This is a long chapter, and you may find the formality difficult, so be sure to allow time. Our focus in class will be on the material on pp. 265-275, but you will need much of the earlier material for context. The end of the chapter is more dispensible for purposes of the class; but it will probably be easier going, and you may find that material interesting.

Hamblin tries to formulate rules of dialogue that extend the ancient elenchus and medieval Obligation Game in a way that allows him to account for more fallacies. He explains his reasons for doing this in a formal way early on (p. 254). He proceeds to discuss formal dialectic in more generality than is necessary for his purposes later, so don't feel you need to sort out all of the details of the discussion on pp. 255-260. Just get a general sense of the sort of game he has in mind. His first example is the Obligation Game (pp. 260-263). His presentation of this is more formal than anything else in the chapter, and it isn't important enough for our purposes to spend a lot of time on it if you don't find it easy. (If you don't know the notation of symbolic logic, you will need to consult the guide below.) His discussion of issues concerning commitment on pp. 263-265 is also not essential though it will help to explain some features of the system on which we will focus.

The notes below are designed to help you follow Hamblin's discussion of the system set out on pp. 265-7 and discussed for most of the rest of the chapter. (In class, we will follow that discussion to around p. 275; but Hamblin goes on to use ideas he has introduced to discuss what he here calls the "Greek game.")

Finally, in the last few pages of the chapter, Hamblin introduces a new sort of game designed to shed light on fallacies concerning inductive reasoning; you may find it interesting (and Hamblin claims to actually have played it) but there won't be time to fit it into class.

Notation from symbolic logic

(i) propositions: capital or lower case letters

Roughly speaking, capital letters may be any (declarative) sentences, simple or complex; lower case letters are reserved for “elementary” (i.e., logically simple) sentences. Strictly speaking, propositions are the meanings of such sentences, so a proposition, unlike a sentence, cannot be ambiguous. (In the examples below, ‘Ann was there’, ‘Bill was there’, ‘Carol was there’ are used as simple examples of propositions A, B, and C.)

(ii) logical operators (specifically, truth-functional connectives): ‘−’, ‘.’, ‘v’, ‘⊃’, ‘≡’

(a) negation: −S is the denial of S

−A says ‘Ann wasn’t there’

(b) conjunction: S.T asserts both S and T

A.B says ‘Ann and Bill were both there’

(c) disjunction: SvT says that at least one of S and T is true

AvB says ‘Either Ann or Bill was there’

(d) conditional: S⊃T commits a speaker to the truth of T if S is true, but it is automatically true if S is false—that is, it amounts to saying that S isn’t true without T being true as well

A⊃B says ‘If Ann was there, then Bill was, too’

(e) biconditional: S≡T says that S and T have the same truth value—i.e., that they are either both true or both false

A≡B says ‘Ann was there if and only if Bill was’

Notation for connectives has never been standardized; but Hamblin’s symbols are less commonly used now than they once were, so they may be new to you even if you have run into logical notation before.

Locutions (see p. 265)

(i) ‘Statement S’ and ‘Statements S, T’

The first is an assertion or concession; the second offers the premises of an argument in response to a ‘Why’ locution (see iv below)

(ii) ‘No commitment S, T, …, X’

This functions either as a refusal to grant an assertion or presupposition or as the retraction of a previous commitment.

(iii) ‘Question S, T, …, X?’

This is a question asking which of S, T, …, X is true. It has the presupposition that at least one of the alternatives is true (expressed symbolically as SvTv…vX). In the special case of ‘Question S, −S?’, the two alternatives are a statement and its denial, so the locution is a ‘yes-no’ question and its presupposition, Sv−S, is a mere tautology saying that either S is true or it isn’t.

(iv) ‘Why S?’

Hamblin exploits the ambiguity of this later (pp. 273f), but the central function is to request an argument supporting S. It carries S as a presupposition.

(v) ‘Resolve S’

This calls for the resolution of a contradictory pair of sentences; that is, it asks that the hearer abjure joint commitment to a sentence and its denial.

Syntactical rules (see p. 266)

S1. Each speaker contributes one locution at a time, except that a ‘No commitment’ locution may accompany a ‘Why’ locution.

Hamblin mentions one rationale for the latter feature on pp. 272f; another is noted in the comment on C2 below.

S2. ‘Question S, T, …, X?’ must be followed by

(a) ‘Statement −(SvTv…vX)’

or (b) ‘No commitment SvTv…vX’

or (c) ‘Statement S’ or

‘Statement T’ or

… or

‘Statement X’

or (d) ‘No commitment S, T, …, X’

This gives the permissible responses to a ‘which’ (or ‘yes-no’) question—specifically, (a) denying the presupposition, (b) refusing to grant the presupposition, (c) providing direct answer, and (d) not answering while granting the presupposition (something that amounts to ‘I don’t know’).

S3. ‘Why S?’ must be followed by

(a) ‘Statement −S’

or (b) ‘No commitment S’

or (c) ‘Statement T’ where T is equivalent to S by primitive definition

or (d) ‘Statements T, T⊃S’ for any T.

These are allowed responses to a request for an argument—(a) denying the presupposition (which would be the conclusion of the argument if one were given), (b) refusing to grant the presupposition, (c) offering as a premise a restatement of the conclusion, and (d) offering a premise T together with a conditional joining the premise and conclusion. Arguments of the sort (c) correspond roughly to what were traditionally labeled ‘immediate inferences’, and arguments of sort (d) amount to “syllogisms” in a suitably broad sense of the term. The specific form (d) is known as modus ponens; but any argument can be put into this form if its premises are conjoined as the statement T and the conditional T⊃S is used to make explicit the connection between premises and conclusion.

S4. ‘Statements S, T’ may not be used except as in 3(d).

This is primarily a convention designed for the most convenient statement of the rules; multiple assertions may still be introduced by conjoining them as a single assertion.

S5. ‘Resolve S’ must be followed by

(a) ‘No commitment S’

or (b) ‘No commitment −S’.

A call to resolve a contradiction requires in response a retraction of one of two contradictory commitments or, more precisely, a rejection of commitment to one of a pair of contradictory sentences. (There is no requirement that there were contradictory commitments to begin with, but there would be little point in issuing the call otherwise.)

Commitment store operation (see pp. 266f)

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).

A speaker is committed to assertions made. To avoid acquiring a commitment, a hearer must make a critical response by denied the speaker’s claim, refusing to grant it, or requesting an argument for it. In the latter case, the hearer acquires the commitment if the argument is offered and the hearer does not respond critically.

C2. ‘Statements S, T’ places both S and T in the speakers and hearer’s commitment stores under the same conditions as in C1.

A pair of premises has the role one would expect for a pair of assertions. One difference is that a request for further argument can be directed only at one; to avoid commitment to the other, the hearer must at the same time issue a ‘No commitment’ locution.

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.

This locution is used both to reject commitments and to retract commitments already made.

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’.

Speakers are committed to the presuppositions of their questions. A hearer can avoid such a commitment only by rejecting the question (by explicitly denying or refusing to grant its presupposition).

C5. ‘Why S?’ places S in the hearer’s store unless it is there already or he replies ‘Statement −S’ or ‘No commitment S’.

Accepting a request for an argument commits a hearer to the conclusion to be argued for; to refuse the request, the hearer must deny or refuse to grant the presupposition. So far this is analogous to a ‘Question’ locution; but, unlike that case, the speaker issuing a ‘why’ locution is not committed to its presupposition.

A sample dialogue (see p. 267). (This is fleshed out with English analogues to the locutions, preserving the references to Hamblin’s notes on pp. 267f. However, don’t expect it to be a sensible exchange; Hamblin has clearly designed it simply to exhibit a variety of aspects of the rules. Hamblin doesn’t say what the axioms are; but, from what he does say, they may well be a set used in a famous work of the early 20th century, The Principia Mathematica; and, if so, the only one instance of an axiom appearing is the one he identifies as such. However, for the sake of simpler commitment-stores, I have assumed that any tautology is an axiom unless that assumption conflicts with what Hamblin says or with the course of the dialogue.)

	Locutions	Formal notation	Commitments
White:	Was Ann there or not?	Question A, −A?
Black:	Ann was there.	Statement A		add A
Wh:	Was Bill there or not?	Question B, −B?	add A
Bl:	Bill wasn’t there.	Statement −B		add −B
Wh:	But Bill was there. [See note 1]	Statement B	add B
Bl:	No, Bill wasn’t there. [See note 2]	Statement −B
Wh:	Why do you hold that Bill wasn’t there?	Why −B?
Bl:	Ann was there. And if Ann was there, Bill wasn’t.	Statements A, A⊃−B		add A⊃−B
Wh:	I don’t grant that if Ann was there, Bill wasn’t. Why do you hold that? [See note 3]	No commitment A⊃−B; why A⊃−B?
Bl:	I retract my claim that if Ann was there, Bill wasn’t. [See note 4]	No commitment A⊃−B		del A⊃−B
Wh:	Bill was there. [See note 5]	Statement B
Bl:	Why do you hold that Bill was there?	Why B?
Wh:	Ann was there. And if Ann was there, Bill was, too.	Statements A, A⊃B	add A⊃B
Bl:	Why do you hold that if Ann was there, Bill was, too?	Why A⊃B?
Wh:	Ann wasn’t there. And if Ann wasn’t there, then if she was, Bill was, too.	Statements −A, −A⊃(A⊃B)	add −A, −A⊃(A⊃B)
Bl:	I don’t grant that if Ann wasn’t there, then if she was, Bill was, too. [See note 6]	No commitment −A⊃(A⊃B)		add −A
Wh:	How do you square your claim that Ann was there with your current commitments?	Resolve A
Bl:	I retract my acceptance of your claim that Ann wasn’t there. [See note 7]	No commitment −A		del −A
Wh:	Ann wasn’t there. [See note 8]	Statement −A
Bl:	How do you square the claim that Ann was there with your current commitments?	Resolve A		add* −A
Wh:	I retract my claim that A was there. [See note 9]	No commitment A	del A
Bl:	Why do you hold that if Ann wasn’t there, then if she was there, Bill was, too?	Why −A⊃(A⊃B)?
Wh:	If Ann wasn’t there, then either she wasn’t there or Bill was. [See note 10]	Statement −A⊃(−AvB)	add −A⊃(−AvB)
Bl:	Why do you hold that?	Why −A⊃(−AvB)?
Wh:	If Ann wasn’t there, then either Bill was there or she wasn’t. And, if that’s true, then if Ann wasn’t there, then either she wasn’t or Bill was. [See note 11]	Statements −A⊃(Bv−A), (−A⊃(Bv−A)) ⊃ (−A⊃(−AvB))	add (−A⊃(Bv−A)) ⊃ (−A⊃(−AvB))
Bl:	Were Ann and Carol both there, or was Ann was missing even though Carol was there.	Question A.C, −A.C?		add −A⊃(A⊃B), −A⊃(−AvB), (−A⊃(Bv−A)) ⊃ (−A⊃(−AvB)), A.C v −A.C
Wh:	I don’t grant that either Ann and Carol were both there or Ann was missing even though Carol was there. [See note 12]	No commitment A.C v −A.C
Bl:	Carol was there.	Statement C		add C
Wh:	I don’t grant that Carol was there.	No commitment C
Bl:	But Carol was there. [See note 13]	Statement C ⋮
Wh:	I don’t grant that.	No commitment C.
Bl:	Why do you hold that Bill was there?	Why B?
Wh:	Bill was there. And if he was there, he was there.	Statements B, B⊃B
Bl:	I don’t grant that Bill was there. Why do you hold that?	No commitment B; why B?
Wh:	Bill was there. And if he was there, he was there. [See note 14]	Statements B, B⊃B ⋮
Bl:	OK, so Bill was there. [See note 15]	Statement B		add B
Wh:	How do you square the claim that Bill was there with your commitments? [See note 16]	Resolve B
Bl:	I retract my claim that Bill wasn’t there.	No commitment −B		del −B

* I suspect Hamblin didn’t intend this to happen; but, to avoid it, he would have had to add ‘Resolve’ locutions as ways of avoiding concessions.

Further rules Hamblin considers. (All but the last are rules, which he says are “discretionary,” that are designed to increase the “degree of rapport” between participants.)

p. 269

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

[A rule to banish the Fallacy of Many Questions.]

‘Statement S’ may not occur when S is a commitment of the hearer.

[A rule to insure that statements give information.]

‘Question S, T, …, X?’ may not occur when any of S, T, …, X is a commitment of the speaker.

[A rule to insure that questions are inquiries.]

p. 270

‘Statement S’ may not occur when S is a commitment of both speaker and hearer.

[A rule to insure that a statement either gives information or constitutes an admission.]

‘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 of S, T, …, X is a commitment of the hearer.

[A rule to insure that a question either makes an inquiry or elicits an admission.]

p. 271

‘Why S?’ may not be used unless S is a commitment of the hearer and not of the speaker.

[A rule to insure that a ‘Why’ locution really invites the heaer to convince the speaker and is not merely ‘academic’.]

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.

[A rule that rules out circular arguments—but also any argument whose conclusion is more than one step from statements already conceded.]

p. 272

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 … or ‘Why X?’

[A strong rule to insure that participants never concede anything except as the result of an argument.]

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, on any occasion on which he is not under compulsion to give some other locution, give ‘Why S?’

[A weaker rule to insure that participants never concede anything except as the result of an argument.]

p. 274

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’.

[An addition to the commitment-store rules to support a rule (which Hamblin doesn’t state formally) that is designed to preclude one way of shifting the burden of proof—viz., addressing ‘Why S?’ to a participant whose commitment-store contains S only as the result of a concession.]