[Foot Note 1_1]

In the following I shall not generally make explicit this second restriction.




[Foot Note 1_2]

Concerning Kuhn's final, restricted, conception of incommensurability see especially Kuhn [1983], [1991] and [1993].




[Foot Note 1_3]

Kuhn [1989], p. 25.




[Foot Note 1_4]

Putnam [1975a], p. 228.




[Foot Note 1_5]

Kuhn [1989], p. 26, n. 28 and [1990], p. 318, n. 25.




[Foot Note 1_6]

Putnam [1975a], p. 224.




[Foot Note 1_7]

Kuhn [1989], p. 28 and [1990], p. 311.




[Foot Note 1_8]

Kuhn [1989], pp. 26 and 29; [1990], pp. 309 and 312.




[Foot Note 1_9]

Kuhn [1989], pp. 29-30 and [1990], pp. 312-313.




[Foot Note 1_10]

Thus some authors such as M. Devitt assert that the reference of terms is multiply grounded; see Devitt/Sterelny [1987], pp. 62-63 and 71-72.




[Foot Note 1_11]

Putnam [1975b], p. 274.




[Foot Note 1_12]

Putnam [1975b], p. 275.




[Foot Note 1_13]

See Nola [1980]. Other authors, such as M. Devitt, call this doctrine «constructivism»; see Devitt [1984].




[Foot Note 1_14]

Searle [1969], p. 169.




[Foot Note 1_15]

Kuhn [1970], pp. 182 f.




[Foot Note 1_16]

See, e.g., Devitt/Sterelny [1987], Sterelny [1983], Sankey [1997] and other references given in Sankey's paper.




[Foot Note 1_17]

This remark agrees with one of Kuhns's aforementioned objections to the causal theory of reference.




[Foot Note 1_18]

Putnam [1973], p. 203; Putnam's italics.




[Foot Note 2_1]

We will not discuss here terminological problems and we will stick to these conventional translations. For a discussion about Frege's notion of Bedeutung, see e.g. (Angelelli 1982).




[Foot Note 2_2]

Our analysis will lead us to quote most of Sengupta's short paper, so that it is not necessary to read it in order to understand Sengupta's argumentation and our refutation of it.




[Foot Note 2_3]

If our supposition that the reference of a sentence is its truth value is correct, the latter must remain unchanged when a part of the sentence is replaced by an expression having the same reference. And this is in fact the case. Leibniz gives the definition: «Eadem sunt, quae sibi mutuo substitui, salva veritate'. What else but the truth value could be found, that belongs quite generally to every sentence if the reference of its components is relevant, and remains unchanged by substitutions of the kind in question ? (Max Black's translation).




[Foot Note 2_4]

This is already an interpretation of Frege, in fact an adaptation to the case where the Satzteil is itself a Satz.




[Foot Note 2_5]

We are not precise in order to include the widest range of semantics (sentential, first-order, Kripke, etc.)




[Foot Note 2_6]

We will stick to this definition, which seems to be the implicit one when someone says that modal logics or intuitionistic logic are not truth-functional. For a discussion about this question, see (Béziau 1997).




[Foot Note 2_7]

Lukasiewicz's three-valued logic, in which both (S1) and (S2) hold, was supposed to formalized the notion of possibility, but nowadays nobody considers this logic as a modal logic.




[Foot Note 2_8]

We will not discuss here the question if it is appropriate to think that A2 applied to the sentence 3. This is what Sengupta assumes and assumes that Frege assumed.




[Foot Note 2_9]

27. For more details on this question see (Béziau 1994).




[Foot Note 2_10]

Here we have the following equation: intension = comprehension = axiomatization. The axioms are the comprehensive way of giving the extension, i.e. the class of models.




[Foot Note 2_11]

However Bourbaki's description of mathematics (as it appears in Bourbaki 1950) gives a key to such a theory.




[Foot Note 2_12]

But model theory reaches great achievements through this line, showing that if we succeed to express a class of structures in a particular way, it reveals important properties of it.




[Foot Note 2_13]

In the above example, we can put instead of «Stone proved»: «Stone believed», «Stone thought», «It is necessary», «It is possible», etc, all these expressions being considered as interpretations of operators of current modal logics or similar logics (epistemic logics, provability logic, etc.). The fact that in the literature these logics are quite commonly presented as intensional logics is typically illustrated by the cover of the second volume of the Handbook of Philosophical Logic: it is said that it «surveys the most significant «intensional» extensions (sic) of predicate logic» (Gabbay 1986).




[Foot Note 3_1]

By contrast, reiteration works for attitudes expressed non-indexically. If the Chair had said, «The Provost is upset about the Dean's report,» then my reiterating his words in indirect discourse would be appropriate. The disparity is well known (Kaplan 1989, 553). The task is to explain it?




[Foot Note 3_2]

See, for example, Castañeda 1966, 1967, and 1989a, 70-76. Similar claims are made in Perry 1979 and Lewis 1983, chp. 10. Castañeda criticized familiar reductions of indexicals, say, `I', to `this person now speaking,' for imputing too much conceptual apparatus to their users, particularly, small children (1989a, 72-5). Nor are the differences in grammatical person reducible to each other, in particular, first-person indexicals are not the most basic (Castañeda 1990a, 736).




[Foot Note 3_3]

See for example, William James, Essays in Radical Empiricism, «The Experience of Activity,» note 14 (Dutton), who describes the expressions `I' `here' and `this' as «primarily nouns of position.» See the perspectival approach in Castañeda 1967 and also Forbes, 1989, p. 470, who explains the difference in sense of two tokens of `that telephone' in terms of «differing viewpoints.»




[Foot Note 3_4]

See Castañeda 1975, chapters 2 and 4, for a defense of the view that intentions are first-person practical thought contents.




[Foot Note 3_5]

Presumably the higher animals can discriminate spatial relations which we would normally express with her, there, near, beyond, etc. Morover, they seem to react appropriately to our demonstrative pointings, and their own interactions may be replete with indexical communication, e.g., the bee's dance (see Millikan 1990).




[Foot Note 3_6]

See, for example, Kaplan 1989, 505-507, 523-524.




[Foot Note 3_7]

See Millikan 1990, 727-728: «to interpret an indexical one must have prior knowledge, one must already know independently and ahead of time, what item bears the indexical's adapting relation to the indexical token. One must already konw both that this referent exists and how it is related ot the token, hence, to the interpreter.»




[Foot Note 3_8]

See Castañeda 1983, 323 and Recanati 1990, 708-709, and 1993 chp. 4-5. John Perry accounts for cognitive significance in terms of the speaker's understanding that the utterance meets the conditions that the character of the sentence establishes for its truth (1993, 246-7). This requires that the speaker has already identified the utterance and, hence, cannot explain its production. Moreover, Perry requires that a thinker not only conceive of the utterance of the sentence but also that the truth-conditions of the utterance established by the character are satisfied. It saddles the speaker with a higher-order thought about the semantics of utterances that cannot be expected of all speakers.




[Foot Note 3_9]

For these reasons, Millikan's repudiation of the essential or irreducible indexical comes to naught. She acknowledges that a person must have some inner name for oneself that bears a special relation to dispositions to act, but since one need know nothing about context in order to determine its referent then it is a Millian name whose semantics is exhausted by its referent. In section 3 I argue that the referential use of indexicals make it necessary to invoke indexical «modes of production» inseparable from the producer's perspective.




[Foot Note 3_10]

I follow Castañeda 1989a in this use of `thinking reference.' Referring terms might express an act of thinking reference, as when one thinks out loud, but one's thinking reference must be distinguished from what one intends to commuincate and from what a hearer is caused to think upon perceiving another's token. Each, in turn, is distinct from the denotation, if any, associated with a linguistic type.




[Foot Note 3_11]

Eddy Zemach has questioned whether talk of referring to oneself qua oneself is informative (1985, 194); how does the second `oneself' indicate anything different from the first? Castañeda argued that while the first is a pure reflexive, merely repeating its antecedent, the second conveys one's experiential confrontation with oneself as «a thinker presently involved in the very experience of making the referring [sic] in question» (1989a, 170). While he elaborated on this in 1990b, 127-139, he also spoke of «a primitive apprehension of the subject one calls «I,» not mediated by any identification procedure» (129), and of the I-properties expressed by first-person pronouns as «indefinable» (1989a, 76). See also my introduction to Castañeda 1998.




[Foot Note 3_12]

See note 2 on irreducibility. The subjectivity thesis was articulated in Castañeda 1981, 1989a, 1989b and 1990a. Analogous reasoning appears in Frege 1967, 25-6 with respect to first-person reference; «everyone is presented to himself in a particular and primitive way, in which he is presented to no-one else.» See also Searle 1983, 220-230; McGinn 1983, 17; and Nagel 1986, chps. 2-4. Boer and Lycan 1980 provides a contrasting view of indexical reference, as do Perry 1979 and 1983, Kaplan 1989, and Millikan 1990, but see Castañeda's responses to each of these positions in Castañeda 1984, 249-256; 1983, 313-328; 1989b; and 1990a.




[Foot Note 3_13]

Modes are not, as such, referred to, nor in need of identifying modes of presentation. This allows us to circumvent the regress argument offered in Schiffer 1990, 255. For a different account of the way in which modes of presentation or senses are employed in accounting for indexicals, see Perry 1977, 1983, the concerns raised by Wettstein 1986, and a reply in Perry 1988. For additional discussion of indexical modes of presentation see Evans 1982, chp. 6 and 1985, chp 10; Searle 1983, 220-230; Peacocke 1983, chps. 5-6; Forbes 1987, 14-25; Smith 1989, 71-79; Recanati 1990, 706-715 and 1993, chps. 4-5; and Bezuidenhout 1996. One benefit of taking indexical modes as internal to propositional content is given in my 1993 where I resolve the problems raised by Richard's context-hopping «Phone-Booth» argument.




[Foot Note 3_14]

See, for example, the Guise-theoretical approach advanced by Castañeda 1989a, chps. 13-14.




[Foot Note 3_15]

Castañeda voiced this view in speaking of first-person self-reference as being reference to oneself qua oneself: «...the locution `oneself (like its substituends) in the contexts `ONE refers to ONEself as oneself' depicts, is a proxy for, a first-person reference attributed to one (or the entity denoted by its substituends). Here `oneself' is what I have called a quasi-indicator, more precisely, a quasi-indexical variable» (Castañeda 1989c, 38).




[Foot Note 3_16]

The terminology of `external occurrence' and `internal occurrence' is employed by Castañeda in 1980, 780-783 and 1989a, chp. 5, and also by Clark 1980, and Forbes 1987. The contrast between external (de re) and internal (de dicto) properly belongs to occurrences of individual terms and noun phrases, an interpretation upheld in Zalta 1988, 171; Castañeda 1989a, 93-97; Richard 1990, 128; and Kapitan 1993, 1994.




[Foot Note 4_1]

Lorenzo Peña cites and approves Unger's and Heller's claim according to which all terms, with the exception of physical predicates (and Peña disaproves even that exception), bring about problems of borderline application and are sorites susceptible (Peña, 1996; 123). Peña explicitly also claims that this fuzziness must be not merely semantical, but ontological, because our language reflects the way the world is. M.Sainsbury (1995) has brought out various problems of intelligibility - and of plausibility - that this last view raises (M. Dummet, in a famous sentence, asserted: «the notion that things might actually be vague, as well as being vaguely described, is not properly intelligible» (Dummett, 1975; in Kefee, 1996; p. 111)).




[Foot Note 4_2]

Kit Fine termed «extensionally vague» the predicate which has actual cases of borderline application, and «intensionally vague» the predicate which has possible but non-actual cases of borderline application («Vagueness, Truth and Logic», in Kefee, 1987; p. 120). My intention here is to claim that only the first case is crucial and properly relevant for vagueness.




[Foot Note 4_3]

Crispin Wright has objected to this move that to try to make precise terms that are in fact vague is contrary to semantics and would prevent its use (Wright, 1976; in Evans & McDowell, 1977; p. 230). I think the second is partially true, but the first seems a matter of priorities: it might be contrary to semantics but in accordance with logic. But, of course, Wright chooses the witggensteinian alternative: if some use of language is contrary to logic,so much the worse for logic.




[Foot Note 4_4]

This line of argument has been developed in Williamson 1990, 114-15.




[Foot Note 4_5]

I mainly aim Lorenzo Peña, 1996 (in fact this paper has prompted the present one). This sort of approach has also been defended in K. Machina, 1976. Machina's option is to gradualize the force of the inference in a sorites argument, so that the more numerous the premises, the less the truth transmited from the premises to the conclusion. For that reason, sorites arguments can begin with premises of value 1 and end up with conclusions of value 0.




[Foot Note 4_6]

This move is made by supervaluationism, maybe the approach which has gained maximal recognition to cope with vagueness in spite of all its difficulties. Cf. a recent revision and highly technical statement in McGee & McLaughlin, 1995.




[Foot Note 4_7]

For that reason, to talk of fuzzy cumules with two sharp boundaries, the one of the beginning of fuzziness, and the one of its end (Peña, 1996; p. 134) is problematic. As T. Williamson, among others, has insisted on, higer order vagueness invalidates these kinds of approach (cf. Williamson, 1994, chaps. 4-5 and 7, and his 1999). M. Tye claims: «I do not accept that «is true» is extensionally vague. And the same goes mutatis mutandis for «is false» and «is indefinite». Of course, in taking this view I am not commiting myself to the position that these predicates are precise. Indeed, it is crucial to my account that they not be classified as precise... they are vaguely vague: there simply is no determinate fact of the matter about whether the properties they express have or could have any borderline instances» (1994, in Kefee, 1996; p. 290). But you could replace just the last sentence by «there is no way to know the determinate fact of the matter...» or even «there is no way to know whether there is a determinate fact of the matter about...».




[Foot Note 4_8]

Among them Crispin Wright in his 1992.




[Foot Note 4_9]

I am not competent to discuss the logical difficulties of this approach. But they do exist (cf. Morgan & Pelletier, 1977).




[Foot Note 4_10]

It is just this supposition which is problematic. As Mark Sainsbury has pointed out (1990, in Kefee 1996; p. 254-6) degree approaches and fuzzy logic seem useless: «one cannot do justice to the phenomena of vagueness, in particular to the phenomena of «higher order vagueness» simply by icreasing the number of sets of individuals associated with a predicate... a predicate which effects such a threefold partition is not vague... This same point is what scuppers the set-theoretic descriptions of vague languages offered by fuzzy logicians and supervaluations theorists... Yet a fuzzy set is a genuine set, a completely sharp object... the fuzzy logician too will be commited to a threefold partition: the sentences which are true to degree 1, those true to degree 0, and the remainder... But we do not know, cannot know, and do not need to know these supposed boundaries to use language correctly».




[Foot Note 4_11]

K. Machina (1972, 27) makes this criticism, claiming that there always are more than one possible -and plausible- translation of observational predicates into scientifical ones, and that any decission in favor of just one precisification would be artificial. I agree with the artificial character of the decission, but you can have good grounds for stipulating one wave lengt instead of another as the corresponding to, for instance, green.




[Foot Note 4_12]

Wright, 1976, 232.




[Foot Note 4_13]

This proposal is made by Crispin Wright in his 1987a (in Kefee, 1996; p. 222). He adds: «We have therefore to acknowledge, surprising as it may seem, that a sorites series of indistinguishable color patches can contain a last patch which is definitely green [red]... It may be difficult or impossible to identify such a patch in a particular case... it should be noted that there is, a priori, no reason to suppose that «the last definitely red patch» would turn out to have a stable reference; if it did not, that would disclose an element of context-relativity in the concept of green which we normally do not suspect» (loc. cit).




[Foot Note 4_14]

This point is made by M. Tye in his 1994 (in Kefee, 1996; p. 289.)




[Foot Note 4_15]

This has been argued by W. Hart in his 1991, and to my mind it has been surprisingly neglected.




[Foot Note 4_16]

Being sensitive to this kind of problems, D. Eddington (1996) has recently and interestingly proposed to take the gradualist approach as merely instrumental, and to develop it's logic in terms of probability calculus, rather than in terms of some or other deviant logic. But she is pretty aware that you cannot replace vagueness with perfect precission.




[Foot Note 4_17]

This has been remarked by Williamson (1994; p. 127).




[Foot Note 4_18]

This line of argument stems from a lecture of Lorenzo Peña slighltly prior to his 1996.




[Foot Note 4_19]

Sainsbury, (1990, in Kefee, 196; p. 259). He has claimed -rightly, to my mind- that the notion of «fuzzy boundary» is incoherent, because any limit or boundary splits logical space into two. According to that, «fuzzy boundary» actually means «no boundary at all». And that is the point: a concept with no boundaries pervades all logical space, and this seems to be not so much incoherent, as absurd. Maybe you could say of all physical objects that are more or less green, even if very very slightly green; but how could you sensibly say that also triangles, feelings, God and justice have some of greeness?




[Foot Note 5_1]

An example of such a pseudo-problem is provided by the traditional controversy between nominalists and realists. According to Reichenbach, nominalists and realists disagree with respect to the existence of abstracta: the former deny, and the latter assert that abstracta exist (Reichenbach 1938, 93-98). The debate in question was also seen by Carnap as a pseudo-problem, basically for the same reasons. In Carnap's view, both factions battle about a so-called `external existential statement', this is a statement in which it is claimed that certain entities exist as such rather than exist `internally' according to the rules of a certain linguistic framework. An external existential statement is a pseudo-statement; it embodies a practical decision rather than a theoretical claim (Carnap 1950, 1963).




[Foot Note 5_2]

As was pointed out to me by Huw Price in private communication, the distinction between abstracta and illata resembles a distinction that is common in functionalist literature, viz. that between role states and realiser states. It seems to me that role/realiser states are not entirely the same as abstracta/illata, although there are indeed similarities. The matter needs to be examined more closely, and I will not elaborate on it here.




[Foot Note 5_3]

On the dual nature of beliefs and desires, see also: Peijnenburg and Hünneman, to appear.




[Foot Note 5_4]

Reichenbach's words here might remind us of what God said to the Mortal in a paper by Raymond Smullyan that became justly renowned:

You can no more see me than you can see your own thoughts. You can see an apple, but the event of your seeing an apple is itself not seeable. And I am far more like the seeing of an apple than the apple itself (Smullyan 1977, 330).

The idea sounds worth exploring: God as an immediate thing, triggered by objective things around us such as apples. About His qualities and existence, however, we do not know anything. Those we have to infer, using the laws of probability and perhaps taking our inspiration from some mediaeval philosophers who attempted to prove His existence.




[Foot Note 5_5]

Recently, Dennett has called himself a «mild realist» with respect to beliefs and desires (Dennett 1991b). He places mild realism somewhere between the «industrial-strength Realism» (with a capital `R') of Fodor and the «milder-than-mild irrealism» of Rorty (Dennett 1991b, 30). Without going into the question of what mild realism actually is (it has to do with the reality of patterns), I only wish to stress here that Dennett applies it to all beliefs and desires alike. By contrast, I think it is more fruitful to claim that some beliefs or desires are real in the sense of Fodor's industrial-strength Realism whereas others are closer to Rorty's irrealism.




[Foot Note 6_1]

«On a version of one of Zeno's paradoxes», Analysis 59 (1999), pp. 1-2.




[Foot Note 6_2]

Infinity: An Essay in Metaphysics (Oxford: Clarendon Press, 1964), pp. 236-39, 254-61, 271-79.




[Foot Note 6_3]

To generate the paradox we need to assume both the reality of motion and the continuity of space. If to solve the paradox we need to surrender one or the other of those assumptions, presumably we will prefer to surrender the latter.




[Foot Note 6_4]

Each of the «acts» consists in (a) determining whether a certain man does or doesn't reach a certain point in space and (b) depending upon that determination, either erecting or refraining from erecting a barrier at a certain other point in space. Priest suggests that the acts might all be performed by a single god rather than the infinitude of gods supposed by Benardete. But there are strong reasons for doubting the logical possibility of an agent's performing an infinitude of distinct acts in a finite time. (See B. Burke, `The Impossibility of Superfeats', The Southern Journal of Philosophy, forthcoming'.) It is undesirable, and unnecessary, to make the new paradox dependent upon that possibility.




[Foot Note 6_5]

Benardete, op. cit., pp. 237-38.




[Foot Note 6_6]

Ibid., p. 258.




[Foot Note 6_7]

Ibid., p. 261.




[Foot Note 6_8]

There is no apparent basis for objecting to (1) solely because of the infinity of barriers it postulates. If there is an objection to «actual infinities», the objection would apply not just to the barriers but to the actual infinity of points and line segments contained within any continuous spatial interval. In general, it's hard to imagine why the infinity of barriers might be logically objectionable if the requisite infinity of spaces is available to accommodate them. As Benardete notes on p. 255, the barriers might have sprung into being spontaneously and simultaneously, or might have been created one per year over the course of an infinite past, or might simply have existed from all eternity.




[Foot Note 7_1]

The reader may find an excellent discussion of copyright-related issues in a FAQ paper (available for anonymous FTP from rtfm.mit.edu [18.70.0.209] /pub/usenet/news.answers/law/Copyright-FAQ). The paper is entitled «Frequently Asked Questions about Copyright (V. 1.1.3)», 1994, by Terry Carroll. We have borrowed a number of considerations from that helpful document.