Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T13:45:15.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Three Remarks on the Interpretation of Kant on Incongruent Counterparts

Published online by Cambridge University Press:  25 March 2011

Rogério Passos Severo
Rogério Passos Severo
Affiliation:
University of Illinois at Chicago / CAPES – Brasilia
Get access Rights & Permissions [Opens in a new window]

Extract

In recent times, a number of authors have systematically criticized Kant's 1768 ‘proof’ of the reality of absolute space. Peter Remnant may have been the first do to so, but many others have since joined him, either challenging the argument itself or showing how relationist conceptions of space can account for incongruent counterparts just as well as absolutist conceptions. In fact, Kant himself abandoned his main conclusion soon after publication, favouring instead the doctrine of transcendental idealism. I do not see how the 1768 proof can be saved, nor will I defend it here. However, in dismissing it some critics seem to have gone too far, and either failed to fully acknowledge Kant's contribution, or attributed to him thoughts he is unlikely to have had. Kant's treatment of incongruent counterparts in his Dissertation of 1770 has also met strong opposition. In particular, his claim that the difference between a pair of incongruent counterparts cannot be apprehended by means of concepts alone has been taken to be a mathematical falsehood. Indeed, incongruent counterparts have been shown to be mathematically distinguishable, with no intuitions needed for that purpose.

Type
Articles
Information
Kantian Review , Volume 9 , March 2005 , pp. 30 - 57
Copyright
Copyright © Kantian Review 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

For comments and criticisms of earlier and later versions I am grateful to Sven Bernecker, Andrew Blom, Mario Caimi, Fabian Domingues, Tiago Falkenbach, Renato Fonseca, José Guerzoni, Nick Huggett, David Potts, Valério Rohden, César Schirmer dos Santos, Márcio Teixeira, João Carlos Brum Torres and three anonymous referees from this journal. I am particularly indebted to Paulo Faria, my teacher and master's dissertation adviser at UFRGS (Brazil), with whom I seriously tackled the issues here discussed for the first time, and to my Kant teacher at UIC, Daniel Sutherland, for his illuminating lectures and a careful reading of the penultimate draft. I would also like to thank the CAPES Foundation (Brazil) for the support of research through a fellowship grant (BEX 1717/00-6).

1 Remnant, Peter, ‘Incongruent counterparts and absolute space’, Mind, 72 (1963), 393–9CrossRefGoogle Scholar ; reprinted in James Van, Cleve and Frederick, Robert (eds), The Philosophy of Right and Left: Incongruent Counterparts and the Nature of Space (Dordrecht: Kluwer, 1991), pp. 51–9.Google Scholar Kant's argument for absolutism (in Von dem Ersten Grunde des Unterschiedes der Gegenden im Raume (1768), 2: 377–83)Google Scholar is discussed in several of the papers in Van Cleve and Frederick. Kant's work is translated into English in Theoretical Philosophy 1755-1770 in the Cambridge edition of the works of Immanuel Kant (Cambridge: Cambridge University Press, 1992).Google Scholar All citations of Kant's pre-Critical works are taken from this edition and references to the Academy edition are given by volume and page number. See also Felix, Mühlholzer, ‘Das Phänomen der inkongruenten Gegenstücke aus Kantischer und heutiger Sicht’, Kant-Studien, 83 (1992), 436–53Google Scholar ; Rusnock, Paul and George, Rolf, ‘A last shot at Kant and incongruent counterparts’, Kant-Studien, 86 (1995), 257–77CrossRefGoogle Scholar ; Huggett, Nick, ‘Reflections on parity non-conservation’, Philosophy of Science, 67 (2000), 219–41CrossRefGoogle Scholar, and ‘Kant and the chiral arguments for substantivalism’ (forthcoming as a chapter of a book by the author); Hoefer, Carl, ‘Kant's hands and Earman's pions: chirality arguments for substantial space’, International Studies in the Philosophy of Science, 14 (2000), 237–56CrossRefGoogle Scholar.

2 According to some, such a defence would be out of place, since Kant never fully embraced Newtonian absolutism. See for example, Walford, David, ‘Towards an interpretation of Kant's 1768 Gegenden im Raume Essay’, Kant-Studien, 92 (2001), 407–39, esp. 433-6CrossRefGoogle Scholar.

3 De Mundi Sensibilis atque Intelligibilis Forma et Principiis (henceforth: 1770 Dissertation), 2: 403.

4 See section 2 below.

5 Hans Vaihinger suggests that Kant might have learned about them from a published work by Segner (1741) to which he had access. See Vaihinger, , Commentar zu Kants Kritik der reinen Vernunft (Stuttgart, 1892; reprinted New York: Garland, 1976), vol. 2, p. 531 n.Google Scholar An anonymous reviewer observed that ‘Two of the Archimedean polyhedra - the so-called “snub cube” and the “snub dodecahedron” - have a “left-” and “right-handed” version’, and that ‘[i]n Part Four of the Principles of Philosophy, Descartes exploits the fact that screws can have oppositely winding threads in order to explain magnetic attraction and repulsion.’

6 See Leibniz, , ‘De Analysis Situs’ (1679) inGoogle ScholarGerhardt, C. I. (ed.), Die mathematischen Schriften von G. W. Leibniz, vol. 5 (Halle: H. W. Schmidt, 1849), p. 179Google Scholar ; and Wolff, , Mathematisches Lexicon (Halle, 1751; reprinted Hildesheim: Olms, 1983), p. 1179.Google Scholar See also Rusnock, and George, , ‘Last Shot’, pp. 260–2Google Scholar, for further references and an excellent exposition and discussion of the topic. The next few paragraphs draw considerably from their paper.

7 Contrary to what Kant suggested, however, this is not a universal rule: there are objects that are not divisible into two symmetrical halves whose counterparts are congruent. Take, for example, a rectangular sheet of paper, pick two diagonally opposing corners, say, the top right and the bottom left, and fold them 90 degrees in opposite directions from the plane of the sheet of paper - that is, fold one of the corners up and the other down 90 degrees. The resulting object will not be divisible into two symmetrical halves (it will have no plane of mirror symmetry) but will nonetheless have a congruent counterpart. For an illustration, see Gardner, Martin, The New Ambidextrous Universe (3rd rev. edn, New York: W. H. Freeman & Co, 1991), p. 14Google Scholar.

8 Later, in the nineteenth century, it was pointed out (originally by Ferdinand Mobius, in ‘On higher space’ (1827), reprinted in Cleve, Van and Frederick, , Philosophy, pp. 39–41)Google Scholar that things that are incongruent in a three-dimensional space can be turned around in a four-dimensional space so as to be enclosed in the same limits as their counterparts. In general, any n-dimensional object can beflippedover in an n+1-dimensional space so as to be enclosed in the same limits as its counterpart. Also movement along a non-orientable space (for example, a Möbius strip, or a Klein bottle) may change the handedness of a particular object. But these mathematical possibilities were physically inconceivable to eighteenth-century thinkers like Kant, and even to nineteenth-century thinkers such as Mobius himself. ‘Space’ then did not mean a mere mathematical construct, but at once the space of physics, geometry and of ordinary experience, and it was conceived as Euclidean and three-dimensional (see Torretti, Roberto, Philosophy of Space from Riemann to Poincaré (Boston: D. Reidel, 1978)CrossRefGoogle Scholar, introduction). Only later was a distinction between physical, phenomenological and mathematical spaces introduced. This explains why Kant only mentions as examples of incongruent counterparts things that cannot be moved and turned around in Euclidean three-dimensional space so as to occupy the same limits: ‘If two figures drawn on a plane surface are equal and similar, then they will coincide with each other. But the situation is often entirely different when one is dealing with corporeal extension, or even with lines and surfaces, not lying on a plane surface’ (2: 381). Kant never mentions flat two-dimensional objects or one-dimensional objects as having incongruent counterparts precisely because they can be turned over in three-dimensional space so as to coincide with their counterparts. For him, three-dimensionality was an actual feature of the (unique) space. One- and two-dimensional spaces were but limitations of the (three-dimensional) space, and higher dimensional spaces were just physically inconceivable (in his 1747 essay on Living Forces, for example, Kant writes that these higher dimensional spaces, if possible, would ‘not belong to our world’). To regard Kant's notion of an incongruent counterpart as limited to oriented spaces of a particular dimensionality – instead of referring to the (unique) space – is an anachronism somewhat diffused in the literature (for example, in Cleve, Van and Frederick, , Philosophy, pp. 8, 22–3Google Scholar ; and Graham Nerlich, ‘Hands, Knees, and Absolute Space’, ibid., esp. pp. 158-9; see also pp. lxix-lxx of the introduction to the English translation of Kant's 1768 essay in Theoretical Philosophy 1755-1770).

9 ‘Last shot’, pp. 260-1.

10 ‘Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another’ (Euclid, Elements, bk III, def. 11, in Heath, T. L. (ed.), The Thirteen Books of Euclid's Elements (New York: Dover, 1956))Google Scholar ; ‘Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional’ (bk VI, def. 1); ‘Similar plane and solid numbers are those which have their sides proportional’ (bk VII, def. 21); ‘Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional’ (bk XI, def. 24).

11 ‘In undertaking an explanation of quality or form, I have learned that the matter reduces to this: things are similar which cannot be distinguished when observed in isolation from each other. Quantity can be grasped only when the things are actually present together or when some intervening thing can be applied to both. But quality presents something to the mind which can be known in a thing separately and can then be applied to the comparison of two things without actually bringing the two together either immediately or through the mediation of a third object as a measure’ in Gerhardt, C. I. (ed.), Die philosophischen Schriften von G. W. Leibniz (Berlin: Hale, 1875), vol. 5, p. 179Google Scholar ; English translation in Loemker, L. (ed.), G. W. Leibniz: Philosophical Papers and Letters (Chicago: University of Chicago Press, 1956), vol. 1, p. 392Google Scholar.

12 ‘… similar are those things that cannot be discerned in isolation’ (… ut similia sint, quæ singulatim observata discerni non possunt) ( Leibniz, , ‘De analysis Situs’ (1679), in Die mathematischen Scriften, vol. 5, p. 180)Google Scholar.

13 2: 382. The surface that limits a left hand could of course be pulled inside out so as to ‘serve as a boundary to limit’ its right counterpart. This is a rather elementary objection to Kant's formulation, and I should like to thank an anonymous reviewer for pointing it out. I guess Kant's reply would be that we ought not to take ‘surface’ here as meaning something like a very thin layer wrapped around a body. Rather, it is meant to refer t o the two-dimensional space which limits a three-dimensional body. And the point is merely that that space cannot be moved rigidly (that is, without stretching or bending) so as to overlap the two-dimensional limits of its incongruent counterpart.

14 Rusnock, and George, , ‘Last shot’, p. 266Google Scholar, maintain that Kant's usage of ‘inner ground’ in the 1768 essay is indeed equivocal. However, the equivocation only shows up if one reads Kant's distinction as mapping onto Leibniz's, in the sense that all qualitative Leibnizian characteristics would count as having an inner ground for Kant, and all quantitative Leibnizian characteristics except the orientation of objects such as hands would count as having an outer ground for Kant. On this reading, Kant would indeed say that orientation has an inner ground sometimes in the sense that it is not discernible in isolation, and sometimes in the sense that it is neither magnitude nor location. There is, however, no need to read this equivocation into the text.

15 2: 380. For an excellent discussion of Kant's use of these examples (as well as of Kant's 1768 essay in general), see Torretti, Roberto, Manuel Kant (Santiago de Chile: Ediciones de la Universidad de Chile, 1967), pp. 120ffGoogle Scholar.

16 ‘On the other hand, where a given rotation can be attributed to the course of those two celestial bodies [sun and moon] - Mariotte claims to have observed such a law operating in the case of the winds: he maintains that from new to full moon the winds tend to change their direction clockwise through all the points of the compass - then this circular movement must rotate in the opposite direction in the other hemisphere. And this is something which Don Ulloa claims to have found actually confirmed by his observations in the south seas’ (2: 380).

17 ‘There is only one way in which we can perceive that which, in the form of a body, exclusively involves reference to pure space, and that is by holding one body against other bodies’! (2: 383).

18 2: 383. There is some controversy in the literature about this reference to a human body. Remnant, ‘Incongruent counterparts’, 398, finds an inconsistency in Kant's argument: ‘We can now see where Kant's own argument goes wrong: it involves the inconsistency of maintaining that it is impossible to say of a hand, considered entirely in isolation from everything else, whether it is right or left, while assuming that it would be possible to say of a handless body, considered by itself, which was its right side and which its left’. See also Huggett, Nick, Space from Zeno to Einstein (Cambridge, MA: MIT Press, 1999), pp. 208–12Google Scholar, and Rusnock, and George, , ‘Last shot’, pp. 265–6Google Scholar, and Pooley, Oliver, ‘Handedness, parity violation and the reality of space’, in Brading, K. and Castellani, E. (eds), Symmetries in Physics (Cambridge: Cambridge University Press, 2003), pp. 258–63.Google Scholar But perhaps the problem with Kant's argument lies - contrary to what these authors suggest - not in the thought-experiment itself, but in the inference Kant draws from it, to the effect that Leibniz's conception of space must be wrong. Although it is true that it hardly makes any sense to speak of a hand being right or left in the absence of any other object to which it could be compared, Kant's thought-experiment does not presuppose that it does. Rather, the experiment relies merely on the fact that a hand has to have a form if it is to count as a hand at all. To be sure, a human body, too, must have a form, and even if we cannot say which of its sides is the right side and which is the left side, it is still the case that a lone hand will only fit one of those sides, not both.

19 For a defence of relationism, and further references, see Nick Huggett, ‘Geometry and topology for relationists’ (this is a chapter in a forthcoming book by the author), also, Huggett, ‘Mirror symmetry: what is it for relational space to be orientable?’ (http://philsci-archive.pitt.edu/archwe/00000767/).

20 For a recent summary of these accounts, and further references, see Pooley, , ‘Handedness’, p. 253Google Scholar.

21 (2: 403). Here is the analogous argument for the one-dimensional case of time: ‘If you think of two years, you can only represent them to yourself as joined to one another by some intermediate time. But among different times, the time which is earlier and the time which is later cannot be defined in any way by any characteristic marks which can be conceived by the understanding, unless you are willing to involve yourself in a vicious circle' (2: 399). Note that in both cases it is orientation that is at stake: the orientation of a three-dimensional spatial form in 2: 403, and of the flow of time in 2: 399.

22 ‘hie non nisi quadatn intuitione pura diversitatem, nempe discongruentiam, notari posse’ (1770) (2: 403).

23 For example, by Gauss, C. F., ‘Theoria residuorum biquadraticorum. Commentatio secunda’, (1831), in Werke (Göttingen, 1863. reprinted: Hildesheim: Olms, 1975), vol. 2, p. 177Google Scholar ; Klein, F., Elementary Mathematics from an Advanced Standpoint (New York: Dover, 1948), pp. 39–43Google Scholar ; Weyl, H., Philosophy of Mathematics and Natural Science (Princeton: Princeton University Press, 1963), pp. 78–84Google Scholar ; Bennett, Jonathan, ‘The difference between right and left’, American Philosophical Quarterly, 7 (1970)Google Scholar - reprinted in Cleve, Van and Frederick, , Philosophy, pp. 97–130Google Scholar ; Mühlhölzer, ‘Das Phanomen’; Rusnock and George, ‘Last shot’; and a few others in Van Cleve and Frederick, Philosophy.

24 ‘Das Phanomen’, p. 452.

25 Similar indications, by other authors, on how to distinguish incongruent counterparts without intuitions can be found in the other papers mentioned in note 23 above.

26 ‘Last shot’, p. 273.

27 ‘It is the business of philosophy to analyse concepts which are given in a confused fashion, and to render them complete and determinate’ ( Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral (1764): 2: 278)Google Scholar.

28 Gegend is commonly translated as region. In this case, as argued by David Walford and Rusnock and George, direction seems t o be a more adequate rendering of the term. See David Walford's notes to his translation of the 1768 essay (in Theoretical Philosophy 1755-1770, pp. 456-7), as well as his ‘Towards an interpretation of Kant's 1768 Gegenden im Raume Essay’ , Kant-Studien, 92 (2001), 407–39Google Scholar ; also Rusnock, and George, , ‘Last shot’, pp. 269–72Google Scholar.

29 Metaphysische Anfangsgründe der Naturwissenschaft (1786): 4: 484Google Scholar.

30 Rusnock, and George, , ‘Last shot’, p. 274Google Scholar.

31 See KrV, B VIII.

32 Rusnock, and George, , ‘Last shot’, p. 274Google Scholar.

33 2: 273-301. The methods of philosophy and mathematics are contrasted throughout the essay. See, for example, the following passage: ‘geometers acquire their concepts by means of synthesis, whereas philosophers can only acquire their concepts by means of analysis - and that completely changes the method of thought’ (2: 289). Similar remarks can be found in KrV A713/B741ff.

34 Ibid. The same point is made in Was heisst: Sich im Denken orientieren (1786): 8: 134–5Google Scholar.

35 See Kant's Logik (Jäsche), §1, where concepts are characterized as repre-sentatio per notas communes.

36 Similarly for ‘after’ and other temporal notions: ‘I only understand the meaning of the little word after by means of the antecedent concept of time’ (2: 399).

37 Later, in the Critique of Pure Reason, Kant would write that ‘reason demands … that no species be regarded as in itself the lowest; for since each species is always a concept that contains in itself only what is common to different things, this concept cannot be thoroughly determined, hence it cannot be related to an individual’ (A655/B683. English translation by Guyer and Wood (Cambridge: Cambridge University Press, 1998)).

38 A similar point seems to underlie Lome Falkenstein's discussion of the perception of a triangle drawn on a sheet of paper in Kant's Intuitionism (Toronto: University of Toronto Press, 1995)Google Scholar : if each point on the sheet is designated by an ordered triple, where the first two elements of the triple are Cartesian coordinates and the third indicates the colour of that particular point, then although ‘each point on the sheet is the subject-matter for a distinct thought, there is nowhere a thought of the appearance of the sheet as single whole, and there is therefore a sense in which the sheet has not been perceived’ (p. 246). Incongruent counterparts are a little more complex in this respect since even if we were somehow capable of grasping part-whole relations from a reading of the ordered triples, that would still tell us nothing about orientation. Falkenstein points out that the form of a triangle cannot be given by taxonomy, mereology is also required. Incongruent counterparts show that in some cases not even that suffices: part–whole relations tell us nothing about orientation. Falkenstein goes on to say that ‘[w]hen I draw a triangle on paper, there is a sense in which the “space” for my activity already exists…. The order of the points is originally fixed by the paper, not by my own decision about how to draw … All I can do … is choose how to run through an order of points that is already given. I cannot create or define the order itself or, to put the point more technically, I cannot change its topology … as I please’ (p. 247). Yes, but also the geometry (not just the topology) cannot be changed as one pleases.

39 The problem is similar to the following: given a description of the colours blue and red in terms of light-rays and their respective wave-lengths, we can perfectly well distinguish one from the other. But nothing in those descriptions allows us to know what those colours look like. The latter knowledge requires a non-conceptual capacity, such as the one paradig-matically exemplified in perceiving red and blue things. This is also corroborated by the fact that it is possible to describe light-rays whose appearance we cannot even imagine (for example, ultra-violet rays). The analogy here is only partial, however, since a conceptual description plus a sensation (the ‘matter’ of an intuition) could perhaps suffice for the identification and recognition of a colour, but does not suffice for the identification and recognition of a spatial form. Sensations only give us indications of the sensory properties of an object (colour, taste, odour, etc.), but not of ‘extensive magnitudes’ (see KrV, A167/B209). And it i s doubtful, to say the least, that spatial properties (extension, shape, continuity, orientation, etc.) could somehow be inferred from sensory properties. In 1768 (2: 380) and again in 1786 (8: 131ff.) Kant does speak of a ‘feeling (Gefühl) of right and left’, but there he means not a feeling of spatial forms per se, but merely a feeling of a difference in the sensations we have on each side of our bodies: the right hand is stronger in most people, the left eyes and ears are said to be more sensitive, etc.

40 A good explanation for the fact that they appear in the latter but not in the former can be found in the different methods of exposition, analytic and synthetic, adopted in the Prolegomena and in the first Critique, respectively. The plainly accessible fact that there are incongruent counterparts is suited for an analytical mode of presentation, which begins with ‘something already known to be dependable, from which we can go forward with confidence and ascend to the sources, which are not yet known, and whose discovery not only will explain what is known already, but will also exhibit an area with many cognitions that will arise from these same sources’ (4: 274-5). English translation by Hatfield, Gary, Prolegomena to any Future Metaphysics (Cambridge: Cambridge University Press, 1997)).Google Scholar The synthetic mode adopted in the Critique, on the other hand, proceeds ‘by inquiring within pure reason itself, and seeking to determine within this source both the elements and the laws of its pure use, according to principles’ (4: 274) Hence, something like an argument from incongruent counterparts, which one might otherwise expect to find in the sections on space of the Transcendental Aesthetic, is nowhere to be found. None of the arguments of the Transcendental Aesthetic begin with empirical facts that are ‘known to be dependable’; they begin instead with general notions and principles. On Kant's methods of presentation, see Caimi, Mario, ‘About the argumentative structure of the Transcendental Aesthetic’, Studi Kantiani, 9 (1996), 27–46Google Scholar, and Shabel, Lisa, ‘Kant's “Argument from Geometry”’ (Journal of the History of Philosophy, 42, 2004, 195–215)CrossRefGoogle Scholar.

41 4: 484. Incongruent counterparts are also briefly discussed in the first few paragraphs of the 1786 essay Was heisst: Sich im Denken orientieren (8: 131ff.).

42 See, for example, Prior, Arthur, ‘Thank goodness that's over!’, Philosophy, 34 (1959), 12–17CrossRefGoogle Scholar, Strawson, Peter, Individuals (London: Mathuen, 1959)CrossRefGoogle Scholar, part 1, and Gale, Richard, ‘Tensed statements’, Philosophical Quarterly, 12 (1962), 53–9.(The examples to be used were elaborated upon the ones discussed by these authors.) In ‘Knowledge by acquaintance and knowledge by description’, Bertrand Russell seems to rely on a similar reasoning (seeCrossRefGoogle ScholarFaria, Paulo, ‘Discriminação e Afecção’, in Marques, E. (ed.), Verdade, Conhecimento e Ação (São Paulo: Loyola, 1999), pp. 145–59).Google Scholar More recent discussions of demonstratives can be found in Schiffer, Stephen, ‘The basis of reference’, Erkenntnis, 13 (1978), 171–206CrossRefGoogle Scholar ; Lewis, David, ‘Attitudes de dicto and de se’ Philosophical Review, 88 (1979), 513–3;CrossRefGoogle ScholarPerry, John, ‘The problem of the essential indexical’ (1979), in Salmon, Nathan and Soames, Scott (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988)Google Scholar ; Stalnaker, Robert, ‘Indexical belief’, Synthese, 49 (1981), 129–51Google Scholar ; Chisholm, Roderick, First Person: An Essay on Reference and Intentionality (Minneapolis: University of Minnesota Press, 1982)Google Scholar ; Austin, David, What's the Meaning of “This”? (Ithaca, NY: Cornell University Press, 1990)Google Scholar ; Martens, David, ‘Demonstratives, descriptions, and knowledge: a critical study of three recent books’, Philosophy and Phenomenological Research, 54 (1994), 947–63CrossRefGoogle Scholar ; and, by the same author, ‘Indexicals’, Stanford Encyclopedia of Philosophy (2001), available online at http:lIplato.stanford.edu/entries/ indexicals/.

43 ‘Demonstrative identification’ here means forms of identification of particular things in which the thing identified varies from context to context even when the words and gestures employed in the demonstration remain the same, that is, are used with the same meanings and intentions. Typically, an ostensive identification, where someone says something like ‘this’ or ‘that’ and points to a certain thing, counts as a demonstrative identification. Also counted are expressions like ‘here’, ‘now’, ‘I’, ‘you’, and ‘to my right/left’, ‘up’, etc., accompanied by gestures or not.

44 The description need not be correct for the identification to obtain. On this and related topics, see Donnellan, Keith, ‘Reference and definite descriptions’, Philosophical Review, 75 (1966), 281–304CrossRefGoogle Scholar.

45 The following passage by William James illustrates the point: ‘If we take a cube and label one side top, another bottom, a third front, and a fourth back, there remains no form of words by which we can describe to another person which of the remaining sides is right and which is left. We can only point and say here is right and there is left, just as we should say this is red and that blue’ (The Principles of Psychology, ch. 20, ‘The Perception of Space’ (New York: Dover, 1890, 1918), vol. 2, p. 150).

46 See Gale, , ‘Tensed statements’, pp. 56–7Google Scholar.

47 Here is an interesting example on the use of ‘I’: ‘An amnesiac, Rudolf Lingens, is lost in the Stanford library. H e reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost … He still won't know who he is, and where he is, no matter how much knowledge he piles up, until that moment in which he is ready to say, “This place is aisle five, floor six, of Main Library, Stanford. I am Rudolf Lingens.”’ ( Perry, John, ‘Frege on demon-stratives’, Philosophical Review, 86 (1977), 492)CrossRefGoogle Scholar.

48 Nelson Goodman objected to a similar argument that a translation without loss into a language without time indexicals is indeed possible as long as a calendar-watch (or, in the case here discussed, where only the identification of places is relevant, something like a GPS device), is available. He argues in The Structure of Appearance (3rd edn, Dordrecht: D. Reidel, 1977), p. 269Google Scholar, that consulting such a device is as legitimate, as far as translations go, as consulting a dictionary when one is translating into or from a foreign language. But how could one know (without demonstrative identifications) that the device works? How can one know whether a watch shows the current time, or whether a GPS device indicates the place where one is, without ultimately relying on some information, gathered from an independent source, of the type: ‘It is now 5 p.m. and that is also what my watch shows’ or ‘We are now at 50 degrees west of Greenwich, 30 degrees south of the Equator, and that is also what my GPS shows’? In fact, Goodman's argument can run the other way around also. Information conveyed by dictionaries, too, ultimately depend on a lexicographer's demonstrative identification of foreign utterances. Using watches and GPS devices to eliminate spatio-temporal demonstratives from our utterances does not entail that the knowledge expressed by such utterances is independent from other pieces of information that must be expressed with the aid of demonstratives. The link between what a watch or a GPS device displays and the time–location one is at cannot be established by a description that does not contain demonstratives. Ordinarily we just take that link for granted. But it obviously must be established at some point. Likewise, the use of dictionaries for translations relies on demonstrative identification of foreign utterances and utterance patterns: the link between the written signs it contains and the actual noises and gestures foreigners make while speaking cannot be established solely by means of descriptions that do not contain demonstratives.

49 That is, descriptions that do not themselves contain demonstratives.

50 To be sure, some demonstratives are essential in tha t sense. Perry, , ‘Problem’, p. 96Google Scholar, suggests that it is plausible to think that ‘I’ and ‘now’ are in fact the only essential demonstratives. ‘Tomorrow’ (the day after the one I am in now), ‘you’ (the person I am addressing now) and all other demonstratives would be expressible in terms of ‘I’ and ‘now’. However, if we are to take up Perry's suggestion, then at least three other demon-stratives, all of them demonstratives of orientation - one for each spatial dimension; ‘right’, ‘up’, and ‘front’, for example - would have to be included in the list. As the passage by James quoted in note 45 above indicates, there is no way of rendering the contents of ‘right’, ‘up’ and ‘front’ in terms of ‘I’ and ‘now’.

51 Hence, also insufficient for determining the extension of a term. See, for example, Putnam's, Hilary ‘The meaning of “Meaning”’, in Philosophical Papers, vol. 2 (Cambridge: Cambridge University Press, 1975), pp. 215–71Google Scholar.

52 The relation between Kant's remarks and contemporary analytic themes is discussed by Yourgrau, Palle, ‘The path back to Frege’, Proceedings of the Aristotelian Society, 87 (1987), 169–210CrossRefGoogle Scholar, esp. pp. 101-3, and Torres, João Carlos Brum, ‘Cognição intuitiva e pensamento de re’, Analytica, 4 (1999), 33–63Google Scholar.