SORITES , ISSN 1135-1349
Issue #07. November 1996. Pp. 6-20.
«The validity of indexical arguments»
Copyright © by SORITES and S.H. Elkatip
The validity of indexical arguments
My concern is mainly the validity of Castañeda's exposition of indexical arguments and particularly its first version as put forth in «`He': A Study in the Logic of Self-Consciousness» in 1966.<1>Foot note 1_1 The following two or three years witnessed other papers by Castañeda on the issue. In 1977 he returned to the topic again with «Perception, Belief, and the Structure of Physical Objects and Consciousness», a paper that «extends Guise Theory to perception»<2>Foot note 1_2
The difference between the earliest 1966 paper and the later 1977 one is that in the latter there are references to Kant and the transcendental deduction while in the former there virtually are none, or, if there is a reference, its tone is very dissimilar<3>Foot note 1_3 In the 1966 paper «`He'» (for short) there is a single reference to Kant and that associates him with Hume: «philosophers (especially Hume and Kant) have known all along, that there is no object of experience that one could perceive as the self that is doing the perceiving»<4>Foot note 1_4 In comparison, «Physical Objects and Consciousness» (for short) ends with an ovation to Kant and «the so-called egocentric predicament, which, to put it in a Kantianesque way, consists in that all judgments and all perceptual fields lie within an implicit I think»<5>Foot note 1_5
In 1977, Castañeda seems to suggest that Kantian philosophy, disagreeing with Humean philosophy which leaves valid knowledge of things such as the self to the imagination, guarantees «the awareness of experiences as part of one consciousness and as having an object, although neither the owner nor the object of those experiences can be found in the experiences as such»<6>Foot note 1_6 There were intimations of the course of development of Castañeda's 1966 indexical argument already in 1967 in «Indicators and Quasi-Indicators» where he begins talking about «Descartes' Cogito and Kant's theses on the transcendental self» and «the fundamental fact underlying the idea of the transcendental self» in the first section<7>Foot note 1_7
Castañeda acknowledges distinctions among «external», «internal» and «transcendental» sorts of knowledge in a reply, in the Tomberlin volume of 1986; to Boër and Lycan's criticism he retorts in the replies section:
At that level, as Descartes, Leibniz, and Kant knew very well, the sceptic is right: all the claims to know are false, except for the cogito claims. We must distinguish a transcendent species of knowledge, from an internal one; the transcendent species of knowledge is a lofty one where nothing more than logical deduction and, perhaps, semantic know-how and perceptual powers are presupposed.<8>Foot note 1_8
Looking back at his work, Castañeda might have viewed it all as Kantian. His preoccupation with «physical space-time» and «visual space-time» as he essays to formulate the «most general properties of visual space» in «Physical Objects and Consciousness» in 1977 may be interpreted as his search for synthetic a priori knowledge. The 1966 indexical argument, however, as I noted above, does not even pay lip service to Kant: its only reference to Kant takes him to endorse Hume on the self, and if knowledge of selves is neither an external sort of knowledge nor transcendent -, then it remains that it is an internal sort of knowledge.
On the one hand, the argument of 1966 for S-used `he' (or `he*') seems to boil down to a projection from a first person point of view to a third person one. While in the first person, it is noted that all references to me are interpreted by me in terms of the first person even if heard or read as third person references. From this observation it is then inferred that all third person references must be interpreted as «referring» to some `I' in the first person.
On the other hand, the argument of 1966 appears to be a purely logical argument. Firstly (i) there is the group of sentences borrowed from Geach:
«a=b and b believes that b is F.» entails «a believes that b is F.» «a=b and b believes that b is F.» does not entail «a believes that a is F.» «a=b and b believes that he himself is F.» entails «a believes that he himself is F.» Castañeda credits Geach with the discovery of the logic of the S-use of the pronoun `he'.
Substitutivity in belief contexts provides another group of sentences (ii) concerning the meaning of personal pronouns. Given that Smith is the editor of Soul, and Smith believes that he is a millionaire, substituting `Smith' or `the editor of Soul' for `he' will obtain for the whole statement different truth values on different interpretations produced by different scenarios about Smith's beliefs about himself: Does he believe that he is Smith? Does he believe that he is the editor of Soul? What is up for grabs here is the doctrine of propositions as held by Frege<9>Foot note 1_9 The applicability of the sense and reference distinction to personal pronouns also comes into question.
And, thirdly (iii) there are the Hintikka sentences: «The man who is in fact a knows that he is a.» «There is a person known to a such that a knows that such a person is a.» By removing Hintikka's restriction that the universe of discourse be limited to persons known to a, Castañeda claims to have improved Hintikka's calculus. He quantifies directly over persons in the universe of discourse, whether they are known to a or not. Having removed the restriction, Castañeda's calculus enables him to write:
(∃xa)(Ka(x = a) & ~¬Ka(x = himself),
where `himself' has a as its logical antecedent.
The domain is now populated with human persons from the outset. Quantification is not over entities known to a, as for Hintikka, and the values of the variables are not metaphysically neutral entities for Castañeda: computers, monkeys, people, angels which interest us only because of the logical properties of their linguistic productions<10>Foot note 1_10
Castañeda was after a logical restriction on the set of sentences he wished to consider. In his 1966 paper he appeals to the logical grammar of sentences with occurrences of the singular first and third person pronouns and formulates four laws, claiming they provide «an exhaustive discussion of, and a rigorous treatment of the logic of, the S-used third-person pronoun»<11>Foot note 1_11 The argument relies on a fork for the meaning of personal pronouns. Its first prong is the replaceability of a personal pronoun by a name or description<12>Foot note 1_12 The second is its replaceability by a demonstrative. Castañeda discusses the fork in detail as he goes through the seven usages of the personal pronouns enumerated, in Castañeda style, from «A» to «G». In conclusion `he*' is distinguished from A to G uses in being baptised as the use of self-consciousness or the S-use.
Castañeda could not choose the sentences to be studied for their logical properties by assessing their meanings. If he did that, then have «I am a composite of a self and a body: I am a human person!», while there is considerable philosophical opposition insisting «No, you are just a very complex body, for all that is known.» Castañeda had to leave out the act of self reference accomplished in a simple sentence like «I am Napoleon.» or «I am a monkey.» These sentences also contain pronouns; why exclude them? Apparently because, granted that Castañeda was arguing for the thesis that all self-reference is reference to a self, one may still claim that one is not a self or a person and contradict his thesis by saying «I am not a person.»
In «On the Phenomeno-Logic of the I» and in «Indicators and Quasi-indicators», Castañeda argues that «I exist.» is necessarily true<13>Foot note 1_13 But «I am a person.» is not discussed. It is excluded from the 1966 discussion not by means of its necessary truth but by two devices which limit the argument to oratio obliqua statements. Castañeda's devices look deceptively like purely syntactical constraints.
His first device is to take an equalitarian approach to «cognitive» verbs and prefixes. The terminology of Latin grammar is implemented by new Castañeda definitions for cognitive verbs and cognitive prefixes.<14>Foot note 1_14 The first allows `to say' to be a cognitive verb. It defines assertive and quasi-assertive verbs to be cognitive along with verbs which express cognitive acts, attitudes or dispositions. The second allows assertive or quasi-assertive verbs to form cognitive prefixes and such cognitive prefixes to function in the main clause for a sentence in oratio obliqua.
Castañeda introduces in addition «an epistemological priority» thesis in . His cognitive verb and prefix definitions permit treating a speech act as a mental act. The device of the cognitive prefix restriction, strengthened by the epistemological priority device limits the set of sentences Castañeda is prepared to consider to sentences all of which are prefixed with some token of the cognitive prefix «to say». All such oratio obliqua sentences in the first person imply no more than that there is a «sayer» or a «speaker».
The oratio obliqua restriction, armed with the cognitive prefix definition and the epistemological priority thesis, successfully circumvents the trouble of addressing sentences like «I am not a person.» and «I am an evolved animal.» which are not evidently contradictory. Allowing such sentences to stay within the set to be explored would be an invitation to an empirical investigation, not a logical discussion, and limiting the set of sentences to be studied thus by the grammatical category of oratio obliqua with the two devices neatly encompasses the Geach group of sentences (i) and two other groups of sentences bearing personal pronouns, (ii) and (iii).
The preliminary doubts which lead to the consideration that the 1966 argument was probably invalid are further entrenched by the persistent confusion of psychological matters with matters of logical analysability. On the one hand, the argument sets out to be a logical study of statements containing tokens of personal pronouns, but, on the other hand, it is a study of knowledge of selves or persons. The logical aspect is made more prominent:
My major contentions are: (a) that the S-uses of `he' are quite different from the other uses of the third-person pronoun; (b) that the S-uses of `he' constitute the employment of a unique logical category, which is not analyzable in terms of any other type of referring mechanism»<15>Foot note 1_15
On the one hand it argues that there is a use of personal pronouns which is irreplaceable by demonstratives or definite or indefinite descriptions, but, on the other hand, it interjects that it is replaceable by the I». Psychological matters play an important role in the claim that S-use has «purely demonstrative reference»:
Thus, we conclude that the pronoun `he*' is never replaceable by a name or a description not containing tokens of `he*'. This suggests that `he*' is a purely referential word.<16>Foot note 1_16
In sum, the S-uses of `he' or `he himself', that is, the uses of the pronoun `he*' can not be analyzed in terms of the demonstrative reference of the strictly third-person pronoun `he'. The only demonstrative reference of `he*' is bound up with that pertaining to the first-person pronoun `I'.<17>Foot note 1_17
Castañeda, rejecting on the one hand replaceability by names, demonstratives and descriptions, nevertheless is advocating that `he himself' must have a demonstrative reference «bound up» with the first person `I', a «pure reference».
Even the illustrations given in the first introductory paragraph of the 1966 article are suggestive of the ongoing confusion: «We say, e.g., `He believes (knows, says, argues, claims) that he (himself) is healthy (rich, tall, heavy, Napoleon, a victim)'». If a mentally unhealthy man announces that he himself is Napoleon or that he is a victim, is he to be taken seriously as Napoleon or as a victim? Castañeda continues: «This use of `he' (to be called the S-use of `he') as a pointer to the object of someone's self-knowledge [,] self-belief, self-conjecture, is the main topic of this study».
Castañeda was not just using the predicate calculus of first order logic to re-write sentences containing personal pronouns. He is after a pronoun which is «ineliminable» for a person:
Privatus cannot remember, or merely consider later on, that he* is , unless he remembers, or merely considers, what he would formulate by saying «I am» or «Privatus is and I am Privatus.» At least the statements of identity «I am Privatus» or «I am the one who» must include an ineliminable use of `I' for Privatus.<18>Foot note 1_18
«Ineliminability for the person» is just the thesis of «epistemological priority» renamed. A most objectionable notion in this argument is «eliminability». Eliminability simpliciter is the notion that an S-use of `he' is bound up with an S-use of `I': that they are correlatives which are eliminable into one another in terms of their meanings. The notion appears again later in John Perry's 1979 paper<19>Foot note 1_19
Eliminability is roughly implication, entailment, analysis or translation<20>Foot note 1_20 and, for Castañeda, the following obtain: Strict eliminability implies eliminability simpliciter, but its converse does not hold<21>Foot note 1_21 I call these «* theses» or just «*». They are crucial for Castañeda's discussion of `he*'.
Thus, Castañeda has divided the notion of eliminability into two sorts. Strict eliminability consists in being eliminable by something other than a token of an S-use of `he', or, when appropriate, other than a use of e I». Eliminability simpliciter of a token of a personal pronoun is its analysis into its correlate<22>Foot note 1_22 It is Castañeda's view that the S use of `he' is the correlate of a use of `I'. He claims that «the only demonstrative reference» of an S-use of `he' is «bound up with that pertaining to the first-person pronoun `I'»<23>Foot note 1_23
Paraphrasing the four laws of S-use in , they read as:
(a) If `I' is ineliminable for the person it refers to in oratio obliqua, then it can be correlated with another person's ineliminable use of an S-use of `he'.
(b) Every sentence which contains a token of S-use of `he' and which is not in oratio obliqua is an incomplete sentence or clause.
(c) From a statement of the form «X knows that p» we can not infer the corresponding statement that p, if p is expressible in sentences containing an S-use of `he'.
(d) A token of an S-use of `he' is not strictly ineliminable in any case other than its subordination to a proximate or approximate antecedent of the token occurring in the main clause of a sentence in oratio obliqua.
I call (a) and (d) «the laws of eliminability simpliciter» or «the access laws» (following John Perry's use of «access» in his 1979 paper). (a) says that somehow, i.e., in terms of pure demonstrative reference, `I' and `he' may concur. (d) says that if `he' occurs in the subordinate clause (with one or more prefixes all having the same antecedent) of an oratio obliqua sentence, then it is strictly ineliminable. But note that by * strict ineliminability may involve eliminability simpliciter. The implication is not annulled in that direction. There are, not counting «ineliminability for the person» because that turns out to be the epistemological priority thesis, (at least) four items involving eliminability: eliminability simpliciter, ineliminability simpliciter, strict eliminability and strict ineliminability.
(b) says, if an S-use of `he' occurs in the subordinate clause of a sentence (with one or more prefixes all having the same antecedent), then it is not eliminable even simpliciter because it is incomplete in a very significant way. It is ineliminable into an S-use of `I'. (b) and (c) together stress that an S-use of the third person singular pronoun in a subordinate clause can not be disentangled from its antecedent. (b) and (c) constitute the laws of ineliminability, since, by *, ineliminability simpliciter implies strict ineliminability. Strict eliminability and eliminability simpliciter do not constitute disjoint sets.
Castañeda's third law (c) captures the importance of the cognitive verb «to know» and his preoccupation with knowing the nature of the self in psychological terms; this is not merely a logical inquiry. It now emerges that «to know» is not on a par with «to say», in spite of the cognitive verb and cognitive prefix stipulations which seem to allow replacing all cognitive verbs with the weakest one of saying.
There are two explanations for (c). On the one hand, psychologically speaking, it is not communally known how each person knows himself, or, on the other hand, the personal pronoun in a dependent clause of a propositional attitude statement expressing self-knowledge can not be replaced by an expression belonging to any other category because it is impossible that there is such a replacement exclusively for logical reasons. However, the former should not be the reason for the latter.
In each case, supplying an appropriate correlate as in the first instance, the sentences below, or sentences resulting from substitutions, all contain personal pronouns:
(1) I ___.
(1') He ___.
(2) I say that I ___.
(3) I think that I ___.
(4) I believe/perceive/know/feel/entertain/cognise that I ___.
(5) I dream that I am back in Spain.
(6) I know that I am in pain.
(7) I know that I am back in Spain.
(b) and (c) prohibit passing from (6') or (7') to (1'). (a) permits passing from (4) to (4'). (d) permits passing from (4') to (4). Sentences in the form of (6') or (7') are entailed by and entail sentences in the form of (6) and (7). The restriction Castañeda falls back on is denying that a sentence in the form of (6') or (7') implies a sentence in the form of (1') but, he is not clear on the entailment of (1) from (6) or (7).
(4), (6) and (7) are similar to (2) in form and could be traded for it in accordance with the cognitive verbs and prefixes stipulations. And, furthermore, some instances of (2) probably do translate into instances of (1), in cases of naming, promising, marrying for instance, although (1) does not always entail (2). If (6) can be exchanged with its counterpart in the form of (2) and (2) with (1), then (1) entails (1') and the result clashes with laws (b) and (c) of S-use.
Although, by the epistemological priority thesis, Privatus is permitted to get (1) from (1'), Castañeda tries to bar, say, Gaskon from getting (1') from (1). In  Castañeda writes, «But the epistemological priority of the demonstrative `I' is only partial. Everybody else must replace a person's references to himself in terms of `I' (me, my, mine, myself) by references in terms of some description or name of the person in question». But, why? If from (1) there is an inference to (1'), there is a formal contradiction in S-logic and the inference clashes with laws (b) and (c).
In the shortest possible oratio obliqua sentence the possible alternatives for `I' and `he' would be as follows:
p1. I ___ that I ___.
p2. He ___ that I ___.
p3. I ___ that he ___.
p4. He ___ that he ___.
According to Castañeda in , in p2 there is not any S-use and in p3 `he' is not in S-use, but `I' is. So is the first token of `I' in p1. Not all uses of `I' in oratio obliqua are S-uses, but, presumably, all uses in oratio recta would be.
However, there is a troublesome point, that is, why the token of `I' in p2 is not in S-use. In  Castañeda announces that «The whole thing is simply that the only ineliminable tokens of `I' for the user of `I' are (I) those occurring in oratio recta and (2) those in oratio obliqua subordinated only to prefixes of the form `I E that»<24>Foot note 1_24 There would be no pride or embarrassment involved in a sentence in the form of «He thinks that I ___ !» unless what was at stake was more than one of the unessential ways of talking about the referent of `I' available to the referent of `he'<25>Foot note 1_25 It could be like finding out that sugar was spilling from your shopping cart, to use Perry's example. The sugar spilling test (or the burning trousers test) qualifies p2 just as well and raises the trustworthiness of asking «What would you do if it were you?» as a test for indexicality.
Secondly, in  Castañeda claims that the pronoun in «Privatus is and I am Privatus.» is an «implicit `I'»:
In order to analyze in detail the connection between a use of `he*' and an implicit use of `I', we need some grasp of the logic of `I'. This does not mean, of course, that whenever, e.g., Privatus hears «Privatus is ...» he is to perform a physically, or psychologically, distinguishable act of translation: «That is, I am...» The point is a logical one: If he only entertains or thinks the statements, without actually making any assertion, we shall speak of his making an implicit use of `I'<26>Foot note 1_26
Privatus knows an implicit logical language. The task is logical; neither Cartesian nor Kantian.
There are doctrinal shifts on the logic of S-use from 1966 to 1969 both about the nature of p2 above<27>Foot note 1_27 and about the modalities of statements and propositions with S-used pronouns. In the context of modalities it is relevant to bring up Castañeda's evaluation of a view defended by Carl Ginet. Castañeda's response is to reject it and to criticise it because «this analysis of `he*' in terms of `I' is at bottom circular»<28>Foot note 1_28 Castañeda complains that Ginet does not make clear the proposition a person believes when he refers to himself; sentences in the form of (1) do not express propositions. Is the answer that the S-use of a pronoun is always subordinate in accord with laws (b) and (c)? Yes, this seems to be Castañeda's answer, but it does not resolve the present inconsistency with the epistemological priority thesis according to which Castañeda depicts Privatus doing a logical translation. If Privatus' implicit logical statement in the form of (1) was explicitly stated, then it was not implicit. But, if it was implicit, then Castañeda, and only Castañeda, knows both the form of the sentence into which Privatus translates things about himself, and that Privatus' translation expresses a complete proposition. Therefore, Castañeda's account is also somewhat circular<29>Foot note 1_29
Castañeda must opt for the first horn of the dilemma, avoid the second one, and go against his own remarks against Ginet's analysis:
There is also the fact that «X believes that He* is H» does not entail that there are any sentences or that «I am H» is a sentence in some language, or that `I' is a word. But Ginet's analysans does require that «I am H» be a sentence and `I' be a word in some language<30>Foot note 1_30
Castañeda's progress on this problem becomes explicit in the 1969 paper in which he argues that «The fact that the first-person pronoun has always largest scope has as its immediate consequence that certain propositions cannot be asserted by anyone<31>Foot note 1_31, in comparison to the 1967 paper in which he declares that «a person's statements of the form `I am not-a-self' are contingent»<32>Foot note 1_32
C.J.F. Williams follows Castañeda in inferring (1) from (2): «The use of `I' indicates that the person who utters it is the very same person as the subject of what is said»<33>Foot note 1_33 He stresses that this inference is not the converse one of deriving (2) from (1): «When Rosie says `I am so-and-so' she does not say or imply that she says of herself that she is so-and so. She says nothing at all about saying<34>Foot note 1_34; but, one of deriving a meaningful use of `I' from an act of saying: `A person's meaningful use of `I' is a sufficient condition, but not a necessary condition, for her having said something about herself»<35>Foot note 1_35
Williams argues that «the concept of personal identity is not wholly an empirical concept<36>Foot note 1_36, but he disagrees with Castañeda, in «Myself,» about the entailment relation of sentences falling into group (ii):
(3') The editor of Soul thinks that he is a rich man.
(3²) The editor of Soul thinks that the editor of Soul is a rich man.
By the inferential relations claimed by Castañeda and discussed above, (3') is not eliminable for the person of the editor of Soul and it is eliminable simpliciter into `I'. In short, (3') entails its substitution instance of (3). For Castañeda, again by the same inferential relations, (3²) does not entail (3). Williams holds that (3²) does not entail (3'). He rewrites (3') as «There is just one man who is editor of Soul and the editor of Soul thinks that that man is rich.» and argues that (3') as such now implies (3²).
Whether (3') entails (3²) or not is a scope distinction between primary occurrence where the entailment holds and secondary occurrence where it does not. Secondly, Williams denies that (3') entails its substitution instance of (3). Consequently, he claims that logically (3') is prior to (3) and, since (3') rewritten as primary occurrence entails (3²), (3') is prior to (3) and (3²). Strawson's epistemological asymmetry in respect to (3') and (3), he maintains, is matched by a syntactical asymmetry explaining why both forms of statements are related to a no place predicate form, possibly like «Rich!», similar to «It's raining!» or «It hurts!»
Morton's example in «Why there is no Concept of a Person» can be added to the list of cognitive verbs in (4'):
(4) He wants that he ___.
His characters Hyperrabbit and Fred are alike because they can say sentences in the form of (4') but they cannot make an inference from (4') to (4) or vice versa. The Hyperrabit, in addition, can not infer (1) from (1') or vice versa. If Fred occasionally infers (1) and (1') from each other, his Korsakoff's psychosis prevents him from making historical inferences about himself. If Fred was more intelligent, imagines Adam Morton, then he, call him «Hyperfred», would learn to infer from (4') to (4). However, Hyperfred can not derive (1) from (4). Note that Castañeda does this through his cognitive verb and cognitive prefix definitions, i.e., via (2). Hyperrabit and Hyperfred are thought experiments demonstrating that it is possible to imagine states of affairs in which inferences with personal pronouns break down. Fred's case is medical and thus real. Adam Morton points out that Fred is similar to the rabbit in his minimalised ability to conceptualise the meaning of an S-used pronoun, but yet dissimilar to her, for he is not just a thought experiment.
One of the possible choices for the meaning of the third person singular pronoun is that it is a proxy for a demonstrative. It could also behave like a relative pronoun or a variable of quantified logic and Castañeda takes that into account in uses D, C and G. For the demonstrative use there are three cases: A-use for «that man», «that woman» and so forth; B-use for `this' or `that'; and, E or body use for `this body'. A-use and B-use are discarded quickly by Castañeda on the grounds that pronouns can refer even when it is possible that the referent is not ostensively within the experience of the speaker or of the hearer.
F-use explains self-reference to take place through a concept, which is known to the referring person, but unknown to all the others. Castañeda and later Perry find this account troublesome, since the presence of a concept correlated with the sense of a pronoun or referring expression in the that-clause is shown to be impossible by (i) and (ii). The logical relations ascertained by Geach would then break down. It will not be entailed that, given a=b and a knows that he himself is F, b knows that he himself is F.
F-use according to Castañeda is de re belief for Perry: Perry thinks that de re belief may be «interesting»<37>Foot note 1_37 and Castañeda finds them «intriguing»<38>Foot note 1_38. The major problem with F-use is its conflict with the doctrine of propositions. By (ii) clearly an S-used pronoun can not be a place-holder for a description because descriptions involve concepts.
Both the E-use and the F-use are rivals for the S-use. In  Castañeda's rejection of E-use is based on common sense: «It is extremely doubtful that the Editor of Soul or Privatus or Gaskon think of a mere body as a millionaire. But even if they all did, we may suppose that in this case they all think of persons. Thus, Privatus' use of `he*' is not a proxy for `this (that) body'»<39>Foot note 1_39 According to Castañeda one knows about one's body through «kinaesthetic sensations, pains, itches, etc., in that body» and there could be moments in which all bodily sensations cease<40>Foot note 1_40 In this respect, the E-use seems similar to the uses in A and B and therefore may be eliminable for the person.
The rejection of E-use has no persuasive force against a proponent of physicalism and it is inconsistent to maintain that persons could speak an actual language or produce the actual sentences the logic of which we are studying, with Castañeda, without having their bodies. Unless thoughts are expressed, the two laws of S-use (b) and (c) can not be applied, since they pronounce a verdict on what counts as a complete thought and thus a proposition and what as an incomplete thought.
Castañeda promises a series of logical studies on the logic of S-use in , but the analysis does not establish that the S-use characterises some usages of the personal pronoun better than the F-use or the E-use. It begs the question by harbouring presuppositions about the nature of a human person. And, it is unclear, because it delineates the set of sentences to be studied for their logical properties by restrictions which are not purely logical.
Suppose as a thought experiment that «a» and «b» are the names of two different halves of brains of two different persons living in the same body after their transplantation for some medical and ethical reasons; then the first and third Geach entailment would fail to hold as well, like the second one, for situations of perceiving, believing, knowing, etc. in which a and b, halves of different brains, do not establish communication. If a is transplanted in c's body and so is b, there will be a person a+b+c and that is numerically identical with itself. But, there will be a sense in which a+c will know things which b+c will not know<41>Foot note 1_41 In Geach's sentences the referents of `a' and `b' are curious things: they have numerical identity and can entertain cognitive structures. If brain halves a and b co-operate to some degree, they would count as one person. We could call this person «a's derivative» or equally «b's derivative» and they would now be the same human person after the transplant operation, but what they know, experience, desire, believe, remember, etc., are, at least for a while, quite different. Logical structure of statements containing personal pronouns does not account for personal identity.
Braude, Stephen E.: «Commentary on 'The Social Relocation of Personal Identity'», Philosophy, Psychiatry, & Psychology, 2, 3, 1995, 205-209.
Cassam, Quassim (ed.) : Self-Knowledge, Oxford University Press.
Castañeda, H.-N. : «`He': A Study in the Logic of Self-Consciousness», Ratio, VIII, 130-157.
Castañeda, H.-N. [1967a]: «Indicators and Quasi-Indicators», American Philosophical Quarterly, 4, 85-100.
Castañeda, H.-N. : «On the Logic of Attributions of Self-Knowledge to Others», Journal of Philosophy, 65, 1968, 439-456; I wonder if it is significant that the title of this paper appears as slightly changed to be about attributions of «Self-reference» in Landini's bibliography in the Tomberlin work .
Castañeda, H.-N. [1967b]: «On the Logic of Self-Knowledge», Nous, 1, 1967b, 19-21.
Castañeda, H.-N. : «On the Phenomeno-Logic of the I» in Quassim Cassam (ed.) ; according to a footnote this paper was first published in 1969, but according to Gregory Landini's philosophical bibliography in Tomberlin's  it was published in 1968.
Hamlyn, D.W. : «Epistemology, History of», Encyclopedia of Philosophy, vol. 3, 8-38.
Hinshelwood, R.D. : «The Social Relocation of Personal Identity as Shown by Psychoanalytic Observations of Splitting, Projection and Introjection», Philosophy, Psychiatry, & Psychology, 2, 3, 1995, 185-205.
Lewis, D. : «Attitudes De Dicto and De Se», Philosophical Review, 88, 513-43.
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