Of those who are approximately Grice’s contemporaries, Quine is one of the very few to whom Grice feels that Grice owes the deepest of debts, the debt which is owed to someone from whom one has learned something very important about how philosophy should be done, and who has, in consequence, helped to shape one's own mode of thinking. Grice hopes that Quine will not think it inappropriate that Grice’s offering on this occasion should take the form not of a direct discussion of some part of Quine’s essay, “Word and Object,” but rather of an attempt to explore an *alternative* to one of Quine’s central positions, viz. his advocacy of the idea of the general eliminability of this or that singular term, including this or that name.   Grice hopes, also, that Quine will not be too shocked by Grice’s temerity in venturing into areas where Grice’s lack of expertise in formal logic is only too likely to be exposed.   Grice has done his best to protect himself by consulting those who are in a position to advise him.  They have suggested ideas for Grice to work on and have corrected some of Grice’s mistakes, but it would be too much to hope that none remain.  It seems to Grice that there are certain quite natural inclinations which have an obvious bearing on the construction of a “subject-predicate” calculus.     They are as follows.    To admit a constant for this or that infividual.    That is, is to admit this or that name, or its representation.    To allow that, sometimes, a name, like "Pegasus", is not the name of any existent thing.    A name may be sometimes 'vacuous.    In the light of this, to allow the constant of an individual to lack a designatum, so that a sentence about Pegasus may be represented in the system.    To regard “Fa” and ~ Fa as 'strong' contradictories.    To suppose, that is, that one must be true and the other false in any conceivable state of the world.    To hold that, if Pegasus does not exist, “Pegasus does not fly" — or "It is not the case that Pegasus flies" — will be true, while "Pegasus flies" will be false.    To allow the inference rules Universal instantiation and Existential generalisation to hold generally, without special restriction, with respect to formulae containing the constant of an individual.    To admit the law of identity ((Vx) x=*) as a theorem.    To suppose that, if is derivable from ,  any statement represented by $ entails a corresponding statement represented by f.    It is obviously difficult to accommodate all of these inclinations.    Given [by (7)] (x)x=x we can, given given derive first a =a by universal instantiation and then (3x)x=a by existential generalisation It is natural to take (3x)x=a as a representation of 'a exists'.     So given (2) and (3), a representation of a false existential statement — "Pegasus exists' — will be a theorem.    Given (6), we may derive, by Existential generalisation, Sx) ~ Ex from ~ Fa.   Given (3), this seemingly licenses an inference from     "It is not the case that Pegasus flies."     to "It is not the case that something flies.”    But such an inference *seems* illegitimate if, by (5),     "It is not the case that Pegasus flies.”    is true if Pegasus does not exist — as (2) allows.    One should not be able, it *seems*, to assert that it is not the case that something flies on the basis of the truth of a statement to the effect that it is not the case that a certain admittedly non-existent thing flies.    To meet such difficulties as these, various manoeuvres are available, which include the following.    To insist that a proper name N is only admissible as a substituend for a constant of an individual.    ‘N’ is only classifiable as a name, in a certain appropriate sense of 'name', if N has a bearer.     So "Pegasus" is eliminated as a substituend, and our third inclination is rejected.    To say that a statement of the form Fa or again one of the form ~ Fa presupposes — implicates? — the existence of a thing named by a.    Such statements lack a truth-value if there is no such thing.     The fourth and fifth Inclinations are rejected.    To *exclude* a constant of an individual from the system, treating an ordinary name as being reducible to a definite description.    The first inclination is rejected.    To hold that "Pegasus" does have a bearer, a bearer which has being, though it does not exist, and to regard (3.x) Fx as entailing not the existence, but only the being of something which is F.     The second Inclination is rejected.    To allow Universal instantiation and Existential generalisation only in conjunction with an additional premise, such as Ela, which represents a statement to the effect that an exists.     The sixth Inclination is rejected.    To admit a constant of an infividual, to allow it to lack a designatum, and to retain normal universal instantiation and Existential generalisation, but hold that an inference made in natural discourse in accordance with this inference-licence provided by the system is made subject to the 'marginal' extra-systematic assumption that every name which occurs in the expression of such an inference has a bearer.     This amounts, Grice thinks, to the substitution of the concept of entailing subject to assumption A' for the simple concept of entailment in one's account of the logical relation between the premises and the conclusions of such inferences.    The eighth Inclination is rejected.    Grice does not, in this essay, intend to discuss the merits or demerits of any of the proposals which he has just listed.     Instead, Grice wishes to investigate the possibility of adhering to all of the inclinations mentioned at the outset; of, after all, at least in a certain sense keeping everything.     Grice should emphasize that he does not regard himself as committed to the suggestion which Grice shall endeavour to develop.    Grice’s purpose is exploratory.    The suggestion with which Grice is concerned involves the presentation and discussion of a first-order subject-predicate calculus — which Myro calls G-hp — the construction of which is based on a desire to achieve two goals:    to distinguish two readings of the sentence "It is not the case that Pegasus flies”  — and of this or other sentence containing the name "Pegasus" which does not *explicitly* involve any negation-device — and to provide a formal representation of these readings.     The projected readings of     It is not the case that Pegasus flies     S,    are such that on one of them it is not the case that an *utterance* of S, can be true, given that Pegasus does not exist and never has existed.    On the other interpretation, an utterance of S, will be true just because Pegasus does not exist.     To allow the unqualified validity, on either reading, of a step from the assertion of S, to the assertion, suitably interpreted, of "Something [viz., Pegasus] does not fly" (S2).    More fully, G-hp is designed to have the following properties.    Universal instantiation and Existential generalisation will hold without restriction with respect to any formula & containing a constant of an individual « [Ф(c)];     no additional premise is to be required.    The steps licensed by universal instantiation and existential generalisation will not be subject to a marginal assumption or pretence that a name occurring in such steps has a bearer.    For some (a), $ will be true on interpretations of G-hp which assign no designatum to a, and some such (a) will be theorems of G-hp.    It will be possible, with respect to any @ (a), to decide on formal grounds whether or not its truth requires that a should have a designatun.    It will be possible to find, in G-hp, a representation of a sentences such as "Pegasus exists".    There will be an extension of G-hp in which identity is represented.    The double interpretation of S, may be informally clarified as follows.    If S, is taken to say that Pegasus has the property of being something which does not fly, S, is false — since it cannot be true that a nonexistent thing has a property.    But if S, is taken to *deny* that Pegasus has the property of being something which flies,  S, is true — for the reason given in explaining why, on the first interpretation, $, is false.    It seems to be natural to regard this distinction as a distinction between this or that SCOPE of the name "Pegasus".     In the case of a connective, a difference in SCOPE mirror the order in which the connective is introduced in the building up of a formula [the application of formation rules.    The difference between the two interpretations of S, can be represented as the difference between regarding S, as being (i)     the result of substituting "Pegasus" for "x" in "x does not fly" — negation having already been introduced —     or     ii)     the result of *denying* the result of substituting "Pegasus" for "x" in "x flies" — the name being introduced before negation.    To deal with this distinction, and to preserve the unrestricted application of universal instantiation and existential generalisation, G-hp incorporates the following features:    A Normal set of parentheses is replaced by a NUMERICAL subscripts which is appended to a logical constants and to a quantifier, and which indicates scope-precedence:    the higher the subscript, the larger the scope.    A numerical Subscript is attached also to the constant of ann individual and to a bound variable as an indicator of scope.    For convenience a numerical subscript is also attached to a predicate-constant and to a propositional letter.     There will be a distinction between    a    and    b)    ~, F,a,.    a) will represent the reading of S, in which S, is false if Pegasus does not exist;   in (a) "a" has maximal scope.     In (b) "a" has minimal scope, and the non-existence of a will be a sufficient condition for the truth of (b).    So (b) may be taken to represent the second reading of S,.     To give further illustration of the working of the numerical subscript notation, in the formula Faz→, Gava H,bs 'v' takes precedence over*→*, and while the scope of each occurrence of "a" is the atomic sub-formula containing that occurrence, the scope of "b" is the whole formula.    The effect of extending an indicator of syntactical scope to a constant of an infividusl is to provide for a formational operation, viz., the substitution of a constant of a infividual for a free variable.     The formation rules ensure that quantification takes place only after this operation has been performed.    A BOUND variable will then retain the subscripts attaching to the individual constants which quantification eliminates.     The following formational stages will be, for example, involved in the building of a simple quantificational formula    There will be, then, a distinction between 3x4 ~ 2 Fixa, and    (a) will, in Q, be derivable from ~, F,a,, but not from ~ , F,az; (    b) will be derivable directly (by E.G.) only from ~, Faz, though it will bederivable indirectly from ~, Fag.     This distinction will be further discussed.    Though it is not essential to do so, Grice has in fact adapted a feature of the system set out in Mates's Elementary Logic.    A free variable does not occur in a derivation, and universal instantiation always involves the replacement of one or more subscripted occurrences of a bound variable by one or more correspondingly subscripted occurrences of a constant of an individual..    Indeed, such an expression as Fix and G,xzV, is not a formula of G-hp — though to refer to it Grice defines the expression "segment.”    Each F,x and G,xy is a formula, but the sole function of the free variable is to allow the introduction of a the constant of an individual at different formational stages.    Faz→, G,agV 4 H, is admitted as a formula so that one may obtain from it a formula giving maximal scope to "b", viz., the formula    A Closed formula of a predicate calculus may be looked upon in two different ways.     A symbol of the system may be thought of as a lexical item in an artificial language, like Deutero-Esperanto.    An Actual lexical entry (a lexical rule) is provided only for a logical constant and a quantifier;    On this view, an atomic formula in a normal calculus, for example     Fa    will be a *categorical* subject-predicate sentence in that language.     Alternatively, a formula may be thought of as the structure underlying, and exemplified by, sentences in a language such as Italian or English the actual lexical item of which is left unidentified.     On this view, the formula Fav Gb will be a structure exemplified by a sub-class of the sentences which exemplify the structure Fa.     The method of subscripting adopted in G-hp reflects the first of these approaches;    In an atomic formula, the subscripts on the constant of an individual is always higher than that on the *predicate* constant, in consonance with the fact that an affirmative *categorical* *subject*-predicate sentence, like     "Socrates is wise" or — name in subject position    "*Bellerophon* rode *Pegasus*” — name in subject position and in object position after transitive verb.    implies the non-vacuousness of the names which it contains.    Had Grice adopted the second approach, Grice should have had to allow not only F,az, etc., but also Fa,, etc., as formulae;     Grice should have had to provide an atomic formula which would have a substitution instance, e.g., F,a,→ G,b, in which the scope of the individual constants does not embrace the whole formula.    The second approach, however, could be accommodated with appropriate changes.     The significance of a numerical subscript is purely ordinal.    So for example, ~ Fa, and ~17 Fa, will be equivalent.     More generally, any pair of "isomorphs" will be equivalent, and G-ho contains a rule providing for the interderivability of isomorphs.     and & will be isomorphs iff (    1) subscripts apart, @ and ( are identical, and (2)     relations of magnitude (=, <,>) holding between any pair of subscripts in @ are preserved between the corresponding pair of subscripts in & [the subscripts in & mirror those in @ in respect of relative magnitudes.    Parsons suggests to Grice a notation in which Grice would avoid the necessity for such a rule, and has provided me with an axiom-set for a system embodying it which appears to be equivalent to G-hp.    Myro makes a similar proposal.    The idea is to adopt the notation employed in Whitehead’s and Russell’s Principia Mathematica for indicating the scope of a definite description.    Instead of an ordinal numerical subscript, normal parentheses are retained and the scope of an individual constant or bound variable is indicated by an occurrence of the constant or variable within a set of a SQUARE-BRACKET, followed by parentheses which mark the scope boundaries.     So the distinction between ~, F,a, and ~, Fa, is replaced by the distinction between     ~[a] (Fa)     and     [a] (~Fa);     and the distinction between Jxy~,F,x2 and 3xa~,F,x, is replaced by the distinction between    (x) (~ [x] (Ex)) and (3x) ([x] (~ Fx)).     Parson's notation may well be found more perspicuous than Grice’s, and it may be that Grice should have adopted it for the purposes of his essay, though Grice must confess to liking the obviousness of the link between a subscript and a formation-rule.    The notion of syntactical scope may now be precisely defined for G-hp.    If y be a logical constant or quantifier occurring in a closed formula , the scope of an occurrence of y is the largest formula in @ which (a) contains the occurrence of n, (b) does not contain an occurrence a logical constant or quantifier bearing a higher subscript than that which attaches to the occurrence of „.    If , be a term (individual constant or bound variable), the scope of , is the largest segment of @ which (a) contains the occurrence of n,    (b) does not contain an occurrence of a logical constant bearing a higher subscript than that which attaches to the occurrence of n.    A segment is a sequence of symbols which is either (a) a formula or (b) the result of substituting subscript-preserving occurrences ofvariables for one or more occurrences of individual constants in a formula.    We may now define the important related notion of "dominance".     A term 0 dominates a segment @ ift @ falls within the scope of at least one of the occurrences, in , of 0.     In other words, 0 dominates @ if at least one occurrence of 0 in @ bears a subscript higher than that attaching to any logical constant in @.     Dominance is intimately connected with existential commitment, as will be explained.    If "n" denotes a symbol of G-ho, “y." denotes the result of attaching, to that symbol, a subscript denoting n.    "Ф(c, a)"= a formula @ containing occurrences of an individual constant a, each such occurrence being either an occurrence of aj, or of..., or of o'.    [Similarly, if desired, for "$(ap,...w,)", where "o" ('omega') denotes a variable.]    "Ф" ="a formula, the highest subscript within which denotes n".    If 0, and 0, are terms (individual constants or bound variables).    *(02/0,) -the result of replacing each occurrence of 0, in d by an occurrence of 0z, while preserving subscripts at substitution-points'.    The upper symbol indicates the substituend.]    A subscripted n-ary predicate constant followed by n unsubscripted variables; a subscripted propositional letter.    If i is a formula, $(*,+m/∞) is a formula.    If is a formula, Vo+Ф(∞/«) is a formula. [NB: Substitutions are to preserve subscripts.]    If m is a formula, 3c, +Ф (∞/x) is a formula. [NB: Substitutions are to preserve subscripts.]    If » is a formula, ~+m is a formula.    If i-m and to-n are formulae, ф 8,4, ф. 4, ф→, 4 are formulae.    is a formula only if it can be shown, by application of (1)-(6), that p is a formula.     [Ass] Any formula may be assumed at any point.    ....中トリャー」&』～コース♥ローキーは。... ф*+~+ ф'.「「ゆく。♥［m-n    v+] etnml)-*-nYa 0    v -] 1f(1) 4[-m)»Ф    Хра- 17+ ф₴ ・がトら、ф° 4) ф' M    → +, CP] If Ф(п-и]- 41-…・・ロートスin-ns then o    [V+] If v*,... w*F then v'.... v*+V@n+m $ (w/∞), provided that a does not occur in '  [V-]V,Ф+ф(x∞), provided that Vo, is the scope of Va.    (*+) +30,+mV, where v is like except that, if an occurs in ф, at least one such occurrence is replaced in & by an occurrence of .    (В-)Зо„Ф, x'... x*Hy if (a/0), x'... x*H/, provided that 3c,ф is the scope of 3o, that a does not occur in any of , x',.... x*, v.    All substitutions referred to in (10)-(13) will preserve sub-scripts.    Rules (I) (13) are not peculiar to G-ho, except insofar as they provide for the use of numerical subscripts as substitutes for parentheses.     The role of term-subscripts has so far been ignored.     The following three rules do not ignore the role of term-subscripts, and are special to Q.    [Dom +]If(1) a dominates ,  p,x,Rtw(a)0), (3) ф, x). x'+* ((2, +m/c,),... (Фк+п/ок)) [m. п> 0].    NB. v, thus altered, must remain a formula; for example, a must not acquire a subscript already attaching to a symbol other than x.]    This provides for the raising of subscripts on a in 4, including the case in which initially non-dominant a comes to dominate f.    A subscript on an occurrence of a may always be lowered.]     [Iso] If @ and y are isomorphs, @+v.    If a dominates @, for any interpretation Z, @ will be true on Z only if a is non-vacuous (only if Ta+exists? is true, where '+' is a concatenation-symbol).     If a does not dominate , it may still be the case that @ is true only if a is non-vacuous (for example if @="~, ~3 F,az" or ="FazV, G,az", though not if ="F,a→,G,az").     Whether or not it is the case will be formally decidable.     Let us abbreviate " is true only if a is non-vacuous" as "ф is E-committal for &".   The conditions in which ф is E-committal for a can be specified recursively:    (1)If a dominates , is E-committal for a.    (2) If =~,~=-mV, and is E-committal for a, then @ is E-committal for a.    3) If =v&,x, and either or x is E-committal for a, then $ is E-committal for a.    4) If =v.x, and both y and & are E-committal for a, then ф is E-committal for a.    5) If =→x, and both ~_* and z are E-committal for a, then ф is E-committal for a [in being greater than the number denoted by any non-term-subscript in 4].    If =Vo, or 3o,v, and (B/∞) is E-committal for x, then ф is E-committal for a.    Since Fja, → ,F,a, is true whether or not "a" is vacuous, the truth of F,a,→, Fa, (in which "a" has become dominant) requires only that a exists, and so the latter formula may be taken as one representation of "a exists".     More generally, if (for some n) a is the only individual constant in » (x) and =→n-m  @ may be taken as a representation of Ta + exists?    An 3-quantified formula 3o,ф will represent a claim that there exists an object which satisfied the condition specified in ¢ iff (a/∞) is E-com-mittal for o.     To illustrate this point, compare (i)  3x4~, Fix, and  (ii)  ヨxュ～3Fix2.    Since ~, Fa, is E-committal for "a" (is true only if a exists) while ~, F,a, is not E-committal for "a", (i) can, and ii) cannot, be read as a claim that there exists something which is not F.     The idea which lies behind the treatment of quantification in G-ho is that while i) and ii) may be taken as representing different senses or different interpretations of "something is not F" or of "there is something which is not F", these locutions must be distinguished from "there exists something which is not F"', which is represented only by (i).     The degree of appeal which G-hp will have, as a model for natural discourse, will depend on one's willingness to distinguish, for example,    "There is something such that it is not the case that it flies"     from    There is something such that it is something which does not fly",     and to hold that (    a) is justified by its being false that Pegasus flies, while (    b) can be justified only by its being true of some actual thing that it does not fly.     This distinction will be further discussed.    Immediately, however, it must be made clear that to accept G-hp as a model for natural discourse is not to accept a Meinongian viewpoint;     it is not to subscribe to the idea of a duality, or plurality, of 'modes of being'.   Acceptance of G-hp as a model might be expected to lead one to hold that while some sentences of the form "Russell _" will be interpretable in such a way as i) to be true, and (ii) to entail not merely "there is something which _ " but also "there exists something which __", sentences of the form "Pegasus _ " will, if interpreted so as to be true, entail only "there is something which _-".     But from this it would be quite illegitimate to conclude that while Russell both exists and is — or has being —, Pegasus merely is — or has being.    "Exists" has a licensed occurrence both in the form of expression "there exists something which " and in the form of expression "a exists";     "is" has a licensed occurrence in the form of expression "there is something which ___", but not in the form "a is".     G-hp creates no ontological jungle.    It would not be surprising if the combination of the admissibility, according to the natural interpretation of G-ho, of appropriate readings of the inference-patternsa does not exist a is not F and (2) a is (not) F something is (not) F have to be regarded as G-Jo’s most counter-intuitive feature.    Consider the following dialogue between A and B at a cocktail party:    Is Bloggs here tonight?    Bloggs?    You know, the Merseyside stock-broker who last month climbed Mt. Everest on hands and knees.    Oh! Well no, Bloggs isn't here.    How do you know Bloggs isn't here?    *That* Bloggs doesn't exist; he was invented by the journalists.    So someone isn't at this party.    Didn't you *hear* me _say_ that Bloggs does not exist?    I heard you quite distinctly. Are *you* under the impression that _you_ did heard me *say* that there exists a person who isn't at this party?    B, in his remarks, seemingly accepts not only inference-pattern (I) but also inference-pattern (2).    The ludicrous aspects of this dialogue need to be accounted for.     The obvious explanation is, of course, that the step on which B relies is at best dubious, while the step which A adds to it is patently illegitimate.    If we accept the first pattern, we should not also accept the second pattern.    But there is another possible explanation, namely that (i given (P) "a does not exist and so a is not F" the putative conclusion from (P),     Something is not F"     C), is strictly speaking (on one reading) true, but    Given that (P) is true, there will be something LITERALLY true, yet wrong, odd, or misleading about saying or asserting (C).    Ignoring such a distinction having proved a common mistake on the part of some philosophers.    In relation to this alternative explanation, there are two cases to con-    a) that in which     the utterer of (C) believes — or knows — that a does not exist, and advances (C) on the strength of this belief or knowledge.    But the non-existence of a is not public knowledge, at least so far as the utterere’s addressee is concerned    (b) that which differs from (a) in that all parties to the talk-exchange are aware, or think, that a does not exist.     Case (a) will not, perhaps, present too great difficulties.    If there is a sense of "    Something is not F"     such that for this to be true some real thing must fail to be F, the knowledge that in this sense something is not F will be much more useful than the knowledge that something is not F in the other (weaker) sense; and     ceteris paribus     one would suppose the more useful sense of (C) to be the more popular,     and so, in the absence of counter-indications, to be the one employed by someone who utters (C).     Which being the case, to utter (C) on the strength of the non-existence of a will be LITERALLY TRUE if misleading.    Case (b) is less easy for the alternative explanation to handle, and Grice’s dialogue is designed to be an example of case (b).     There is a general consideration to be borne in mind, namely that     it will be very unplausible to hold both that there exists a particular interpretation, or sense, of an expression E,     and     that     to use E in this sense, or interpretation, is always to do something which is *conversationally* objectionable.     So the alternative explanation will have (l) to say why such a case (b) example as that provided by the dialogue *is* conversationally objectionable, (2) to offer some examples, which should presumably be case (b) examples, in which the utterance of (C), bearing the putative weaker interpretation would be conversationally *innocuous.*    These tasks might be attempted as follows.    To say "    Something is such-and-such"     Or    It is not the case that something is such-and-such    might be expected to have one or other of two conversational purposes;     either to show that it is possible (not) to be such-and-such,     countering (perhaps in anticipation) the thesis that nothing is even (not) such-and-such,     or     to provide a prelude to the specification, perhaps after a query, of an item which is (not) such-and-such.     A's remark —     So, it is not the case that someone is at this party.    — cannot have either of these purposes.     First, Bloggs has already been agreed by A and B NOT to exist.    And so, the utterance cannot provide a counter-example to any envisaged thesis that every member of a certain set — e. g. leading local business men — is at the party.     Bloggs, being non-existent, is not a member of any set.    Second, it is clear that A's remark is advanced on the strength of the belief that Bloggs does not exist.    So, whatever specification is relevant has already been given.    The following example might provide a conversationally innocuous use of (C) bearing the weaker interpretation.     The cocktail party is a special one given by the Merseyside Geographical Society for its members in honour of Bloggs, who was at the last meeting *elected a member.* as a recognition of his reputed exploit.     A and B have been, before the party, discussing those who are expected to attend it    C has been listening, and is in the know about Bloggs.    Well, someone will not be at this party.    Who?    Bloggs    But it's in his honour!    That's as may be, but he doesn't exist; he was invented by the journalists.    Here C makes his initial remark (bearing putative weak interpretation), intending to cite Bloggs in specification and to disclose his non-existence.    It should be made clear that Grice is not trying to prove the existence or admissibility of a weaker interpretation for (C).    Grice is merely trying to show that the prima facie case for it is strong enough to make investigation worth-while.    If the matter is worth investigation, the formulation of G-hp is one direction in which such investigation should proceed, in order to see whether a systematic formal representation of such a reading of "Something is (not) F" can be constructed.    As a further consideration in favour of the acceptability of the weaker interpretation of "Something is (not) F", let me present the following "slide":    To say     Bloggs is at this party    would be to say something which is not true.    To say     It is not true that Bloggs is at this party.    would be to say something which is true.    To say    It is not the case that Bloggs is at this party.    would be to say something which is true.    Bloggs is not at this party.    Bloggs can be truly said not to be at this party.    Someone, viz. Bloggs, can be truly said not to be at this party.    Someone is not at this party, (viz. Bloggs.    It seems to Grice plausible to suppose that remark (I) could have been uttered with truth and propriety, though with some *inelegance*, by B in the circumstances of the first dialogue.     It also seems to Grice that there is sufficient difficulty in drawing a line before any one of remarks (2) to (7), and claiming that to make that remark would be to make an illegitimate transition from its legitimate predecessor, for it to be worth considering whether one should not, given the non-existence of Bloggs, accept all seven as being (strictly speaking) true.     Slides are dangerous instruments of proof, but it may be legitimate to use them to back up a theoretical proposal.    So far as Grice can see, there will be no difficulty in formulating a system G-hp as an extension of G-hp which includes identity..     In a classical *second*-order subject-predicate calculus one would expect to find that the formula     (VF) (Fa→Fb) (    or the formula     (VF) (Fa-›Fb))     is a definitional sub-stituend for, or at least is equivalent to, the formula     a = b    Now in G-hp, the sequence Fa→Fb will be incomplete, since subscripts are lacking, and there will be two significantly different ways of introducing subscripts, (i F,as→2F,be and (ii) Faz→, F,b,.     In (i "a" and "b" are dominant,    and the existence of a and of b is implied; in ii)     this is not the case.     This difference of subscripting will reappear within a *second*-order predicate calculus which is an extension of G-hp.    we shall find both (    i) (a) VF,F,a,→, F,b, and     (ii) (a) VE,F,a2→4 F,b,.     If we introduce the symbol * into Q, we shall also find iii) VF, F,a,,F,ba and (iv) VF,F,a,**F,b,.     We may now ask whether we want to link the identity of a and b with the truth of (iii) or with the truth of (iv), or with both.     If identity is linked with (iii)     any affirmative identity-formula involving a vacuous individual constant will be false;     If identity is linked with (iv) any affirmative identity formula involving two vacuous individual constants will be true.    A natural course in this situation seems to be to admit to G-hp two types of identity formula, one linked with (iii) and one with (iv), particularly if one is willing to allow two interpretations of (for example) the sentence    Pegasus is identical with Pegasus"    on one of which the sentence is false because Pegasus does not exist, and on the other of which the sentence is *true* because Pegasus does not exist     — just as "Pegasus is identical withBellerophon" will be true because neither Pegasus nor Bellerophon exist).     Cf the null set and extensionalism.    We cannot mark this distinction in G-hp simply by introducing two different identity-signs, and distinguishing between (say) a,=,b, and a,=, b3.     Since in both these formulae "a" and "b" are dominant, the formulae will be true only if an and b exist.     Just as the difference between (iii) and (iv) lies in whether "a" and "b" are dominant or non-dominant, so must the difference between the two classes of identity formulae which we are endeavouring to express in G-hp.    So G-hp must contain both such formulae as az=,b, (strong' identity formulae) and such formulae as aj=,b2 ('weak' identity formulae).     To allow the constant of an infividual to be non-dominant in a formula which is not molecular will be a temporary departure from the practice so far adopted in G-hp.    but in view of the possibility of eventually defining "=" in a *second*-order calculus which is an extension of G-hp one may perhaps regard this departure as justified.    Q' then might add to G-ho one new symbol, "=";  two new formation rules;  ' =,? is a formula,  If aj+ =, Bj+, is a formula, &,+ =-Bj+, is a formula, where m> j+k and m> j+ 1.  (c) two new inference-rules  A-Vo,+,C0,-,-,0,-, [a weak identity law]  a,  Be. ф+ф(Ba).     There is substitutivity both on strong identity and on weak identity.    Grice hopes that these additions would be adequate, though Grice has not taken steps to assure himself that they are.     Grice might add that to develop a representation of an interesting weak notion of identity, one such that Pegasus will be identical with Pegasus, but not with Bellerophon, I think that one would need a system within which such  a psychological notion, such as "it is believed that,” is represented.    The task of providing a semantics for Q might, Grice thinks, be discharged in more than one way;     the procedure which Grice suggests will, Grice hopes, continue the following features:     it will be reasonably intuitive,      it will not contravene the philosophical ideas underlying the construction of G-hp by, for example, invoking an imaginary or non-real entitiy    it will offer reasonable prospects for the provision of proofs of the soundness and completeness of G-hp though Grice must defer the discussion of these prospects to another occasion.    The provision of an interpretation Z for Q will involve the following steps:    The specification of a non-empty domain D, within which two sub-domains are to be distinguished: the special sub-domain (which may be empty), the elements of which will be each unit set in D whose element is also in D; and the residual sub-domain, consisting of all elements of D which do not belong to the special sub-domain.    The assignment of each propositional letter either to 1 or to 0.    The assignment of each -ary predicate constant y to a set (the E-set of y) of ordered n-tuples, each of which has, as its elements, elements of D.     An E-set may be empty.    The assignment of each individual constant a to a single clement of D (the correlatum of a).     If the correlatum of a belongs to the special sub-domain, it will be a unit-set whose element is also in D, and that element will be the designatum of a.     If the correlatum of a is not in the special sub-domain, & will have no designatum.     Grice has in mind a special case of the fulfilment of step (4), in which every constant of an individual has as its correlatum either an element of the special sub-domain or the null-set.     Such a method of assignment seems particularly intuitive.    If an individual constant a is, in Z, assigned to a correlatum belonging to the special sub-domain, Grice shall say that the assignment of a is efficient.    If, in Z, all individual constants are efficiently assigned, Grice shall say that Z is an efficient interpretation of G-hp.    It will be noted that, as Grice envisages them, interpretations of G-hp will be of a non-standard type, in that a distinction is made between the correlation of a constant of an individual and its description.     Every constant of ann individual is given a correlatum, but only that which on a given interpretation is non-vacuous has, on that interpretation, a designatum.     Interpretations of this kind may be called G-ho type interpretations.    Grice uses the expressions "Corr (1)" and "Corr (O)" as abbreviations, respectively, for "correlated with 1" and "correlated with 0"    *. By "atomic formula" Grice means a formula consisting of a subscripted n-ary predicate constant followed by a subscripted individual constant.    Grice shall, initially, in defining "Corr(1) on Z" ignore quantificational formulae.    If ф is atomic, @ is CorrI) on Z iff i) each individual constant in has in Z a designatum (i.e. its correlatum is a unit set in D whose element is also in D), and ii) the designata of the individual constants in , taken in the order in which the individual constants which designate them occur in , form an ordered n-tuple which is in the E-set assigned in Z to the predicate constant in ф.    If no individual constant dominates , is Corr(1) on Z ifl (i    If =~,V, y is Corr(0) on Z;    If =v&,x. v and z are each Corr(1) on Z;    If ф=wv. X, either or y is Corr(1) on Z;    If =/→,x, either is Corr(0) on Z or x is Corr(1) on Z    If (x) is a closed formula in which & is non-dominant, and if is like « except that & dominates $, then is Corr(1) on Z iff i) v is Corr(1) on Z and (ii) a is efficiently assigned in Z.    If a closed formula is not Corr(1) on Z, then it is Corr(0) on Z.    To provide for quantificational formulae, some further notions are required.    An interpretation Z' is an i.c.-variant of Z iff Z' differs from Z (if at all) only in that, for at least one individual constant a, the correlatum of a in Z' is different from the correlatum of a in Z.    Z' is an efficiency-preserving i.c.-variant of Z iff Z' is an i.c.-variant of Z and, for any a, if a is efficiently assigned in Z a is also efficiently assigned in Z'.    Z' is an efficiency-quota-preserving i.c.-variant of Z iff Z' is an i.c.-variant of Z and the number of individual constants efficiently assigned in Z' is not less than the number efficiently assigned in Z.'    Let us approach the treatment of quantificational formulae by considering the 3-quantifier.     Suppose that, closely following Mates's procedure in his “Elementary Logic,” we stipulate that Jw,ф is CorrI) on Z iff $ (a'/∞)is Corr (1) on at least one i.c.-variant of Z, where a is the first individual constant in Q.     We assume that the individual constants of Q can be ordered, and that some principle of ordering has been selected.    In other words, 3w,ф will be Corr(I) on Z iff, without altering the assignment in Z of any predicate constant, there is some way of assigning &' so that ф (a/∞) is Corr(l) on that assignment.     Let us also suppose that we shall define validity in Q by stipulating that @ is valid in Q iff, for any interpretation Z, ф is Corr(1) on Z.    We are now faced with a problem.     Consider the "weak existential" formula 3x2~, F,x,.     If we proceed as we have just suggested, we shall be forced to admit this formula as valid;     if "a" is the first individual constant in G-ho, we have only to provide a non-efficient assignment for "a" to ensure that on that assignment ~, Fa, is Corr(1); for any interpretation Z, some i.c.-variant of Z will provide such an assignment for "a", and so 3x4~3 F,x2 will be CorrI) on Z.     But do we want to have to admit this formula as valid?     First, if it is valid, Grice is reasonably sure that G-ho, as it stands, is incomplete, for Grice sees no way in which this formula can be proved.     Second, if in so far as we are inclined to regard the natural language counterparts of valid formulae as expressing conceptual truths, we shall have to say that e.g.     It is not the case that someone will be at this party    If given the 'weak' interpretation which it was supposed to bear in the imagined conversation, will express a conceptual truth;     while Grice’s argument does not demand that the sentence in question express an exciting truth, Grice is not sure that he welcomes quite the degree of triviality with which is now threatened.    It is possible, however, to avoid the admission of 3x,~,F,x2 as a valid formula by adopting a slightly different semantical rule for the 3-quantifier.     We stipulate that 3o,$ is Corr(I) on Z iff @ (c'/co) is Corr(I) on at least one efficiency-preserving i.c.-variant of Z. Some interpretations of G-hp will be efficient interpretations, in which "a" will be efficiently assigned; and in any efficiency-preserving i.c.-variant of such an interpretation "a" will remain efficiently assigned;     moreover among these efficient interpretations there will be some in which the E-set assigned to "F" contains (to speak with a slight looseness) the member of each unit-set belonging to the special sub-domain.     For any efficient interpretation in which "p" is thus assigned, F,a, will be Corr(1), and ~ , F,a, will be Corr(0), on all efficiency-preserving i.c. -variants.    So 3x4~gF,xz will not be Corr(1) on all interpretations, i.e. will not be valid.    A similar result may be achieved by using the notion of an efficiency-quota-preserving i.c.-variant instead of that of an efficiency-preserving i.c.-variant; and the use of the former notion must be preferred for the following reason.   Suppose that we use the latter notion;(ii)(iii)that "a?" is non-efficiently assigned in Z;  that "a" is the first individual constant, and is efficiently assigned in Z    that "F" includes in its extension the member of each unit-set in the special sub-domain.     ~, Faz is Corr(1) on Z, and so (by E.G.) 3x2~, Fix, is Corr(1) on Z.     But "a" is efficiently assigned in Z, so ~g F,a, is Corr(0) on every efficiency-preserving i.c.-variant of Z (since "F" includes in its extension every designable object).     So x~, F,*z is Corr(0) on Z.    This contradiction is avoided if we use the notion of efficiency-quota-preserving i.c.-variant, since such a variant of Z may provide a non-efficient assignment for an individual constant which is efficiently assigned in Z itself; and so 3xz~, F,x, may be Corr(I) on Z even though "a" is efficiently assigned in Z.    So Grice adds to the definition of "Cort(I) on Z", the following clauses:     If =Vo,k, is CorrI) on Z, iff V(a'/a) is Corr(1) on every efficiency-quota-preserving i.c.-variant of Z.     If ф =3o,/, is Corr(1) on Z iff y (x'/c) is Corr(1) on at least one efficiency-quota-preserving i.c.-variant of Z.    In each clause, "a is to be taken as denoting the first individual constant in Q.]    Validity may be defined as follows:    ф is valid in Q iff, for any interpretation Z, ф is Corr(1) on Z.    Finally, we may, if we like, say that p is true on Z iff p is CorrI) on Z.    It might be objected that, in setting up G-ho in such a way as to allow for the representation of this or that vacuous name, Grice has ensured the abandonment, at least in spirit, of one of the desiderata which Grice had in mind;     for(it might be suggested) if G-ho is extended so as to include a Theory of Descriptions, the constant of an individual will be seen to be indistinguishable, both syntactically and semantically, from an unanalysed definite description;     The constant of an individual will be related to a representation of a description in very much the same way as a propositional letter is related to a formula, having lost the feature which is needed to distinguish it from a representation of a description, namely that of being interpretable only by the assignment of a designatum.    Grice does not propose to prolong the essay  by including the actual presentation of an extension of G-ho which includes the representation of a description, but Grice hopes to be able to say enough about how he envisages such an extension to make it clear that there will be a formal difference between the a constant of an individual of G-hp and a definite description.     It is a familiar fact that there are at least two ways in which a notation for representing a definite description may be developed within a classical system;   one may represent     The haberdasher of Spurgeon is bald    either by     (1) G(1x. Ex) or by (    2) (9x. Fx) Gx;     one may, that is, treat     "ix. Fx"     either as a term or as being analogous to a (restricted) quantifier.     The first method does not allow for the representation of a difference in syntactical scope, so a general decision will have to be taken with regard to the scope of a definite description, for example that they are to have maximal scope.     The second method does provide for scope-distinctions;     there will be a distinction between, for example,     (ix. Fx) ~ Gx     and     ~(1x. Fx) Gx.     The apparatus of G-hp, however, will allow us, if we wish, to combine the first method, that of representing a definite description by a term, with the representation of differences of scope;     we can, if we like, distinguish between c.g.,     ~,G,ax,F,x,     and     ~,G,1xgF,xz,     and ensure that from the first formula we may, and from the second we may not, derive E!, 1x, F,*2.     We might, alternatively, treat a description as syntactically analogous to a restricted quantifier, if we so desire.     Let us assume (arbitrarily) that the first method is adopted, the scope-boundaries of a descriptive term being, in each direction, the first operator with a higher subscript than that borne by the iota-operator or the first sentential boundary, whichever is nearer.    Let us further assume, perhaps no less arbitrarily, that the iota-operator is introduced as a defined expression, so that such a formula as nitional substitution for the right-hand side of the formulaG, xgF,x2→4G,x,F,x2, together with applications of the rules for subscript-adjustment.    Now, as Grice envisages the appropriate extension of G-hp, the formal difference between a constant of an individual and a descriptive term will lie in there being a legitimate step (by Existential generalisation from a formula containing a non-dominant constant of an individual to the related "weak' existential form,     e.g.. from ~, Faz to 3x4~, F,x2, while there will, for example, be no analogous step from ~ G, 1x, Fxz to 3x4~, G,x2.     Such a distinction between a constant of an individusl and a descriptive term seems to Grice to have, at least prima facie, a basis in intuition;     Grice has at least some inclination to say that,     if Spurgeon has no haberdasher,      it would be TRUE, though no doubt conversationally odd, to say     "It is not the case that Spurgeon's haberdasher is bald"     (S),     even though no one has even suggested or imagined that Spurgeon has a haberdasher;     even though, that is, there is no answer to the question who Spurgeon's haberdasher is or has been supposed to be, or to the question WHOM the utterer means by the phrase " Spurgeon's haberdasher."     If that inclination is admissible, it will naturally be accompanied by a reluctance to allow a step from S to     "Someone is not bald"     (S,) even when S, is given its 'weak' interpretation.     Grice has, however, already suggested that an utterance of the sentence "    It is not the case that *Spurgeon* — never mind his haberdasher — is bald    S')     is not assessable for truth or falsity unless something can be said about who *Spurgeon* — never mind his haberdasher — is or is supposed to be;     In which case the step from S' to S, weakly interpreted, seems less unjustifiable.    Grice can, nevertheless, conceive of this argument's failing to produce conviction.     The following reply might be made:     If one is given the truth of S, on the basis of there being no one who is haberdasher to Spurgeon, all one has to do is first to introduce a name, say 'Bill', laying down that 'Bill' is to designate whoever is haberdasher to Spurgeon, then to state, truly, that     it is not the case that Bill is bald     — since there is no such person — and finally     to draw the conclusion, now legitimate, that     someone is not bald     — on the 'weak' reading of that sentence.    If only a stroke of the pen, so to speak, is required to legitimize the step from S to S, weakly interpreted, why not legitimize the step directly, in which case the formal distinction in G-hp between a constant of an individual and descriptive term must either disappear or else become wholly arbitrary?"    A full treatment of this reply would, Grice suspects, be possible only within the framework of a discussion of reference — not predication — too elaborate for the present occasion;     Grice can hope only to give an indication of one of the directions in which Grice should have some inclination to proceed.     It has been observed that a distinction may be drawn between at least two ways in which descriptive phrases may be employed.    A group of men is discussing the situation arising from the death of a business acquaintance, Smith, of whose private life they know nothing, except that, as they think, he lived extravagantly, with a household staff which included a butler.     One of them says     Well, Smith’s butler will be seeking a new position.    Earlier, another group has just attended a party at Smith’s house, at which their hats and coats were looked after by a dignified individual in dark clothes and a wing-collar, a portly man with protruding ears, whom they heard Smith addressing as "Old Boy", and who at one point was discussing with an old lady the cultivation of vegetable marrows.    One of the group says     Smith’s butler got the hats and coats mixed up.    The utterer in example (1) could, without impropriety, have inserted after the descriptive phrase "Smith’s' butler" the clause "whoever he may be".     It would require a *special circumstance* to make a corresponding insertion appropriate in the case of example.    On the other hand, we may say, with respect to the second example,  that some particular individual has been 'described as', 'referred to as', or 'called' Smith’s butler by the utterer.    furthermore, any one who was in a position to point out that Smith has no butler, and that the man with the protruding ears was Smith’s *gardener* — or someone hired for the occasion — would also be in a position to claim that the utterer had misdescribed that individual as Smith's butler.     No such comments are in place with respect to the first example.    A schematic generalized account of the difference of type between examples (I) and (2) might proceed along the following lines.     Let us say that X has a dossier for a definite description & if     there is a set of this or that definite description which includes &,     all the members of which X supposes (in one or other of the possible sense of 'suppose") to be satisfied by one and the same item.     In a type (2) case, unlike a type (I) case, the utterer intends his addressee to think, via the recognition that he is so intended,    a) that the utterer has a dossier for the definite description & which he has used, and (b)     that the utterer has aptly apositively alla Urmson selected from this dossier at least partlyin the hope that his addresssee has a dossier for & which 'overlaps' the utterer’s dossier for & (that is, shares a substantial, or in some way specially favoured, subset with the utterer’s dossier).     In so far as the utterer expects his addressee to recognise this intention, he must expect his addressee to think that in certain circumstances the utterer will be prepared to replace the remark which he has made (which contains 8) by a further remark in which some element in the utterer’s dossier for & is substituted for d.     The standard circumstances in which it is to be supposed that the utterer would make such a replacement will be (a) if the utterer comes to think that the addressee either has no dossier for &, or has one which does not overlap the utterer’s dossier for & (i.e., if the addressee appears not to have identified the item which the speaker means or is talking about), (b) if the utterer comes to think that & is a misfit in the utterer’s dossier for , i.e., that & is not, after all, satisfied by the same item as that which satisfies the majority of, or each member of a specially favoured subset of, the descriptions in the dossier.     In example (2) the utterer might come to think that Smith has no butler, or that though he has, it is not the butler who is the portly man with the protruding ears, etc., and whom the utterer thinks to have mixed up the hats and coats. (iii)     If in a type (2) case the utterer has used a descriptive phrase (e.g., "Smith’s butler") which in fact has no application, then what the utterer has said will, strictly speaking, be false;     the truth-conditions for a type (2) statement, no less than for a type (I) statement, can be thought of as being given by a Russellian account of a definite description — with suitable provision for unexpressed restrictions, to cover cases in which, example, someone uses the phrase "the table" meaning thereby with the implicated quasi-demonstrative "the table in this room.”    But though what, in such a case, an utterer has said may be false, what he *meant* or signifies may be true — for example, that a certain particular individual [who is in fact Smith’s gardener] mixed up the hats and coats).    Disimplicature: meaning less than one explicitly conveys.    Let us introduce two auxiliary devices, ordinary and capital let-ters, to indicate to which of the two specified modes of employment a reported use of a descriptive phrase is to be assigned.     If I write "S said '    The Fis G',    "Grice shall indicate that S was using "the F" in a type (1), non-identificatory way, whereas if I write "S said "THE F is G",' I shall indicate that S was using "the F" in a type (2), identificatory way.    It is important to bear in mind that Grice is not suggesting that the difference between these devices represents a difference in the meaning or sense which a descriptive phrase may have on different occasions;     on the con-trary, Grice is suggesting that a descriptive phrase has no relevant systematic duplicity of meaning or significance or signification or Fregeian sense.    Its meaning is given by a Russellian account.    We may now turn to names.     In Grice’s type (1) example, it might be that in view of the prospect of repeated conversational occurrences of the expression “Smith’s butler," one of the group would find it convenient to say     "Let us call Smith’s butler 'Bill'."     Using the proposed supplementa-tion, Grice can represent him as having remarked     Let us call Smith’s butler 'Bill'."     Any subsequent remark containing "Bill" will have the same truth-value as would have a corresponding remark in which "Smith’s' butler" replaces "Bill".     If Smith has no butler, and if in consequence it is false that Smith’s butler will be seeking a new position, it will be false that Bill will be seeking a new position.    In the type (2) example, also, one of the group might have found it convenient to say     "Let us call Smith’s butler 'Bill',"     and his intentions might have been such as to make it a correct representation of his remark for Grice to write that he said     Let us call SMITH’s BUTLER 'Bill'."     If his remark is correctly thus represented,  it will nor be true that, in all conceivable circumstances, a subsequent remark containing "Bill" will have the same truth-value as would have a corresponding remark in which "Bill" is replaced by "Smith’s butler".     For the person whom the utterer proposes to call "Bill" will be the person whom he meant when he said "Let us call SMITH’S BUTLER 'Bill'," viz., the person who looked after the hats and coats, who was addressed by Smith as "Old Boy", and so on; and if this person turns out to have been Smith’s gardener and not Smith’s butler,     it may be true that Bill mixed up the hats and coats     and false that     Smith’s butler mixed up the hats and coats.     Remarks of the form "Bill is such-and-such" will be inflexibly or rigidly tied, as regards truth-value, not to possible remarks of the form     "Smith’s butler is such-and-such",     but to possible remarks of the form "The person whom X meant when he said 'Let us call Smith’s butler "Bill"' is such-and-such".    It is important to note that, for a definite description used in the explanation of a name to be employed in an identificatory way, it is not required that the item which the explainer means (is referring to) when he uses the description should actually exist.     A person may establish or explain a use for a name & by saying     “Let us call THE F &" or "THE F iscalled &"     even though every definite description in his dossier for "the F" is vacuous;     he may *mistakenly* think, or merely deceitfully, of playfully — the loyalty examiner —  intend his addressee to think, that the elements in the dossier are non-vacuous and are satisfied by a single item;     and in secondary or 'parasitic' types of case, as in the narration of, or commentary, upon fiction,     Hamlet saw his father  Macbeth saw his enemy    that this is so may be something which the utterer non-deceitfully pretends or feigns.    So a name introduced or explained in this way may be vacuous.    Grice may now propound the following argument in answer to the objection that any distinction in G-ho between a constant of an individual and a descriptive term will be arbitrary.     For a given definite description 6, the difference between a type 1 and type (2) employment is not to be construed as the employment of o in one rather than another of two systematically different senses of .    A name a may be introduced either so as to be inflexibly or rigidly tied, as regards the truth-value of utterances containing it, to a given definite description ô, or so as to be not so tied (6 being univocally employed);     so the difference between the two ways of introducing a may reasonably be regarded as involving a difference of sense or meaning for a;     a sense in which a may be said to be equivalent to a definite description and a sense in which it may not.    It is, then, not arbitrary so to design G-hp that a constant of an individual is to be regarded as representing, among other linguistic items, a name used with one of their possible kinds of meaning, namely that in which a name is not equivalent to a definite description — e. G. Pickwick, Bunbury.    Grice does not propose to attempt the important task of extending G-hp so as to include the representation of a psychological verb-phrase, but Grice should like to point out a notational advantage which any such extension could be counted on to possess.     There are clearly at least two possible readings of such a sentence as     "sue wants someone to marry her",     one in which it might be paraphrased by     sue wants someone or other to marry her"     and another in which it might be paraphrased by     Sue wants a particular person to marry her" or by "    There is someone whom sue wants to marry her".     Symbolizing "a wants that p" by Wap, and using the apparatus of classical predicate logic, we might hope to represent reading (    1)by W°(3x) (Fxa) and reading (2) by (x) (WªFxa).     But suppose that Sue wants Bunbury to marry her    having been deceived into thinking that her friend Betty has a highly delectable brother who goes by Bunbury though in fact Betty Bunbury is an only child.     In these circumstances one is inclined to say that     "sue wants someone to marry her    is true on reading (2),     but we cannot now represent reading (2) by (3x) (WªFxa), since Bunbury does not exist.    The apparatus of G-ho should provide us with distinct representations for two familiar readings of     sue wants Bunbury to marry her    , VIZ., (a)  Wy F,ba, and (b) W9*F,b,a,.     Given that Bunbury does not exist only(b) can be true.     We should have available to us also three distinct 3-quantificational forms (together with their isomorphs):  (i)W93x,F,xzas;  (ii)(iii)    Since in (iii) "x" does not dominate the segment following the 3-quantifier, (iii) does not have existential force, and is suitable therefore for representing "sue wants a particular person to marry her" if we have to allow for the possibility that the particular person does not actually exist.    . [ and (ili) will be derivable from each of (a) and (b): (ii) will be derivable only from (a).]    Grice has in this essay developed as strong a case as he can in support of the method of treatment of a vacuous name which he has been expounding.    Whether in the end Grice should wish to espouse it would depend on the outcome of further work on the notion of reference.    Grice is particularly indebted to Parsons and Boolos for some extremely helpful correspondence, to Myro for countless illuminating suggestions and criticisms, and to Mates for assistance provided both by word of mouth and via his book Elementary Logic, on which Grice has drawn a good deal.    Grice owes the idea of this type of variant to Myro, whose invaluable help was essential to the writing of this section.    9 c.g. by Donnellan, 'Reference and Definite Descriptions', Philosophical Review;     as may perhaps be seen from what follows, Grice not sure that Grice is wholly sympathetic towards the conclusions which Donnellsn  — never mind Kripke — and cf Grice’s friend Patton, draws from the existence of the distinction. h. P. Grice