[Foot Note 1_1]

We have tried here to define the main terminology in an objective way, independently of any philosophical taste. In the literature, the terminology varies in function of philosophical doctrines, for example some people consider that definite descriptions are proper names, that reference is different from denotation, that it is better to call «sense» what we have called meaning, etc.




[Foot Note 1_2]

(Haack 1978, p.56) says that «Some formulations of the predicate calculus employ singular terms (`a', `b' ... etc.) as well as variables. (...) Singular terms are usually thought of as the formal analogues of proper names in natural languages».

Let us note that what Haack here calls singular terms are usually called `constants' in a book of mathematical logic and that the terminology `singular terms' is rarely used in such a book...

It is not obvious, as we assume here as Haack does, that constants of a formal language are counterparts of a proper names of natural language (see the quotation of A.Church below).




[Foot Note 1_3]

«Possible worlds» has a relatively precise meaning in Kripke semantics for modal logic; however in the philosophy of language this expression is used in a rather general and informal way (by Kripke himself), which seems coherent with the present interpretation.




[Foot Note 1_4]

(Church, 1956, p.9) says «We adopt the mathematical usage according to which a proper name of a number is called a constant, and in connection with formalized language we extend this usage by removing the restriction to numbers, so that the term constant becomes synonymous with proper name having a denotation.

However, the term constant will often be applied also in the construction of uninterpreted calculi - logistic systems in the sense of #7 - some of the symbols or expressions being distinguished as constants just in order to treat them differently from others in giving the rules of the calculus. Ordinary the symbols or expressions thus distinguished as constants will in fact become proper names (with denotation) in at least one of the possible interpretations of the calculus.»

Thus according to Church, «0» is not a proper name, but only something like «n(0)» is. If we adopt strictly this point of view, «n(0)» is trivially a rigid designator. To be coherent, Church should consider «n(s0)» as a definite description and not «s0». (In fact Church considers definite descriptions proper names; see Church 1956, p.3).




[Foot Note 1_5]

In the case of a first-order theory, which is complete but not categorical, the differences cannot be expressed by first-order properties.




[Foot Note 1_6]

I once heared a famous philosopher of language, explaining Kripke's theory, saying that a typical example of a rigid designator is a mathematical expression like «û2». First notice that «û2» is a definite description rather than a proper name. Second, the reference of «û2» can vary even when it is used by a mathematician who is not a logician and believes that he is working with categorical theories only.




[Foot Note 1_7]

There are various possible counterparts of formal (i.e. axiomatic) theories in natural language; a theory can be a knowledge database, information common to a community of people, etc.




[Foot Note 1_8]

In a language without the description operator terms can be eliminated by simulating individual constants with symbols of monadic predicates, and symbols of functions with symbols of relations. As regards the description operator, Russell himself showed how it can be eliminated.




[Foot Note 1_9]

In principle it seems that there are no difficulties to turn pseudo-formal set theory into formal set theory. But a lot of things have to be checked. The operator of description is a vbto (variable binding term-forming operator) and one has to check that the usual syntax and semantics of first-order logic and the correlative results can be extended to vbtos. Such work has been carried out by Corcoran, Herring, Hatcher and da Costa. References can be found in (da Costa/Mortensen, 1983) which is a kind of survey.




[Foot Note 2_1]

M. G. Yoes, «When Is If,» Sorites 1(April 1995): 96-99.




[Foot Note 2_2]

Joseph S. Fulda, «Material Implication Revisited,» American Mathematical Monthly 96 (March 1989): 247-250.




[Foot Note 2_3]

Joseph S. Fulda, «Denied Conditionals Are Not Negated Conditionals,» Sorites 2 (July 1995): 44-45; Joseph S. Fulda, «Counterfactuals Revisited,» Sorites 5 (May 1996): 35-38.




[Foot Note 3_1]

Laudan thus considers relativism as not desirable and hence he considers rationality as valuable. This is important to remember because his meta-methodology intends to be a naturalistic one. The question is whether the normative recommendations made by Laudan's theory are provided only by a descriptive or empirical study of the history of science, or whether the normative judgments made by Laudan's theory are instead the result of tacit evaluations.




[Foot Note 3_2]

«What does give comfort to relativism is a failure to address the question: `How are methodological rules or standards justified?'» (Laudan 1989, p. 370)




[Foot Note 3_3]

Cf., Laudan (1989), pp. 370-1




[Foot Note 3_4]

Cf., Laudan, 1996, p. 143




[Foot Note 3_5]

Such as Chapter 8 of Laudan's 1996.




[Foot Note 3_6]

Since «unreasonableness» and «irrationality» are terms of abuse or opprobrium, there is an implicit recommendation in favor of being rational, also compare note # 1.




[Foot Note 3_7]

Cf., Laudan 1996, p. 78




[Foot Note 3_8]

Numerous scientists have highly valued and searched, at least prima facie, explicative truth. Garré of Basel, a disciple of R. Koch, for example, risked his health and life by inoculating himself with staphylococci, he did this to find out whether the hypothesis of a bacterial cause for anthrax was true.




[Foot Note 3_9]

If Laudan answers by proposing a selection of past scientific achievements as exemplary work, the norms would be there already in his selection. In other words, `exemplary' is a normative term, and if one were to try to infer the standards of exemplariness from a selection of past scientific work, one would only obtain the standards that one put in, since to select the exemplary we must first assume some standards of exemplariness.




[Foot Note 3_10]

Cf., Laudan 1996, pp. 148-9.




[Foot Note 3_11]

Cf., note # 2 above.




[Foot Note 3_12]

Many of the following arguments were inspired by various helpful conversations I held on these topics with John Worrall.




[Foot Note 3_13]

This aim is in the American Declaration of Independence.




[Foot Note 3_14]

Doubts arise, even in this case, when we recall that Calvinists -- as declared in the Synod of Dort -- aspire to salvation, even though it might be impossible for them both to attain it and to promote it. This because they could be one of the unfortunates unknowingly predestined for damnation., and this regardless of their faith, love, or merit, or lack thereof. Calvinists live then in a permanent state of doubt and apprehension just hoping for the best. A similar situation may arise, when one applies inductive methods, methods that one cannot justify to one's satisfaction -- say, without circularity -- in such a case, one uses induction without being commited to it. One proceeds hoping for the best and fully aware that one lives precariously.




[Foot Note 3_15]

Cf., J. Elster, Chap. 1.




[Foot Note 3_16]

«the Serbs and their allies suffered a defeat that has become hallowed in several great heroic ballads. (...) They have become lenses through which subsequent creators of national mythology have come to see their past, endow it with deep metaphysical import, and imagine the attributes of the nation in essentially spiritual terms. Kosovo was turned (especially during the 19th century) into the Jerusalem of the Serbs.» History of Serbia, Encyclopaedia Britannica CD 99 Multimedia.




[Foot Note 3_17]

29. Cf., Plato's Crito.




[Foot Note 3_18]

Oscar Wilde, at the Cadogan Hotel in 1895, after his failed action against Lord Queensberry, rejected -- as Socrates had -- the achievable option of flight to await inevitable arrest. Wilde may appear in this act, to be self-destructive and irrational, however, in another reading of this event, Wilde's act shows him to have been determined not to yield to the pressures of a hypocritical society. Wilde stayed in England, and did forced labor, because at the Cadogan Hotel, Wilde decided to search an ideal, the ideal of self and social consistency, the ideal of self and social authenticity. Wilde stayed because he wanted to fight hypocrisy, and he was ready to suffer forced labour for the sake of this goal. A goal -- that given what we know of human nature -- is an impossible goal, and it is a goal that can only be approched.




[Foot Note 3_19]

Francis' goal may also be irrational for Laudan, because it is also possibly both semantically vague, and epistemically utopian.




[Foot Note 3_20]

It could still be argued that the numerous people that have admired idealist conduct, have been the victims of self-deception, that they have really admired something else, but what could this something else be? Besides, the hypothesis of self-deception would require of a colosal amount of self-deception, or false consciousness, which appears as an implausible thesis.




[Foot Note 3_21]

Or at least people widely believed to have been idealists.




[Foot Note 3_22]

This psychological fact may be exemplified by a phenomenon such as that of the idealized and valued Medieval `courtly love'. This love was a longing that lasted as long as it was not physically satisfied, and therefore the lovers avoided consummating their love.




[Foot Note 3_23]

For Rawls (cf., Section 67) self respect is one of the primary goods, that is, one of the goods necessary for the framing and successful execution of a rational plan of life.




[Foot Note 3_24]

As shown by the fact that Simeon was visited at his column by many pilgrims, by the fact that Simeon became a role model for many who were still emulating him as late as the XIXth century, and by the fact that his advice was even sought by the Imperial Court.




[Foot Note 3_25]

Rawls says that, finding our person and deeds appreciated and confirmed by others who are likewise esteemed and their association enjoyed, helps us to gain self-esteem.




[Foot Note 3_26]

Cf., Diotima's discourse in Plato's Symposium.




[Foot Note 3_27]

Laudan has criticized Popper for his conventionalism about scientific aims and methods, and Laudan has criticized Lakatos for his intuitionism. Cf., Laudan (1996), pp., 15 -- 16, and Laudan (1986) respectively.




[Foot Note 3_28]

A similar argument has been developed by J. Worrall, 1996, p. 8




[Foot Note 3_29]

It is a `demonstrably utopian' aim, because if we understand proper justification (as Laudan does) as an argument in favor of a statement, method, or goal, then logic tells us that the search of justification must lead to an infinite regress, circularity or dogmatism, this because every argument has premises.




[Foot Note 3_30]

Laudan, 1990b, p. 53.




[Foot Note 3_31]

Or as John Worrall has argued: `relativism as Laudan defines it, is inevitable' (Worrall, 1989, p. 381.)




[Foot Note 3_32]

Cf., chap. XIII of Kuhn's The Essential Tension.




[Foot Note 3_33]

This example of incompatible aims was argued at length by I. Berlin, cf., p. 12.




[Foot Note 3_34]

The weighing of ends is also needed to fine tune the means chosen to approach or attain some aims, since the means are often underdetermined by the desired end states. For example, if the only aim of a community were egalitarianism the way it was approached (say through revolutionary terror or through gradualist reform) would be irrelevant. Other weighted aims are needed, such as human rights and democratic freedoms, to help narrow the underdetermination of chosen means. If not one coud end with results as disimilar as Maoist China and the Japan of the 60's, two communities which were allegedly quite egalitarian.




[Foot Note 3_35]

Cf., chap. XIII of Kuhn's The Essential Tension.




[Foot Note 3_36]

Cf., note # 30.




[Foot Note 3_37]

Cf., N. Rescher, The Strife of Systems, chapters 7 & 8.




[Foot Note 3_38]

To narrow the range of possible rational life plans Rawls introduces the `Aristotelian Principle', a principle that supposedly states a natural fact, and that says: other things equal, human beings enjoy the exercise of their realized capacities (their innate or trained abilities), and this enjoyment increases the more the capacity is realized, or the greater its complexity. (Rawls, p. 426.)




[Foot Note 3_39]

Since some axiological inconsistencies can be only pragmatic, it is not always clear whether some collection of ideals is mutually inconsistent.




[Foot Note 4_1]

An entity persists from t to t' if and only if it exists at t and t'.




[Foot Note 4_2]

Four-dimensional objects are perduring objects, not enduring ones (Johnston's terminology, see Johnston 1984).




[Foot Note 4_3]

I leave aside another alternative: to impose temporal restrictions on Leibniz's Law. As far as I can see, this is the way chosen by Myro (1986), who aims to hold that Leibniz's Law is valid exclusively for cases of synchronic identity. To my mind there is no rationale to maintain this easy way out of the puzzle that the problem of change poses: friends of continuants are distinguished precisely by their insistence on the universal application of the Law at all costs (I am thinking of the dispute related to constitution and identity, where they take the Law as demanding modal indiscernibility too), so how can they now justify a restricted reading of it?




[Foot Note 4_4]

The first theory is defended by Quinton (1973), the second by Haslanger (1989) and Johnston (1993) and the third by Merricks (1994). An excellent critical introduction to all of these theories can be found in chapter 6 of Denkel (1996).




[Foot Note 4_5]

Where `t/φ' means: the property φ as it occurs at time t.




[Foot Note 4_6]

This appears to be the «solution» offered by Coburn (1976, 174).




[Foot Note 4_7]

It is worth noting here that we may talk of `intrinsic relations'and `extrinsic relations' in such a way that the intrinsic feature is not something that belongs exclusively to the notion of property. A relationship is intrinsic when it «supervenes on the intrinsic natures of its relata» (Lewis, 1986, 62).




[Foot Note 4_8]

The reason why I will not deal with the second modification of the relative property theory is because it is in the long term subject to the same criticisms as the original theory. Those who maintain that objects are (partially or not) composed of particularized properties need, in order to explain the identical causal effects of some of those properties (being white at t and non-being white at t') to admit certain degrees of similarity between them. Similarity can be primitive or not. If it is, what justifies the identity of causal effects between different particularized properties is that they belong to the same set. If this is not the case, it is understood that such properties are strictly instantiations of universals, so their identical causal potential is due to their being instantiations of the same universal. In the first case, the property of being white is the set in question, in the second case it is the universal. And, unless we relativize to times the properties of belonging to the same set or of being an instantiation of the same universal, the problem of temporary intrinsics rises from its ashes. To reformulate the issue in the terms which the new theory requires, the problem consists in explaining either how it is that the same object possesses particularized properties which belong to sets of complementary properties or else how it is that the object is constituted by instantiations of complementary universals (where a complementary universal is, given the universal f, the universal which corresponds to the predicate `not-f').




[Foot Note 4_9]

See his paper «Is there a problem about persistence?», in H.W. Noonan (1993, 261-289).




[Foot Note 4_10]

D. Lewis (1988, 66, note 1).




[Foot Note 4_11]

I imagine that Merricks (1994) interprets this theory analogously when he accuses it of introducing esoteric properties such as being-at-t or tly white.




[Foot Note 4_12]

This appears to be the solution of Merricks (1994). On p.177 he says: «My exemplifying `being F at t', does not imply I exemplify `being F', for t may not be present. My being F at t, therefore, is compatible with my being not F». On p. 178: «the only properties an object has are the properties it has now». And note 18: «My claim that the only properties an object has are the ones it has now is consistent with the claim that an object O can have a property F at a time t other than the present-just so long as O's having F at some time t means that O now has the property `being F at t'».




[Foot Note 4_13]

Lewis (1988, 66) believes that the most serious defect of this theory is that it denies the reality of the past and future and regards them as ersatz times. Indeed, I assume that this is the basic metaphysical deficiency from which stem all the inadequacies of the theory that I outline in the text below.




[Foot Note 4_14]

The term is from R.M. Adams (1981, 23).




[Foot Note 4_15]

I know of only one theory, highly psychologistic by the way, which takes this into consideration: that of Augustine of Hippo, according to which there are three times: present of past things, present of present things and present of future things (see Confessions, XI, 20, 26)puede




[Foot Note 4_16]

The expression was coined by D. C. Williams (1951). The idea is also present in Prior (1968, 1).




[Foot Note 4_17]

I have no wish to go into detail over questions relating to the ontology of time, since the subject is excessively problematic to be dealt with here and the most sensible course is to leave it aside for the moment.




[Foot Note 4_18]

Lowe (1988, 72-73).




[Foot Note 4_19]

Ibid., p. 73. It is surprising that his metaphysical argument of fundamental particles contributes absolutely nothing in terms of referents for singular terms in his semantics.




[Foot Note 4_20]

Evans (1985) believes that if we take modal semantics as our model for a temporal semantics, we accept implicitly that metaphysical background. Of course, although the evaluation of temporal sentences varies with the time, it seems clear that the way in which the truth of a modal sentence depends on the truth of a certain sentence in the real world is not analogous to the way in which the truth of a sentence in the past depends on the truth of another sentence in the present: the truth-value of `Richard Nixon left the White House' does not depend on any true sentence concerning our present.




[Foot Note 4_21]

Montague's syntactical categorization is easily understood. I shall offer here a brief guide to it, as I shall be using his notation in part of this section. Proper nouns and individual variables are of type e, sentences are of type t, monadic predicates are of type <e,t>, diadics are of type <e, <e,t>>. In general, an expresion α is of the type <x,y> if and only if when taking as arguments expressions of the type x, it yields as values expressions of the type y.




[Foot Note 4_22]

Richard (1981) and (1982).




[Foot Note 4_23]

Kaplan (1977), in Almog, ed. (1989), especially p. 503, no. 28, where he contrasts his temporalist semantic theory with an eternalist theory.




[Foot Note 4_24]

Evans considers previously to T3 another theory, T2, which, in his opinion, also accounts for the relevant linguistic phenomena. According to this theory `N' is ambiguous as regards its predicative or enunciative value. It displays an enunciative value (of type t) in so far as it contains a reference to the time of the utterance owing to the implicit indexical `now', which eternalizes the content of `N'. Without the implicit indexical it would merely have a predicative value (it would be of type <e,t>), it will be a kind of propositional stem. In line with this theory, the temporal operator `now' would belong to a syntactic category distinct from the rest of temporal operators, as, unlike them, it would be the only one capable of offering a sentence as a value, when applied to the eternalization of `N' executed by a different operator. For example, `yesterday', when applied to (1) would offer a predicative expression: `yesterday [Richard Nixon resigns]', which only acquires enunciative value when embedded in `now[N]', i.e. as `now [yesterday [Richard Nixon resigns]]'. Therefore, `now' is of type <t, <e,t>>, while `yesterday' (and all other temporal operators) is of type <<e,t>,<e,t>>. Nonetheless, this odd asymmetry in the treatment of one temporal operator with respect to the others appears rather artificial.




[Foot Note 4_25]

Salmon (1989, 366).




[Foot Note 4_26]

My classification is based on that of Haslanger (1989, 7-8), substituting my (4) for his possibility (iv).




[Foot Note 4_27]

Assuming that the metaphysically committed interpretation of Merricks' theory that I offered in section I is correct, how would one explain those propositional attitudes whose content were singular propositions referring to past objects?




[Foot Note 4_28]

Evans (1985, 362-363) says that to relativize the evaluation of sentences to times is to commit oneself directly to modal and temporal possibilism.




[Foot Note 4_29]

Perry (1972, sec. V) offers a clear exposition of the two basic semantics of temporal parts. According to the first, supported by Smart, proper nouns would refer to temporal parts of four-dimensional objects; according to the second, they would refer to four-dimensional objects themselves. Although the two positions can account for the facts, I feel it is more convenient to adopt the second, as I shall explain below, since in this way, we can minimize the discrepancies between the analysis and the truth value customarily attributed to many identity sentences. See below in this section. See also Inwagen (1990).




[Foot Note 5_1]

See, for example, Lucas (1989) and Markosian (1993).




[Foot Note 5_2]

See, for example, Harris (1988), p. 20.




[Foot Note 5_3]

Schlesinger's proposal has been subjected to penetrating criticism by Oaklander (1984), pp. 70-77.




[Foot Note 5_4]

McTaggart does not explicitly state that events approach «us.» In all other respects, Schlesinger's interpretation closely parallels McTaggart's description (1908, esp. p. 460) of temporal becoming.




[Foot Note 5_5]

Grünbaum, «The Status of Temporal Becoming,» in Gale (1967), pp. 322-353.




[Foot Note 5_6]

See Gale (1968), pp. 231-239, Capek (1976), p. L, and Harris (1988).




[Foot Note 5_7]

See, for example, Smart (1980), pp. 9-10.




[Foot Note 5_8]

Grünbaum, «The Status of Temporal Becoming,» pp. 338-340.




[Foot Note 5_9]

For a discussion of these views, see Smart (1980), pp. 11-14.




[Foot Note 5_10]

See P. Frank's, «Is the Future Already Here?» in Capek (1976), pp. 387-395, for discussion and criticism of Jeans' philosophical interpretation of relativity theory.




[Foot Note 5_11]

For an elaboration on these metaphors, see Smart (1949) and Gale (1968), p. 230, respectively.




[Foot Note 5_12]

Only four of the conditions which are necessary for event A will be represented.




[Foot Note 5_13]

In regards to those philosophers who maintain that event statements are uninformative, it appears that the postulate could also be expressed in terms of «fact-causation.»




[Foot Note 5_14]

The theory outlined herein is neutral with respect to the question of whether time is absolute or relational. However, because of its simplicity, I support a relational theory of time.




[Foot Note 5_15]

Whitrow, «Becoming and the Nature of Time,» in Capek (1976), p. 530. Originally published in the Natural Philosophy of Time (London: Thomas Nelson and Sons, 1961), pp. 288-296. See Gale (1967), p. 353 for a retort from Grünbaum to Whitrow's question.




[Foot Note 5_16]

Broad, «Ostensible Temporality,» in Gale (1967), p. 131. Originally published in An Examination of McTaggart's Philosophy (Cambridge: Cambridge University Press, 1938), Vol. II, Pt. I. C. W. K. Mundle has modified Broad's statement in the following way to better reflect the Russellian position: «The Battle of Hastings precedes the Battle of Waterloo and both precede this.» For this statement, see «Broad's Views About Time,» in Schilpp (1959), p. 370.




[Foot Note 5_17]

For a comprehensive discussion of scaling methods, see Torgerson (1958).




[Foot Note 5_18]

From Grünbaum (1963), p. 320. Originally published as H. Reichenbach, «Les Fondements Logiques de la Mécanique des Quanta,» Annales de l'Institut Henri Poincaré, Vol. XIII (1953), pp. 148-154.




[Foot Note 5_19]

I am indebted to Richard Taylor for his work in the articles entitled «Causation.» See Taylor (1963) and (1967).




[Foot Note 5_20]

See Broad, «Ostensible Temporality,» pp. 131-132, for criticism of this way of thinking.




[Foot Note 5_21]

See Broad's, «Ostensible Temporality,» p. 124 and «A Reply to My Critics,» in Schilpp (1959), pp. 766-767.




[Foot Note 5_22]

See, for example, Smart (1969).




[Foot Note 6_1]

Quantum-theoretical, branching worlds would of course be temporally related to each other; however, such worlds would not be merely possible in the sense needed for a philosophical account of modality. I shall discuss branching possibilities later in this paper.




[Foot Note 6_2]

In fact, of course, I'm referring to the set of those possible worlds that include the situation with which I'm concerned (England's winning the Ashes), and which are close enough to the actual world to be of interest to me.




[Foot Note 6_3]

I should like to thank Dorothy Edgington for her comments on an earlier draft of this paper.




[Foot Note 7_1]

Unfortunately we cannot yet handle TeX or LaTeX files. The convertors we've tried have proved useless.




[Foot Note 7_2]

In the case of WordPerfect 5.1, the procedure is as follows. Suppose you have a file called `dilemmas.wp5' in your directory c:\articles, and you want to submit it to SORITES. At your DOS prompt you change to your directory c:\articles. We assume your WordPerfect files are in directory c:\WP51. At the DOS prompt you give the command `\wp51\convert'; when prompted you reply `dilemmas.wp5' as your input file whatever you want as the output file -- suppose your answer is `dilemmas.ker'; when prompted for a kind of conversion you choose 1, then 6. Then you launch your communications program, log into your local host, upload your file c:\articles\dilemmas.ker using any available transmission protocol (such as Kermit, e.g.). And, last, you enter your e_mail service, start an e_mail to to <sorites@ifs.csic.es> and include your just uploaded dilemmas.ker file into the body of the message. (What command serves to that effect depends on the e_mail software available; consult your local host administrators.)

With WordPerfect 6 the conversion to kermit format is simple and straightforward: you only have to save your paper as a `kermit (7 bits transfer)' file.




[Foot Note 8_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.