 'admissions'; and questions a corresponding function as no-liability admission-elicitations; and in this case what is stated may or may not be a prior commitment of the hearer but is definitely not one of the speaker, whereas a question may or may not have an answer among commitments of the speaker but definitely does not have one among those of the hearer. Hence the rules given need to be weakened at least to
'Statement S' may not occur when S is already a commitment of both speaker and hearer.
and similarly for 'Statements S, T'; and
'Question S,T,. . ., X?' may not occur when any one or more of S, T, . . . , X, is a commitment of the speaker and any one or more a commitment of the hearer.
These rules are still strong enough to eliminate certain possible repetitious inanities such as 'Question A, B? Statement A. Question A, B? Statement A ...'.
These rules might be acceptable in a pure question-and-answer system but in the present system at least the first of them is still too strong, since it would prohibit the use of axioms in the justification of their consequences. Let S be an axiom and T a formula equivalent to it by definition: then we want to license 'Statement T. Why T? Statement S' but, since S is inerasably in both commitment-stores, 'Statement S' is permanently forbidden. The rule would need to be weakened even further at least to the extent of excluding statements made in answer to 'Why' locutions. The rule in respect of questions can probably be retained.

Another kind of repetitiousness, exemplified by

'Statement A. No commitment A.
Statement A. No commitment A',
is more difficult to ban. What is needed is an elaboration of the commitment-store operation to have it register second-order commitments of the form 'No commitment A', when a locution of this form is uttered. This is not an impossible extension but we need not pursue it here.

A possible condition on answers to questions concerns (what I shall call) 'whole truth commitment'. When it is said of an answer that although it is true it is not the 'whole truth', what must be understood is that the answer should properly be replaced by a stronger one which gives additional information; and that, by giving the weaker answer, the answerer has 'implied' that he is not in a position to give the stronger one or that the stronger one would be false. It would be possible to build 'whole truth commitment' into answers by treating every answer to any question as if it were accompanied by a 'No commitment' locution with respect to such other possible answers as are not actually implied by the one given. Certain restrictions on the formulation of questions are entailed by this stipulation, but the result would be at least a partial explication of what we mean by 'the whole truth'.

Can we introduce rules corresponding with the criteria of argument in the previous chapter? Argumentation appears in this system only in a rudimentary form, since the statement or statements which follow a 'Why' locution are not necessarily to be regarded as the ultimate premisses of an argument and the depth to which the participants probe is unregulated. If the utterer of a 'Why' locution is regarded as inviting the hearer to convince him, a reasonable rule is

'Why S?' may not be used unless S is a commitment of the hearer and not of the speaker.
(Otherwise the 'Why' is 'academic'.) The specimen dialogue gives us several examples of argument in a circle, and we might look for a rule which would outlaw these. The simplest possible such argument is
'Why A? Statements A, A ⊃ A';
and, if S and T are statements equivalent by definition, another is
'Why S? Statement T.
Why T? Statement S'.
An unnecessarily strong rule is the following:
The answer to 'Why S?', if it is not 'Statement -S' or 'No commitment S' must be in terms of statements that are already commitments of both speaker and hearer.
This achieves the object of outlawing circular reasoning but makes it impossible to develop an argument more than one step at a time; that is, a participant cannot make, and succeed in justifying, any statement which cannot be deduced in one step from statements his opponent has already conceded.

Let us try another tack. Even if circles appear in an argument we might regard it as a satisfactory one provided it is capable of being restated without them. Thus we might regard an extended argument developed in answer to a string of 'Why' locutions as a satisfactory one provided the ultimate premisses are commitments of both parties; and, in one important particular case, if they are axioms. Now one easy way of ensuring 'goodness' of all the extended arguments in the system is to stipulate that participants always rigorously question the credentials of one another's statements with 'Why' locutions, and never concede anything except as the result of argument. There are two possible formulations which recommend themselves: the stronger is

If there are commitments S, T, . . . , X of one participant that are not those of the other, the second will, on any occasion on which he is not under compulsion to give some other locution, give 'Why S?' or 'Why T . . . or 'WhyX?'
This enjoins extreme fractiousness of the participants, and can be weakened in the first clause to read:
If one participant has uttered 'Statement S' or 'Statements S, T' or 'Statements T, S' and remains committed to S, and the other has been and remains uncommitted to it, the second will (etc.)
Both rules are rather drastic in effect since they imply that the process of questioning with 'Why' cannot stop until it reaches premisses a priori agreed between the two participants; and they provide no guarantee that such premisses will ever be reached. Nevertheless it will be the case that no argument which does terminate can be circular when seen as a whole, and we have succeeded in banning the Fallacy of Begging the Question.

These rules present arguments as ex concesso; and there are other kinds of argument. One participant may feed the other with 'Why' locutions without admitting any step of the argument himself. We have, however, allowed for this possibility in allowing forms such as

'Statement S. No commitment S; why S?
Statement T. No commitment T; why T? . . .', where T is equivalent by definition to S, or forms such as
'Statement S. No commitment S; why S?
Statements T, T ⊃ S. No commitment T, T ⊃ S; why T? . . .'
and so on; namely, forms in which a 'Why' locution is accompanied by a 'No commitment' one. Black will not now be committed at any stage of the argument, yet still demands that White produce the argument. Our rules do not need to be altered to deal with this version of argument.

What other relevance does the system have to the analysis of traditional fallacies? The Fallacy of Misconception of Refutation is committed, according to modern accounts, when someone undertakes to prove one thing and proves another instead. There is no close analogy in this system of 'undertaking to prove' a thesis, but a participant who answers a 'Why S ?' with a 'Statement' or 'Statements' locution (other than 'Statement -S') could be held to have undertaken to prove S. The form 'Statement S. Why S? Statements T, T ⊃ U', which is already banned by syntactical rules, might serve as a generic representation of this Fallacy, though it misses the spirit of most of the examples that are given. The Boethian version of the Fallacy does not turn at all closely on dialectical considerations.

A formal Fallacy such as (the modern version of) Consequent can, of course, be represented, as can any feature of Formal Logic. Its most explicit representation would be in the syntactically illegal

'Statement A. Why A?
Statements B, A ⊃ B'.
There is no danger here, as there is in some formulations, of confusion with argument from example.

This might be the place for a comment on the ambiguity of 'Why'. This is at least triple. In the present formulation, 'Why S?' is clearly a request for a deduction or proof of S, and a proof is a special kind of justification of an act of statement-making, subject to certain provisions such as that the occasion is one that is appropriate to meticulous truth-telling. Seen more generally, however, 'Why' can ask for a justification of a given statement-act independently of these assumptions: it can shade off into

'Why did you say that?', which can be answered
'In order to impress X',
'Because it seemed the right thing to say',
'For practice' or
'Because I had a fit of absent-mindedness'.
These answers are so different from the previous kind that it seems appropriate to regard 'Why' as having two different possible meanings; though it is not so clear that some kinds of answer (such as inductive justifications) traditionally classified with the first are not more properly classified with the second.

A third meaning of 'Why' makes it a request for a causal or teleological explanation:

'It's cold in here. Why?
Because the heating system is off', or 'John is in the library. Why?
Because he has an essay to finish'.
We have noticed that the Fallacy of Non-Cause as Cause originally referred to failures of deductive proof rather than failures of causal explanation, and this confusion would be more natural in a system of Dialectic that incorporated the ambiguity of 'Why' than in other kinds of analysis. Hence our system has some explanatory power that is independent of its logical merits. An analysis of Non-Cause as Cause in its original sense requires a dialectical system incorporating reductio reasoning, and is simpler in a system of a slightly different kind.

The concept of Burden of Proof is replaced in this system by the somewhat simpler concept of initiative. Generally, as in the Law of Evidence, [Quoted by Sidgwick, Fallacies, p. 150, from Sir James Stephen's Digest of the Law ofEvidence, 3rd edn., p. 100.] 'He who asserts must prove', in that 'Statement S. Why S? clearly puts the onus on the first speaker. The cruder attempts to shift the burden, such as in 'Why S? Why -S?' are outlawed by syntactical rules. Consider, however, the piece of dialogue

'Statement S. Statement T.
No commitment S; why S?'.
This is not at all illegal, for 'Statement T', in failing to repudiate S, implicitly concedes it; and the first speaker, who is quite entitled to change his mind and repudiate S himself, may then question the concession. This is quite sophistical and points the need for a special rule. One approach would be to regard commitments which are the result of concession rather than of personal statement as different in character from the others, and mark the difference in the commitment-store entries. Thus let a commitment-store contain 'Sc' rather than 'S' when S is conceded rather than stated: we might add to the commitment-rules.
When S is written into a commitment-store it is written 'Sc' if the other participant's commitment-store already contains 'S' or 'Sc'; otherwise it is written'S'.
We might then interpret the rules above to stipulate that 'Why S?' cannot be addressed to a participant whose commitment-store contains merely 'Sc', not 'S'. This is an ad hoc solution of a kind we might disapprove of on the grounds that it makes life too easy for the man who passively makes concessions. An alternative way out of
'Statement S. Statement T.
No commitment S; why S ?'
would be to guarantee that when one participant gives 'No commitment S' the other always, at least, has an opportunity to do likewise before being confronted with a 'Why' locution. In fact the present system is not impossibly unfair in this respect since 'No commitment S; why S?' can always be followed by 'No commitment S'. Our rules err, if at all, on the side of allowing potential sophists too many easy escape routes on either side of the argument.

The 'discretionary' rules we have been discussing vary in force and it is not to our purpose to make a once-for-all selection of them. Various particular systems of differing character can be obtained by making different selections. I make, moreover, no claim to completeness of this discussion: many dialectical infelicities remain as systematic possibilities even when the strongest of our rules are enforced, and it is not even certain that it is possible to legislate for good sense by purely dialectical means. The system as outlined may, however, serve as a demonstration of how much can be achieved with comparatively meagre resources.

Emphasis on words or phrases sometimes has a straightforward meaning analysable in terms of commitment. Let us suppose we have a language built on just four elementary statements

'John likes tea',
'Molly likes tea',
'John likes coffee', and
'Molly likes coffee',
but with the possibility of emphasis on the nouns 'John', 'Molly', 'tea', and 'coffee'. The simplest kind of emphasis, to be called italic emphasis and indicated by italics, is that indicated in speech by the tone '√' as in 'John likes tea' when this means 'John likes tea, whether or not he likes coffee', or in 'Molly likes coffee' when this means 'Molly likes coffee, whether or not John does'. Commitment to 'John likes tea' is therefore equivalent to commitment to the unemphasized 'John likes tea' together with non-commitment to 'John likes coffee', and similarly. It is in order to couple an italically emphasized statement with the denial of its counterpart, as in 'John likes tea but he doesn't like coffee', but not with the affirmation; and 'John likes tea, and he likes coffee' is a curiously inept formulation resembling a self- contradiction, which we would use in practice only if there were also some question about John's liking for, say, cocoa or orange juice. Copi's example of the change of meaning, as various words are emphasized, of 'We should not speak ill of our friends' (see p. 24 above) can be analysed in this way. But there are also other kinds of emphasis. Thus SMALL CAPITAL emphasis (tone ¯\) indicates definiteness, as when 'John likes TEA' means 'What John likes is tea. not coffee', and carries commitment to 'John does not like coffee' as well as to 'John likes tea': similarly 'JOHN likes tea' means 'The one that likes tea is John, not Molly'. Combination of emphases gives us even more resources: 'John likes TEA' (√- ¯\) says that John's distinct preference is tea, whatever Molly's is, and couples commitment in respect of 'John likes tea' and 'John does not like coffee' with non-commitment in respect of 'Molly likes tea'. These examples suggest that there may be other features of stress and tone with easily analysed dialectical force, though it is also possible that speakers of other languages than English may arrange matters differently. The remark should be added that these kinds of emphasis are not to be confused with the larger kinds that involve whole locutions, arguments, points or theses.

It would be instructive now to conduct some kind of formalization of the conventions of Greek public debate. For various reasons this is a project of great difficulty and I shall not attempt it in detail. Some remarks and comments are, however, in order; particularly with reference to the Fallacies that may be exemplified within it.

The 'Greek game' of Plato's earlier dialogues resembles the Obligation game (which derives from it) in having, in any given phase, two participants with specialized roles, the 'questioner' and the 'answerer'. Also as in the Obligation game, the questioner is 'Socratic' in a sense we can now make definite: his locutions carry no commitment and he has no commitment-store. When Plato has Thrasymachus complain, in the Republic (337)

Socrates will do as he always does -- refuse to answer himself, but take and pull to pieces the answer of someone else.
he is objecting to the practice of having one participant make no assertions but merely ask questions of the other; and when Socrates replies
. . . how can any one answer who knows, and says that he knows, just nothing;. . . ?
he is putting up a not-entirely-sincere justification of a procedure which Plato elsewhere holds to be appropriate to the search for philosophical truth. [See Robinson, Plato's Earlier Dialectic, p. 80.] The questioner, nominally at least, has no thesis of his own and accepts, within the limits of logic, whatever the answerer tells him.

Only if we attempt to construct a rationale for the arrangement of the questions might we be inclined to alter this view. In fact Socrates emerges, in the long run, as someone with strong views of his own. Biased or loaded questions are not infrequent; and something might be deduced from the way in which questions are phrased in expectation of one answer rather than another. Socrates frequently says such things as 'But our recovery of knowledge from within ourselves, is not this what we call reminiscence?' or 'Then, Thrasymachus, do you actually think that the unjust are sagacious and good?'; and he cross-questions with zeal when he disagrees, but desists when his answerer gives the answer he wants. These tactics are not necessarily disallowed by the rules of the game, but they introduce another dimension into it. In order to formulate the rules we would first have to elaorate a theory of interrogative commitments and their interaction with indicative ones, and this would take us out of our way. There are, in effect, two Greek games, of differing degrees of sophistication; and we confine ourselves here to the simpler one.

Questions must be 'definite' or 'leading' ones with small numbers of possible answers, so that our model 'Question S, T, . .., X?' represents them reasonably well. Since the aim of the questioner is to refute the answerer he must be equipped with means of bringing about this refutation, and some such locution as 'Resolve S' must be permitted to him; but he need have no other form of locution besides these two.

The answerer's commitment-store is initially empty and his locutions are all single statements of the form 'Statement S' except that, in answer to 'Resolve S' he must say 'Withdraw S' or 'Withdraw -S', and that he may say 'Don't know S, T, . .., X'. The point of distinguishing our previous 'No commitment' locutions into these two categories will appear in a moment.

A feature of the game that it is difficult to formalize is its dependence on the views of the onlookers or 'the majority'. These people are the ultimate arbiters both concerning the admissibility of a given statement or argument and in judging the final outcome. We could, perhaps, try the following formulation: There is given, in connection with the game, a list of statements representing 'popular beliefs'. The shape of the possible plays of the game is critically dependent on this list, which is (generally understood to be) large and unsystematic. It need not be consistent. Its function is to provide prima facie answers for the answerer. Thus when the questioner asks 'Question S, T, . . ., X?', and one or more of S, T, . . ., X are 'popular beliefs', the answerer gives one of these as his answer; at least when this would not be inconsistent with anything in his commitment-store.

The answerer starts play with a locution 'Statement T', where T is the thesis, and play ends if the answerer gives 'Withdraw T'. Unless T is self-contradictory he cannot be compelled to do this -- the system is semantically unforced -- but he may be trapped into doing so. There must be rules, that is, requiring him to concede consequences of his various admissions. Again, this is difficult to formalize realistically. Any question, we might say, such that just one possible answer W is a consequence of the answerer's previous statements by definition or modus ponens or syllogism must be answered 'Statement W; with corresponding provisions where two or more answers are so implied. But Plato also often uses argument from example or induction, and sometimes arguments from the authority of poets and others, and these are expected to dispose the answerer towards appropriate admissions though reserving to him the possibility of resistance, at least until evidence becomes overwhelming.

A special rule of the Greek game is that every question must be followed through; and this involves the postulation of some kind of store of 'unanswered questions', so that the game cannot properly end while this is non-empty. Hence we must distinguish a 'Don't know' answer from a 'Withdraw'. The rules for the answering of a question will be something as follows: To 'Question S, T,. . ., X?', if any of 'Statement S' or . . . or 'Statement X', or alternatively 'Statement -(SvTv . . . vX)', is forced by an inference-rule, the answerer must give one such; otherwise if any is a popular belief he gives one such; or otherwise he may give any one; or if no one of them is in his commitment-store, he may give 'Don't know SvTv . . . vX' or 'Don't know S, T, . . ., X'. If the last of these is given it is itself placed in the commitment-store, placing the question, as it were, on the notice-paper. A 'Don't know' locution placed in the commitment-store in this way is removed only when the corresponding question is re-asked and properly answered.

It does not need saying that all the Fallacies of Aristotle's list can be realized within this framework in some shape or form; though we shall suspend consideration of Fallacies Dependent on Language until the next chapter. There is nothing much to add about some of the others, but we should notice now that since it is the questioner's task to disprove what the answerer says, there is an implicit burden of proof which makes possible the realization of Begging the Question in its full sense. The questioner commits the Fallacy of Begging the Question when he asks a question one of whose alternatives is the negation of the Thesis T, or some statement which is the last link in a deduction that would result in the disproof of T, or some relevant statement which (in the required Aristotelian sense) is less certain than the negation of T. There could be, in principle, a precise rule forbidding such questions.

The questioner may also implicitly employ reductio ad impossibile reasoning and even, literally, reductio ad absurdum, if what is 'absurd' is what is contrary to strong majority opinion. This means that the classical Fallacy of Non-Cause as Cause can be realized, and that a rule prohibiting it could be formulated.

How often may an answerer change his mind? And how long may he hold out against an inductive consequence of popular beliefs? We cannot formulate precise rules regarding these matters (and some others) unless by arbitrary stipulation. The ultimate weakness of Aristotle's own attempts to formulate precise rules is his reliance on the 'majority opinion' to enforce them, since what the majority cares to enforce is, at the very least, a contingent matter.

The systems so far considered have all turned around deductive justification of theses. It is instructive to conclude by considering one based primarily on induction from 'empirical' evidence. The game to be described is quite unambitious and designed purely to make the point of principle that an analysis of inductive procedures is possible.

The two participants are assumed to have access to a stock of empirical fact, namely, knowledge of existence of various objects characterized by sets of properties. For example, it may be known that there exists a large red chair, a red table of unknown size, a not-large not-beautiful bookcase of unspecified colour, and so on. Some of the facts may be public, some initially private to individual participants.

Each locution is of one of the following kinds:

  1. A generalisation of the form 'All things are As' or 'All As are Us', where A and B are affirmative or negative terms. A generalization when made is 'tabled', and must not be equivalent to any already tabled.
  2. A denial of an already-tabled generalization. Unless successfully challenged, a denial replaces the generalization it denies.
  3. A challenge to a tabled generalization or denial. A challenge is counted successful unless met as in [4] or [5].
  4. An exemplification of a generalization. 'All things are As' is exemplified by giving an example of a thing which is an A; and 'All As are Bs' is exemplified by giving an example of a thing which is both an A and a B or, in view of the equivalence to 'All non-Bs are non-As', a thing which is both a non-A and a non-B. [Cf. the 'paradox of the ravens', in an extensive literature starting with Hempel, 'Studies in the Logic of Confirmation'. My rule is not very satisfactory at this point, but no simple rule will be any better and it would take us too far off course to formulate one that is.] The example may be public or (hitherto) private.
  5. A proof of a generalization or denial, by deduction from tabled generalizations or denials, and/or by the giving of one or more examples as in [4].
  6. A concession, or empty move. Successive empty moves, one from each participant, end the dialogue.

All examples and proofs must be logically valid: that is, any question of validity is resolved outside the dialogue proper. The same applies to objection to a generalization on the grounds of its equivalence to an already-tabled one.

A proof by combined deduction and example, as in [5], can occur in the following form. If 'All As are Bs' is already tabled, the denial of 'All Bs are Cs' may be proved -- even though there is no known example of a B which is not a C -- by giving an example of an A which is not a C (but of which it is not strictly known whether it is a B or not). Similarly, if 'All As are Bs' is tabled, the denial of 'All non-As are Bs' may be proved by producing a simple example of a non-B.

'Good' dialogue is that which sets up as many generalizations as possible, subject to consistency and to rigorous testing. We can imagine the process as a competitive or as a co-operative one, as we please.

If a generalization is tabled and not denied in spite of known empirical support of the possible denial, this is a case of selection or suppression of evidence, of the kind often listed as one of the abuses of Scientific Method. When a generalization is put forward of which there is no known exemplification, and it is not challenged, the result is a species of argumentum ad ignorantiam.

As the possible locutions have been described, a good deal depends, in a competitive dialogue in which generalizations are credited to the participant putting them forward, on initiative and tactics; and, under these circumstances, a generalization will often be rebutted by reference to a previous one which is no more firmly supported than itself. When this happens, a version of the (classical) Fallacy of Non-Cause has been committed. In certain versions of the system it would be desirable to introduce a modification to the rules to avoid this contingency.

A participant who succeeds in tabling all of the six related statements

'All As are Bs',
'All Bs are As',
'All As are Cs',
'All Cs are As',
'All Bs are Cs', and
'All Cs are Bs'
before having any of them denied would seem to be proof against challenge to any of them since, whichever one is challenged, there are always two others from which it can be proved deductively; but this would be an example, of course, of Arguing in a Circle. Actually, as the rules are stated, they generally avoid this case since empirically-supported denials are given preference over deductive proofs. It could consequently occur only if there were no evidence to support any denial.

The system could form the basis of an actual game, in which the empirical evidence was represented by cards, and generalizations received scores. [I am indebted to V. H. Dudman for the use of some hours of his time helping me check out a trial version of such a game.] An important feature in securing realism is sufficient complexity of the empirical evidence to discourage participants from attempting to survey it exhaustively. This is, however, easy to achieve and difficult to avoid. (Compare chess, in which the logically perfect game is beyond the capacity of the largest computer.)

The system could be elaborated in various directions to model other features of inductive reasoning and its abuses.